mechanics of hoisting machinery - Forgotten Books

MECHANICS OF HOISTING MACHINERY

THE ME CHANICS

HOISTING MACHINERYINCLUDING

ACCUMULATORS, EXCAVATORS,AND

FILE - DRIVERS

TEXT - BOOK FOR TECHNICAL SCHOOLS AND A GU IDEFOR PRACTICAL ENG INEERS

DR. JUL IU S WE I SBACHAND

PROFES SOR GU STAV HERRMANN

AUTHORISED TRANSLATION FROM THE SECOND GERMAN ED ITIONBY

KARL P. DAHL STROM,M. .E

,

LATE INSTRUCTOR OF MECHAN ICAL ENG INEER ING AT THE LEH IGH UNIV ERS ITY

d’ o w

W ITH 1 77 l LLu s

’

TnA’

Ns

New 320th

THE MACMILLAN COMPANY

A l l rights re served

TRANSLATOR’

S PREFACE

THE translation h e re w ith presented to the engineering public

has been made from Professor Herrmann’s revised edition o f

Weisbach’s great work on Engineering Mechanics. Of this

work several volumes are already familiar to English readers

through the translations completed successively by Messrs. Coxe,Du Bois

,and Klein

,and treating respectively of Theoretical

Mechanics,Steam - engines and Hydraul ics , and Machinery of

Transmission. Th e present section,however

,h as never hereto

fore appeared in English print,although its great value has

been recognised by all the above able translators,and by

institutions of learning all over the world . As the need of

suitable text - books for the more advanced courses in theMechani cs of Machinery h as long been felt at our technical

schools, the translator w as induced to undertake the work of

editing the volume on Hoisting Machinery,in ord er to make a

beginning towards alleviating this need .

References in the text to previous volumes of Weisbach’s

Mechanics,allude to the Engl ish translations unless otherwise

specified. The metric and English measurements are used,the

latter being enclosed in brackets.

The translator is indebted to Professor J. F. Klein o f the

Lehigh University for much valuable aid in the preparationof the work .

October 1 89 3 .

3 3 7561

CONTENTS

INTRODUCTION

CHAPTER I

LEVERS AND JACKS

CHAPTER II

TACKLE AND D IFFERENTIAL BLOCKS

CHAPTER III

WINDLASSES, WINCHES, AND L IFTS

CHAPTER IV

HYDRAULIC HOISTS,ACCUMULATORS

, AND PNEUMATIC HOISTS

CHAPTER v_

HOISTING MACHINERY FOR MINES

viii MECHANICS OF HOISTING MACHINERY

CHAPTER V I

CRANES AND SHEERS

CHAPTER

EXCAVATORS AND DREDGES

CHAPTER VIII

FILE - DRIV ERS


INTRODUCT ION

1 . THE object of all hoisting machinery is to raise andl ow er masses. Such apparatus is extensively used in extractin gmineral products

,in raising and distributing building materials

,

and in granaries,warehouses

,machine—Shops , and factories .

In all hoisting arrangements the motive power is expendedin two ways:first, in performing u sefu l work, namely , the productQh of the weight Q of the load and the height h throughwhich its centre of gravity is lifted ; and , second ,

in overcomingw astefu l resistances. It is usually unnecessary to take intoaccount the energy stored up in the lifted body by virtue ofits velocity

,Since the arrangement is generally such that th e .

velocity of the load when it reaches its destination is equal to zero .

When a hoisting apparatus is intended for intermittentservice only

,and absorbs but a small amoun t of power

,it is

usually operated by hand,as is th e case with the various forms

of jacks,hand - cranes

,etc .

On the other hand,when the machine is to be in continual

use,some other source o f energy

,chiefly steam power

,is

employed,which is the case in hoisting machinery for mines

and nearly all large works of engineering o f the present day.

With reference to economy of power, that hoist is generallyconsidered the most efficient in which the ratio of hurtful touseful resistances is least. If no wasteful resistances werepresent all hoisting machines would be equally efficient asregards expenditure o f energy

,for according to the principle

o f virtual velocities we shou ld have for every construction

Qh P3)

where 3 denotes the distance , in the direction of motion,E B

MEcHANIQS‘ OF HOISTINC MACHINERY

through whi ch the point of application of the effort P hasbeen moved whi le the weight Q has been lifted through aheight h . Therefore

,in the absence of friction

,the theoretical

effort,whi ch in the following will be denoted by P

0,would be

Now let Ww denote the total work performed in overcomingthe prejudicial resistances

,while the weight Q is bein g raised

or lowered through a height h — that is,let Ww represent the

sum of the products obtained by multiplying each prejudicialresistance W into the .distance w through which it has beenovercome

,then the expression for the work performed in

rai sing the weight isQh Ww P3

,

From this follows that,under all circum stances

,the actual

force P IS greater than the theoretical force P,as long as the

resistances W act in the same direction as the load Q,or as

long as the force P acts to raise the load . Thi s constitutes thef orw ard motion as distinguished from the backw ard or reverse

motion,which results when the weight Q is lowered ; here the

load Q is the cause o f the motion , and P is to be consideredas the resistance which acts to prevent acceleration .

Let (P) denote the force required to prevent accelerationin the latter case

,and let (W)w denote the work performed

in overcoming the wasteful resistances ; then, for the reversemotion

,the prejudicial resistances W are acting in the same

direction as (P), and (P)3 + (W)w = Qh solving this equationw e find

Qh (W)w,

S(P)

a result which Shows that (P) is less than the theoreticalforce P

0.

It is customary in hoisting as well as in other machines todesignate the ratio

A 2 2 Q"77"

P Qh + Ww

INTRODUCTION 3

of the effort When the hurtful resistances are neglected to theeffort actuall y exerted by the term eficr

’

ency . Thi s ratio,

which accordi ng to the above is always less than unity, represents that part or percentage of the effort P which is employedin performing the useful work . Similarly we speak of theefficiency (77) of the hoisting machines for the reverse motion ,understanding by this the ratio of the actual effort (P) requiredwhen the load Q is being lowered, to the effort P0 requiredwhen hurtful resistances are neglected

,and then w e have

This value also is always less than unity,and even becomes

negative when (W)w > Qh . For the limiting case (W)w : Qh ,w e have (77) and consequently (P) equal to zero ; in otherwords

,this means that the forces of the machine are balanced

without the additional e ffort (P). Therefore a negative valueof (n), for which (P): ( 77)P0 is also negative, shows that duringthe lowering of the load Q an additional force (P) is to beappli ed

,which will act in the same sense as Q .

A negative sign (77)may therefore be taken as an indicationthat the machine is capable o f holding th e load suspendedwithout running backward when the application of motivepower ceases

,a property which under certain conditions bel ongs

to the worm wheel gearing. The efficiency 77 for the forwardmotion is of course always positive .The introduction and use of this fraction to express the

efficiency is a great convenience in practical calculations,for

even in th e most complicated machine the “theoretical force

h

8

can always be determined from the relations b etween thedistances h and s

,and thus the knowledge o f the efficiency 7)

immediately gives the actual effort required

p i e.

7)

But the value o f 77 can easily be computed, when we knowthe value s o f the efficiencies Of the separate pieces and mechan


isms of which.

the machine consists. In symbols let 771 , 772 , 773m,denote the efficiencies of the several parts of the train

,

then the efficiency of the whole machine i s 7;= 771 772 073

Since the simple mechanisms o f which all hoisting machinesconsist can be reduced to a very limited number of classes

,as

wil l be seen in the following,it is easily understood that a

knowledge of the mean value of 77 for these simple mechani smswill in most cases lead to results sufficiently exact for practicalpurposes. As w e proceed this will become more evident .A general remark may here be made

,however

,in regard to

the above mentioned selflocking hoistin g apparatus,whose

efficiency ( 77) in the reverse motion w as found to be negative,

namely,that their efficiency in the forward motion always is

comparatively small. The truth of this statement will b eevident from the following reasonin g.

Assuming the limiting case (n) O,in whi ch the machine

is still selflocking,w e shall have

Qh (W)w .

For the forward motion w e have the general expression

Qh"“Qh + w w

Under the supposition that both values W and (W) areequal

,and therefore that Qh Ww

,w e have

In this case,accordingly

,w e obtain the result th at th e

efi ciency of a h oistingmach in e w h ich au tomatica l ly p revents th e load

from ru nn ing d ow n ,

”d oes not exceed 50 p er cent u nd er th e most

favou rabl e circumstances,and that it must be even smaller in al l

cases for which (77) is negative, that is to say (W)w > Qh .

As a matter of fact,however

,the work performed in over

coming the wasteful resistances has a value Ww for the forwardmotion which is different from the value (W)w for the reversemotion

,inasmuch as the wasteful resistances are dependent

upon the forces in action , namely, W upon P and Q , and (W)upon Q and (P). In general w e can assume that W is largerthan (W), because P alw ays exceeds the value of (P), although

INTRODUCTION 5

in a few exceptional cases the resistance W may b e even lessthan (W). Therefore

,although the result obtained above is

not strictly general,but holds under the supposition that the

wasteful resistances do not consume more work during thereverse

,than during the forward motion

,we may

,nevertheless

,

assume that in all cases the efficiency o f hoisting mechanismswhich automatically hold the load suspended without runningdow n is small

,and therefore their employment is

,from

economical reasons,not recommended in cases where great

expenditure of power is required.

On the other hand,where they are not to be in continued

operation,such machines are very useful

,owing to the con

ve n ie n c e with which they may be worked,and because there is

no danger of their accidentally running down .

NOTE — Sin ce th e re lation found above for the e fficiency o f amachine compose d of seve ral me chanisms

,also holds good when it

runs backward,w e find

,re taining th e same notation

,that

(772) (713 ) (on)

From this e quation w e se e that (77) cannot b e negative , unle sssome one of th e factors in th e right hand membe r h as th e negativeSign

,and w e conclude that a machine is capable of supporting th e

load automatically wheneve r any on e of its mechanisms has thisfe ature . It is hardly ne ce ssary to state that w e are not to infe r apositive value for when two o f th e factors of th e right handmembe r are negative , as th e first of th e me chanisms which have thisse lf- locking fe ature w ill prevent th e load from running dow n ; as

regards th e remaining me chanism, w e can no longe r speak of a.reverse

,only a forward motion in one dire ction or th e other.

CHAPTER I

LEVERS AND JACKS

2 . Th e Lever is frequently used for lifting heavy loads bythe application o f a small effort. The height to which a loadcan be lifted by one sweep of the lever is usually very Slight,

a fe w centimetres (one inch) b eing the average ; therefore , inorder to obtain a greater lift

,it is necessary to raise the

fulcrum o f the lever gradually,while the load is being su p

ported in some suitable manner,and then repeat the sw mgi ng

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MECHANICS OF HOISTING MACHINERY CHAP.

A disadvantage in common to the tw o styles of jacks justdescribed arises from the fact that after every lifting movement the load has to be lowered a certain distance duringthe return of the lever. Designating the angle of sweep o f

the lever by a ,and the distances of the points o f application

of the load from the bolts K and L by a =KF and a1

(L

27

and that the load is lowered 2 a 1 sin -gfor every return movement— that is to say , the total lift is only

LF,w e find that the lift for every forward sweep is 2 a sin

h 2 (a al )sin

921 2KL sin

This height h is to be taken as the distance between teeth,or centres of holes in the same row o f the post. Neglectingthe wasteful resistances o f pin friction

,

‘ the useful workperformed by either of these two jacks is found to be

a a KLKFA’

which is only a fraction o f the total work A expended at th e

lever handle E, and it becomes a smaller quantity in the sameratio as the distance

“

between the bolts K and L is reduced.

The Sw ed ish lever - jack,Fig. 3

,is not subject to this

disadvantage. In this apparatus each of the four uprights isprovided with a row o f holes for the pins K and L

,and it is

evident that the load,which rests at the middle of th e lever

LEVERS AND JACKS 9

EE,and in the figure is represented by the beam DC

,used for

uprooting the stub S,can be raised by reciprocating either end

of the lever.This construction is frequently used

,in modified form as in

Fig. 4 ,in hoisting gears for Operating lock gates. The lever

EE is then movable about a pivot C ,fixed in the post GG

,

each side of which it operates alternately on the bolts K andL

,wh ich are inserted in the Slotted bar AB. This bar is

guided in its vertical movement b y the pivot and also by the

central portion FF of the lever EE,which is likewise slotted

in order to prevent Side movement.The manner in which the reciprocatin g motion of a lever

may be utilized,with the aid of a brake, for raising a load,

may be learned from vol. iii. 1 , 1 72,of Weisbach’s Mechan ics.

Denoting the lever arm CK of the load by a ,and that of

the effort by b,w e find the theoretical effort required for

lifting the load Q from

If w e now assume the radius of the journal C to be r,and

that o f the pin K r], and let (I) represent the coefficient of

1 0 MECHANICS OF HOISTING MACHINERY CHAP.

journal friction, w e get,after the lever has been swung an

angle a , the following equation

Pba Qaa <f>(Q P)t'

a n rla,

when th e pressure on the journal is expressed by P Q ,which

gives the required lever effort

and accordingly the efficiency

For the return motion,or when the load being lowered

,

the effort (P) is obtained

and the efficiency

To determine P by graphical methods,describe in Fig. 5,

with C and K as centres, and with gbr and gtrl as radii, thecorresponding friction circles

,

and take the directions o f thereaction Z and the load Qtangential to these circles at01and k

lfor the forward

motion,and at c

2and h

2for

the backward motion. If nowEF

,which is drawn parallel

to these tangents,be made

equal to Q ,the length Is

lll ,

determined by drawing Fcl ,will represent the force P ; and

the length kzl2 ,determined by producing Fc

2 ,will give (P).

In hoisting machines the lever arm a o f the load is muchsmaller than the arm b o f the effort. The size of the journalis fixed by the principles of the strength of materials, and it

LEVERS AND JACKS ” 1 1

is best to use steel in order to reduce the diameter anddiminish the friction as much as possible . As an example ,let us

,

assume the very unfavourable case with respect to

efficiency, that r r1fl

,and let the coefficient 4) 00 8 ; then ,

2

after making the supposition that r r1 ,we obtain th e

fo l l ow mg table for different ratios 5of th e lever arms.

TABLE OF THE EFFICIENCY OF LEVERS.

The small difference in the values of 77 will allow us toassume as a mean 77 0 96

,as in most cases r+ r

,is smaller

a

2

3 . Gear Wh e e ls — The osc illating motion o f the lever issubject to many inconveniences, and for this reason mosthoisting machines aredriven by a rotating shaft.To this end let us imaginethe tw o l ever arms of thejack to be replaced bytwo wheels AC “and BC(Fig. 6) having the radiir and R respectively

,and

fixed to a shaft 0 . TheSmaller of the two is aSpur - wheel gearing with a rack which sustain s the load Q .

If now a force P be allowed to act constantly at thecircumference of the large wheel

,the load Q may be raised

w ithout interrupting its motion. When the action of the

F ig. 6.

1 2 MECHANICS OF HOISTING MACHINERY . CHAP.

w heel is to be greatly increased, however, its diameter wouldh ave to be made so large as to render this means of increasingthe power inconvenient and difficult. In such cases vi e canmake use of the following arrangement. Instead of allowingthe driving force to act directly on CB, this wheel is providedwith teeth and made to gear with a small pinion o f radiusDB = r

l ,which is fixed to the Shaft D . Th e latter may be

driven by a crank DE, or another wheel of radius DE l .

A machine containing one such pair o f wheels, as CB and DB ,

is said to be single - geared.

The action of this simple mechanism is to reduce themotion in the ratio o f r

1to R

,for during one turn of the

crank E,the point of application o f the force moves through a

distance 2 7rR1 ,while the Shaft C is making only a fractional

part o f a revolution, and the load Q is lifted through“ a

7’

distance 2 7rr —1 only. In proportion as the velocity d im inishesR

an increased load is practicable, for which w e have theequation

which gives

when all the wasteful resistances are neglected.

If the value of P proves inconveniently large, E may al sobe made into a spur wheel and allowed to gear into a pinionon a second shaft

,which is acted upon by the driving force

,

and so on indefinitely. Thus,w e distinguish windlasses by

saying that they are singl e , d ou b l e , or treb l e -

geared cases wheremore than three pairs o f gears are used are to be counted asexceptions. While w e may thus arbitrarily increase thep ow er of the Windlass

,it is of course impossible to increase the

w ork d on e during one revolution of the crank ; on the contrary ,with each additional pair '

of gears other wasteful resistancesare introduced

,which consume work and correspondingly

reduce the efficiency o f the whole machine.Owing to the frequency with which cog wheel gearing

LEVERS AND JACKS 1 3

occurs in hoisting apparatus, we deem it necessary to investigate“more thoroughly the wasteful resistances which areoccasioned by these mechanisms.

In Fig. 7 let the driver having the radius CA z r gear withthe larger wheel MA on theshaft M ; let Q be the resistance at A

,acting in the dire c

tion o f the tangent of thepitch circles and opposing therotation of the Shaft M ; then ,in the absence of wastefulresistances

,the force P re

quired at the end of thelever arm CB R is given

b y R= Q% .

But wasteful resistancesarise whenever w e have rel ative motion between machineparts

,hence in the present case they occur between th e teeth

at A and between the journal C and its bearing.

The friction between the teeth,according to iii. 1

,

79,is

l I 1 1

when the slight deviation in the direction of the pressurebetween the teeth from the tangent AO to the pitch circlesis neglected

,and z

1and s

2denote the number of teeth in the

wheels CA and MA. Putting

(INT

w e find the force which is required at A to overcome theresistance Q of the Shaft M to rotation

,to be P

I: ( 1

I ence the efi ci ency of the pair of toothed wheels is

P0 1

77

Th e value of gincreases as the number of teeth dimin ishes ,


and for the gears o f windlasses,where z

2is always considerably

larger than sl ,it is materially affected by the number of teeth

s1of the small Wheel or pinion. In most cases this number

ranges from 7 to 1 2 it seldom exceeds 2 0,and it is only in

the simplest arrangements,waggon jacks for example

,that

the number of teeth in the pinion is less than 7. Let usz

d enote the velocity ratio —1of the wheels by D, then w e may

1 1w ) (I v);

2] Z2 z l

hence

z, + 0°

3 3 ( 1

This value of 77 can always be easily computed, but to obtaina rapid estimate it will be convenient to u se the table below.

This table gives the value of the efficiency

1 z,

a + 06 fl l r fi’

fer the number o f teeth ,z, 5

,6, 7, 8 ,

1 0,1 2

,1 5

,2 0

,in the

pinion,and for the velocity ratios, v = l

,07 5, 0 3

,

0 1,and v 0 for the rack .

TABLE OF THE EFFICIENCY OF TEETH.

Froin this .table w e see that .for the. proportions most fre



tical importance,however

,as in all probability there is greater

error in accepting the coefficients of friction which are d ete rmin e d empirically than in neglecting th e error which arisesfrom the assumption Z P PI . Moreover, w e may add thatwhen a crank CB is fixed to the shaft

,the d irection of the

force P wil l continually change,cau sing the angle a. to assume

all values between 0 ° and and hence the determinationof P

,referred to above as giving a more exact value

,would

only hold for a definite position of the crank.

Under th e above supposition,therefore

,we obtain from

PR PF <1>(P For

1‘

P= P7

,

1l‘

‘ fR‘

and since, in the absence of friction,

P =P

w e have , for the efficiency of the pinion shaft

1 — 4>

r

Introducing the ratio of the lever armsR

v, In thi s

formula, w e find that the expression for the efficiency can bewritten

for which in most cases w e may put approximately

n= 1

The ratio 5, that is to say, the ratio of the radius r of th e

r

j ournal to the radius r o f the smaller wheel , varies between02 and 0 4 in windlasses it is only in waggon - jacks which

LEVERS AND JACKS 17

employ the smallest size of pinion that this ratio will exceed04 , and it is only in shafting that it will fall to 0 1 andbelow. In order to rapidly estimate the influence of thejournal friction in windlasses and hoisting gear

, w e can referto the fol lowing table, which gives for the ratio

0

7°

R h"h, A, 5, and S:and for

0-

5,0-

4,0 -

3,0

-

2,and 0 -

1 ,

the values of the efficiency,

n= 1 <1 w as;

th e coefficient of journal friction being assumed to be 4; 8.

According to this table the e ffiCie n cy of the shaft ranges from0 940 to 09 9 1 , and for the common gears used in windlasses,

r1

c orresponding toR Z

and

e fficiency to be about 7.

If w e wish to determine the efficiency of the combination,

considering both the friction of the teeth and that of thej ou rnal, w e must put

0 3,w e may assume the

TABLE FOR THE EFFICIENCY OF GEAR SHAFTS.

0-

5 09 40 0 -947 0 -950 0-953 0 -955

if 0 4 0 -

95 2 0-

957 0-

960 0-

963 09 64o 0

- 3 09 64 0-968 0 970 09 73

f”; 0

-

2 09 76 0-

979 0 -980 0-98 1 0

-98 2

5 0 -

1 09 88 0 -989 0-

990 0-

99 1 0-991


Therefore for the most common proportions w e may take amean value of

77 x 9 92 2,

or in round numbers For proportions differing mate rially from the above we can find the exact value from the

general formula. Wemay add that the e ffi

c iency (77)for the reversemotion is found from thesame formula by prefixing the contrary Sign tothe terms containingfor

,during the reverse

motion, all the re sistr

an ce s act opposite to thedirections they possessduring the forwardmotion. Hence for thereverse motion

1

(P) <1 0912

and the efficiency,

(1 o (1 95)T

as w e are now considering may beshown in the following pages thatexists in all mechanisms.

4 . Rack and Pinion - Jack . For raising;

loads to small

If1 + ¢R

f

The values of (77)calcu late d from the formuladiffer So l ittl e

”fro

’

m'

77

that the efficiencies forthe forward and reversemotion of such a . traintaken as equal. It will besuch equality by no means


heights th e jack,worked by a

“

pinion and rack, is largelyused in practice. Its arrangement is evident from Figs. 8and 9.

Fig. 8 represents a jack in the form in w hich it is employedin expediting building operations andin the erecting - shops

,while, for

placing heavy pieces of work in thelathe the jack illustrated in Fig. 9 isused. In Fig. 8 the load Q actseither in the axis of the rack at Eor on a claw D . In the latter casethe action Q gives rise to friction atthe bearing surfaces F and H . Thepinion A

,which has but a small

number of teeth ( 5 to meshes withthe rack

,and receives its motion

directly from a crank on the shaft Cwhen the load is small.With greater loads the wheels B

and N and a shaft J are inserted,and

a crank JK is fixed to the latter.A ratchet wheel on this shaft

,held

by a pawl fixed to the frame,prevents

the load from running down whenthe power is removed from the crank.

In order to ascertain the force Prequired to lift the load Q , we mustfirst determine the friction at thebearing surfaces F and H

,Fig. 8.

Let T represent the equal reactionof the guides F and H,

the point of

applications being assumed at themiddle o f the surfaces in contact ;let l represent the vertical distancebetween these horizontal forces ; e thehorizontal distance between the loadQ and the lifting force Q1 , which actsin the pitch - line of the rack ; an d , finally

,let c denote the

a lgebraic sum of the distances o f the guiding surfaces F and Hfrom the point 0

,which represents the intersection o f the lines

2 0 MECHANICS OF HOISTING MACHINERY CRAP.

of action of the force Q1 and the lower reaction T,then th e

equation o f moments about O as a centre is

at Tl

in which the upper sign corresponds to the lifting,and th e

lower to the lowering of the load. Using the upper Sign w e

obtain

so that the total friction of H and F equals

2 ¢T 2 ¢Ql _

e

¢c°

This gives for the lifting force exerted by the rack

on the other hand,when the load is lowered the force exerted

by the rack on the pinion A is given by

(Q1) Q 2 ¢T

Q(1To balance this force Q ,

friction of teeth and journals beingneglected

,would require the application of a force

T

Ql R E

2

2

to the crank JK R2 ,where r

1and r

2denote the radii of th e

pitch circles of the wheels CA and JN,and R

Ithe radius of

the wheels CB. If 771denotes the efficiency of the rack and

pinion CA and the shaft C,and 772

the efficiency of the pinionJN and its shaft J

,the required driving forces will be

,

1

771772

1Q1 % R

2771 772 <1 + 2 ¢ l —

6

¢0>QR1R2Since, w ithout wasteful resistances ,


the efficiency o f the jack for the forward motion becomes

P0

177 13

771 772771772 773 9

i f the value

e

l — c

is regarded as the efficiency of the prismatic guides of the rack.

The force (P)which must be applied to the crank to prevent the running down of the load is determined in the samemanner

,and found to be

0 7°

(1 2 9 5 M)9 17

11

1R“

? (71007907013

0,

where

1 2 9+

3

4,

EXAMPLE — Let Q 400 kilograms [882 l b s ], l = me tree = me tre and c = O

°

O6O me trethen assuming th e coe fficient of friction (sliding)to b e <1)

th e lifting force exerted by th e rack is

and th e force required for lowering is80

= 400 1 - 0(Q1) 3 °400+ 0

°

1 5 x 603 76 -7kg. [83 0 l b s.]

hence th e e fficiency of th e guide s for lifting is400

42 4‘

5773 :

and for lowe ring

400

Let each pinion have 6 te e th, and th e whe e l CB 3 6, then fromth e table on page 1 4 th e e fficiency of th e rack is 09 48

,and for

th e pair o f whe e ls 09 40. If r1

3 0 mm. r2= 2 5 mm .

RI: 1 50 mm . and R

2: 2 00 mm.

then, for a ratio of th e journals

2 2 MECHANICS OF HOISTING MACHINERY" CHAR

th e e fficiency o f th e shaft C,according to table , page 1 7, is

r1 3 0

H] 150

and th e e fficiency of th e shaft J is

V

09 64

Conse quently th e re sulting e fficiency of the shaft C,toge the r

with th e rack and pinion,is

771=O°948

and that o f th e shaft J is-

940 x

This give s for th e e ffort re quire d1 1 3 0 2 5

42P x09 06

x 4 5 x1 50

x

2 001 2 85 kg [2 8 3 l b s ]

As th e theore tical driving force is3 0 2 5

P0 _ 4OOxm x

200— 1 0 kg. [2 2

the e fficiency o f th e machine is1 0

0778, or ne arly 784.

We also find77=n1 772773 =0

'

91 2 x 09 06 x 09 43

This comparative ly small value of 77 is mainly du e to th e smallnumbe r o f te e th and the comparative ly large size of th e journals.

To low e r th e load require s th e application of a force3 0 2 5

P = °9l 2 0°

6 3 k .0 x 90 x 76 778 g [1 7 l ]

to th e crank.

The application of graphical methods for determining th eforce P and the efficiency 77 o f hoists

,and indeed o f all

mechanisms,is to be recommended as simpler than the

numerical calculation,particularly when drawings of the

machine are at hand.

The simple principles u nderly ing such a graphical investigation follow directly from the character o f the angl e of friction ,

and are briefly stated in the appendix to vo l . iii. ,part 1 ,Weisbach’s

Mechan ics (see also Zu r graph isch en Stat-ilc d er Masch inengetriebe ,

von Gustav Herrmann).



equal to that made by the actual line o f action of the teeth .

But the effect of the friction of the teeth is to transfer thetheoretical line of action (which passes through the pointsof contact a and n of the pitch circles) parallel to itself

through a distance 4: (PT, so that the leverage of the

driving force relatively to the axis of the driver is increasedby this amount. Then will 0

3a1represent the line of action

of the pressure Plexerted between the teeth of the rack

and pinion,and 0

47111the line of action of the pressure P

2

between the teeth of the wheels . With the radius (tr drawthe friction - circles about the points C and J ; then thedi rections of the reactions o f the

,j ournals Z

1at C and Z

2at

J are represented by the respective tangents 03c and o

4i to

these friction circles,and passing through the intersec tion

03o f the forces P

Iand P

2and the intersection 0

4o f the forces

P2and P. The shaft at c is acted upon by the three forces

PI ,P2 ,and the reaction Z

1 ,and the shaft J by P

2, P,and the

reaction Z2

. After drawing these lines of action,the polygon

of forces 011 2 3 45 is easily obtained

\from the load l o l by

draw mg1 2 | | ee 1 ; o

l2 | |01 0

(in the figure the latter lines coincide— that is to say , Q ismeasured from the point o f intersection further draw

013 | | b1 b ; 2 3 l|02 o3 ; 3 4 lo c

° 2 4H03 04 ; 45 | |04i, and 2 5 | |04K .

The length 2 5 represents the magnitude o f the driving forceP exerted on the crank K

,and is drawn on the same scale

as Q ,and at the same time the sides of the force polygon

represent the pressures PIand P

2between the teeth o f the

gears,the reactions T

Iand T

2of the guides

,and the reactions

Z1and Z o f the bearings. These forces can now be used for

determining the dimensions of the teeth,j ournals, bearings,

parts of the frame,etc.

The method here shown by a Single example remainsessentially the same for all kinds of mechanisms ; hence weshall only exceptionally give such full details in the followingpages. By constructing a diagram sufficiently large w e obtaina degree of accuracy which suffices for every case. As regardsthe accuracy o f this method, compared with that o f computa


tion,hitherto exclusively used in practice, we may say that

with the graphical method it is unnecessary to make anyapproximate assumption, such , for example

,as that the

pressure of the teeth is perpendicular to the line o f centres.It is only necessary to add that, for the determination of thevertical force P

0,the diagram is constructed in the same

manner by taking the angle of friction,the radii o f th e friction

circles,and the quantity Cal l equal to zero

,consequently the

reactions T normal to the bearing surfaces. For the reverse

motion of the jack the diagram is altered only in this par

Q

Fig. 1 1 . Fig. 1 2.

ticu l ar ; the directions of the reactions , etc.,are inclined to th e

normals of the bearing surfaces at an angle equal to the angleo f friction, but in a contrary direction to that drawn for theforward - motion

,and the reactions of the bearings are re pre

sented in direction by the other of the two possible tangentstouching the friction circles.

5. Jack Screw s — For lifting greater loads to smallheights screws with square threads are frequently used

,and

by turning the screw or its nut, motion is imparted to theload. In the simple jack

,Fig. 1 1 , the screw A is made . to

advance in the fixed nut D by turning the lever E,thus

2 6 MECHANICS OF HOISTING MACHINERY can .

lifting the load which rests on the head C , while in the liftingjacks represented in Figs. 1 2 and 1 3 the advance of the

screw is produced by turning thenut. On the other hand

,Fig. 1 4

,

which is used to lift a rail restingat B on the lever EC

,is worked

by turning the screw A,whose

nut forms a part of lever EC .

Also in the jacks employed for

lifting locomotives for the purposeo f removing or replacing axles

,

etc.,the screw turns and the nut

advances. Such jacks , which arealways employed in pairs

,consist

,

when constructed according toFig. 1 5

,of a vertical screw A

connected with the wooden frameL by the box D and the Step C .

By employing two pairs of gearsFG and HJ the rotation com

Fig. 1 3 mu n icate d to the crank K isimparted with redu ced velocity to the screw

,compelling the

nut M to slide up between the guides on the frame L ; theresult is the lifting of the cross - beam T and its load (1000

F ig. 1 4.

motive , boiler, etc ), the ends o f the beam resting on thenuts M of this double jack.

The object in choosing a pair o f Spur and a pair of bevelwheels is n ot only to obtain the required increase o f power bya reduction in speed , but also to make the working o f thecrank more convenient for the labourers. For very heavy

LEVERS AND JACKS 27

loads the reduced velocity is sometimes obtained by using a

F ig. 17.

Worm wheel an d worm instead of spur wheels. Th is is seen

2 8 MECHANICS OF HOISTING MACHINERY OHAP.

in the apparatus,Fig. 1 6, used for adjusting the vertical

millstone spindle with its runner. The screw A,which is

prevented from turning by the square part B,receives its

vertical motion by revolving a nut,which i s made asa worm

w heel gearing into a worm E,operated by the crank K.

Again,in the jack

,Fig. 1 7, the rotation o f the nut M is

e ffected by the screw S on the crank arbor C .

AS regards the purchase o f a screw or ratio borne by theresistance to the driving effort

,it is shown in vol. iii. part

1, § 1 2 6, of We isb . ,

Mech,th atP

1=Q

1

M+

driving force applied to a point at a distance r from the axisequal to the mean radius of the thread

,and there

,over

coming the load Q , acting along th e axis o f the screw. , In

this formula journal friction is neglected, p. represents the

coefficient of sliding friction of the thread in its be aring,and

Sthe velocity ratio o f the screw is n :

fiz th e tangent of the

angle of the inclination of the helix . Furthermore let r;

denote the lever arm of pivot friction due to the pressureacting in the direction of the axis of the screw

,and rz the

lever arm o f friction between the neck - j ournal and its bearing,

due to the force P acting at right angles to this axis then,

the driving force acting with a leverage R was found to be

r

Q ("I ‘LL

where 4) denotes the coefficient of j ournal friction.

,w here P is the

The theoretical force requi red is Poz nn

,therefore the

efficiency is

R q21 np. r

and hencer

(P) Rn ,

u

LEVERS AND JACKS 29

It w as also noted in the article referred to,that for the

same angle o f inclination of the helix,the efficiency is materi

ally diminished by increasing the radii rland r

2. Therefore

,

in all apparatus of thi s class,in which the n u t is tu rn ed

,a

Smaller effi ciency is to be expected than in those machineswhere the sp in d l e of the screw is turned.

- In the screw jacks as usually constructed,the velocity ratio

n of the helix is seldom greater than 0 1,nor less than

Further, when the screw turns, we may assume as suitable thevalues r

1 0°5r and r2 r. When

,however

,the nut is

rotated,it is provided with a collar - shaped bearing

,having an

inner radius r w e may then generally assume the leverage ofthe collar friction to be r

;1 °5r

,and that of the neck - journal

r

r2

2 r. In the above formula the effect of the ratioRuponthe efficiency is but of secondary importance, for the friction of

the neck - journal of radius r2 depends upon the lever arm R of

the driving force P, only this friction diminishing as R increases.For windl asses, R always considerably exceeds the radius r of

the screw, so thatEseldom amounts to more than

The following table of the efficiencies 77 and (77) for differentvalues of the pitch w as computed on the supposition of a leverarm R= 8r

, jar - 0 1

,and

This table shows the important influence of the wastefulresistances upon the efficiency of the screw - jack

,and that an

estimate made without considering frictional resistances woul dnot be even approximately true. Owing to their smallefficiency

,screws should not be employed in hoisting apparatus

intended for continu ou s and heavy service . On the other hand,

their application is often to be recommended for apparatuswhi ch run intermittently

,owing to th e great security which

they insure against running down by virtue of their self- lockingproperty. That this feature belongs to all the screws containedin the table foll ows from the fact that the values of (77) arenegative throughout.The values of 77 in the table, which refer to the case in

which the screw tu rns, can also be employed for the efficiencyof worm gears

,as is shown in vol. iii. 1 ,

1 3 2,We isb .

MECHANICS OF HOISTING MACHINERY CHAP.



thus th e driving force requ ired isPo 8

7 m— 41 5 kg.

In orde r to de te rmine th e force which must b e applie d to th ecrank to low er th e load, w e find for th e scre w

1 500 -06 - 0 - 1

-084 1 607

(T1 50 0 0 8 x 80 00 06) 00 604

2 55°

As th e the ore tical force , which acts in th e pe riphery o f th e beve lwhe e l of radius 1 50 mm. [5 9 1 in.] is

3 000 x 00 6 x1g):48 kg. [ 1 05

-

8

it follows that th e actual force at this point is48 x kg. [2 69 9 l b s.]

Th e e fficiency o f th e b e ve l gearing be ing 909 66 x 3 09 40,

the re is e vidently ne eded an exertion of1

x 1 2 2-

4 xPE A

- 2 1 7 kg. [47-

85 l b s.]3 00

on th e crank,in orde r to cause th e load to de scend .

EXAMPLE 2 .— Ii th e nut

,by th e addition of a rim

,is made into

a worm whe e l,having a radius ‘

of 1 00 mm . then th ee fficiency of th e screw will b e given by

1 00 x 80 00 60 0 -006)1 00

(P)

60

— 0-2 00.

0 00 06)x 00 840

Now,l et th e mean radius of th e worm b e 40 mm . and

th e ve locity ratio n = and l et u s choose a length of cranke qual to 2 00 mm. [78 7 in .] furthe r, l et u s assume th e leve r arm of

th e pivot to b e rl

1 0 mm. and th e radius of th e journalof th e worm shaft to b e r

2= 1 5 mm. in .] Then (sinc e th e

friction be tween th e worm whe e l and its bearings has already be enincluded in de te rmining th e force required at th e periphe ry of th eworm whe e l — that is to say , included in th e expre ssion 77 02 00)th e e fficiency of th e worm gear will b e

2 00 008 x 1 5 00

-

994 0 -3 93 .

2 000

-

1 8 (1 0 8

Hence th e e fficiency of th e jack screw is-2 00 x 0

-

3 93 00 79.

As th e the ore tical force require d at th e crank is40 40

. r3 000 x 0 06 x1 00

x 0 08 x2 00

1 1 52 kg. [2 0


th e actual forc e w ill b e1 °1 52

P00 79

kg . [3 2- 2 l b s.]

EXAMPLE 3 .

— Finally,l et u s suppose that th e scre w ,

w ith th e

same dimensions, is driven by two pairs of gears as in Fig. 1 5,and

l et u s assume th e radius o f th e pivot to b e 2 0mm. [ 79 that ofth e e nd journal to b e 40 mm. and that of th e spur whe e lon th e scre w shaft 450 mm . 2 then th e efli cie ncy of th e

screw is found to b e450 x 40 m en 0 -006)

4500 — 0

-

006)x 0°

08 xgLet th e spur whe e l s have 1 5 and 75, and th e be ve l whe e ls 1 2 and

48 te e th, then th e re spe ctive e fficiencie s of th e te e th are

1

1 + 0-

3 3 (l1 51

75

— 0-973 .

If now w e assume th e journals of th e ve rtical shaft on which th ewhe e ls are fixe d to have a common radius of 3 0 mm .

and th e beve l and smalle r spur whe e l to have th e re spe ctive radii3 00 mm . in .]and 90 mm . th e e fficiency of thisshaft will b e

3 01 - 00 8 x

3 00

3 01 + 00 8 x

90

In like manne r w e de te rmine th e e fficiency of th e crank axle to b e

1 - 0-

08 x2 0

400

1 + 00 8 x 29

75

by taking its radius e qual to 2 0 mm . 9 th e le ngth o f

crank 400 mm. [1 57 5 and th e radius of th e beve l whe e l75 mm. in .] Consequently

,th e e fficiency o f th e machine

be come sn=0

°2 96 x 09 75 x 09 66 x x

As th e the ore tical force re quired at th e crank is40

x1 5 1 2

00 0 6-

e k . 1 -98 1b .,3 0 x 0 x

400 75 48g [ 3 ]

th e actual driving force required is

kg. [7-s6 1b s.]

3 4 MECHANICS OF HOISTING MACHINERY CRAP."

If w e wish to apply th e principle s o f graphical statics in orderto de te rmine th e e ffort re quire d to ope rate a jack scre w

,w e may

proce e d as follows. LetA,Fig. 1 8

,repre sent th e axis of th e scre w

,

having a me an radius AB ab th e nut o f th e screw carrie s a whe e lof radius AJ this whe e l is drive n by th e spur whe e l HJ fixe d toth e axle H o f th e crank HK. Let th e bearing surface of th e nutb e repre sented by th e ring having a radial width BR br

,and l e t

F ig. 1 8.

its mean radius ac b e taken as -th e leve r arm o f friction. Assume3 8 to b e th e dire ction o f th e thre ad midway be twe en th e oute r andinne r e dge s at a, and a. its angle o f inclination to a plane normal toth e axis. Furthe r, if an

,is th e normal to this line

,and th e angle

nae is constructe d equ al to th e angle of friction p, then, makingda AQ,

and drawing th e horizontal line de through d , w e obtainin th e length dc ace tang (a p)th e force s p 1 o f th e couple actingat th e circumfe re nce of th e screw. Th e force s o f this couple are


repre sente d by DE and DlEl. Now draw th e line af, making an

angle with th e axis o f th e screw e qu al to th e(

corre sponding angleof friction p l , be longing to th e supporting surface 0

,then, similarly,

th e length df will repre sent th e force s p 2 of th e couple,d u e to th e

friction of th e pivot, which couple acts in th e circumferenc e of th e

c ircle AC. Let th e force s o f this couple b e repre sente d by DF andDlFl. By combining th e tw o couple s p 1 and p 2 w e find th e re sultant

c ouple p ,whose force s are repre sente d by DG and DIGI. Let J

b e th e point -o f contact of th e whe e ls, and J1J th e dire ction of th e

p re ssure exe rted by th e te e th, whose inclination to th e line of

c e ntre s is about then th e actual pre ssure,taking friction into

account,will b e e xe rted along th e line LL paralle l to J

1J and at a

d istanc e,u. 2(se e Appendix III. 1 ,We isb . Mech .)from th e latte r,

trepre senting th e pitch and,a th e coe fficient of friction of th e te e th.

The pre ssure PIexe rte d by th e te e th in th e dire ction LL calls forth

a re action in th e bearing of th e nut,whose radius is AR

,w hi ch

re action also acts in, th e dire ction LIL1 tangent to th e friction circleo f AR. But th e tw o couple s p and PI must b e e qual

,a condition

fulfilled only when th e line 0102joining th e points o f interse ction o f

each pair of force s coincide s with the ir re sultant. The re fore , making 0

11 l G

l ,and drawing through 1 a paralle l 1 2 to 0

102 ,th e

length 2 01will give th e force PI as th e actual pre ssure exerte d by

th e te e th o f th e whe e l HJ on th e whe e l AJ . Th e force P requiredat th e crank is now obtaine d simply by comple ting th e triangle of

force s of which 2 01repre sents on e side

,th e other tw o be ing re spe ct

ive ly paralle l to th e dire ction 03K

,and to th e tangent o3 h drawn

from 03to th e friction circle of th e axle H

,th e tangent repre senting

th e dire ction o f re action o f th e be aring. Th e re sult give s as th e

driving forc e P th e length o f th e line 2 3 in th e po lygon 011 2 3 .

6. Differen tial Screw - Jack s.

— Another class o f screwjacks has been constructed

,whi ch depends upon the principle

of differential metion,so that a load can be lifted by imparting

rotation to both screw and nut. As the motions are in thesame direction

,but differ in amount

,the motion axially of the

piece will be proportional to the difference of the rotations.A modern example of this class of lifting jacks is shown in

Fig. 1 9 . Here the motion of the crank K is transmitted bymeans of the bevel wheels D and E to the nut M

,and by

means of C and B to the screw A ; for this purpose the holeo f the wheel B is provided with a feather, which fits a longitu d inal key - way in the screw.

’

Owing to the velocity ratiosc hosen for th e bevel gears

,the screw is rotated faster than the

3 6 MECHANICS OF HOISTING MACHINERY CRAP ,

nut,although the reverse of this arra ngement can be .used .

‘

In order to lower the load at a greater velocity,the bushing J

inf which the crank shaftturns , is made eccentric, so

that a half turn will raise itsufficiently to throw thewheels C and B

,as well as

D and E,out of gear

,leaving

only the wheels C and B1in

gear with each other toOperate the spindle A

,as in

the ordinary jack screw. Thismode of transmitting motionfrom C to B

1is also adapted

for lifting lighter loads,which

requirei

a smaller velocityratio.The action o f this class o f

jacks has been fully investigated

\in vol. iii . 1 , 1 3 0,W e isb .

Al ech .,and it was there found

that a large effi ciency can onlybe obtained by making thepitch of the screw as coarseas possible

,and reducing the

area of the supporting bearings as much as is practicable ; twosuch bearings are employed in the present case

,one for the

Spindle and one for the nut. Under this assumption theefficiency of the apparatus given in the example of theparagraph cited

,for an angle of inclination ct r — 4 5

° or n : 1,

w as found to be 07 1 5. This represents an exceptionally largeefficiency for screws

,and the explanation lies in the unusual

proportions assumed. It is easy to Show that the arrangemento f Fig. 1 9

,using the ordinary proportions (n : to

can have but a very small effi ciency,and that it is reduced

by d iminishing the d ifference between the velocities o f thescrew and nut.

In order to prove this,let the respective angles through

w hich the screw and nu t turn in a given time be denoted by(61and (3

2 ,and again let r express the radius of the helix mid


w ay between the outer and the inner edges of the thread,the

2 7 WThus the load Q Is

lifted through a distance (a)1 662)rn ,

and the useful work performed is expressed by Q ( co 1 (5

2) rn . In addition , work hasbeen performed in overcoming the friction between the threads

,

as well as in the jou rnals and supporting bearings. For thepurpose o f simplifying the calculation

,let the comparatively

unimportant journal friction be entirely neglected,and let us

only take into account the friction between the th reads andthat produced by the load Q at the support at L,

and betweenthe nut and its support at G. The friction generated at thetwo latter surfaces depends on Q ,

and is given by n . Lettingthe mean lever - arm of friction for the bearing at L be rl , andfor the nut w e can express the useful and lost work by thefollowing equation

way"HQ<w i (“

elf ¢Q<w 1rl ( 02th) Q[(w 1 weld”I‘)

w2r2)]

Therefore,neglectin g the friction due to transverse action of

the driving force,the efficiency becomes:

velocity ratio of this helix being n :

Use fu l w ork (to l w 2)rn

En e rgy e xpe n d e d w2)r(n [.L) w

2r2)

If in this expression we put n : 00 6,as in the examples of

the precedi ng paragraph,and place 0

°

5r and 1°

5r,as

being the smallest possible values ; and if w e further assumethe velocity ratio to be a) :w w e shall obtain an e ffici

1 2

ency:(4 3 )0

°

06r

(4 0 °06)r + x 0 5 3 x 1°

5)r x

0 08 8,

that Is not quite The friction of the neck - journalsfurther reduces the efficiency. When the difference betweenthe angular velocities 60

1and (5

2is taken smaller than the above

assumed values,the effi ciency will be stil l smaller. Construo

tions of this kind,therefore

,give a great efficiency only when

the pitch of the screw is coarse and the radii of the bearingsare small.

CHAPTER II

TACKLE AND DIFFERENTIAL BLOCKS

7. Pu lle ys — The hoisting arrangements thus far mentionedare suitable for small lifts only. FOr greater heights rop es or.chains passing over pulleys or drums are made use of. Thesimplest arrangement o f this kind is shOw n in Fig. 2 0

,which .

illustrates the single fixed or gu id e p u l l ey commonly employedin practice .A rope sustaining the load Q upon the part BC passes over

the p li l l ey A,which turns in a fixed bracket or support G

,and

the load i s lifted by applying a pullP to the other end o f the rope in thedirection DE.

As the distances through whichthe driving force and resistance act

are equal,the theoretical force

P02 0The wastefu l resistances in the

present case are: stiffness Of" the

rope,or friction connected with the

u se of the chain,and journal friction ;

taking these into account th e actualpull P is determined as follows. Let

0 denote the coefficient o f the resistance Opposing th e motionof the rope or chain as it moves on or leaves the pulley ;according to vol. i . 2 00

,W e isb . Mech ,

this resistance isproportional to the tension Q in the advancing part o f therope

,and is to be taken equal to a Q ; its effect is the same

as if a force arQ resisted the motion of the rope at the points '

B and D at which the rope is bent. Denote by Z the pressure

Fig. 20.


40 MECHANICS OF HOISTING MACHINERY CRAP.

This gives for the effi ciency o f the reverse motion

as in the case of the forward motion. When the two portionsof the rope are parallel a more exact value for It is given bythe equation

Qr e o Pr (MP Q)r,

which gives

hence

a value which in most cases differs b u t little from the above

given 1 2 0 °

In fixing a value for 0'

w e must make a distinction betweenchains and ropes . It has been shown in vol. i. 2 00

,W e isb .

Mech,that for chains the friction at the joints where bending

occurs,due to the tension Q ,

is given by

8

¢1Q273

where 951 represents the coefficient o f friction for the links,

and 8 the diameter of the round iron in chain . We thereforehave for chains

In the case o f ropes, fuller information concerning theresistance due to stiffness is also to be found in vol . i . 2 02

and following of the work referred to. Basing our calculation son the formula of Egte lw ein ,

the resistance due to bending the

II TACKLE AND D IFFERENTIAL BLOCKS 41

rope to the curvature of the pulley and then straightening itagain

,is

3 2

2 0 'Q O'OI8FQ

T,

where 8 and r are expressed in millimetres.

3 2

[ 2 0 Q Q when 8 and r are in inche s]7.

Therefore for ropes we have3 2

2 o = 0°

457

For the ordinary chain pulleys,as used in hoisting - tackle and

windlasses,it is customary to take the radius r o f the pulley

not less than 1 08. Assuming this proportion and a co

e ffic ie nt of friction TI 02,w e find for chains

82 0 ° 2 x 0 2 x

2 08

that is,a value independent of the diameter o f chain iron.

A suitable radius for rope pulleys is r: 48,which gives82

that is,a value directly proportional to the diameter of the

rope.Assuming a diameter of pin

2 1? d 3 8 for chain pulleys,

2 r d 8 for rope pulleys,

and a coefficient o f journal friction ct 00 8,the values o f the

efficiency of the fixed pulley

Re dte n b ach e r give s, accord ing to th e expe riments o f Prong,

52

(for metre s)

th is w ou l d give

52

(for mil l imetre s)


have been calculated for arcs of contact 2 a = andand tabulated as follows

TABLE OF THE EFFICIENCY OF THE F IXED PULLEY.

l77 k r

sm a

Diam eter o f Rope . 1 0 mm . 2 0 mm . 3 0 mm . 40 mm . 50 mm .

-

3 9 in . ]-

79 in . ] [ 1-

1 8 in . ][ 1-57 in . [ 1

-

97 in .

Ch ains

2 a 1 80°

09 3 9 09 01 08 66 08 3 3 08 03 09 58

2 a 1 2 0 09 42 09 0 3 08 68 08 3 5 08 05 09 60

2 a = 90°

09 44 09 06 08 70 08 3 7 08 07 09 64

In the preceding calculation th e weight of the pulley h as

been neglected,as its effect on the journal friction is slight in

comparison with that of the forces acting on the rope or chain ;in individual cases more exactness may be desirable

,and then

the pressure on the jou rnal should be increased by thisamount.The influence of the weight of the ascending and descend

ing ropes and chains will be examined later.The ratio between the effort and resistance for the mov

abl e p u l l ey can be easily derived from the relation P = lcQalready found for the fixed pulley. For this purpose let thepulley A

,Fig. 2 1 ,

having the two parts o f the rope parallel,

be suspended from a fixed hanger AF,and let the tension pro

du c e d in the part BC by the load carried be denoted by S ,then in order to bring about motion in the direction of thearrow

,a force kS must be applied to the part DE,

so that thehanger has to resist a total pressure Z = S+ lcS = S( I + h).In this case

,when the pulling end o f the rope passes over a

certain distance 8,the load Q at the other end must rise through

the same distance. The mutual relations between the forcesQ ,P

,and Z will not be altered

,no matter what motion is

given to the whole system,consisting o f the pulley with its

hanger and both ends o f the rope,as the relative motions of

the individual parts will remain the same as before. Therefore, if we introduce at each instant an additional motion


equal to that of Q ,only in opposite direction

,that is

,if the

whole system be shifted vertically downward a distance 3,then

the load Q will come to rest, and the end C of the rope maybe considered as attached to a fixed point. The pulley, together with the force Z

,is shifted a distance 8 in a direction

contrary to that in which Z acts,while the pulling part DE

,

besides its previous motion measured by s, receives an equal

additional motion,so that the point of application of the force

P moves through a distance 2 8 in the direction in which th e

latter acts.Through this reasoning w e can pass from th e

fixed to the movabl e p u l l ey, which in Fig. is represented in

P=k S

F ig. 2 1 .

th e usual inverted position. Here the end of part BC is attach e d to the fixed point C

,which reacts with a force S’

,while

,

as before,the pulling force P hS

’

,tends to impart rotation to

the pulley,and thus lift the load

,which is now represented by

the pressure Z S( 1 h) on the pin. The energy exerted isexpressed by kS x 2 8, while the useful work performed is

S(I k)x 3 .

Thus the efficiency of the movable pul ley is found to be

1 k

which is greater than the efficiency 1 of the fixed pulley,

79

since 79 is always greater than unity.

44 MECHANICS OF HOISTING MACHINERY can .

By communicating motion to the movable pulley in thedirection of the load Z

,w e can also determin e the formulae

applicable to the reverse motion , during which the pointof application of P is moved downward . In this case Prepresents the useful resistance

,and Z the driving force .

During the descent o f the pulley the part DE is woundon

,and the . part BC unwound, so that the tension in BC

becomes equal to hS,while that in DE will be denoted

by S. Accordingly,the bearing pressure Z is again given by

S( 1 As the energy expended is expressed by S( I + 75)x s,

and the useful work performed by S x 2 8 , the efficiencythe reverse motion of the movable pulley becomes

S2 E 2

i + k

This expression may be obtained directly from the value forthe forward motion

1by substituting

hfor h

, and taking the reciprocal of the

result,inasmuch as

P <P>7) 193 11 61 07) P

0

°

It also follows th at the value (77, for the reverse

motion must be less than the value 77: for the

motion,since 2 x 2 h < ( 1

For example,if for a particular pulley w e had

h = 1 + 2 o 2 3 2-

4 1 1,

the efficiencies would be

a. 77 (77)llI

09 09 for th e fixe d pulley.

09 55 for th e forward mo tion o fmovable pulley.

09 52 fo r th e reve rse motion o f movable pulley.

I I TACKLE AND D IFFERENTIAL BLOCKS 45

The relation between effort and resistance in the pulleycan be easily determined by graphical methods. Let BC andDE

,Fig. 2 3 , again represent the centre lines of the parts of

the rope ; then draw parallel to them and at a distance8

0 o°

0098°[o 02 2 882]for ropes , or ¢1§for chains

,the lines

o f action bc and etc of the forces , and from the point o f inte rsection 0 draw the corresponding tangent ou to the frictioncircle o f the journal

,which circle is described with a radius

(tr. In this construction the lever arm Ab of the resistancemust be taken larger

,and that of the effort Ad smaller

by the amount 0° than the radiu s r o f the pulley. Making

0 1 z Q,and drawing 1 2 parallel to ol e

, the force P will begiven by 1 2

,and the reaction of the bearing by 2 0.

Fig. 24.

For the movable pulley,Fig. 2 4

,draw the lines o f action

cb and ed of the forces at a distance 0 ' from and parallel to thecentre lines o f the rope, and assume the reaction 0a of thebearing tangent to the friction circle of the journal and parallelto the parts of the rope. Make a 1 = Z

,draw th rough 1 the

horizontal line e 1 c,and connect at and c ; then the driving

force P will be represented by 1 0 eg, and the reaction of th e

fixed poin t C by oa hb .


In the following

TABLE OF THE EFFICIENCY OFo

THE MOVABLE PULLEY

Diam . o f Rope . 1 0 mm . 2 0 mm . 3 0 mm . 40 mm . 50 mm .

8: in .] in . ] in . j in . ]

09 70 09 50 09 3 3 0 91 7 09 02

09 68 09 46 09 2 8 09 09 08 91

are contained the results for the forward and reverse motionobtained under the same suppositions as previously for thefixed pulley, that is

r 48 and 2 1° d 8 for rope s.

r 108 an d 2 1° d 3 8 for chains.

8 . Hoisting - Tack le — VVith th e"aid o f the preceding

paragraphs it now becomes an easy matter to determine therelations between the forces acting in the many differentsystems o f pulleys used in practice under the name o f tackl e .

There is but one rule to be observed in such contrivancesnamely

,that in every case w h ere a rop e en circl es a p u l l ey , th e

tension in th e u nw in d ing p art is equ a l to 76 times th e ten si on in

th e advan cing p art; h as before representing the coefficient ofresistance for the pulley

All combinations o f pulleys are included under the headof tackle

,but we may make a distinction

,though not very

.

marked,between the arrangement in which each b l ock in the

combination has but a single pulley or sh eave,and that in

which the several sheaves are mounted side by side In a frameor block.

A simple combination o f pulleys o f the former kind is shownin Fig. 2 5 . Here the weight Q is suspended from the movableblock A

,which hangs in the bight of a rope

,one e nd o f Which

,

called the su sp end ing part, is attached to the fixed point F1 ,



As the pull on the Spindle o f the pulley B is S w e find ina similar manner the tension in the part J to be

k k 2

S2 1 + lc

SI (1 + k Q’

and for the part Kk k 3

°3

_

1 + ks2 <1 + k>Q ‘

Fin ally,for the tension S4 in the hauling part L of the

fixed pulley we haveIt

1 + lcS4= kS

3= k(

In general for one fixed and n movable pull eys the actualforce required is

and the efficiencyPO

1 1 + h

>7

f’7

"

P 1? 2 15 x

If the tackle shown in Fig. 2 5 were inverted and su s

pended by the pulley A,the fixed pulley D being omitted

,and

the driving force made to act directly on the part K,then the

load may be carried on the three parts M,N

,and O at the

points F1 ,F2 ,F3. For this case let S denote the tension in

F1M

,and S’ and S”the tensions in F

2N and F

30 ,then for the

part H we haveSIkS

,

from which we deduce the tension in F2N

,

1 k— S.

1 + 1681 1 k

Similarly for the part J we h ave,

S2kS

' k S.

hence the tension in F Ol h 2

Sl 19

82 (I k)

1 1 TACKLE AND DIFFERENTIAL BLOCKS

and in the ply K the tension

P ;S3kS k S

accordingly for the load Q we obtain

75 101Q S + S + S s

and consequently the driving force

Without wasteful resistances w e Should have

P0= S

3= S

therefore= 7S = 7P

and the efficiencyPO

1 3 k 3 k2

’7 P 7133

Another arrangement of tackle is Show nin Fig. 2 6. Here th e ropes , which are

made fast to the blocks A, B,and C

,

are passed around the three pulleys,D

,

E,and F

,from which the load Q is

suspended. Supposing a force P to beapplied to the part G

,then

,without

hurtful resistances,the tensions in J and

H will be P,and thus in each o f the parts

K , L, and M there will be a tension o f

3 P. Consequently the force acting in partN will be 9P

,which also represents the

tensions in O and T ; by adding togetherthe forces we obtain

Evidently the distances travelled bythe points of application o f the effort andload are also in the same ratio of

Owing to the varying dimensions o f pulleys

49


ropes, the values of h differ for the different pulleys. If

a mean value of

( 1 + 2 0‘

+

0

2 35)be assumed for all th e pulleys

,then the application of a force

P to the part G wil l produce in J the tension

further,in H

,the tension

and consequently the force acting in K will be expressed byP( 1 77

In the same manner we find the tensi on In the parts

L to be P( l 17 and in M to b e P( l 27

thus giving the pressure on the pin in the block B equal toP( 1 n

For the part T we find the value

P(1 °

2 778277,

and for OP(1 n 770

27729 ;

therefore the force exerted on the hook U is

P( l 7)

For the load Q,which is equal to the sum of the tensions in

the parts H,J,M

,L

,. O

,and T

,we find

Such tackle find very l ittle application in practice forraising heavy loads by means o f a small effort

,as even for

moderate lifts the height required by the arrangement is consid e rab l e , which fact is a pparent from Figs . 2 5 and 2 6 . In

Fig. 2 5,for example

,a lift h o f the load requires a space 2 h

between the pulleys A and B,and a space 4h between B

and C,so that the height of the fixed pulley D above th e

lowest position of the load must be at least six times the lift h .

Ir TACKLE AND D IFFERENTIAL BLOCKS 51

Iri Fig. 2 6 it appears that the arrangement is still more

unfavourable in this respect . On the other hand,such systems o f

pulleys are frequently to be met with in the modern hydraulichoists

,where . the stroke of the piston working under high

pressure is greatly multiplied,and thus increases the range o f

motion o f a comparatively small load. This is effected byinverting the system so as to carry the load at the free endof the rope, while the movable pulley, say A,

Fig. 2 5,is acted

upon by the effort P. More detailed information on this classof hoists will be found in the following.

On the other hand,the Second class o f tackle mentioned

on page 4 6 is far more generally used,bein g employed for

lifting heavy weights to considerable heights by the applicationo f a small force

,hand power for instance.

A clear idea of the mode of action is obtained from Fig. 2 7,

in which the pulleys of each b l bck are placed on se parate pins,

although in reality thearrangement generallypreferred is to placethe sheaves either sideby side on a commonstud in the block

,or

below each other onseparate pins . Themanner of suspending Pthe load Q from thel ower block which contains the sheaves C

,E

,

G,and the mode o f

F ig' 27°

passing the rope over the sheaves,is evident from the figure.

The most common arrangement is to place the same number of sheaves in each block ,

this number frequently beingthree

,seldom or never more than four. On e block may be

given an extra sheave,however, for instance , by omitting the

sheave G,and securing the rope to the lower block , or by

leaving out the fixed sheave B ,and allowing the driving force

to act on the part rising from C .

In the arrangement represented in the figure the load Q issustained by six plies o f the rope, the tension in each , neglecting all wasteful resistances

,being equal to the force P

0in


the haulin g part BA. Therefore in this case Q 6P0 ; or in

general for n carrying parts Q nP. Taking friction andstiffness of rope into account

,the .tensions in the different

parts wil l not be equal . Then if SI , S2 , S3 S7represent

the tensions in the plies,and k the coefficient of resistance

73 : 1 (which is assumed the same for al l the

sheaves), w e have S2

S176 S

3S213 S

lk2

,etc.

,and in general

for the uth ply S,= S1 1

3“. The tension S

7in the pulling

end A is given by P _

—_ S

7= S

173“

,or In general for n sheaves,

by Sn+ 1

SI75”

.

The load Q is found by means of

or in general for n sheaves

kn- 1)

- S

Sin ce P the efficiency o f a tackle having six sheaves is

P0 go It“- 1

’7P as 6k6(k

and generallyh"1

’71)

The pull on the upper block is given by

Therefore , when the lower block is fixed,and this force Z is

employed to raise a load Q z Z,the efficiency is

1 1

P9 n + 1 u + 1 hn'H — l

P sn+ 1 sle — 1)

which expression , for the movable pulley, that is, for n = 1 ,

becomes equal to the value already deduced,namely


In order to determine the efficiency for the reverse motion,

with a view to calculating the force (P)which must be appliedto the free end A o f the rope so as to balance the load Q,

w e

first substitute for Is and find (P) and as in this case

1

l 1 len — l= S

l kn- 1(lc

l

the efficiency becomesS ukn

- lac 1 ) u (h 1)

P

The graphical determination of the forces acting in a tackleis easil y obtained by applying the methods previously employed.

Let A,Fig. 2 8

,be the middle o f

,a

horizontal diameter BC: 2 r o f asheave

,measured from centre to

centre of rope ; lay o ff Bb and Coequal to a on the same side o f theextremities of this diameter ; makeAal equal to the radius (tr of thefriction circle of the journal

,so

that alb r 0

°

ctr, and alc r

(7 + ctr. Now lay o ff upon thevertical through b the length b l

equal to the tension S1in the

fixed part of the rope,and draw

the straight line l al2 then the

portion c 2 of the vertical throughc will represent the tension S asaccording to the construction

S1 (r o (tr) S2 (r o ctr).

In order to find the tension in the remaining parts,we have

onl y to make ca2

bal , and draw a line from 2 through a

2then

b 3 will represent the tension S3 ,and drawing 3 a

1we shall have

04 S4 etc. Thus b7 will give the pu ll in g force P for a tacklehaving six sheaves ; and the load will be represented by thesum o f the lengths

b l

0

F ig. 2 8.


This diagram also holds for th e reverse motion ; though inthis case the pull exerted on the free end of the rope is re pre

sented by the length b l,when the running block descends

under the action of a load

The following table gives the efficiency of tackles both forthe forward and reverse motions the number of sheaves rangesfrom two to eight

,and the chains and sizes o f rope are those

which occur most frequently in practice.The relations of the radii o f the pins and sheaves to the

diameter of the rope or round iron composing the link (in thecase o f chains) are the same as those previously assumed for

the fixed and movable pulley.

TABLE OF THE EFFICIENCY OF TACKLE.

The table shows how in tackle operated by large ropes theresistances are considerably greater than in chain tackles

,the

efficiency of the latter being independent of the diameter o f

link iron,under the above assumption that the radii of pulleys

and pins are directly proportional to the size of lin k iron .

The preceding results also apply to the ordinary tackle,Fig.

2 9,page 55

,in which sheaves of the same diameter are placed

side by side in a block,and turn loosely on a common shaft or

pin. Were the sheaves secured to the shaft,and the latter



and 6. With this form of tackle,designed b y

'

Wh ite,a small

gudgeon may be employed,thus reducing the friction

,but it is

not much used in practice,as the resistances due to stiffness of

rope are largely increased when small sheaves are employed.

Besides,on account o f the rope thickness it is impossible

wholly to prevent slipping.

Sometimes the blocks are arranged one above another,

Fig. 3 1,in which case the sheaves o f each block have different

diameters so as to prevent the plies of rope from rubbingagainst each other. The deductions already made are alsoapplicable to this form o f tackle

,only w e must here for each

sheave substitute the value of

r

pertaining to it. This arrangement is riot to be recommended,

for here again the resistances due to stiffness of the rope areunnecessarily large for the smallersheaves

,and moreover

,owing to

the increased length Of theblocks

,the efficient height to

which the load can be raised isto ‘ some extent diminished.

So far the weight o f therope itself has been neglected.

As regards its effect upon thepin fric tion and on the resistancedue to stiffness o f the rope, it isadmissible in almost every caseto neglect this factor on accounto f its in sign ificanc e . On theother hand

,the work which must

be expended for ra1s1ng thew eight of the rope , as also thework performed by the rope inits descent

,demand special con

sideration in many cases.Let the weight o f a unit of length (metre) o f rope be put

equal to g, and l e t it be assumed that in the case o f the fixedpulley R

,Fig. 3 2

,the point of application A o f the effort, th e

F ig 3 2 . Fig. 3 3 . F ig. 3 4.


position of the workman , for instance, is at a height AB = a

above the position of the load Q. In raising this load Qthrough a height BC = h

,a portion o f rope o f the length h

,

and weight hg, and represented by its centre of gravity S ,reaches the level of A. The energy expended in raising this

hweight of rope through a height SA = a

2,

hL = hg<a

For h = 2 a, L : 0, and for a greater lift L would evenbecome negative ; that is , the energy exerted by the portion o f

rope between R and A in its descent would be greater thanthe work performed in lifting the portion between Q and R ;this case deserves attention when blocks are employed on highscaffoldings where the driving force is applied below.

In the movable pulley B,Fig. 3 3 ,

when the load Q israised through the same height BC = h

,a weight of rope

h2 hg is lifted a distance SA = a accord ingly the corre

2

spond ing work performed is expressed by L 2 72g(a g).If a second pulley D ,

Fig. 3 4,is suspended from B at a

distance a1therefrom

,it will be seen that when the load Q

has been lifted through a height DE = h,the pulley B wil l

have passed over a distance BC = 2 h ; consequently the path

of the lower piece of rope is expressed by SIS and"

ithat o f the u pper piece by SA = a — h . Thus the workperformed is found to be

L 4hg(a h) 2 hq(a1 g) hg(4a 2 a1

3 h).

If a third movable pulley be suspended from D a distancea2below it

,w e shall in like manner find for the total work

required to raise the three parts of rope

L 8hg(a 2 2) 4hg(al h) 2 hg(a,hg(8a 4a

12 a

21 1 h)


In order to obtain the maximum effective lift in sucharrangements

,the pulleys must be brought as near together as

possible in their lowest position ; therefore, putting a 1 a 0,

w e have2

L hg(8a 1 l k),

and in general for n movable pulleys

2 2”- 1 1

3h).

For an ordinary tackle with n Sheaves which correspond tothe fixed and movable pulleys in Fig. 3 3

,- w e find the work

consumed for lifting the rope to be

hL = ngh<a

EXAMPLE — In an 8 - sheave d tackle with a lift of 6 me tre sand whe re th e rope w e ighs 05 kilograms pe r me tre

pe r foot), th e work re quire d for lifting th e rope is

L= 8 x 05 x m etre kil ograms (3 47 fo ot pou n d s),3

when th e workmen are located 5 me tre s ft.) above theload.

Assuming th e workmen to stand at a he ight o f 3 me tre s aboveth e load, th e w ork require d for th e same purpose would b e reduce dto zero

,and we re they place d on a leve l with th e load, w e shou ld

findL= 8 x x 72 metre kil ograms 52 2 ft. l b s.]

Supposing th e we ight of th e load Q : 400 kilograms [882th e assistance rende re d by th e we ight of th e rope would b e

72

400 x 6

driving force,th e we ights o f th e running blocks are

,o f course

,to b e

adde d to th e load lifte d . Th e e ffe ct o f th e we ight o f th e sheave supon th e pin friction may b e negle cte d, inasmuch as th e action of

this we ight is to diminish th e pre ssure on th e pin o f th e lowe r blockby th e same amount as this pre ssure is increased in th e uppe rblock.

Th e u se o f tackle is confine d chiefly to building ope rations andth e rigging o f ships. Such appliance s are not adapte d for heavyservice o n acco unt o f th e inconvenience attending both th e returno f th e running ,

block when empty, and th e handling of long rope sand chains. On th e other hand, this form . of hoisting ge ar is of

3 pe r cent of th e total use ful work. In de te rmining th e


gre at value for temporary se rvice in lifting mode rate loads,which

accounts for its u se in building ope rations, and also for manoeuvringsails

,etc .

,on board ships. From th e table on page 54 it appears

that,as a rule , th e e fficiency of a chain tackle is gre ate r than that

o f a large rope tackle .

§ 9. Th e Differential Pu l ley - Block . Th e comparativeSimplicity of this form o f h oisting gear, as constructed byWeston

,has led to its extensive adop

tion in machine shops and in buil ding operations . Its name is due tothe fact that a movable pulley isemployed

,which is caused to ascend

with a velocity proportional to thedifference of the motions of the twoparts o f the chain passing over it.The contrivance consists of twopulleys running in separate blocks

,

A and F,Fig. 3 5

,the lower GH

being an ordinary movable pulleycarrying a hook J for attaching theload Q . The upper pulley is providedwith two grooves for the chain

,one

of these DE having a somewhatlarger diameter than the other BC .

An end l ess chain K connects the twopulleys in a manner shown in thefigure

, passing first over the smallerpulley in the direction CB

,then

downward to the movable pul leywhi ch it supports in the loop GH

,

and finally up over the large pulleyED . The load is lifted by hauling onthe part DK

,thus imparting motion

to the upper pulley in the directiono f the arrow. For if w e imagine thispul l ey to have moved through acertain angle

,say one complete

revolution , then a portion 2 7rR Of the cham will be woundon at E, while a portion equal to wil l be unwound onthe other side of the smaller pulley at B

,when R and r


denote the radii o f the two pul ley grooves . In Consequence,

the portion of the chain which carries the movable pulley isshortened by the amount

2 rr(R

so that the pulley F,together with its load Q , is lifted through

a height 71-

(R r) equal to one—half that distance . Since theeffort P has travelled the path 2 7rR,

we obtain,when wasteful

resistances are neglected,the theoretical force required

As the tension in part CK of the chain is very slight,due

as it is to the weight of this portion of the chain only,i t is

evident that the chain,unl ess checked

,would slide down

over the upper pulley on account o f the far greater tension S,

generated by the load Q in part BG ; in order to prevent suchsliding motion

,the upper pulley is provided with pockets

made to fit the links of the chain , Fig. 3 6 . Here we find thereason why the use of ropes is n ot feasible in this type of

hoists.This hoistin g gear

,as commonly constructed

,is capable of

sustaining the load automatically,a feature of prime importance

in many cases,although it is combined with the

disadvantage of a small efficiency as previouslyreferred to . In order to determine the latteras well as the actual effort P required

,let R

denote the radius of the larger pulley groove AD,

r that o f the smaller groove AB,and that o f the

movable pul ley FG,the latter two most always

being made of the same or nearly the samesize ; further, let r denote the radii o f the pins

A and F, the c o efiic ient of friction for the chain, <1) the

coefficient of friction for the pin,and 8 the size of the round

iron of which the cham Is made . Then,denoting the tension

in the part BG by S,and that in HE by SI , we shall have for

the movable pulley F as before

Sl r Sr (4158- 8 95158 1 S

l )’


from which follows

if,for the sake o f brevity

,we place

Moreover,since

it follows that

s Qand S

as in the ordinary movable pulley.

For determining the equation o f moments for the fixedpulley

,w e will regard the tensions s in the chain BG and P

in the part DK as the drivin g forces,and the tensions S

Iin

EH,together with all the wasteful resistances

,as the opposing

forces we then obtain the equation

PR Sr S,R S

,)R (ing—!Sr S S,)r,

from which,after dividing through by R

,we get

8 r r

7°1 “ T1

527.

RI1

Since R and r always differ by a small fraction only (ordinarily9 1 4

TOR to

T5R)’ we can put

81 - ¢ 1 2R

_

and thus place the coefficient o f SIequal to 76. As result w e

obtain17

‘

P : Sl

'k SR: QR 1 + k

(°1 + cc

62 MECHANICS OF HOISTING MACHINERY CHAP.

Placing the ratio n,w e have

and as w e have found

R — 7' l — n

PO

L—”Q M Q

2,

w e obtain for the efficiency

P0

1 — n 1 + lc77 P 2 kz — n

'

For the reverse motion of the block all wasteful resistances actin the opposite direction hence

,in order to obtain the formulae

applicable to this motion,we have only to give the terms con

taining <1) and 961 Opposite al gebraic signs ; that is, in place o fthe quantity

8 r

8 t

o o

8 rl — e f

2 ’

1 + gl> —8 r

12 7‘ 7

'

Thus w e find for the reverse motion the force applied

and for the efficiency

QP) 2 1 — nk2

l — n k2 + k

In the differential block the radu R and r

ch ain pulley depend on the proportions of thechain

,as the inside length of the link must be



In the following table will be found th e values of 7) andcorresponding to the ratios

0

R 07 5, o-

so, 0

-

9, 0-

9 3 3,

for a mean value o f

TABLE OF THE EFFICIENCY OF DIFFERENTIAL PULLEY-BLOCKS .

2 1 — nk2

(77)l

1 06

This table plainly shows the slight efficiency of ordinarydifferential pulley - blocks with slightly differing radii, and it istherefore evident that they are also to be cou nted among thekinds of hoists which are not to b e recommended for continu ou sservice

,on account of their want of economy of power. On

the other hand,owing to their self- sustaining property

,they

must be regarded as useful apparatus for occasiona l u se in

machine shops,erecting shops

,and in building operations.

They possess the advantage over the screw - jack of being moreeasily adjusted for greater lifts

,besides being simpler in con

struction and mode of application . Their disadvantage, in common with all chain pulleys

,consists in the stretching of the

chain under the stress to whi ch it is subjected,the result

being that the links no longer fit accurately in the pockets ofthe pulley groove.Th e negative value o f (n) signifies that the block is self

7°

sustaining,and the limit o f the ratio n

R’at which this self

locking property commences,is found from the equation

1

(77) 0, hence I - nk2 = 0,or n

132,

1 1 TACKLE AND D IFFERENTIAL BLOCKS 65

For example,if k 6

, the limiting value o f this ratio is7°

given by n

R08 89.

In order to determine graphically the pul l P which isnecessary to drive the differe ntial pulley w e may proceedas follows

If GH,Fig. 3 7, is the

movable pulley,then draw in

the direction in which theload Q is assumed to act th evertical tangent ff l to thefriction circle of the pin

'

F,

which circle has a radiusFurther

,draw the lines Mg

and Oh,which represent the

tensions S and SIin the chain

parallel to the line o f action8

o f Q ,and at distances 0

°

gb 1 2

from the tangents at G andH

,the former at G away from

the latter at H,toward the

centre F. Now,divide the

load Q M 1 at N,so that

MN l = Of l zf1M ;

for this purpose draw MO

perpendicular to M 1,connect

O with 1,and through f 2 , th e

point o f intersection betweenthe lines 0 1 and f l f , draw thehorizontal line f2N thus MN Fig° 3 7°

S will give the tension in the chain BG,and N1 S

Ithat

in EH. These forces are supposed to act on the fixed pulleyalong the ve rtic l e s b and c

,which lie at a distance 0

° from thevertical tangents at B and E

,and are located inside the chain

which winds o ff at B and outside that which winds on at E.

Besides,the force P acts in the vertical d at a distance 0

° fromthe tangent at D . These three parallel forces are held in

F


equilibrium by the reaction Z S + S1+ P of the bearing A

,

which reaction is represented by o z, located at a distance

(film! from the centre A.

The problem is thereforeso to determine P that theresultant o f S

,SI ,and P

shall coincide with za . Herew e may use the polygon of

forces MN1 with O as thepole . For this purposedraw through any point I)o f th e line of action of S

,

the l ines but and parallelto the pole rays OM andON ; further

,draw

,87

parallel to 0 1,and join

Then afy will give thedirection in which 0 2 is tobe drawn

,which line to

gether° with 0 1 determinesthe length 1 2

,which

,

measured according to thescale assumed

,will repre

sent the required force P.

If we wish to investigate the reverse motion bythis nie th od

,S and S

I

must be interchanged,that

is,make

lay o ff 0 and (pr in directionsopposite to those of thepreceding construction and

,

with the aid of the lines o faction of the forces

,com

pl ete the force and equ il i

b rium polygons,as show n

in the figure by the dottedlines. The length re

presents the force (P), and the upward . d irection in whichit is drawn shows that the tackle is selflocking, as during

II TACKLE AND DIFFERENTIAL BLOCKS 67

the reverse motion the upward force (P) turns thepulley D in the same direction in which the load Q tend sto turn it.

1 0. Oth er Forms of Tackl e — A great variety of tacklehave been constructed

,a fe w o f which we will now describe

in detail. In the arrangement shown in Fig. 3 8,the load Q

i s suspended from the hook G of a running block F,one end

o f the chain being made fast to the upper block at C,while

th e other end is carried over the pulley AB and down to N,

where it is secured to the chain CD by means of a ring. As

in the differential tackle,the pulley B is provided with pockets

for the links of the chain,in order to prevent slipping.

Motion is imparted to this pulley B by a worm wheel Mattached to it

,and gearing with a worm S

,which is operated

by an endless chain K passing over the pulley J . For heavierloads two or more pulleys can be connected side by side onthe Spindles A and F

,as in the ordinary tackle. By th e

employment o f worm gearing this hoisting gear is made selflocking

,so that in order to lower the load it is necessary to

apply power to the other end o f the driving chain K. As h asbeen previously explained

,the efficiency of this arrangement is

considerably reduced by the use of worm gearing,and for this

reason the conclusions arrived at in the case of jack screwsand differential pulley - blocks hold for this form of hoistingapparatus as well. In accordance w ith our previous deductions

,

the efficiency,as also the driving force, are found to be

where 771represents the efficiency of the tackle, and

772that of the worm gearing (see tables , pages 54 and

Take,for instance

,the case of a chain tackle with two sheaves

where we had found combined with a worm andworm gear of efficiency 772

0 3 5,then we should have

7, 0 -9 3 x 0-

3 5 0 3 2 5.

Assuming the worm wheel M to have 1 5 teeth,and the

radius o f its pitch circle to be 7,while that o f the drivin g

pulley J is equal to then the theoretical pulling forceWill be given by

1 1 7° 1

P0: Q2 1 5 221 57 75Q

= Q 01 3 3 Q°


while the actual pulling force is

00 1 3 3

03 2 5Q 00 40n

Thus a force o f lbs . would have to be exerted for each1 00 lbs. lifted , whereas in the absence of wasteful resistancesonly lbs. would be necessary.

In another form o f hoisting apparatus,as constructed by

Co l l ct and Enge l hard of Offenbach,and which properly comes

F ig. 3 9.

under the head o f windlasses,a

worm driven by a chain wheeland chains is also made use of.

This worm communicates oppositerotations to two worm wheelsplaced on th e shafts of two chaindrums. Consequently the twochain s

,from which the load is

directly suspended without theuse of a movable pulley

,are

shortened by equal mounts, so

that th e load rises with doublethe velocity to what would be thecase were a movable pulley employed . With reference to asoertaining the useful effect

,we may.

regard this arrangement as acombination o f two equal windlasses

,each o f which lifts half the

load. The efficiency of the wholeapparatus is then equal to theproduct o f the efficiency o f theworm gearing into that o f thedrum

,the wasteful resistances of

the latter consisting of the frictiono f the journals and the resistance due to friction in the chainas it

'

winds on to the drum.

For information on this point we refer to the followingparagraphs.

A peculiar tackle shown in Fig. 3 9 h as been invented by

,II TACKLE AND DIFFERENTIAL BLOCKS 69

Earl e . l Here the chain which sustains the load passes over achain pul ley B provided with pockets to prevent slipping

,so

that th e load Q can be suspended from either end H or Hlo f the chain. The chain pulley B

,which is loose on the stud

A,has cast into it an internal gear D

,which latter is driven

by a spur wheel C,having one tooth less than D . The centre

E o f this wheel is therefore at a distance AE z c 12 71“

the centre o f A,t representing the pitch o f the gears. The

stud A is provided with an eccentric A'

,on which the driver

C turns loosely,friction rollers F being also introduced in order

to reduce the friction of the eccentric. Rotation is communicatedto the stud A by means of the chain pulley J

,the latter being

operated by the chain K as in the tackles just described. Thecentre E o f the driver will then

,revolve about the stud A in a

circle having the radius 6,while the wheel C is prevented from

turning about its own axis. The result is that,while the

centre E moves in the aforesaid circle about A,a line connect

ing any two points of the wheel C will always remain parallelto itself. Al l points o f C must move in circles described withradius c

,and therefore the motion will not be on e of rotation

,

but o f translation in a circular path . In order to accomplishthis movement a peculiar _L- shaped piece is employed on thehorizontal arms T o f which the lugs G and L of the wheel Cslide back and forth ; while the upright arm is guided by thestirru p N

,and the stud A is capable o f a vertical motion

,in

which the driver C must take part on account of the lugs Gand L. From this it is evident that by combining a horizontaland a vertical movement it is possible to impart a circulartranslation at each instant to the wheel C .

In consequence of this arrangement,it follows that for one

complete revolution o f the chain wheel J and shaft A thetoothed wheel D is made to turn through the space of onetooth

,as the following considerations will show. Let us first

suppose both the toothed wheels and the shaft A to make onecomplete turn in the direction of the arrow

,and then assume

the wheel C to be turned in the opposite direction about itsaxis E through on e complete revolution . The effect of the

1 Se e Engine er, 1 867, p . 1 3 5,and Ze itsch . Dcntsch . Ing. 1 868, p. 2 7.


latter motion is to cause the wheel D to turn back through a

fractional part 62 of a revolution, where z2 denotes the numberz

o f teeth in th el

d rive r C,and z

1the number in the internal

wheel D . Accordingly, for one complete revolution of thechain wheel J with its shaft A

,the internal wheel D with the

pulley B has been turned in the same direction as the shaft Athrough the fraction

+ l — fi F

of a revolution,i .c. through the space of one tooth, if w e assume

to be one less than zl. From this we may also deduce the

velocity - ratio or the relation between the distances traversedby the po ints

'

o f application of driving force and load. Supposing the shaft A to have made one revolution

,then the force

w ill describe a path 2 7rR,and the load a path 1 2 71- 7

,when 7

z2

denotes the radius o f the pulley B,and R that of the driving

wheel J . In th e tackle constructed by Ead c z z 3 1,z2

3 0,

and therefore for° a ratio12 g, the velocity ratio would

be6

1—

2, hence the theoretical effort

P0:z ”7

22

I§Q = 61

The actual driving force required is considerably larger thanthis

,owing to the large wasteful resistances

,which in addi tion

to a Q and GP,due to bending the chain over the pulleys B and

J respectively,consist o f the following:the frictional resist

auces of the shaft A in the hanger N,those of th e chain

pulley B on A,and the wheel C on its eccentric E,

the frictionof the teeth of the wheels

,and

,finally

,the resistances due to

the sliding friction of the piece T against the lugs G and L,

the stirrup N,and the shaft A.

These resistances are computed in the following mannerLet 7 be the radius of the pulley B upon which Q acts, andR the radius of the chain wheel J to which the force P isapplied ; further, let 7 1 and 7

2denote the respective radii o f


72 MECHANICS OF HOISTING' MACHINERY CHAP.’

will vary w ith th e position of the eccentric,as in the slotted

slider crank,consequently the force PI acting at E will not be

strictly constant: But a mean value of same,during one

revolution o f the shaft A,is found from the equation pertaining

to the work done by the various forces

P12 7re Q

21

2 2 2 7r7°2 qSP1 2 7r(r e) acm e 2 pU4e .

If we wish to consider the influence of the friction rollersupon the magnitude of P

I ,we must substitute ugt for (j) in the

term ¢Pl 2 7r(r c), which expresses the Work performed inovercoming this friction

, v representing the ratio of theof the pin to the radius of the rollers .From the above expression w e obtain the force P

must be exerted at the centre E of the eccentric,andwhi ch

requires the application of a force P to the driving chain.

Taking into account the friction of the chain and that of theshaft A in its bearings

,w e obtain the equation

P<I 0 )R P16 MP.44For,

from which

Expressing P directly in terms of known quantities wouldInvolve the use of some inconvenient formulae, and thereforean example has been chosen to elucidate the subject.

EXAMPLE — In a differential tackle of this form l et zz

andz1= 3 1 b e the numbe r of te e th of the gears, 72 1 50 mm. ih .]

and 71 233 1 50 1 55 mm . in .]th e radii of th e pitch circle s,

and thus c = 71

mm. [0°

2 0 in .] Furthe r, l et 7° = 8O mm.

[3°

1 5 in .] b e th e radius of th e pulley B,R : 1 60 mm. [6

°

3 0 in .]th e radius of th e chain Whe e l J, r 1 5 mm. [0

°59 in .] th e radiuso f th e shaft A

,thus th e rad ius of th e e cc entric r c 2 0 mm. 79

in .] Then, for coe fficients o f journal friction 0°

08, and sliding

friction,a and assuming a value 0 02 -

8O we find

2 08

th e force Q1 acting in th e te e th o f th e inte rnal whe e l

1 55 x 1 5


Taking friction of th e te e th into account, w e obtain th e re sistancein th e circumfe renc e of th e drive r

Q2 = [ 1 0 0°

53 4Q.

If n ow th e arms o f th e couple s VV and UU b e 0 (Z 2 00 mm .

[78 7 which supposition also make s V U,and friction rollers

b e employed with a ratio of th e journal V : 13 then th e force PIacting at th e c entre E o f th e e ccentric will b e obtaine d from

1 1 1 1 50PI5=o

~

53 4oéfi

x 0°

08P1 2 0+-

2x 0 - 1 5 x 4 x 5 x

which give sQ: 0

°

747Q.

Hence w e obtain final ly th e driving force5 0

-

08 x‘

1 5

which indicate s that eve ry 1 00 l b s. lifted require s an exertion o f

l b s.

Since without friction

Q=0°

01 61Q,

th e e fficiency is found to b e

Assuming th e above data,the re fore

,, Eadc’

s tackle apparentlygive s a greater e fficiency than th e common differential tackle , about45 pe r cent of th e ene rgy exe rte d be ing lost in ove rcoming th ewasteful re sistance s

,and 55 pe r cent be ing employed in lifting th e

load. In orde r to asce rtain whe the r th e tackle is se lf- locking, w e

must give opposite signs to qt, ,a, f, and If the se substitutions

give a positive value for (P), w e must conclude that, for th e abovedim ensions

,th e apparatus doe s not posse ss th e se lf- locking feature ;

On th e _whole,this tackle de se rve s no spe cial re commendation on

account o f its small e fficiency, and , e ven for th e case that it we remade se lf- locking

,th e diffe rential pull ey block is to b e pre ferre d

ow ing to its greate r simplicity.

CHAPTER III

WINDLASSES,W INCHES

,AND LIFTS

1 1 . Wind lasse s,

- The various f orms of tackle describedabove are employed chiefly for lifting moderate loads . °For

heavier service and greater l iftsa drum is ordinarily made useo f around which the rope

'

orchain is coiled . The arrangement is then called a w ind lass

,

and is identical in principlewith that shown in Fig. 40

,

th ough instead of rotating thedrum by means of spoke wheelsor hand spikes

,a large toothed

wheel is placed on the drum shaft and made to gear with apinion on a separate crank shaft . The action of such gearing has already been explained in 5 3 .

A simple Windlass worked by spokes is shown in Fig. 4 1 .

It consists of a tripod ABCD,two legs AD and BD of which

are firmly joined in order to serve as a support for the drumE and guide pulley F

,while the third leg C is jointed to the

others by the pin D . When the requisite space or support iswanting

,this third leg may be dispensed with

,and the per

manent legs stayed by one or two ropes,DH

,termed guys ,

which are securely anchored to the ground. The resolutionof the load Q into components acting in the directions o f thelegs AD and BD and the strut CD will give the pressures on thelegs

,or

,when guys are used, will give the pull whi ch the anchor

stay must withstand.

In place o f a tripod,a d errick

,as illustrated in Fig. 4 2

,

F ig. 40.

CRAP. III WINDLASSES,W INCHES

,AND LIFTS 75

may be used. Here the post AB is mortised into a timberplatform S

,and is held in its vertical position by several

ropes,or chains radiating from the top B. The load Q is

suspended from a movable pulley E,one end of the rope being

secured to the cross - beam at K,while the other end is led

over “the guide - pulleys F,G

,and H to the drum of a geared

Windlass W,which is mounted on the pl atform S . By employ

ing the movable pul ley the purchase is doubled, but its u se

Fig. 41 .

n ecessitates a correspondingly longer drum for holding theincreased length of rope.For lifting very heavy loads

,such as locomotives

,marine

boilers,etc.

,tackle containing from four to eight sheaves are

frequently used in place of single blocks,not only for the sake

of gaining an increase of power,which might easily be effected

by inserting an additional pair of gears,but chiefly with a

view to avoiding excessively heavy chains,which in turn

w ould necessitate the u se of very large winding drums.Fig. 4 3 shows the arrangement of the Windlass employed.

The drum D has its bearings in cas t - iron standards ABC,and

carries the. large spur wheel H,which gears with the pinion

G on the crank shaft E operated by the cranks F and F’.

76 MECHANICS or HOISTING MACHINERY CRAP.

Th e pawl 3 , which either engages with a special ratchet wheelon the crank shaft or directly with the teeth of the pinion

,

F ig. 42 .

the drum from reversing its motion under theof the load when the application o f power ceases — thisdevice being necessary in all windlasses which are not se l filocking. .If it is desired to .uncoil the rope from the drum

,a

too rapid rotation of the crank shaft may be avoided b v

m WINDLASSES, WINCHEs,“AND LIFTS 77

shifting th e latter in its bearings, thus throwing the pinionand wheel H out o f gear. A latch f suspended from the crossstay BB’ prevents any unintentional shifting o f the crankshaft

,and must be swung out of the position indicated when

the shaft is to be shifted.

A double - geared Windlass is shown in Fig. 44. Here thedrum G receives its motion from the crank shaft A throughthe medium of tw o pairs of gears B,

C and D,E

,of which the

F ig. 43 .

pini on D and the wheel C are keyed to an intermediate shaftH. With this arrangement

,which is used when heavier

weights are to be lifted,the velocity o f rotation o f th e drum

CEof that o f the crank shaft.

For obtaining a more rapid rotation of the drum,when lighter

loads are to be lifted,the Windlass is also arranged to Operate

with a single pair o f gears only, the wheels B and C beingthen disengaged by shifting the crank shaft A axially, thusal l owmg the pinion F on the shaft A to gear directly into thewheel E on the drum shaft. The ratchet wheel S againsustains th e load until the pawl S

Iis raised clear of the teeth .

will be only a fractional part


Unless provision be made to check the motion when the pawlis released

,the load would drive the mechanism backward with

an accelerated motion,which might easily lead to breakages

,

and by the rapid rotation of the cfank s endanger the lives ofthe workmen. To prevent such an occurrence

,machines of

this kind are always provided with a brake,which generally

consists of a drum or pulley N encircled by an iron band or.

strap operated by a lever L. The arrangement and mode Of

F ig . 44.

action o f such friction brakes have been fully investigated invol. iii. 1 78 ,

W e isb . Mash ,where attention is called to

the fact that the most advantageous results are obtained whenthe brake is applied to a rapidly revolving shaft. The frictionpulley is therefore generally placed either on the intermediateor on the crank shaft

,and only in rare cases is it attached to

the drum. In the above - mentioned paragraph it is alsopoin ted out that the brake lever should be so arranged that itwill act directly on the driven end J

2of the strap, and not


80 MECHANICS OF HOISTING MACHINERY CHAP .

In order not to subject the shaft of the drum to a torsionalstrain the large spur wheel is generally bolted directly to thedrum instead Of being keyed to th e shaft

,the drum being

provided with a flange for this purpose. The gears aregenerally made Of cast iron

,and it is only for pinion s or to

secure additional safety that wrought iron or steel are used asmaterial ; the shaft should always be made of wrought iron orsteel.When a Windlass is to be worked by several men

,and to

this end is '

provid e d with two cranks, it is advisable to placethese at an angle o f 1 80

° in order to equalise the powerexerted by the men operating the cranks. As the resistanceto be overcome in a hoisting machine is uniform

,fly

- wheelsneed not be employed ; in fact, their u se would render difficultthe exact stopping of the load

,and under certain conditions

might lead to breakages. In machines .o f this class, whereowing to the varying resistance a fly - wheel cannot be d ispen se d with , for instance in th e case of dredging machines , thewheel should be given a yielding connection with the hoistingdrum

,by the introduction o f a friction - coupling, for instance .

For all windlasses the ratio of the theoretical driving forceP0to the load Q is directly given b y the velocity ratio, and

therefore denoting the radius of the drum by and the lengtho f th e crank by R,

w e have7”

FO= Q—

Rn1n2

where nl ,n2

represent the velocity ratios of the re spe c

tive pairs of wheels that is, the ratios o f the number o f teethin the drivers to the number o f teeth in the followers .The actual driving force P ‘ is easily deduced from what ‘

h as preceded. When the load Q acts with a lever arm equalto the radius 7

'

of the drum (measured to the centre of therope or chain), the force PI , which must be exerted at theradius R

Iof the large gear on the drum ,

taking into accountfriction of the journals and the re sistan c e

'

d u e to stiffness,is

determin ed from the equationP R

whi ch gives

III WINDLASSES, WINCHES, AND LIFTS 81

Here , as before , r denotes the radius of the journal of the drumshaft

,and 0

° the coefficient due to stiffness o f the rope or chain,

the most u nfavourable case being assumed,namely

,that the

forces Q and PI are parallel and acting each side of the centreof the journal. If the weight G of the drum were to be takeninto account

,which would be necessary only in the case of

large winding drums for wire rope,we should have

610 4><Q G)rRI q

As the theoretical force in the circumference of[

the large gear

of radius RIis given by Q

1; the efficiency of the drum 1 s1

r .7‘

I:p, 1

=

QRI =M

(

l771 P

I 1 + U + ¢E7’

Again, let 772 and 773denote the respective efficiencies of the

first and second pairs of wheels,each of these coefficients re

presenting the product of the efficiency o f the teeth (seetable

,page and that of the gear shaft (se e table , page

then the total efficiency o f the Windlass is andconsequently

P -

7

1

;P0

The coefficient a' for the stiffness is estimated as in the case ofpulleys

8 80

'

(jag02 —

2?for chains,

for hempen rope

Assuming the most unfavourable case,namely

,that the

spur wheel is keyed to the_drum shaft

,thus subjecting this

shaft to a twisting action,the radius r of the journal may be

taken equal tor 07 58 for rope s

,

r for chains,


as is shown by the following calculation . Accordin g to vo l;iii. 1 , 1 1 6

,W e isb . Mcch .

,we find for hemp ropes

8= JQ,or Q = 0

°78582

[8=°

03 JQ in in che s, o r Q = 1 1 1 682 in

and according to vol. iii. 1,1 4

,we find the diameter o f a

wrought - iron shaft,which is subjected to a twisting moment

Q7°

,to be

2: 1 -02 3 6; [2 1° 06 907

Substituting in this expression 7° 48 and Q 0 78552

[Q we obtain

r= 0 x 43 3 07 453

Similarly for the chain we find the size of link,according to

vol. iii. 1 , 1 1 9,from

8= O°

3 2 6 JQ,or Q = 9

°42 82

[8=°00858 JQ,

or Q

hence for a radius of the drum 7 1 2 8 We have

t 0-42 x 1 2 83 = 2 473

Thus the ratio o f th e d iame te r of j ournal to that o f the drum

may be taken equal to 02 whether rope or chain is used,

since in the case of ropes w e haver 07 58

7° 48

and for chains

Substituting this value for7,

in the above expression for 771 ,

7° 1

and assuming a mean value forR 4

we can compute the1

efficiency of the Windlass corresponding to different sizes of“

rope and chain ; these values are contained in the following;

table. It may here be noted that the ratioFfvaries from—f

1

III WINDLASSES, W INCHES, AND LIFTS 83

to £3 for the ord inary'

w in'

d lasse s ; as this proportion h as but as l ight influence on the effi ciency o f the machine

,however

,it is

sufficiently exact,when making estimates

,to assume

7

_

E4:

in the table. These proportions are to be regarded asapproximations only which are near enough to the truth inthe ordinary Windlass working with rope or chain ; but forproportions departing from the above

,as for instance the drums

o f winding engines working with wire rope,the efficiency in

‘every case must be computed according to the general formulae.This matter will be more fully treated in connection with thelatter class of machines.

TABLE OF THE EFFICIENCY OF HOISTING DRUMS.

l‘

1 — ¢fi 1:7°

EXAMPLE — A load Q 3 000 kg. [661 5 l b s.] is suspended froma chain made o f iron 1 8 mm. in .] in diame te r by means of adouble -

geare d Windlass. What force must b e exerted by th e

workmen at th e cranks, if the se have a length of 400 mm.

5 and w e assume th e radius of th e drum to b e 7 :

me tre s that of th e spur whe e l on th e drum shaftR1= 0

°75 me tre s and th e ve locity ratios of th e twopairs of gears to b e 7

1

;and

Th e the ore tical force is2 00 1 1

P0: 3 000 400R350 kg. [1 1 0 2 5 l b s.]

Assuming th e radius of th e journal to b e r 40 mm.

th e e fficiency of th e drum is


A ccording ‘ to th e table s on page s 1 4 and 1 7 l et u s assume ‘

th e

e fficiency o f th e first pair o f whe e ls to b e 772 x

and that of th e se cond pair to b e 773 3x then w e

have for th e e fficiency of th e Windl ass 77 x x

hence th e force

0 82_

— 60°

9S0C 61 kg. [1 3 4°5 l b s.

If it is de sired to de termine th e re sistanc e (P)which must b eproduce d by a brake in orde r to prevent th e acce le ration o f th e

load during its de scent, l et u s assume th e brake -Whe e l to have a

d iame te r o f 05 me tre in .] and to b e locate d on th e gearShaft ; then, without waste ful re sistance s, (P)be come s

I

2 00 1

256kg. [882 l b 8. ]

Owing to th e waste ful re sistance s,how eve r

,which of themse lve s

oppose the backward motion,th e actual re sistance require d o f th e

brake is only 400 kg. 882 l b s.]whe re (771)and (712)denote th e e fficiencie s of th e drum and th e first pair of whe e ls ;the se value s in th e pre sent case diffe ring but slightly from 771 and

772 . Hence th e re sistance to b e offe red by th e brake is to b e takenat x x 400 3 6 1 kg. [796 l b s.] How to find th e tensionsin the brake strap require d for producing this re sistanc e is fullye xplained unde r th e head of Brake s in vol. iii. 1 , 1 78.

In order to determine by graphical methods the force Prequired to drive a double geared Windlass

,let us first draw

the line ccl ,Fig. 4 6

,o f the load Q parallel to the centre line

EQ of the sustaining rope,and at a distance Ec 0

° therefrom.

If throu gh the points o f contact D and B of the pitch circleswe lay o ff the directions DD’ and BB’ of the pressures betweenthe teeth at an angle of 75° with the lines o f centres HG andAH

,then the lines o f action of the actual pressures Z

1and Z

2

will be parallel to these directions,and at the distances Dd

and Bo equal to Cfrom them . The direction of the force P isto be taken perpendicular to the crank AK at the point K.

If now through the points 01 ,o and o

s— representing the

2 ,

respective intersections between the lines of action o f theforces Q

,

and '

Z1 ,Z1and Z and Z

2and P— w e

‘

draw thecorresponding tangents o

lg,027i,and 0

3a to the friction l

circles of the journals G,H

,and A

,then these lines will give

the directions o f the corresponding reactions RI ,R2 ,and R

3of

the bearings. Using the lines of action of the forces thus

III W INDLASSES,WINCHES

,AND LIFTS 85

e stablished , w e obtain the polygon of forces as follows:make011 Q,

draw 1 2 parallel to 0102 ,2 3 parallel to o

2h

,and 1 3

parallel to 0203 ,and finally draw 1 4 parallel to 0

3K and 3 4

parallel 03a . The length 1 4 will give the driving force P

,

and in the remaining Sides o f the force polygon 011 2 . 3 4

w e obtain the respective forces Z and R exerted between theteeth and at the bearings

,from which the dimensions of these

parts together with the proportions of the framework may be

Fig. 46.

computed. For the sake o f clearness the part 1 3 4 of th e

polygon is magnified five times in 1 3’ Were w e to

assume the quantities Q’

,and the radii o f the friction - circles

equal to zero,that is to say ,

were the lines o f action of theforces drawn through the points E

,D

,and B

,as also through

the centres G,H

,and A, we should obtain the force PO, while

for the reverse motion we must lay o ff the quantities a andgin d irections contrary to those for the forward motion, andthen draw the lines of action of the actual forces parallel to


the theoretical directions. In a similar manner the reactionsof the bearings are determined by the tangents drawn fromthe points o f intersections o to the‘ other Side of the frictioncircles .

1 2 . Wind lasse s operate d b y Ste am Pow er.

— A11 thehoisting machines thus far mentioned have been assumed to bedriven by hand power. When some other source o f energy,such as steam or hydraulic power

,is employed for the purpose

of performing a greater amount of work in less time, the onlyalteration in the arrangement of the Windlass is to replace thecrank by a sui table mechanism for receiving the power. Thus

,

in the case o f hoists used in Shops and warehouses,the driving

shaft is usually operated by means of,a tight and a loose pulley

driven by a belt from a continuously rotating shaft . By shiftingthe belt when in motion from the loose to the tight pulley, orthe reverse

,the hoisting apparatus can be engaged or disengaged.

This arrangement is applied to sack - h oists,for instance

,used in

flou r - mil l s for lifting sacks of grain,and is also employed in

saw - mills for hauling logs. In vol . iii. 1,

1 70, is Shown aform o f hoist also used in flou r- mills

, which is directly drivenby a belt running over a pulley on the winding drum. Thesame article also describes the method of effecting a uniformdescent of the load by means of a ’

b rak e . Where a Windlass isused for hoisting only

,not for lowering

,the brake is usually

dispensed with,as the hook then is not lowered by power

,being

instead brought to its lowest position either by means of a lightweight or by a direct pull on the chain . Concerning thevarious forms of hoisting apparatus arranged to run bothforward and backward

,a full description will be given under

the head o f Lifts.

Windlasses are frequently combined with a Special smallsteam - engine

,where it is desired to hoist heavy loads quickly

,

and no other source of power is available. This is the case inloading and unloading vessels

,for which purpose we find steam

hoisting gear extensively used. The engine is usually of th e

simplest possible construction,Since in cases where occasional

service only is required,simplicity of construction and safety in

Operation are matters of greater importance than economy of

fuel. Condensing engines are therefore rarely employed for

this purpose, and expansion of the steam is only used so far as


88 MECHANICS OF HOISTING MACHINERY can ».

As a rule the limit of velocity of the load in steam hoists ism. [05 ft] per se e . A steam hoist for u se on board

Ships is illustrated in Fig. 47.

1oTh e piston rods o f the two

oscillating cylinders A are connected with the driving shaft B,

and the reduced motion of the drum is obtained by means o fthe pin ion C and gear E . The brake pulley F is fixed to the spurwheel E

,and the flexible strap is applied by means of a lever

as heretofore explained. The distribution of the steam takesplace through the trunnions Z on the cylinders oscil l ate

,

Fig. 47.

and the engine is reversed by the action of a suitable valve, S.

For the purpose Of Operating the hoisting drum by hand whenrequired

,a special shaft

,not Shown in the figure

,is provided

,

having square ends for receiving th e crank handles . By shiftingthis shaft in its bearin gs

,a pinion keyed to it is made to gear

with the wheel E. Drums K are also attached to each end of

the drum Shaft for winding rope when desired.

The steam - cylinders are m . [59 in .] in diameter ; thestrok e

‘

is m. and the crank shaft makes 1 00revolutions per minute .

» The number of teeth o f the gears are

1 Se e Oppermann,Portefeni l l e économique d es Mach ines

,1 868, p. 1 8, and al so

Ruh lmann , A l lgem . Masch in en l ehrc, vo l . iv.

III WINDLASSES,WINCHES

,AND LIFTS 89

1 1 and 68 respectively , and the diameter of the drum Shaftm . and thus the velocity of the chain is

1 00 1 1

60 680 -5200 x 3 1 4 m .

and the energy expended by the steam - engine in lifting a loadof 1 800 kg. [ 3 970 lbs .] with this velocity is

1 800 x 3 04 kg.-m . [2 1 98 ft. l b s.] h .

-

p.

As due allowance must be made for wasteful resistances,the

engine evidently must develop more than five horse power.1 3 . Oth er Forms of Ho ists — In the apparatus shown

In Fig. 48, and known u nder the name of the Difi’

erentia l

or w ind lass,the action is the same as in the above

mentioned differential pulley blocks. The load is suspendedfrOm the movable pul ley A

,both ends of the rope being

fastened to the drum BC,so that when this is turned one end

is unwound while the other is wound on . Owing to thediffering diameters o f the drum at B and C

,more rope is

wound on than is unwound,and consequently the load rises

with a velocity corresponding to the difference In the diameters.Letting R denote the radius o f the larger portion o f the drumB

,and 7

° that o f the smaller part C,then

,after one revolution

of the drum,the portion o f the rope which hangs below the


Windlass will'

have been shortened by an amount 2 7r(Rand the load accordingly has been hoisted a distance equal toone - half o f this length

,that is Assuming that no

wasteful resistances exist,the effort at the crank D of length 2

w ould be found fromR

P02 4 1 :m(R which give s P

0 Q2;

T

The stiffness of the rope,however

,as well as the friction

in the bearings,make a far ‘ greater effort necessary

,and

essentially reduce the efficiency o f this apparatus,as was also

the case in the differential pulley block. Denoting by a thec o efli c ie nt due to stiffness of the rope in winding on or Off, andassuming a mean value for this coefficient in common for boththe drum and the sheave in the block

,we obtain the following

equation,with reference to the tensions S in the unwinding

part at C and SIin the part whi ch winds on at B:

SI= S Sic

where is the radius of the sh eave, and 131that o f the pin on

which it turns. We also have

If r denotes the radius of the journal o f the drum BC ,w e

can now deduce the equation

Pl S( I S1 ( 1 + 0

°

)R ¢ (P S S,)r,

or, after substituting

and S

Pl ”Q“

( l 1k G <7)R (MP Q)r.

The value of P may thus be derived from

1 — 070P( l g k

r w r

The efficiency of a hoisting apparatus of this description isvery small

,and when ropes o f large size are used it is even

smaller than that o f the differential pulley block, owing to the



to be ’ recommended, and for this reason a detail ed analysis ofthe same will not be presented.

A peculiar h oisting mechanism -has been designed by Zong,1

Fig. 50. A scroll - shaped cam ABC,projecting from a di sc S

on the crank Shaft , Operates an intermediate shaft by means ofa star wheel J provided with friction rollers mounted on studs

F ig. 49.

E in its circumference. A'

pinion F on the intermediate shaftdrives the gear G on the wind drum H. For every revolutiono f the disc S the star wheel J is evidently moved through onedivision in a manner similar to the action o f a worm andworm gear. The ratio of the forces at work may also bedetermined similarly

,the theoretical effort required at the

crank o f a length l beingTl

r 1PO

L

7?

1 Se e Civi l Engine er and Arch itect’

s Jou rna l , Ju l y 1 852 , and Dingl e r’

s jou rnal ,

III W INDLASSES,W INCHES, AND LIFTS 93

where r1 ,

'

Rl ,and r are respectively the radn -

of"the "gears F

and G and the rope drum,the number of studs E being denoted

by 77. As may be readily seen,however

,the efficiency is

greatly reduced :by friction,as is also the case in worm gearing.

For let a be the mean radius of the scroll,which may be shaped

like an Arch imed ean sp ira l“with a radial pitch equal to the

pitch 3 o f the star wheel,then the work required for over

coming the friction between the cam the studs when in

will for every revolution o f the disc be expressed by

,q 2 7ra,

when Q 1denotes th e resistance acting through the space 3 in

the circumference o f the Star wheel. Taking for mean radiusa of the scroll as low a value as 2 3 , and assuming a coefficientp. the work spent in overcoming friction wil l still be

x 2 x x 2 8Q1 = 1'

2 56Q1 3 ,

which exceeds the useful work Q 3 thus w e Obtain the e ffici1

m .0 44 3 only.

It is possible to reduce the friction to one - half of. the above }

ency of the scroll disc alOn e to be

°


amount by the use of friction rollers,but in spite o f this fact

a very small efficiency is always obtained from the. Wind lass asa whole . Consequently it would

.b e advisable to employ a

more eflicie nt mode o f driving— another pair of gears,for

instance.In single windlasses

,as used in building enterprises

,the

winding drum is sometimes Operated by a lever AC (Fig.

provided with a pawl B,engaging a ratchet C on the drum

,

the load thus being raised by depressing the lever AC,w hile a

second pawl D attached to the framework prevents it fromrunning down. Besides comparative S implicity and efficiencythis type o f Windlass possesses the advantage o f being lessrestricted as to the length of the lever arm CA than is the

F ig. 51 . Fig. 52 .

case with the diameters of gears and radii of cranks in otherconstructions. Thus the length Of the lever may always bechosen to suit different loads. The non - continuous movementmust be counted as

"

a disadvantage,however.

When the lift is considerable it is necessary to make thewinding drum of large dimensions

,in order to be able to wind

on the great length of rope. In such cases the rope is notmade fast to the drum

,only placed around it in a fe w coils

,

one end being allowed to unwind while the other is windingon , thus leaving always the same number of coils on the drum.

A sufficient number o f coils must evidently be left on thelatter to prevent the rope from slipping.

One of the simplest hoisting machines arranged accordingto this plan is the cap stan (Fig. Here several coils o frope are placed around the vertical drum C

,which is rotated

by m eans of handsp ikes E th rough the pinion a attached to


96 MECHANICS OF HOISTING MACHINERY ° CHAP.’

th e° second groove of G at a

,etc.

,it final ly

'

leaves the lastgroove of the drum H at b.

As before,the Object to be gained by repeatedly carrying

the rope around the drums is to prevent slipping,and therefore

w e have also for this case the general equation S Slew,when

ry denotes the sum o f allthe encircled arcs of thetwo drums. If n is th enumber o f grooves hal f

A e n c irc l e d , which may bean even or odd number

,

then ry= n 7r. For hoist

ing the load the drums Gan d H must be rotatedin the same direction

,at

the Same velocity,which

is accomplished by thepinion F on the driving .

shaft C gearing into thetw o equal drum gears Dand E.

In order to determinethe relation between dri vrng force and load for the hoists .

under consideration,let S Q denote the tension in th e tight '

part a e,SIthat in the part col which passes from drum G '

to H,likewise S

2the tension in the second part ba w ind ing

on to G,etc. , so that S,, will denote the tension in the final

,

leaving part,when in all n grooves are half encircled. Then

,

for the limit w hen the ropef is on the point of slipping, w e

have

F ig. 53 .

S Sle‘P”S2 e2‘P”S3 e 3W Sne’w

”After one revolution of the drums, of radii r, in thedirection of the arrow, the resistance S Q has been overcomethrough a distance 2 777 , the driving force P during the operation evidently being aided by the tension S

,,in the last,

receding part bf. Neglecting the influence o f friction and thestiffness o f the rope

,the tensions S

I ,S2 ,S3".

i

Sn _ 1

'

in therespective parts between the tw o drums will then have neitherperformed nor

'

absorbed work,as each tension furthers the

11 1° WINDLASSES

,WINCHES

,AND LIFTS 97

motion o f one drum equally as much as it impedes that of th eother. Thus , in the absence of wasteful resistances

,the

theoretical driving force P0at the circumference of the drums

is :P0S.

To find the actual effort required at the circumference ofthe drums

,let 0 ° denote the coefficient of stiffness and r the

radius of the journals. The pressure on the journals of thesh aft A will then be

and of the shaft B

Under the assumption that the tension S,is just sufficient

to prevent slipping,thus S S

nel l”

,or S

,we shall

obtainZ S(I e

'

f”r e“2W + e

‘ m- l wr

)

Z1S(e

‘

¢W e' w

The resistances due to the stiffness of rope at the drum Gwill be

and at the drum H

U1= 0 (S + S

z+ s

s+

Consequently,the force P required at the circumference o f the

drums is obtained from the equation

Pr (S Sn)r 0°

(Z Zl )r <1>(Z Z

1

or with the above values of Z and Z1

P(r a) (10 w e»: (o r N 91


Hence w e may derive P,and from P

0 Q the efficiency

2 9 may be obtained. From the force P at the circum77P

ference of the drums , we may further calculate the effort PI

acting with a lever arm RIon the crank shaft C

,when due

attention is paid to the journal friction o f the shaft C,and the

friction between the teeth of the gears CF,AD

,and BE.

Further explanation will be Obtained from the followingexample

EXAMPLE .— In a hoisting apparatus of th e kind shown in Fig. 5 3

,

th e rope runs around th e tw o drums thre e time s, th e load is 3 00 kg.

(66 1 5 lb s ), th e radii o f th e drums are m. and th e

ratio of th e gearing is 0 2 . What is th e driving e ffort require d atth e e nd o f a crank m. in.) in length 7Here n 6

,hence , assuming ,a 8

,w e obtain

e

e

which give s a tension in th e slack e nd o f th e rope of

S6: 3 00 x o-

oo51 2 ='

1-

54 kg. l b s.]

Assum ing th e size of rope 8 J 3 OO 2 0 mm.

shall find from th e formula given by Eyl e lw e i n

82 4000 :0 01 8

5 ;

(0°

(P4573:o°4572 x 3

°

94

and for a radius of th e journal 1: 1 5 mm. in .]w e have1 5

1—

0—

00 01 2 .

Hence w e get

P(1 o Q(1 o O3 6+ O 01 2 )Q(1 + 0 41 5)

Q(0°

9949

which give sQ= 1

°1 2 4Q=3 3 72 kg. [743-5 l b s. ]

As P0 Q, when waste ful re sistance s are negle cte d, th e e fficiency

of th e two drums will b e



means o f the hook H attached to the movable pul ley D .The

slack end K’o f the chain is guided by a closed casing LMN

,

F ig. 55.

in which it slidesback and forth underthe action of th e

driving wheel B,thus

preventing entanglement o f the links

,the

chain being alwayskept tight b y theweight o f its lowerend. This construotion is not used inpractice to any greatex t e n t

,h ow ev e r

,

chiefly on account of

the large amount of

friction generated atthe pins of the linkch ain

,and besides

,in

common with allmachines employingchains for driving

,it

is liable to the disadvantages due to thegradual elongation of

the links . The resistanc e s generated bythe chain in runningon and ofl

' the pulleysmay be calculated inthe same manner as

that employed for ascertaining the friction between a rackand its pinion .

In Bern i er s Windlass the chain which carries the load Qpasses over the fixed guide - pulley H,

Fig. 55, and is thenbrought around two shafts A and B

,which are o f triangular

cross - section at the points where the chain is carried . Slippingo f the chain is made impossible in this 'manner

,and the load

1 Se e Ruh lmann,Al lgem. Masch inen l ehre

,vo l . iv, p:402 .

J O d d

WINDLASSES,WINCHES

,

‘

ANC Liraisz

is therefore raised if the two shafts A and B are rotated inopposite directions. Th e Opposite rotation is accomplished bymeans of two gears o f equal size placed on the shafts andgearing together

,the motion being transmitted from the crank

shaft GK to the notched shaft A th rough the gears E and F.

The slack end o f the chain might be allowed to drop freelyfrom the shaft B

,but in order to secure a uniform tension and

prevent entanglement,it is usually suspended

,as at O

,and

carries in its height a movable pulley J together with a tensionweight L.

This hoist,besides requiring no chain drum

,is evidently a

very powerful c ontrivan c e,inas

much as the lever arm o f theload is . equal to the smallradius o f the chain shaft only.

The friction as well as the wearof the chain is considerable

,

however,owing to the small

radius. This evil is of greatc onsequence in this machine

,as

it is capable o f smooth running only as long as the linksretain their correct lengths.

In Stauf er’

s Windlass thisrequirement of links of a constant length

,wh ich can scarcely

be depended on in the longrun

,is a matter of little

.moment. Here a cha in l ock is also made use o f,Fig. 56

,

w ith depressions for the links,but since the chain is not

carried around the shaft,only between the shaft and a

drum B,very fe w links are grasped at the same time

,

and for this reason a slight elongation will do no harm. Thishoisting machine

,besides

,offers several advantages

,as for

in stance with reference to safety in lowering.

a load andkeeping it suspended . The above - mentioned drum B is castin one piece with the pinion C

,and is operated from the crank

K through the clutch coupling D . Thus,while the chain shaft

is slowly revolved by means o f the gears C and E,the chain is

at the same time pulled through the lock between A and B.

Fig. 56.

MECHANICS“OF HOISTING MACHINERY car p .

The ratchet wheel H on the crank shaft and the pawl J preventa reversing of the motion as long as the drum is connectedwith the crank by means o f the cl utch D. By pressing thecrank slightly backw ards the clutch may be disengaged fromthe drum

,however

,and the load Q thus released. The drum

being loose on the Shaft,will then under influence o f the load

run backwards with an increasing velocity depending on theratio o f the gearing. By simply quitting hold of the crank theclutch is automatically again thrown into gear

,and the motion

arrested by the pawl J. In order to obtain a uniform velocityin lowering

,a braking resistance is

,by the motion of the drum

shaft,produced in the following ingenious manner. In the

circumference of the drum a number o f leaden ' segments areapplied in such a manner as to be forced outward by the actionof the centrifugal force during the rotation o f the drum

,thereby

producing the necessary frictional resistance. This resistance,

increasing with the velocity,soon reaches a point where no

further acceleration of the load is possible . To avoid Shockswhen the load

,after the crank has been dropped

,is brought to

a sudden stop,the clutch is made yielding to a certain extent.

This hoist undoubtedly is a perfectly safe contrivance,since the

load is brought to a stop merely by releasing the hold of thecrank

,an Operation which requires no effort whatever on the

part of the workman .

1 4 . Lifts — This class of hoisting apparatus is used forlifting building materials

,grain

,coal

,ore

,etc .

,and receives

names to correspond,such as brick

,grain or coal elevator

,and

furnace - lift. We may divide these machines into two classesthose in which the hoisting action is continuous

,being pro

du c e d by means of an endless chain , and those in which theload is carried at the end o f a rope or chain in the mannermade u se o f in the windlasses just described.

In lifts which employ an endless chain the latter is eitherprovided with special receptacles for the load

,or with hooks

for its reception,the material being occasionally placed in a

so - called cage . In either case the continuous motion of thechain and the lifting o f the load are accomplished by revolvinga shaft on which the wheel or wheels are fastened

,around

which the endless chain 1 s carried .

The second class o f lifts either Operates with a drum upon


1 04 MECHANICS OF HOISTING MACHINERY. CHAP.

the car h as been emptied it i s returned to a platform whichdescends on the otherside of the lift

,and

upon reaching thebottom it is againremoved and refilled .

Should the removalof a full or empty carbe neglected at anytime

,no loss worth

mentioning wou l dresult

,since the car

would then only com

pl ete another revol u tion

,which would

.require practically noextra expenditure of

energy,owing to the

fact that the workperformed by theempty car in itsdescent would nearlyequal that absorbedduring the ascent .By providing the

endless chain withstuds or hooks forreceiving the load

,

the platforms may bedispensed with . In

the furnace - lift,partly

illustrated in Fig. 58,

the truck A which isto be raised has itsSides fitted with hooksd a which are su s

tain e d by the studsbb of the chain until

F ig ' 59° the truck has reachedthe top . The trucks are brought to the hoist by a railway

Fig. 58.

III WINDLASSES,W INCHES

,AND LIFTS 1 05

at the bottom,and removed by the Same means at the top.

The upper railway is sufficiently in clined to convey thetruck from the lift to the mouth of the furnace by the actiono f gravity

,the empty cars being returned to the shaft by a

second railway. To prevent any deviation which,owing to

the one - sided action of the load,might cause them to run o ff

the pulleys,the chains are provided with stiffening links cc

,

and the wheels CE are surrounded by fixed guides BDB for

these links .An inclined lift Operated by an endless chain is shown in

Fig. 59,which represents its lower portion

,and makes clear

the method employed for taking hold of the trucks by meansof hooks attached to the chain . The truck A is brought to thehoist on a railway B

,the endless chain CDEF passing over a

Sprocket wheel engaging the links of the former. At intervalsof 3 metres ( 1 0 ft.) the links , which are about 03 m . ( 1 2 in .)in length

,are made in the shape of hooks (d ogs) CEF

which grasp the rear axle G of the car,and thus raise it to

the top,w here it unhooks itself

,and is conveyed to the mouth

of the furnace on an inclined railway. The upper sprocketwheel is located above the charging platform

,and through suit

able gearing it is driven by water or steam power.In case the chain should break

,the cars are prevented from

running down the incline by means of small e lbo w - shapedlevers H attached at several points along the railway. Theselevers

,while they permit the axles o f the car to pass on the

upward journey,are so arranged as to arrest any backward

motion . The empty cars are lowered on a second railway bymeans of a windl ass controlled by a brake .

Neglecting wasteful resistances,the power required for the

Operation o f a lift with an endless chain can easily be compu te d as follows . Let Q denote the weight of the material tobe raised on the truck

,h the height to which it is to be lifted ,

and n the number o f trucks to be hoisted per minute . Thenthe useful work expended in hoisting each truck will be Qh ,and the work performed per minute will be t ,

or persecond

nh ,L

60Q

This expression,however

,is true only when the descending


platform or truck G,as in Fig. 57, isentirely counterbalanced

by the ascending one . In every other case we must place

nO

L66<Q G)h .

The velocity of the load in the vertical direction is 7) sin a ,

where 7) denotes the Speed of the chain,and a the angle o f

inclination o f the railway to the horizon .

The arrangement of an e l evator, as used in flou r- mill s for

F ig. 60. Fig. 61 .

carrying grain to the upper story,is shown in Fig. 60. In

place o f an endless chain , an endless belt carried by the twosmoothly finished pulleys A and B is here employed

,con

tinu ou s motion being communicated to the upper pulley bythe driving - belt pulley C . At equal distances along the hoisting - belt small sheet - iron buckets G are placed which

,after

the grain has been coarsely ground at D,carry it to the top

story,where it is finally discharged at H. In order to give

to the belt a sufficient degree of tension"to prevent sl ipping,


1 08° MECHANICS OF HOISTING MACHINERY can »

.

are made with double bottoms , forming reservoirs which canbe filled with water at the top from

'

tanks D “and E,and

emptied below by means of the valve b.

All that is required when a loaded platform is to be hoistedis to fill the reservoir in the empty platform with water

,the

weight o f which causes it to descend, and at the same timelifts the load. When the descending platform reaches thelowest point, a release valve is opened by striking again st aprojection K

,and thereby causes th e water to run out. This

platform may now be loaded, and then hoisted by filling the

Fig, 62.

upper reservoir in turn with water. A brake - wheel F,

Operated by a treadle R,controls the speed during the ascent

and descent.Fig. 6 3 shows a large fu rnace - h oist driven by water or

steam power. It consists of two parallel railways A and B,

inclined at an angle o f 3 0° to and having a length correspond ing to the height o f the furnace. On each railway runsa car

,C or D

,mounted on wheels o f unequal diameters

,and

provided with a horizontal platform for receiving baskets;buckets

,or trucks containing ore

,coal

,etc . Both cars are

attached to the same rope EFG,which passes over the drum

I II W INDLASSES,WINCHES, AND LIFTS 1 09

F,the rotation of the latter thus causing one o f the cars to

ascend while the other descends. In order th at the ascent o fthe l oaded car may take place alternately with the descent o fthe empty one

,the drum must be arranged to rotate in either

direction,and for this purpose a reversing motion must be

employed. This may be Operated either by gearing orby belts running on tight and loose pulleys . In th e abovehoist the latter arrangement is used . On e o f the two belts

,

H and K,which transmit motion to the drum shaft

,is

open,and the other is crossed ; by means of a

’

forked lever

F ig. 63 .

LMK either belt may be Shifted to its corresponding tightpulley

,thus causing the drum shaft to rotate in either d ire c

tion. Should the rope break at any time the car will bebrought to a stop by the pawl N or O engaging with thetoothed rail along th e track.

Let G be the weight o f a car,including the empty receptacle

which is placed u pon it,and Q the load placed in the other

receptacle,then for the state of rest the tensions in the portion s

E and G o f the rope are SI (G + Q) sin a

,an d S

2G sin a

respectively,where a. is the angle o f inclination o f the plane

to the horizon . Let 7/ denote the efficiency for the ascent o fthe mechanism consisting o f the car C

,the rope E

,the pulley

1 1 0 MECHANICS OF HOISTING MACHINERY'

CHAP. III

R, and the drum F ,and let be the efficiency of the corre

spond ing parts belonging to the car D for the descent ; thenthe resistance to be overcome at th e periphery o f the drumis expressed by

W P g1; (77

’

)S2-

}7(G Q)sin a (77

'

)G sin a .

77 7)

In the absence o f wasteful resistances,that is to say, for

77'

1 w e have W = P0= Q sin a ,

and therefore theefficiency of the whole hoist becomes

a r

From this we see that the dead weight o f the car,including

the receptacle,may have considerable influence on the efficiency

of the hoisting machine,which proves the fallacy o f the su p

position upon which the calculation is often based,namely

,

that the dead weight can be left out of account,because th e

tw o cars balance each other.

EXAMPLE.

—In an incline d furnace - lift,similar to th e on e in Fig.

63,a : 3 0

°

is th e angle of inclination, th e use ful load o f a car i s

1 000 kg. ( 2 2 00 l b s ), and th e we ight o f th e car,including th e

empty re ceptacle , is taken at 800 kg. [ 1 764 l b s.]Assuming the e fficiency o f th e car

,th e guide pulley, and th e

drum,to b e 77

: 0°

90, and to b e th e same for th e ascent and de scent,

unde r which supposition th e frictional re sistance s of th e journals ofth e car and pulley and th e re sistance d u e to stiffne ss o f th e ropeconsume 1 0 pe r cent of th e energy e xe rte d

,then w e shall have for

the re sistance at th e pe riphery o f th e drum1

sin 3 0°

x 800 sin 3 60= 640 kg. [ 1 41 0 l b s.

where as without waste ful re sistance s P0

1 000 sin 3 0°

500 kg.

[1 1 00 hence th e e fficiency o f th e hoist is 77 228— 0 78 1 .

If w e assume th e circumfe rential ve locity of th e drum to b eme tre s ft.] per se cond, th e powe r to b e transmitte d by th ebe lt will b e 640 x 3 2 0 kg.

-m . [2 3 1 5 ft.- l b s.]pe r se cond, corre

3

7

2

5

0 horse powe rs h. p .] Th e time required

to lift a load to a he ight h 1 6 me tre s ft] is

spond ing to

64 se c o nd s.


1 1 2 MECHANICS OF HOISTING MACHINERY CHAP .

A very interesting form of hoist 1 was employed in buil dingthe Suez Canal

,the material raised by the dredges being carried

to the banks on inclines. The essential features of this elevatorare show n in Fig. 64 . Two large iron girders A

,securely

braced to form a strong frame,carry the rails a o f an inclined

track upon which a four - wheeled car W travels . This carsupports the drum on which two chains are wound

,from the

ends of which a box K,filled with the dredged material

,is

suspended. This framework rests at C upon a movable platform running on a track along the canal bank

,and also at E

upon the dredge - boat S,which contains the steam - engine for

operating the Windlass. The framework A and the boat areconnected by a kind of universal joint, enabling the frame toadjust itself to changes in the water level

,and the platform D

is made movable about a vertical axis,as in the case o f a turn

table . The steam - engine drives the drum T of a Windlass,

thus wind ing on two parallel wire ropes s,which are carried

over fixed pulleys L at the apex o f the frame,and ultimately

secured to two large drums V carried by the front axle o f thecar W. Two smaller drums are cast on to the drums V,

andthe box K is suspended from chains attached to the former.AS the wire rope is wound upon the drum T the drum V is

made to rotate with its smaller chain drums , thus causing thebox K to rise vertically. This vertical motion continues untilthe box

,by means of two roll ers 75 fixed to its hind end

,strikes

against the guard rails X arranged at the Sides of the frame.These prevent any further vertical motion o f the box

,and

hence any further rotation of the drum V. Any additionalpull exerted by the wire rope on V causes the car W with itssuspended box K to .travel along the rails a ; during this motionthe box is kept in a horizontal position by guiding the rollers10 between the parallel rails X and Y . At the apex Of theframe the rails X and Y are curved in such a manneras to tip the cage K

,which thus automatically discharges

its contents. At this point the engine is stopped,and then

reversed after the box has been emptied,thus allowing

the empty car W to roll back under the action o f its ownweight

,whereupon another loaded car may be lifted in the

same manner.1 Se e Oppe rmann , Portcfcu i l l c d cs Mach ines

,1 869

, p. 2 8.

III WINDLASSES, W INCHES, AND LIFTS 1 1 3

In building the Suez Canal eighteen of these elevators wereemployed ; the average slope of the inclines w as aboutthe extreme ends o f the frame were 3 metres [ 1 0 and 1 4metres [4 6 ft.] above the water level, and each cage had acapacity of ab out 3 cub. In . [4 cub. yds ]

CHAPTER IV

HYDRAULIC HOISTS,ACCUMULATORS

,AND PNEUMATIC HOISTS

1 5. Hydrau lic Hoists.

—Recently a form o f hoisting apparatus has come into use

,founded on th e principle o f th e

hydrostati c press that is,water under great pressure acting

on the surface of a piston,which fits water - tight in a cylinder

,

is employed to raise a load resting upon the piston . Theessential arrangement of a hydrostatic or Bramah press is

shown in Fig. 65. By means of a small force - pump,w hose

plunger A receives a vertical reciprocating motion by th e

application of muscular or steam power,the water, drawn

from a reservoir through the suction pipe BC is forcedthrough the tube DD into a strong cast - iron cylinder E.

During this motion the suction valve a and the delivery valveb act like the valves of a common force - pump. The loaded


1 1 6 MECHANICS OF HOISTING MACHINERY CHAP.

spond ing coefli cie nt of friction,the force exerted by the press

plunger will not exceed ( 1 — P. Fu rth er information con

cerning the values of 4; will be given later.Fig. 66 represents an hydrau l ic l ifting jack, in which F is

the press cylinder and K the lifting plunger projecting throughthe upper end of the cylinder, the enlarged base G serving asa reservoir for the liquid. The pump cylinder B forms a part

Fig. 67.

of the frame , and the figu re shows how the plunger A receivesits motion from the lever CD oscillating about C . The reservoir is filled through an opening S

,and

,to prevent freezing

,oil

or glycerine is generally used. When the load is to belowered the communication between th e cylinder F and th e

reservoir G is effected by a valve worked by a screw H.

Owing to their exposed position the pump cyl inder andthe valve chamber are liable to injury and fracture. To avoidthese dangers various arrangements 1 have been devised in

1 Se e Ze itschr. d e u tsch Ing. 1 866, p. 707.

Iv HYDRAULIC AND PNEUMATIC HOISTS 1 17

.w hich th e sensitive parts are placed in the interior of th e

jack . By this means greater security against injury has beenobtained, but the parts are less accessible. We wil l onlymention one o f these arrangements, the apparatus of TangyeBros ,

Fig. 67. The jack is provided with a projecting clawK 1 and the tube EE Sliding on the cylindrical standard F,

being fitted with a water - tight join t in the shape o f a leathercup M ; a feather c

,sunk in the cylin der E

,and fitting in a

groove cb,guides the cylinder and prevents it from rotating.

The reservoir K is above the cylinder,the oil is admitted

through a screw - hole h,and by means of the reciprocating

motion o f the plunger A it is drawn through the valve 3,and

forced through the valve d into the space 6 bounded by theplunger F and cylinder E. The manner o f Operating thepump plunger by the l ever CBG is evident from the figure.When the load is to be lowered b y the action o f its own weight ,the lever G is depressed into its lowest position G’

,when the

plunger A opens the delivery valve,at the same time pulling

back the suction valve 3 by - means o f a projection a . Toenable the end of the plunger A to strike the valve d

,the

spindle of the valve 3 is made ring - shaped . It is calcu latedthat this jack will raise a maximum load of kilograms l b s.] when the cylinder E has an insid ediameter of 89 mm. [ 3 5 and the pump plungerA has a diameter of 1 9 mm . in .] For ra ising thetubular girders of the Britannia Bridge

,

1 very powerfu lhydraulic presses were applied . These were placed inrecesses purposely constructed in the towers

,40 feet above

the permanent bed of the tubes,and the force - pumps were

operated by two steam - engines of 40 h .-

p . each . Each tube was4 60 ft. long , and weighed, with the additional weights raised,1 72 6 tons . Each was provided at the ends with cast -i ronframes

,to which two lifting chains made up of sets of eight

and nine links alternately , were attached . These chains weresuspended from the cross - head o f the plungers of the hydraulicpresses. The manner of arranging the apparatus and securingthe chains which carry the ends o f th e tubes will be understoodfrom Figs . 68 and 69 . In both illustrations A is the pressplunger

,B the cylinder

,and C the pipe through which water

1 Se e Cl ark , Th e Britann ia and Conw ay Tu bu lar Bridges.


is forced by the engines. DD are the walls of the tower,E F and G cast - iron girders

,and H is a cast - iron support

for the press cylinder B . Furthermore , K represents thecross - head from which the l ifting

°

ch ains are suspended,and

N the cylindrical guide rods, which pass throu gh the crosshead

,and are secured above to the cast - iron girder 0 ,

whilebelow they are firmly attached to the cylinder. The cross

Fig. 68.

head is provided with clamps a which hold the ends of thechains and are screwed up firmly against the links. Whenthe lifting piston has completed its stroke two other sets ofclamps b are screwed up tight and hold the chains whil e a se to f links is removed

,thus permitting the cross - head to be

lowered for the purpose of commencing a new stroke. Toprevent the tube from falling in case the press should burstor the chains break

,the ends o f the tube were followed up by

masonry during the ascent.



of the hoisting apparatus for the Britannia Bridge by2

3 543 . With the usual‘rigid combinations, wheels ,

screws,etc such large purchases can only be produced by

employing additional mechanisms of the same kind,and this

greatly reduces the efficiency. In comparison with thesecombinations the wasteful resistances of the hydraulic hoists aretrifling. These consist principally of the friction between thepress plunger and its stuffing box, an d

l

of the hydraulic resistancesof the pump . By omitting all pipes for conducting the fluid as inthe jack

,Fig. 67, a pump efficiency of at least is realised

,and

assuming in addition a loss of about 5 per cent for the frictionof the press plunger (se e below), w e , c on c l u d e that 7) isa suitable value. for the efficiency of such hydraulic hoists.It is Of course understood that these h oists sustain the loadautomatically when the supply of water into the press cylinderceases

,for the delivery valve is then closed and acts as a pawl.

It is also unnecessary to provide this class of hoists with brakes,for by regulating the opening of the escape valve the descent ofthe load isperfectly controlled and acceleration made impossible.Nevertheless

,when worked only at irregular intervals they

are apt to get outO

of order, and in winter to be destroyed,unless oil or some other fluid Which is not liable to freeze isemployed in place of water.

EXAMPLE — If in th e lifting jack o f Fig. 67 th e diame te rs of

th e plunge rs are assumed to b e 1 9 mm. [0 75 in .]and 89 min.

[3 5 and th e maximum load to b e lifte d is kg .

[6 then,basing our calculations on an e fficiency 77 0 75

,

1 92

th e force to be exe rted by th e pump plunge r must b e W x

1 8 2 3 kg. [402 0 l b s.]If th e leve r arm of th e pump plunge r is taken e qual to 40 mm .

and th e e ffort o f th e workmen is applie d at th e e nd o f aleve r 1 me tre ft]long, this e ffort be come s 0 040 x 1 8 2 3 72 9

kg. l b s.] Th e ratio borne by th e re sistance to th e e ffort is892 1

given In thi s case by1 92

5485 .

1 6. Pre ssure Re servo irs — Instead o f forcing the waterinto the cylin der o f an hydraulic hoisting apparatus by meansof a pump

,an elevated reservoir may be employed to furnish

Iv HYDRAULIC AND PNEUMATIC HOISTS 1 2 1

the necessary head. To lift the load it is necessary that thenatural head shou l d exert on the lifting piston a pressureFH'

y , greater than the weight Q ; here F again denotes thearea o f the lifting piston

,«y the weight of water per unit of

volume,and H the height o f the pressure column measured

from the surface o f the water in the reservoir to the bottom of

the lifting piston. It is understood that Q represents the weightto be lifted

,including the friction

o f the piston and other wastefulresistances . In cases where thenecessary head of water is availabl e

,for example

,in places where

the water mains give sufficientpressure

,hydraulic hoists may be

conveniently employed,as they do

not then require a special primemover. This has led to their u se

in many of the larger h ote ls andw areh ou ses for lifting persons andgoods from one story to another.A well - known example of thiskind is the hoistin g apparatus(constructed by Ed oux 1

) employedto carry visitors to the

, top of

the exhibition building at th e

Universal Exposition at Paris in1 867, and used in Vienna in1 873 for a Similar purpose.This li ft is illustrated in Fig.

70. The holl ow lifting plunger Fig' 7°

A,made o f cast iron in several pieces (see vol . iii. 1 ,

Fig. passes water - tight through the cylinder cover B , andsupports the cage C ,

which is arranged to carry passengers.The greater portion of the cylinder is sunk in the ground.

The cage is guided by four vertical standards D,and attached

to chains E,which are carried over the pulleys F

,and loaded

at the free ends with counter - weights G placed within thestandards. By this means the weight o f the cage and its load

1 Se e Lacro ix, Etu d es swr l’

Evposition dc 1 867, 6 Série .


is partly counterbalanced , the excess of weight of the cagebeing sufficient to ensure its descent. The water is admittedthrough the pipe H

,and to control the descent o f the cage a

regulating valve J is introduced, which , after Shutting o ff thesupply

,all ows the water to be discharged from the lifting

cylinder. In the present case the diameter o f the liftingplunger A was m . [9 8 and the maximum pressureexerted upon it was 1 500 kg. [ 3 3 00 which correspondsto an effective head o f water of

1 5003 0

-

57 m. [1 00 3 ft.]0 2 5 221 000

Fig. 71 shows a Simi lar lift, and represents an arrangement used in the locomotive works of tBorsig in Berlin forli fting the locomotives in the erecting- shops to the height ofabout 2 metres [6% ft.] to the track o f the Stettin railroad.

Here the platform C,constructed of iron beams

,is ' provided

with rails upon which the engines run. It is then lifted bythree lifting pistons A working in Cylinders placed side byside

,the water being conducted through the pipe H from a

supply reservoir lying about 1 8 metres [59 ft.] above . thecylinders. The platform is guided vertically by two standardsD fixed to it

,each of which is held by three rollers attached to

brackets E projecting from the walls . To support the platformwhen in its highest position

,there are four pillars G and two

sliding shoes which may be introduced under the ends of thelifted pillars. The platform is lowered as in all such contrivan c e s by discharging the water from the lifting cylinder.To shut off the supply o f water at the right time

,a dog K

fixed to the platform strikes against a lever F when the platform reaches its highest position . The apparatus is so arrangedthat for l ight loads the two outer cylinders can be disengaged

,

and therefore their lifting plungers are not fastened to theplatform. Each lifting plunger has a diameter of metre

ft.]When the available head of water is insufficient

,a special

motor may o f course be employed to drive a set of pumps,to

force the water into an elevated reservoir from which the lifting cylinder may then be supplied. Al though this arrange



of powerful motors for intermittent work is avoided by employing the indirect mode of action mentioned above. In this caseth e motor can be employed during the whole time of an Operation to pump water into an elevated reservoir

,where it may

be at once available,during the intervals o f actual lifting.

For this reason these elevated reservoirs,especially when made

in the form in which they are represented in the followingarticle

,have received the name of accumu lators. It is evident

from what precedes that a motor, which is unable to lift theload directly

,can easily perform the work when a reservoir is

employed . For let T denote the time of a complete Operation ,t the time during which the crane is rising, and N the horsepower o f a motor which is capable of directly performing thework of lifting, then the continually and indirectly working

75motor needs only to exert energy to the amount of

TN horse

powers,provided the additional wasteful resistances arisin g

from the indirect action are neglected.

Moreover, it is evident that any prime mover alreadyemployed for other purposes

,as a ste am - engine driving the

machi nery of a shop,can be used to work a pump to supply

the reservoir.An other advantage o f the indi rect system

,and under certain

circumstances a very important one,is that we have a con

ve n ient means o f easily di stributing a large amount o f

mechanical energy to considerable distances ; such a case ariseswh en a large number of hoists are to be driven at once by asingle prime mover. For

,since the water pressure can be

conducted to the hoisting apparatus through a series o f pipesadapted to the local features of the ground

,we have a method

o f transmitting motive power to long distances which is freefrom the disadvantages of having many bearings

,bevel wheels

,

and rope - pulleys,all of which must be estimated in considering

the cost o f a transmission o f power by shafting or wire rope,

other things being equal Nor would it be advantageous toemploy steam - hoisting machinery on account of the great losso f heat due to the condensation o f steam in the long pipes.These circumstances explain satisfactorily the advantage o f

employing an hydrauli c hoist driven by an elevated reservoir inall cases where the machine works intermittently

,and where

HYDRAULIC AND PNEUMATIC HOISTS 1 2 5

a“ large amount of work must be performed in a shorttime.

1 7. Accumu lators.

— The pressure Fn exerted upon alifting plunger

,increases in direct proportion to the height H

Of the free surface of the water in the reservoir above theplunger

,hence by increasing

the natural head of water H,

the cross - section F can becorrespondingly reduced. Butthe erection o f elevatedreservoirs is generally attendedwith considerable expense andgreat difficulties as soon as theheight becomes considerable

,

and where they are employedit is seldom possible to obtaina head of water o f more than3 0 m. [ 1 00 ft.] A smallhead will generally involvelarge dimensions for the liftin gcylinder

,and

,as will be shown

hereafter,will involve a rela

tive ly large loss o f work dueto wasteful resistances , so thatsuch a construction cannot berecommended as an e cono

mical one.For this reason Armstrong’s

invention,an accumu lator which

replaces the elevated reservoir,is of great importance.An accumulator, Fig. 72 ,

consists essentially o f a strongcylinder B

,whose plunger passes

,water - tight

,through th e

stuffing box C . This lifting plunger is heavily loaded by aweight receiver which consists of two wrought - iron cylindersE and F suspended from a cross - head D . Let us now supposewater to be pumped into the accumulator cylinder through thepipe H , during which Operation the pipe K is closed ; then thelifting plunger A is forced upward by the pressure of the wate r


u pon its lower surface, and in this manner the weight G is

raised as in a hydraulic hoist. Here again w e have G = Fp ,

where G denotes the fixed weight,F the area o f the lifting

plunger A,and p the water pressure per unit of area ; this

expression does not take into account the friction of the stuffingbox

.The water contained in the cylinder B is therefore

subjected to a pressure p per unit of area expressed by p 9.

FThis water pressure could be obtained by replacing the loadedpiston A by a pressure column o f the same cross—section F andweight G

,and its height would therefore be found from G

FHry, to be E

. Thus the water in the accumulatorF7

cylinder B is under the same pressure as though the cylinderwere connected by means o f a pipe with an elevated tank , theheight of the free surface o f the water above the bottom of the

lifting piston being H If,therefore

,by opemng the

V

cock K,water is conducted from this cylinder through the

pipe V to any hydraulic hoist,the machine will perform its

functions in the same manner as if the reservoir with theabove head of water were employed. In other words

,with

reference to its action on the hoist the accumulator replaces aG

pressure column of HF"

. The available quantity o f water”Y

in the accumulator is likewise given by its dimensions,and is

equal to V F l where l denotes th e distance through wh ichthe lifting plunger A can fall when the cock K is opened ; thatis

,it denotes the height to which the plunger w as previously

raised by the pump. Furthermore,w e se e that while the

water is being conducted through the pipe V to the hoist,the

pump may replenish the accumulator continuously through thepipe H. If the water which is forced by the pump is justsufficient to drive the hoist

,the lifting piston will remain

stationary ; on the other hand , it will fall or rise according asthe hoist uses a greater or smaller quantity of water than thepump can supply during the same time . We may thereforeregard the accumulator as a regulator which stores up or giveso ff the difference between the energy supplied and that consumed.



Armstrong h as made use of a pressure o f 50 atmospheres,

which corresponds to a head of about 500 metres [ 1 650such a head evidently would hardly b e obtainable by the useo f elevated reservoirs . The employment of great water pressuremakes possible the use of small sectional areas for the workingplungers

,and by this means the hydraulic resistances in the

supply ‘pipes are considerably reduced. For example, let ussuppose the water o f the accumulator to be conducted to theseparate hoists through water - mains of diameter d and lengthl,which latter quantity is sometimes very great

,then for a

velocity 7) the quantity o f water under a head H which passesd 2

through the pipes in each second is QW

477,and wh en

wastefu l resistances are neglected,represents the work

7rd 2

A. QHy T’

v .

But on account of the friction of the water in the pipesthere is a loss of head, which, according to vol. i. 455, W e isb .

Mech,is given by i

772 l

Fe d- 7 °

this shows that the loss is independent of the head H,i .e . for

equal values o f l , d , and 77,but different values of H

,the loss

of head is a constant quantity. If therefore the ratio betweenthe loss of work expressed by

7rd 2

AO T

ul l/07,

d h”d 2

an t e energy expended AT

eHry, i s determi ned, w e shall

obtain the relative loss o f work due to the transmission of

water in pipes ; that is to say ,the loss of work corresponding

to each unit of energy expended,will be expressed by

t l c2 l

0

A‘

H' fd zn

’

and therefore varies inversely as the head H. Similar remarksapply to the other hydraul ic resistances ; for . example

,to th

IV HYDRAULIC AND PNEUMATIC HOISTS 1 2 9

loss of pressure due to the passage o f th e water through thecontraction caused by regulators

,bends

,branch pipes

,etc. ,

for

the loss of head at these places is independent o f the absolutehead H. From this point o f V iew the hydraulic transmissionof power with a large head of water is very economical .

‘

On the other hand,owing to the high pressure the con

struction of water pipes in accumulator plants requires thegreatest care

,as even Slight leakage is attended with consider

able loss o f power.In consequence of the large head under which the water o f

an accumulator works,there is another peculiarity belonging

to the class of lifts under consideration. When the load is tobe lifted through a moderate height only

,it is customary to

form the upper part o f the lifting plunger into a platform for

its support,as illustrated in Figs . 70 and 71 . But for a great

length o f stroke this construction would lead to practical inconveniences

,as the plunger w oul d project out of the cylinder

to a considerable distance,which would be a matter o f great

consequence,inasmuch as the diameter of the plunger would

be comparatively small,especially when the load is light

,the

plunger for this condition assuming the character o f a longslender pillar whose strength against fracture from bu lgingwould be insufficient. To meet this d ifficulty the commonArmstrong mode of construction in such cases is to give theplunger a short stroke and to gain an increased range of

motion by suitably arranged tackle . The action of these liftsis the reverse of that mentioned in 8

,inasmuch as the load

to be lifted acts at the free end of the chain,while th e motion

of the pulley or block is directly effected by the plunger. Theforward motion during the raising o f the load therefore corresponds to the reverse motion o f the ordinary tackle . Of

course it follows that the effort which the piston exerts on thelifting tackle is greater than the load to be lifted in the proportion o f the velocity ratio. The high pressure o f the waterrenders it always easy to exert the required force by correspon d ingly increasing the sectional area of the plunger

,the

further advantage thus being gained that the resistance offeredby the latter against compression is increased .

When an hydraulic plant is employed for both heavy andlight work

,then instead of using a single hoist it is more

K

1 3 0 MECHANICS OF HOISTING MACHINERY CHAP. IV

economical to use several so arranged as to work either separate ly for light loads , or together for heavier loads . If thisarrangement were not followed it would b e necessary to entirelyfill the hoist cylinder in both cases , and a very small efficiencywould result.That it is possible to stop or retard the motion of a hoist

ing apparatus by simply closing the supply pipe is self- evident,and w e have mentioned above that by adjusting the openingo f the passage in the supply pipe w e can control the descending load. When a platform is employed it is generally madesuffi ciently heavy to cause the descent by its own weight, andit is often necessary to balance a portion of this weight by th euse of a counter - weight. It is also common practice to utilisethe excess of platform weight over counter - weight to force thedischarge water into an elevated tank which supplies the forcepumps of the accumulator.When there is no platform

,as in the case of cranes and

many other lifts where the load is attached to a hook,it is

generally necessary to load the latter with a special weight toensure the backward motion of the lift. AS this weight, besideskeeping the chain tight and overcoming the resistances o f thepulleys, must cause the descent of the lifting plunger, thelatter is frequently connected with a cou nter -

p lu nger having a

smaller sectional area,but the same stroke as the lifting plunger

,

thus avoiding the use o f a heavy weight on the hook. As th ecounter - plunger takes part in the direct motion o f th e workingplunger

,it is forced into its cylinder during the forward motion

of the latter,and then driven out again by the water pressure

,

thus causing the return o f the lifting plunger. The weightattached to the hook

,therefore

,only serves to give the chain

the necessary degree of tension. Ropes are seldom employedin hydraulic hoisting apparatus . The class o f hydraulicmachinery under consideration

,besides being used for the

actual lifting of weights,is frequently employed to perform

other kinds o f work,for example

,to lift Sluice gates

,and to

swing crane - jibs. (See chapter on Cranes .) It is also employedin Bessemer works to rotate the converters

,and in boiler works

to form bo iler heads, etc. ,but only in cases where intermittent

power is required . For machinery which is to work contin u o u sly the accumulator is not an advan tageous prime mover



on accoun t of its indirect mode of action. In the followingpages a fe w lifts operated by accumulators will be described.

g 1 8. Hydrau lic Lifts.

- In Germany one of the firsthydraulic plants constructed according to Armstrong

’

s systemwas devised in 1 856 for effecting railroad communicationbetween Homberg and Ruhrort

,being employed for lifting cars

from the steam - ferry to the level of the rails . To effect thiseach station is provided with the hoisting apparatus shown inFig. 73 . The lifting cylinder is placed in the massive towerT

,and fastened to two wrought - iron beams D . The plunger

A has a diameter of 0 3 1 4 m. and carries a crosshead C from which the chains K spread downward to theplatform P

,which is to be raised. The latter is provided with

tracks upon which are generally placed two loaded cars, eachweighing about 3 00 cw t. kg.] These can be rundirectly from the ferry upon the platform when in its lowestposition. The vertical motion o f the platform is secured bymeans o f guides f attached to the walls of the tower

,and is

effected by admitting water through the pipe r leading fromthe accumulator. The weight of the platform amounting toabout 560 cw t. [2 kg] is partly balanced by two counterpoises

,together weighing kg. l b s.] w hich

weights working in passages in the walls,are connected with

the cross - head C of the lifting plunger by chains 75,which pass

over pulleys s. The distance through which the platform isto be raised changes with the varying height o f the water o fthe Rhine, the maximum lift being metres [2 ft.]This is also the estimated length o f stroke of the plunger A.

There is still another plunger AIhaving a diameter of 0 1 96

metres in .]and a length o f stroke one - half that of plungerA. By means o f the movable pulley R attached to the crosshead, and th e chain 16

1, the smaller plunger can assist in lifting

the platform when the weight o f the load demands it. Besides,

it is employed alone in li fting the empty platform,preceding

the lowering o f the cars,no water being admitted into the

large cylinder. In order that the latter may still be suppliedwith the water needed as a brake during the next descent

,

there is located in the u pper part of the tower an auxiliaryreservoir into which the water used in the cylinder is forcedas the platform descends. By means o f valves, water from the

IV HYDRAUL IC AND PNEUMATIC HO ISTS

accumulator maybe suppliedto one or both cylinders asdesired

,the Cylinder into

which no water pressure isadmitted being at thesame time placed in commu n ication with theauxiliary reservoir 0 . Thevalves are worked by hand

,

but a selfacting d ise ngag

ing device is introduced,

by which the platform,

during the last two metres

[6 5 ft.] o f its up and downstroke acts upon a systemof levers

,causing a

'

gradualclosing of the admission ordischarge port

,in order to

prevent the shocks whichwould occur if the motiono f the masses were suddenlyarrested.

The accumulator,whose

pumps are driven by asteam - engine of 3 0 horsepower

,has a diameter o f

0 4 1 8 metres in .]and a stroke of metres

[ 1 75 so that itscapacity approximatelycorresponds to that of thetw o hoist cylinders for theirmaximum stroke of 8 72

metres ft.] andmetres [ 1 4 3 ft.] respective ly. The weight on theaccumulator plunger is estimated to produce a pressureo f 4 3 kg. per sq. centimetre[6 1 1 l b s. per sq. in .]

Fig. 74.

1 3 3

1 3 4 MECHANICS OF HOISTING MACHINERY a r.

Fig. 74 shows an A7mstrong lift for warehouses, Fig. 75

representing the hoist cylinder A on a larger scale . Thepiston K is driven downward by the water pressure causingthe movable pulley carried by the cross - head C of the piston

Fig. 75. Fig. 76.

rod to haul upon the rope that passes over the fixed pulley E.

On e end of this rope is made fast to the cross - head C,while

the other end is fixed to the block of the movable pulley'

F .

From the latter,in the manner shown in the figure

,a second

rope passes over the fixed pulleys G and H,whence it is

carried horizontally between the guide - pulleys Z over the



since the use o f the latter is accompanied by considerablefriction due to the great pressure of the water, which makes itmore difficu lt to handle. 0

Since water is practically incompressible, it is necessaryin all hydraulic hoisting machinery to u se special precautionsagainst shocks which occur when masses in motion are suddenlybrought to rest. Let us

,for example, suppose the platform of

the lift,Fig. 73 , to be descending, and let its motion be su d

d e n ly arrested by the closing of the discharge valve, then theM7)

2

2

pended in producing shocks,in consequence of

'

w h ich the pressure of the water in the hoist cylinder might become sufficientlygreat to cause fracture. In order to avoid this straining action ,a relief valve is introduced into the pipe connecting th e

cylinder with the valve chamber ; thi s valve , subjected on itsupper surface to the water pressure in the accumulator, isgenerally kept closed

,and is Opened only when the pressure

within the cylinder becomes excessive ; when this happens, acertain quantity of water from the cylinder is forced back intothe supply pipe communi cating with the accumu l ator. Ashock would also occur if the upward motion o f the platformwere suddenly arrested by cutting o ff the supply o f water ;this may be prevented by a valve— in this case

,a suction valve.

For example,let us suppose the platform to reach the end of

its u p- stroke with a velocity then after suddenly cutting

Off the supply of water, it would stil l be capable of rising to

actual energy stored in the moving mass M, would be ex

2

a height h 24gdue to this velocity

,the effect of which would

be to produce a vacuum or empty space,having a volum e

Fh . Now, immediately following the formation of such avacuum, the platform would drop through this distance h , and,on striking the water

,would cause a shock. To prevent the

platform from thus falling,the pipe connecting the cylinder

with the valve chamber is provided with a second valve . Thisis lifted during each u p

- stroke,and draws water from the dis

charge pipe in to the cylinder,thus preventing the formation

of a vacuum, and afterwards by its action as a brake, regu l ating the descent o f the platform . The arrangement of theserelief valves is best seen in Fig. 77, which represents the valve

Iv HYDRAULIC AND PNEUMATIC HOISTS 1 3 7

gear of the Ruhrort -Homberg lift. The water from the accumu lator is admitted through the pipe a , and , after it has beenused in the cylinder

,is conducted through the pipe b to the

auxil i ary reservoir 0 in the top o f the tower. By opening thestop valve 6 the water reaches the chamber d , from which itmay pass either through valve g and pipe g1 to the large hoistcylinder, or through 75 and 161 to the small hoist cylinder, or itmay be conducted at the same time through 9 and h to bothcylinders

,in which case the discharge valve f must be closed.

If,after closing c

,the d ischarge valve is opened

,the plunger

complete its return stroke,since the water then escapes

F ig. 77.

from g1 and h l through f into the pipe b. At c we have therelief valves already mentioned

,whose lower side is acted on

by the pressure of the water in the accumulator,while 777 and n

represent the suction valves. During the ascent o f the platform these valves will be Opened

,if the pressure in the h oist

cylinder falls below the pressure exerted on the lower surfacesof the valves by the water o f the auxiliary reservoir 0 . Atth e same time the valves m and n provide either cylinderwhen not in communication with the accumulator— with waterfrom the auxil iary reservoir

,to act as a brake in the manner

already described.

We see that the valves e , m ,and n cannot extend their

action to the balance weights connected by chains with the


platform,and that these chains are exposed to unavoidable

shocks by the sudden stopping of the machinery. To preventthese straining actions it is always advisable to gradually retardthe motion

,and it is with this object in view that the self

actin g disengaging device mentioned above is made use o f.1 9. Action Of Accumu lators.

— It stil l remains for us to

F ig. 78.

G establish the principles whichQ I govern the working o f hydrauli choisting machinery by accumu

lators.1 For this purpose letthe fixed weight resting uponthe accumulator plunger bereplaced by a col umn o f watero f equal weight

,having the

same sectional area F1as the

plunger,and a height repre

sented in Fig. 78 by BG = h .

Let us also suppose the parto f the weight of the liftingplunger and platform

,which is

not balanced by counter - weights,

to be replaced by a column o f

water having the same sectionalarea F as this plunger

,and a

height AC go, and let the usefu l load Q to be lifted be represented by a similar column

,

having the height CD = g, so

that Q = Fgfy, where «y

(

repre

sents the weight of a unitvolume o f water. F

2may

represent the sectional area o f the horizontal supply pipe,

l its length,BA and l

' the length o f the discharge pipeAH having the same cross—section F

2. Finally the height

above the pipe BH o f the water level J in the auxiliary reservoir—from which the pump replenishes the accumulator— will be

denoted by HJ h/ . The water levels D and G in the figurecorrespond respectively to the l ow est position o f the liftingplunger, an d the h igh est position of the accumulator plunger.

1 Se e artic l e b y L . Putzrath, Ze itschr. d . Vcr. De u tsch . Ing.

,1 878, p. 505.



w here V denotes the quantity of water Ftc that has passedfrom the accumulator into the cylinder o f the hoist . In performing this work a volume o f water F1y z c z V has beenconveyed from the space GG’

o f the accumulator to the reservoir J

,and at the same time the centre o f gravity of this water

has,according to the figure

,descended through the distance

h

Consequently the work performed by this mass of water infall i ng is expressed by

h h’

We therefore see that the expression V ¢y<h + h

’— v§ repre

sents the loss o f work which attends the lifting o f the load,and that the efficiency of the hydraulic lift is represented by

The question n ow is under what conditions the above lossbecomes a minimum and the efficiency a maximum. This is

evidently the case when the value h + h’ v2 is made assmall as possible. If the frictional resistances a o f theplungers in their stuffing boxes, and 4; of the water in thepipes di d not exist, we see that the height h , or the difference o flevel between G an d D in the two cylinders at the beginning of

the stroke,would be at least h y z a( l v), thus h z: for

equal cross - sections F and F 1 of the plungers,because when

the lifting plunger is in its highest position the column of waterin the cylinder A must be balanced by the column in B .

Likewise during the descent of the plunger the height h’ cannot be less than zero even in the absence o f friction, for thelevel C in the hoist cylinder

,corresponding to the empty plat

form,cannot fall below the level J in the auxiliary reservoir.


Under these ideal conditions of freedom from all frictionalresistances , the loss of work for a complete Operation becomes

V 7 (h + h’

( 1 + v)+ 0 —v

Hence for F F1the loss isnga'

. A portion V vy(It—

50+ 79

)21 v

n w —

2of th1 s work Is lost during the ascent

,and the

£13

remainder V 7 (h’

+5) V 72 during the descent o f the plat ~

The explanation of this is found in the fact that thevolume of water Re which has de scended does not

,as would

be the case with a rigid body,rise above the level D’ or J in

consequence of its velocity,the assumption being made that

the velocity communicated to the water is destroyed by eddiesor internal motion.

In reality,however

,the loss o f work is much greater owing

to the friction o and 0 1o f the plungers , and the friction <1) in

the pipes. Taking these frictional resistances during theascent o f the platform into account

,the figure shows that the

minimum value of h must satisfy the condition

-

1+ qs.

Further,let the height o f the water . column which corre

sponds to the friction o f the stuffing box during the descent ofthe lifting plunger be denoted by a

' C’N CN, which height

is henceforth to be deducted from the water column AC’ 90 ac,

and let : JO denote the height o f the water column correspon d ing to the friction in th e discharge pipe AH, then w elikewise find the least value o f h’ to be

77 (r'

47.

Assuming these mi nimum,i .e . most favourable

,values

,the lost

work during the raising o f the load Qn 'y to a height a:

becomes

V y (h + h’—

vg>V 7 1 +


If now the lift be arranged so as to fulfil these conditions,i .e .

if the effective heads h and h ’ be so chosen as to satisfy therelations

h + V)

h'

(If) 0,

then although the ascent and descent would be theoreticall ypossible

,yet for practical purposes the working o f the machine

would require too much time,inasmuch as the raising and

lowering o f the water levels at D and G during the up stroke,

and at C’ and J during the down stroke,would take place in a

manner similar to that observed when communication is Openedbetween two vessels containing water to unequal heights

,as in

the case of a canal lock.

As the actual problem,however

,is to »lift the load to a

certain height in a given time,and as the same conditions

must be fulfilled for the down stroke,the solution requires

that we assume the effective heads h and h’ greater than theminimum heads determined above. The problem is thusreduced to finding the relation b etw e e n ‘

th e assumed effectiveheads h and h ’ and the time required for the ascent and descent.From what has preceded it follows that the loss o f work during

CC

the up stroke,found to ben (h h

’v

5), must increase withh and h ’

,so that Obviously th e efficiency o f the hydraulic lift

diminishes in proportion as the velocity of the ascent anddescent increases .

In order to determine the speed of the lifting plunger,it

is necessary to consider the mass of the counter - weight Wbalancing the platform. Let this counter - weight be replaced

WFry’

equal to the area F of the lifting plunger,while go represents

the height o f the water column corresponding to the tota l

weight Q0 o f the platform. Further,let 7) be the efficiency of

the system o f pulleys used in connection with the counterweight ; then during the up stroke the excess QO 77W o f theweight o f the platform must be overcome

,and the descent of

the platform must be effected by the excess Ofw e ight QOW7?

by a water column o f height w whose sectional area is



Now the driving force P,and hence the acceleration c

,

diminish with every instant,this diminution being due not

only to the reduction in effective head h by ( 1 v) times theincrease in a

,but also to the expenditure o f a portion o f this

head towards giving motion to the water. A clear idea of

this fact may be gathered by noting the difference between thehydrostatic pressure of water when at rest, and the hydrau l icpressure when it is in motion. According to vol. i. 4 2 7,W e isb . Mech ,

the hydrau l ic head , at a point where the waterflows with a velocity f

v2 ,is less than the hydrostati c head at

0

the same pomt by 29

the water at the entrance. In accordance with this principlethe pressure whi ch causes the acceleration of the mass M is

determined as follows. Suppose the liftingplunger to be inits lowest position

,and the valve S just Opened to the water

,

then for the effective head h — o ‘71—91’ at this point,

the in itial hydrostatic pressure is f (h — ar— <rl—qb)ry, where

h h — g—go+ 77w ,

and f is the area of th e passage offered bythe valve to the water. But the pressure diminishes after themotion of the plunger has begun . For example

,assuming

that the lifting plunger has reached a height DD’= £U,at

which instant its velocity may be taken equal to thenfrom what precedes a diminution o f the hydrostatic head h

,

equal to a + y = a°

( 1 v), occurs ; besides , the hydraulic heado f the flowing water in S is less than the hydrostatic head by2 2

772

771

29

Now 77 F CF,hence 77

1 F7) V7) , and o

zf e F,hence

1

F F—7) where

,u. denotes the ratio of the sectional area

f fof the l ifting cylinder to that of the inlet. Consequently thehydraulic head at S at this instant is

where 771denotes the velocity of

where 772and 77

1denote the velocities in S and tG

’.

,02

o - «i— e — u i - cx - w — e 2 9

.

in which expression evidently v2 can be disregarded in com

parison with,ufi,as v is always less than 1 , while ,

u. generallyl ies between 2 0 and 40

,thus making v

2 equal to hardlyTIC


per cent of,uz. We thus obtain the acceleration o f the

lifting plunger at the position referred to,that is at a

distance a from its lowest position

U -

O’

l

where for the sake of brevity w e put

h 0°

(1) a

and

Substi tuting the general value c W for the accelerati on,

8and placing 77 5, w e finally obtain the equation applicable

to all hydrauli c hoisting machines

a ( 1 v):c ,u.2

a

The integration of this differential equation offers greatdi fficulties

,but it is easy to obtain a solution sufficiently

accurate for our purpose. According to the above investiga172

tion,the height“25; due to the velocity increases from zero

at the beginning to a value depending upon the speed 77 of thelifting plunger. The velocity 77 is usually small in all hoistin gmachines

,owin g to the large masses put in motion

,seldom

exceeding 0 3 metres ft.] per second ; consequently,though the corresponding velocity of the water through the

Fsupply valve is greater in the proportion of

‘7,the head due

to the latter velocity is nevertheless small compared with thelarge hydrostatic heads employed in the accumulator plant.The error wil l therefore be trifling if

,when determining the

accelerating force,instead of simply subtractin g the abo ve head

at the instant corresponding to the maximum speed 77 o f the


lifting plunger,we subtract it throughout from the beginning

of the motion. Conducting the calculation in this manner,we

shall find that the time t of the up stroke as obtained from theformula will be slightly in excess o f the actual time required

,

as in reality the acceleration is somewhat greater than weassume at the comm encement o f the motion

,in view o f the

fact that the head which properly Should have been deductedfrom h at this point o f the stroke

,would fall short of the

maximum value actually deducted. Thus the principalequation (5) developed above , changes to

where h no longer represents the actu al excess o f head of thewater level G above D

,Fig. 78 , but a quantity which h as

2

been diminished bym;. .g

In order to deduce an expression for this time t from

equation let us substitute 21

;for c,then

87) a ( 1 v).ri

at b 9°

l l .

Multiplying this formula by

w e havea ( l v)x

7787) gPb

from which by integration w e get

[if (i _ Li fx2>+ co t2 g”bx 2

,u b

u s .

Since 7) 0 when a : 0,we find const. 0. Hence

(8x

)2 2 a 1 V



Corresponding to this velocity of the lifting piston w e havefor the velocity o f the water through the orifice o f the supplyvalve 77

2 la y , and if w e add to h the head

7722 2 as ( l v)s

2

27; 2 6h

due to this velocity 772 ,we shall obtain the effective head by

which the water level in the accumulator must exceed that ofthe lifting plunger in order to accomplish the desired object ;that is

,in order to pass through the length of stroke 3 in the

given time t.The formulae for the down stroke are determined in the

same manner. For this case the acceleration c’of the moving

masses,when the lifting plunger is at a distance a’ from its

highest position,and the valve opening is f

’

7.

is determined by

.fl

(hl

0"¢

I

x!

)

when we note that here 90 represents the driving water columnand k’ w the driven . Hence we must assume for the effectivehead 1

k’

and v= O,77

as the area of the free surface of the auxiliary reservoir is manytimes greater than the area of the plunger. Analogous to thecalculation for the up stroke

,w e have placed

if; — O

°'

a'

and

Likewise,multiplying by 77

’ will give

and by integration2 am

(85, —g [

blx

hence the velocity of the platform when it reaches its lowestposition is


For the time t’ of the descent,w e have from the

equation ”l b , 8x!

hence

arc cos (18

)J 2 a’

x'

a'

from which w e deduce

Therefore we have

w k’

l'

)

to which value we must again add th e head

,2 a

’

s 82

2 b'

due to the velocity of the water through the di sch arge orifice,

In order to obtain the head of the water level 90 relatively tothe discharge tank

,it being assumed that the time of descent

is limited to t’ seconds.From careful experiments made by John Hick,1 the friction

of a plunger working through a leather collar varies directlyas the water pressure per unit of the surface of the plunger

,

and as the diameter o f the latter, but is independent of thedepth of the wearing surface of the collar.According to these experiments

,the tota l friction of the

plunger is R [cg where K is the tota l pressure on the plunger

expressed in kilograms,D the diameter, and x a coefficient

depending upon the state o f lubrication,which ranges from

1 0 09 to when D is expressed in millim etres [1c rangesfrom 0 03 98 to 0 0977, when D is expressed in inches and Kand R in pounds]. Let this friction be expressed in the form

1 Engin eer, Ju n e 1 1 866, and in ab stract Verhand lg. d . Var. z. Bg. d . Gew .

1 866.


of a pressure column having a head 8, and an area of cross2

section F equal to the area of the plunger ; then this0

head in metres can be determined from77

°D 2 0° K 76

K

4 1 000 D D 4 1 000’

where k is the head which measures the plunger pressure K .

G K K 77°D 2 G

1 44 D D 4 1 44

where D is expressed in inches , 0 in feet, and G is the weighto f a cubic foot o f water.]Hence we have

which varies between

mm .

Therefore, for a plunger diameter of 1 00 mm.,the loss o f

head is, roughly, from 1 to per cent. According to theolder estimates of Rankin e

,the friction of the plunger in

hydrostatic presses is much greater,and amounts to about 1 0

per cent of the load in ordinary cases. In an article onAccumulators, Zeitschr. d eu tsch . Ing. 1 867, page 65, Horn er

assumes 5 per cent o f the load as a mean value for thisfriction . Hence, corresponding to each set of dimensions; wemust assume a different value for The frictional resistances(j) and (3

1of the water in the pipes are to be computed accord

ing to the rules laid down in vol. i. s’ec. vii . ch . 4 ,W e isb . Me ek .

If we suppose that the load Q ,instead of resting upon the

lifting piston— as assumed in the preceding pages— is indirectlyconnected with the ram

,say by interposing pulleys

,as illus

trate d in Figs . 74 and 76, the calculation remains the same,except that Q will then represent not the load itself, but a

n Q

77

denotes the velocity ratio o f the mechanism and 77 its efficiency.

pressure column equivalent to the resistance where n



the friction o f th e leather packing to b e 3 per cent of th e pre ssure

on th e plunger (according to Hick w e should have only if?00 08 for th e lifting plunge r, and if:0 006 for th e accumulator),w e must place

me ) 0 3 68 0-

95 x m . ft.]

0° =0 -

03 x 43 1 = 1 3 m . [42 6 ft.]

In orde r to de termine (f) w e may take th e mean ve locity of th e

lifting plunge r at i—g 0 1 94 m. so that th e mean ve locity

of flow in th e supply pipe o f diame te r d mm. [4 1 2 is2

x 0-75 m. [5 74 ft.] Hence th e loss of head

according to vol. i. 456,

[

We isb . Mech,is given by th e formula

I 772 50f " 57 25 0T0

“

4 27 97811 5 m ’ [4 9 ft ]:

and w e have roughly 0°

01

cf) : 1 0 + 1 3 + 1 5 2 5 In . [82Furthe r, th e ve locity with which th e lifting plunge r reache s th e

e nd of its up stroke is found from ( 1 3 ) to b e

3 6 2 57 3 68 3 02 43 1 50

Th e corre sponding ve locity of th e wate r through th e opening o fth e supply valve is there fore ,

a i) 3 6 x 0 3 70 1 3 3 m.

th e producing of which require s an additional head

2 x 9 8 19

-

04 m. ft.]

Consequently th e minimum e ffe ctive head require d to work th e

machine is

In . ft.]

In th e pre sent case th e available balance actually amounts to

k q (g, nw )=43 1 2 57 3 68 m . [3 05

which prove s that th e working of th e lift is sufficiently ensured,and

that if w e de sire to prevent th e platform from moving at a greate r

IV HYDRAULIC AND PNEUMATIC HOISTS 1 53

Spe ed, th e exce ss of head must b e reduced by throttling th e openingo f th e supply valve .

For th e de scent of th e platform w e have k' = 1 8 m . [59l’

0,ct

’

0, ,a

’

1 9 hence , again assuming th e time for lowe ringto b e 45 se conds

,w e find according to ( 1 6)

1 3 0 m . ft.]

Th e final ve locity o f the platform may then b e de te rmined fromwhich give s

From this w e obtain th e ve locity through th e opening of thedischarge valve to b e 1 9 x m. whichrepre sents a head of metre s ft.] If w e assume a value of

7 7

19) 0 -03 x ( 3 68 In . [40 ft.]

for th e friction of th e le athe r packing, th e e ffe ctive head requiredwill b e

m . [54 3 3 ft. ]

As,howeve r, th e available e ffe ctive head has th e greate r value ,

repre sented by

7)k

'= 3 68 3 1 8 m . [ 1 05

th e time for th e de scent of th e empty platform may b e reduced.

De ducting, for instance , from the se 3 2 m. a head of say 5 m.

ft.]for overcoming th e friction of the packing, and producingth e required ve locity through th e discharge valve , the re stillremains a head of a

’

2 7 m. which give s th e time t’

required for lowe ring fromi i are cos (l — i)g a

1 9 xarc cos (1 g ) 3 0 2 se conds.

It is e vident that when th e platform is loaded, too rapid motionmust b e prevente d by throttling th e discharge valve .

2 0. Pne umatic Hoists.

— At the present day pn eumatic


hoists have gained an extended application . Two furnace - liftso f this class are illustrated in Figs . 79 and 80. That show nin Fig. 79 w as designed by Gibbons for four blast furnaces nearDudley

,and has been in operation for a number o f years . It

consists of a wrought - iron tube AB m. [57 4 ft.] wide ,and 1 6 m. [5 ft.] long, which is filled from below with

Fig. 79. Fig. 80.

compressed air. The load Q is placed on a platform at thetop A

,and IS lifted together with the tube by the action o f the

air. The latter 1 s supplied through the pipes CDEFG fromthe blast chamber which provides the furnace with air, and thelower end o f th e tube AB is closed by the water which nearlyfills the pit BEF

,that is enclosed by brick work. In its

lowest position,the tube AB rests on a support at the bottom

o f the pit,and it is guided during its upward motion both by

rolls KK inside the pit,and by four columns above the latter,

which are reached by the fou r arms LL at th e top of the tube .



rings,travels in a vertical tube A which is accurately bored

out. A square platform B is connected to this piston by fourropes D

,one in each corner

,these ropes being carried over

four guide - pul leys C placed' diagonally. By this arrangementany movement o f the piston K causes an equal and oppositemovement of the platform. The piston K is made of sufficient

weight to balance the platform,to

gether with the empty ore and cokewaggons

,as well as part o f the

load .

By means of steam . power the airis pumped out from the cylinder Athrough the pipe a

,when the

piston is in its highest,and con

se quently the platform in its lowest,position . The atmospheric pressurenow forces the piston down , andthus causes the platform to rise.For lowering the latter

,after the

loaded cars have been exchanged forempty ones

,the vacuum pump by

means of a valve motion is transformed into a compression pump ,which forces air into the cylinderthrough the pipe a

,until the excess

o f pressure on the underside o f thepiston compels the latter to ascend .

In the furnace - lift at Schwech at 1

the excess o f pressure amounts to 71F ig. 81 .

atmosphere for a load of ore havingan unbalanced weight of 2 tons ,

while ‘

Ila

‘ atmosphere is sufficient for an unbalanced load of

coke weighing 412ton .

The calcu l ations for a pneum atic hoist may be made in thefollowing manner — Let W denote the resistance to be overcome by the piston

,including wasteful resistances , and with

due attention paid to the counter - weights ; further, let Frepresent the area o f cross - section of the piston , and p 0 the

1 Excu rsionsbe ri cht. vo n Rie d l e r, 1 876, Sk etch 74.

IV HYDRAULIC AND PNEUMATIC HOISTS 1 57

outside, and p the inside pressure of the air per unit of area,then

W FU’ ‘

Pok

When the piston has travelled through a distance 3,it has

performed an amount of workAO

Z F<f7 “p 02 3 V<P “P0,

if the volume Fs passed through by the piston is denoted by V.

In order to determine the power whi ch must be developedby the engines which drive the air pumps

,let f be the area

and l the length o f strokeo f the pump piston B

,Fig.

8 2 . While the latter travelsfrom B to B

1 ,the

the cylinder is compressedfrom the original pressure

p O to p . Beyond this pointno further compression takesplace

,the air in the pump

cylinder during the reF1g° 82 °

main d e r o f the stroke BlC z l

1being instead forced into the

lifting cylinder through the pipe D,thus causing the piston

to move through the distance 3 from A to A1 ,so that Fs

f l 1= V . According to vol . i . g 4 1 5 ,

the work done by th eengine during the period o f compression is given by

A. fl l p l og.

4 — fi o<l 4)P0

V}? loge “12° V ?“l l ),1170 1

as the external atmosphere acts with a force fp 0 through th edistance ( l l

l ).The work done during the second period B

lC _

- l1is

As=f (f7 —

Po)l i W}?an d consequently the total work performed by the engine forone stroke o f the piston is

V zg—OU —

p o)= Vp l oge0 1

V 3?“l l ) V<P1


The efficiency 77 of the pneumatic lifting cylin der is thusfound to be

77fig 10

“170

A19 log, _

11 V loge v

210

when the ratio o f compression fl is denoted by v.

10 0For the vacuum - lift

,Fig. 8 1

,in which W = F (p0 p),

obtain in a similar manner the useful work

when the ratio of density 230 is denoted by v.

20

The work actually expended will be

A =f lre Y4. tog,

or,as f l 1 F8 V

,and lp = l 1p0,

A =V (ii — 10 ,

10O

(V ir l o e170P

g19

170 g 1’

which gives for the vacuum - lift an efficiency

By further investigation we find that the efficiency of

pneumatic hoists decreases as the ratio of densities 17 increases ,and that the result is more un favourable in vacuum - lifts thanwhen compressed air is employed. This may be seen from? thefollowing table

,which gives the efficiencies 77 and 71

’ deducedfrom the above formulae for different values o f v.

TABLE GIV ING THE EFFICIENCY OF PNEUMATIC HOISTS.

0 95 3 09 1 4 08 78 08 2 2

I

77 02 5 1v2 log, v 1


CHAPTER V


2 1 . Brak e s_

for Low e ring— These devices are used for

retardi ng the motion in lowering a load,so as to obtain a

Fig.

’

83 .

smooth and uniform descent,and prevent

shocks when the load reaches its pointo f destination .

A simple brake is sometimes employed as a life - saving apparatus at fires

,

for letting down persons from the upperstories of burning buildings . Here thecoil friction ac ting between a rope and acylinder is utilised

,as may be seen from

Fig. 8 3 . The apparatus consists of aspool - shaped object C

,around which the

rope AB is wound in several coils . Theupper end of the rope is secured in aSuitable manner

,while the lower e n d

hangs down freely. Now,if the person

is suspended from the h o ok , b y means o fa belt

,the coil friction is brought into

play by the sliding of the cylinder along therope. The friction may be estimated in the following manner.Let the tension in the upper end o f the rope

,which is equal to

the suspended load,be denoted by S

I ,and that in the free end

by S2 ,then

,according to vol . i . 1 99

,when 4) is

the coefficient of friction and a the arcs surrounded by therope. Thus the friction is F S

IS2

S2 (e

¢“ which isindependent of the diameter o f the cylinder, and it is evidentthat it can be greatly increased by increasing the number o f

CHAP. v HOISTING MACHINERY FOR MINES 1 61

coils of the rope . To check the sliding motion,it is only

ne cessary to apply a slight force at the free end o f the latter,

which may be done at will by the occupant of the apparatus .Assuming q!) 03

,and that the rope makes two full coil s

around the cylinder,then

e‘P“ 43 - 3

,

and consequently F 4 2 ° 3 S which shows that for arresting

Fig. 84.

the motion,the application of a force equal to

117

of the weightof the occupant would be sufficient. The lower end of therope may be secured to the knobs D

,when it is desired to stop

the descent for any length of time.In machin ery

,the mechanism employed for lowering loads

consists chiefly in a horizontal shaft or barrel provided with abrake wheel or disc . Around this barrel the rope whi ch holdsthe load is wound

,and gradually unwinds during the descent ,

while the brake lever or strap is pressing against the wheel.M


A brake winch,as used for lowering machin es and materials

into shafts o f mines,is shown in Fig. 84 . AB is a common

tackle,and C is the load attached to it ; D is the w inch drum ,

DE the crank,and FG the brake disc

,which is fast on the

drum. The brake beams,which are movable about K and M

,

are forced again st the disc by means o f the lever PR whi chturns on the fixed stud R. While one workman applies thebrake lever

,and thus counteracts the weight of the load C

,

another slowly turns the crank DE,thus causing the rope to

unwind from the drum,and allowing the load to descend.

If Q is the load , and n is the number of ropes AB in thetackle

,then

,neglecting the wasteful resistances

,the force at

the circumference of the letting b denote the

radius of the drum,including half the thickness o f the rope

,

and a the radius o f the brake disc,w e now Obtain the force

required at the circumference of the latter R éQ l“2

a na

Placing the braking force at the end o f the brake lever P andKL MN

2

of the load are KF MG b and RS RT b2 ,the coefficient

of friction at the brake disc being then R ct? %P henceI 2

its lever arms a and RP a2 ,while the lever arms

w e get

which gives

PQ

o

aa la2

(tn

As the frictional resistances assist the action of the effortapplied in all apparatus for lowering

,it follows that the force

P actually required falls below the value just deduced.

EXAMPLE — A load Q we ighing 1 000 kg. [2 2 05 l b s.] is to b elowe re d by means of th e brake winch in Fig. 84 th e ratios of le ve rarms are I

1128 ,a]

and( 1 2

—TU ,

th e numbe r o f rope s in th e tackle AB is n 6,and th e co efli cie nt of



England for lowering coal cars to vessels,as shown in Fig. 85.

AB is a track on which the cars C,arrive ; DE is an arm

whi ch swings about the point D,and carries a platform

T ; in its highest position thi s platform forms a continuation of the track AB

,and is made to receive a coal - car.

A rope EK attached to the end E of the lever,unwin ds

from the drum K, w hen the loaded car is lowered to the

vessel,and causes the empty car to return when wound on

to the drum. In order to accomplish the latter operationwithout the aid o f special motive power

,a counter - weight G is

made use o f,which is suspended partly by the arm GM pivoted

at M,and partly by a rope GK

,which is wound on to the

drum K while the car is being lowered,thus causing G to rise

and storing up sufficient power'

for the return of the empty car.A large brake wheel RS operated by a strap S

,is fixed on

the drum K with a view to securing a uniform motion and amoderate rate of speed during both ascent

'

and descent.In designing a drop of this kind

,the counter - weight should

be so chosen that the braking force required to counteract theaccelerated up and down motions of the caf will be as small aspossible

,and also the same in both cases.

For the calculation let us assume that,when the car is in

its lowest position,both arms DE and MG are horizontal , and

that it is sufficiently correct to place

DK = DE = a and MK=MG = b.

Now let for any position 2 a denote the angle EDK whi ch theload arm makes with the vertical

,and the angle GMK

which the counter - weight arm makes with the horizon further,

let Q be the load in the car,W the weight o f the latter empty,together with the platform and one - half of the arm DE

,and G

the counter - weight,including one - half o f the arm MG . By the

use o f the parallelogram of forces,we then find the tension in

the rope EK during the lowering o f the loaded car amou nts to

(Q +W)2 sin a,

and while the empty car is being hoisted

S'

lW2 Sin a .

HOISTING MACHINERY FOR M INES 1 65

The tension in the rope KG is in both cases

The force P acting in the circumference of the rope drum,

and which must be overcome through the brake action , is inlowering

P = SI

sin a— G

and in hoistingcos 2BP = S

z- S

I= G

78W 2 sin a .

If these forces are to be equal , as required, w e Obtain

sin a co sBG (Q 2W)

co s

Evidently this requirement cannot be fulfilled for all valuesof a and

,8 ; assuming, however, that this condition holds for

the lowest position,when 2 a. 90

° and B 0,then we get

sin

Besides,it is possible to make the two brake pressures equal

in a second position if the relation between the angles a. and,8 is suitably chosen . If this occurs in the highest positi on of

the car,in which the angles may be denoted by 2 a 1 and

w e have the equation

2W)sin c

lco s

,81

co s

sin 81co s B, co s fl ,

from which when a l is given we Obtain

When the arrangement is contrived in the above manner,it

is then evident that the braking force required for uniformlowering

,either in the highest or lowest position

,equals that


needed for hoisting. In order to establish the desired relationbetween the angles a 1 and ,

8 1 , it is necessary to give the properlengths to the arms a and b .

These will be determined with reference to the fact thatthe same length of rope is wound on to the drum K on oneside as is unwound on the other

,so that in general

KC EDfl EK,

or for the highest position

2 b sin 181 2 a sin al

.

If now the lever arm a of the load is known as well as itsangle 2 a 1 w ith the vertical in the highest position , w e mayeasily compute

,8 1 and b from the equations given . The con«

di tion regardin g equal braking force for lifting and lowering isonly approximated to in the intermediate positions .

EXAMPLE — A drop is to b e constructed like that in Fig. 85 for

a l oad Q : 1 000 kg. [2 2 05 th e car toge the r with platform ,

etc. ,having a we ight W = 4OO kg. [882 lbs.] In this case th e

counte r-we ight must b e made e qual to

G: (1 000 2 x °7071 1 273 kg. [2 807 l b s. ]

Th e force require d at th e circumfe rence of th e drum w ill b e

P= ( 1 000°41 4 400 x kg. [ 1 558 l b s.]

For a diame te r of brake wh e e l o f 6 time s that of th efriction at th e strap must equal 1 1 8 kg. [2 60 1b s.] Th e calculationsfor ascertaining th e require d pre ssure at th e leve r are treate d of invol. iii. 1

,We isb . Mech , in th e chapte r on brake s.

If th e load is to b e l et down from a h e ight h 1 2 m. ft.]and th e arm from which it is suspende dmake s an angle of 2 0

° withth e ve rtical in its highe st position, so that a 1 then th e lengthof this arm will b e

h 1 2

cos 2 a 1

_

0 °93 971 2 77m . [41 2 ft.

Th e angle ,81is obtaine d from

sin 1 0°

4 sin 2 1 0°

cosB,2 a/5

z 0771 3 ,



track. In Fig. 8 6 an arrangement o f this kind is il l ustrated,

as carried out in practice at the Saarbrncker mines . l The carW travels on the rails a

,between Which a second and lower

track b is placed for the counter - weight Gr,which is made of

cast iron and provided with small rollers . The rope S leadingfrom the car unwin ds from the drum B on the shaft A

,while

the rope SIsecured to the counter - weight is wound on to the

smaller drum C on the same shaft. It is evident from th e

figure how the motion may be controlled by the brake wheelD and the lever E.

Such inclined railways have been constructed for a varietyof grades

,ranging as low as 1 ° 50’ where the inclin ation is so

slight,however

,it would be impossible to attain the desired

result without the exercise of great care in the construction so

as to reduce the hurtful resistances to a minimum.

If for the inclined plane in Fig. 86 Vere denote by Q theweight of the load in the car

,by W that of the empty car

,by

G the counter - weight,and by a. the inclination of the railway

to the horizon,then w e obtain for the turning moment exerted

on the shaft A when the car is descending

[(Q W)b Ge] sin a,

where b and c are the radii o f the rope drums B and C , andwhen it is ascending

,the moment is

(G6 Wb) sin a,

neglecting wasteful resistances . ‘By placing these two expres ;sions equal

,we find that it would be necessary to make

In order to determine the minimum inclination of theplane , w e must take account of the frictional resistances . Let

4) be the coefficient of journal friction, v the ratio of the radiusof the car journals to that of the wheels

,and v1 the same ratio

for the counter - weight,r the radius of the drum shaft A,

and 0'

and 01 the coefficients due to th e

'

stiffn e ss of the ropes S and

1 Ze itschv. f . d . Berg Hittien u nd Sa l ~ Wesen ,1 856.

v HOISTING MACHINERY FOR M INES 1 69

SI , then the turning moment actin g on the drum inwill be

(1 0'

(fig)(Q +W) (sin a vq!) co s a)b

(I 01 (sin a v

l gb cos a)o,

and in lifting

(1 01

<1>20>G (sin a v

lqt cos 000

(I (sin a q co s a)b.

These expressions should always give values considerablygreater than zero

,in order to make the motion possible.

g 2 2 . Mine Hoists.

— These are used,as the name implies ,

for lifting ore,coal

,etc.

,in the shafts of mines . The direction

in which shafts are sunk may approach to the p erp en d icu lar,when the angle varies from 75

° to 90° to the horizon,or it

may . be nearly h orizonta l , in which case the angle is 1 5° or

less . The essential part o f a mine hoist is a drum with tworopes so attached that wh il e one is wound on to the drum theother is being unwound . Thus if a loaded receptacle hangs atthe end of one of the ropes

,and an empty one at the other

,the

former may b e lifted while the latter is lowered. After anexchange of receptacles at each end the operation may berepeated by turning the drum in the opposite di rection. It ischiefly by this arrangement

,which is similar to the foundry

hoists already described,that the mine hoists differ from

common winches and ordinary lifts,which

,as a rule

,are pro

vid e d with only one rope carrying a hook or a cage.

In cases where small loads only are to be hoisted frommoderate depths

,the comm on w inch is made use of

,which

may be operated by two or more workmen. For greater loadsand considerable depths the w hin

,or upright drum

,is employed ,

which is either driven by hand power or revolved by horses oroxen . All hoisting of any great consequence

,however, is

nowadays done by water or steam as th e motive power, thehoisting machine being provided with a drum which

,in most

cases,is horizontal. Evidently the arrangement differs accord


ing as a w ater - w h ee l,tu rbin e

,w ater- motor

,or a steam - engine is

made use of as the prime move r. More recently com

p ressed a ir1 has been introduced for the same purpose

,the

air being compressed by steam or water power,and afterwards

used in a motor coupled to the hoisting machine,in a manner

similar to the mode o f using steam in a steam - engine.The arrangement of a mine winch is shown by Fig. 87.

A is the drum around which a rope B is wound ; at the ends0 and D of the latter the iron - bound buckets are suspended.

Onl y the arriving or departing bucket E at the top of theshaft is shown in the cut , the other bucket at the samemoment being near the point where the loading is being done.

F ig. 87.

Th e journals o f the drum rest on the posts EH,secured to

the timbers KK,placed horizontally over the mouth of the

shaft. At their upper ends the posts are provided with ironlined slots for the reception of the journals. The workmenstand on a platform LL

,supported by the timber framework

KM placed over the shaft. The rod a running parallel withthe drum

,and fastened to the posts at each end by means of

iron brackets,serves as a hand - rail for the workmen in remov

ing the loaded bucket and replacing an empty one . Finally ,in order to prevent the falling into the shaft o f objects whichmight create obstructions

,the doors N and O are made u se

1 And e l ectric motors. Translator's remark .


172 MECHANICS OF HO ISTING MACHINERY CHAP.

in the following manner . Let s be the length o f the ropewhich is to be wound on to the drum

,r the radius

,and l the

length o f the latter, then for a thickness d of the rope the

number o f coils in each layer is represented by‘ n i. Ford

m layers of rope,that next to the drum has a radius o f r +

i

and the radius o f the outside layer is r + (m

mean radius is to be taken equal to r + -

2

W—

Ld . Consequently

the total length of the rope will be

which equation gives

and hence

m “

771+

03‘

d

The mean radius is therefore

or approximately

The methods employed for equalising the influence of theweight o f the rope by varying the radii of the drum

,will be

explained in the following .

In order to make possible the use o f a win ch for heavyloads

,a gear and pinion are occasionally employed for driving

the drum. This is necessary,owing to the fact that the

.diameter of the drum cannot be reduced beyond a certain sizeconsistent with proper strength

,and also depending on th e

stiffness of the rope , and besides it is not practicable to makethe cranks longer than the usual measure of from to m .

HOISTING MACHINERY FOR MINES 173

(from 1 4 to 1 65 inches). Mine winches with tw o sets of gearsare rarely employed .

A geared winch is shown in Fig. 8 8 . Here the drum Ais about 0 3 or 04 m . [ 1 2 or 1 5 inches] in diameter, andcarri es a large gear BD with 40 to 60 teeth , while the pinionE is keyed to the crank shaft EF (not shown in the fig.) Asa rule one workman is stationed at each crank , though it isevident that provided the crank handles are of sufli c ient length

,

F ig. 88 .

three 0 1° four men may profitably engage in the hoisting

operation.

The distribution of labour may be so contrived that,whil e

two men are regularly employed at the cranks,a third one

attends to the emptying of the buckets,besides assisting at the

cranks part of the time. The wire ropes used for winches ofthis kind are made from four strands

,each consisting of four

wires twisted together. The thickness of wire is from 1 tomm. to 0 06 in .] The drum and crank shaft aresupported by two pairs of posts K

,K which are let into

the timbers L,L placed across the Open ing o f the shaft , th e

drum being carried by the beams M,M

,and the crank shaft by

the cross - pieces N,N. The floor serves to give a firm

footing to the workman.


2 3 . Hand and Horse - Gins.— Th e general arrangement

of vertical drums operated either b y jiand or horse power isexplained in vol. ii . , We isb . Mech

,and it is here only intended

to treat of their application for mining purposes . The essentialfeature of the arrangement is the rope drum

,which may be

either cylindrical or conical . It is usually made in two parts,

one o f which can be di sconnected from the shaft in order toallow of a change being made in the hoisting depth wheneverrequired. The di sengagement takes place when th e bucket

,

operated by this part o f the drum,has reached the top

,motion

on the shaft being prevented by means o f a brake arrangement.In the meantime

,the lower empty bucket is transferred from

the previous point o f loading to its n ew location . When thishas been accomplished

,the loose part of the drum is again

rigidly connected with the shaft,and the hoisting may go on

as before . The rad ius of the drum is generally equal to on e

fourth o f the length of the sweep,and the length of the drum

is from 3 0 to 60 centimetres [ 1 to 2 feet]. By the use of

flanges at each end o f the drum the rope -may be wound on toa depth of 0 3 to 06 metres [ 1 to 2 feet]. On e of the flangesalso serves as a brake wheel

,the brake being arranged essentially

as described in vol. iii. 1,W e isb . Mech .

The horizontal direction in which the rope leaves the drumis changed into a direction parallel with the shaft

,by the use

of guide - pul leys or idlers,placed about 6 m. feet] above

the mouth of the shaft . These pulleys are about 2 or 3 m.

to feet] in diameter, and provided with a groove forthe rope . It is advisable to make the distance from the guidepulleys to th e drum equal to at least twenty times the heighto f the coils of rope

,in order to cause the rope to wind uniformly

on to the drum. The portion of the rope between theguide - pulley and the drum should also

,for this purpose , be

supported by cou nter - w eights. The plane in which each guidepulley is to be placed

,is determined by the d irection o f the

rope in the shaft,and that of the part leading from the d rum

to the pulley. When the shaft is vertical,both guid e - pulleys

will be placed vertically when it is inclined and “the horizon taldistance between the two ropes in the shaft is less than thediameter of the drum (which is usually the case), the guidepulleys as well as their journals will be inclined to the horizon.



ft.] in length, and secured to the former, the ends being

grasped and pushed forward by the workmen. The pivot

HOISTING MACHINERY FOR MINES 1 77

the spindle rests in a step which is let into the block C ,and

the upper end is held by a bearing secured to one of the overhead beams ih the hoisting shed . The two drums E and R

I

are fast on the vertical shaft. The ropes EFG and ElFlGr1pass

over the rope - pulleys F and F 1 placed side by side, one abovethe other

,and are thus given the proper in clination correspond

ing to the slope of the shaft. On e of the buckets H has justarrived to the surface

,and has been grasped by the dumping

hooks ; the other has at the same moment reached the place ofloading

,and for that reason is not visible in the figure . The

guide - beams K,K

,etc.

,may be seen as well as the u pper ends

of the stringers at L,on which the bucket travels by mean s o f

the wheels a,b,

Two of the four dumping - hooks whichare attached to the guide - beams are shown at c and d . MN isthe so - called co l lar

,or the horizontal timbering which surrounds

the ladder shaft at M,and the two divisions of the working

shaft at N. The lower flange o f the drum also serves as abrake wheel when a brake is required . The brake is operatedby pulling down the lever OP

,which is movable about 0 ; by

means of a vertical rod (scarcely noticeable in the figure), thislever acts on a bell - crank QR,

movable around R,and connected

through the bar S with the well - known block brake TUV.

The labourer may be assumed to move at a velocity of onemetre ft.) per second. Hand power is nowadays seldomused in this kind of hoisting, as the efficiency of a workmanoperatin g a vertical drum is less than when he is turning acrank.

1

In Fig. 90 is show n a Saxon h orse -

gin . As before,A is the

upright shaft,B the sweep

,and C the supporting block for the

former,provided with a step for the steel pivot. Of the two

drums D and D I the lower one is fast to the shaft , whil e th eupper one is movable . For regular working the upper drumrests on the lower one

,the two being connected by means of

pins protruding from the arms of the lower drum and lockedinto corresponding recesses in the upper one . When it isdesired to move the position o f the empty bucket in the shaft

,

the upper drum may be lifted and thus disconnected from th e

lower one by means of the winch a,which operates the horizon

tal shaft d by the action of the chain b and an arm 0,and

1 See Serl o,Le itfad en d er Bergbau ku nd e , vo l . 11 .

178 MECHANICS OF HO ISTING MACHINERY CHAP.

ultimately lifts the upper drum by the carrying chains 6. It

is now possible to rotate the upright shaft together with thelower d rum

,and thus move the bucket to a higher or lower point



The apparatus is generally driven by one or two horses(seldom four), for which may be assumed a velocity o f 09 m.

[ 3 and a pulling force of 45 kg. [ 1 00 lbs .] for eachhorse. The length o f sweep is usually taken to be from 6 to1 0 m. to and the radius o f the drum,whichis determined by the load to be hoisted

,is generally from 1 8

to 2 m . [59 to ft.]when one horse is used, and from 3 5

to 4 m . to ft.]when two horses are employed:The average velocity o f the load may be assumed to be about03 m . [ 1 and rarely reaches m . ft.] per second.

’

g 2 4 . Ho isting Mach ine s operate d b y Wate r Pow er.

Water - wheels are frequently employed for driving hoistingmachinery in mines . In most cases no gears are made use o f,the drums

,one movable and one fixed

,being secured directly

to the shaft o f the water - wheel. It is then"° evidently impo ssible to carry the ropes to the drums horizontally from theguide - pulleys above the shaft of the mine. A special shaftmust be constructed when the water - wheel is located at somedepth below the surface

,and the ropes conducted through it to

the drums after passing over two pairs of lguide - pulleys at thetop. It is thus necessary to increase the length of the ropesby an amount equal to the depth of the special shaft

,as com

pared with the case where the drum is located above ground.

Although the journal friction is increased by this mode of

driving,the loss o f power ensuing is not so great as would be

the case were the drum located ab ove ground and a rod conn e ction employed for driving it from the water - wheel below.

The arrangement of a rod connection is based on the varioustypes of parallel cranks de 'scribed invo l . iii. 1 , 1 3 7,

°W e isb . Me

'

eh .

_

Eachend of th e (water - wheel shaft

,as well

as the drum shaft,is provided with

a double crank with pin s diametrallyopposite

,as in Fig. 92

,the cranks on

one side being se t at 90° to thecranks on the other side. Four

connecting rods of equal length connect the correspondingcrank pins. Evidently dead centres are avoided by thisarrangement ; and besides , the advantage is gained that therods will be submitted to a pulling strain only, which is a

F ig. 92 .

HO ISTING MACHINERY FOR M INES 1 81

matter o f great moment,inasmuch as it would be impossible

to arrange suitable guides for them owing to their swingmotion.

An essential feature in this kind of hoisting apparatus isthe reversing w h e e l . In order to hoist the two buckets alternate l y the drum must revolve alternately in opposite directions .~As a simple water - wheel turns in one direction only

,it would

be necessary to employ a reversing motion were such a wheelused to drive the hoist. With a view to greater safety

,h o w

ever,a water - wheel with two sets of buckets and two gates

placed in opposite di rections is made use of. Accordi ng as thewater is let into one or the other of the tw o sections of thewheel

,the latter

,together with the drum

,will be made to

rotate in one direction or the other.The gates are operated by a double lever

,which is movable

about a point between the two gate rods,and passes through

longitudinal slots in the latter. The double lever is operated bya single lever placed above ground

,from which a rod leads down

to the former. When the machine is to be stopped after th eloaded bucket has reached the surface

,the operation consists

in closing the gate,and at the same time applying the brake

,

which acts on the partition between the buckets in the rim of

the water - wheel . The arrangement of this brake is essentiallythe same as that employed with drums driven by horses. Thenecessary brake lever is located beside the gate lever

,and near

the levers for pulling up and down the dumping - hooks.As a rule the buckets are larger than when horse power is

employed,and move at a greater velocity. While in the latter

case they are made to hold 8 or 1 0 baskets (hibb l es), and moveat speed of 03 to m . to they are made o fa capacity of from 1 2 to baskets when water power is used

,

and allowed to move at a velocity of from to 1 m.

to ft.]The method of filling the buckets quickly and with the

least possible travel is shown by Fig. 9 3 . A is the bucket tobe filled

,which travels along the guide - beams BC on the rollers

aa,and during the filling rests on the timbers DE placed on

the traverse beams. FH is a car or truck (or buggy) containing the ore or coal

,and travell ing on rails to the point of

loading. The load is dumped into the bucket by tipping the

MECHANICS OF HOISTING MACHINERY CHAP. v

box - shaped top around a shaft in the front part of the truckw hen the car holds the same quan tit

yas the bucketthe least

possible time is lost.Still less time is required for filling when the method shown

in Fig. 94 is made u se of. Here the car A in which the orearrives on the railway is placed on a cage BCD

,which hangs

on the rope in place of the bucket,and travels between the

gu ide - beams EE,FF by the side rollers aa . When the

machine is at rest the cage is supported by the struts G andH

,which are movable around a horizontal axis

,and must be

Fig. 93 . Fig. 94.

thrown out of the way when hoisting at greater depth is to b edone.The general arrangement of a hoisting machine operated by

a water - wheel d irectly is shown by two views in Figs. 95 and96. A is the reversing wheel

,B

,B1are the two drums

which are fast on their own shafts,and connected to the

water - wheel shaft by means of releasing couplings a,a,

which consist o f two discs and a pin passin g throughdiametrally.

The rope which passes around the drum B is carried aroundthe pul leys C in the rope shaft

,and then over the idlers D and


1 84 MECHANICS OF HOISTING MACHINERY CRAP. V

E located under the roof of the hoisting shed,wherefrom it

hangs down in the working shaft in ~ the direction ‘

E,F. The

rope leading from the d rum B1passes around the guide - pu l l ey

C1 ,and over the idler D

lEl ,finally having the direction E

lF1

in the working shaft. Fig. 96 shows at G the dumped bucketand at H the safety catches

,which allow the bucket to travel

clear up to the idlers,in case the machine should be stopped

too late,but prevent it from falling back into the shaft. At

K the levers are show n which serve for Operating the gates,

brakes,and dumping - hooks . In the latter figure the double

brake is represented at L,LI ,which acts on the middle rim of

the wheel,and is connected with the brake lever above ground

by means of the pull rods M,M

1 ,the double bell - crank N

,and

the rod 0 . Finally,at P

,Fig . 95 shows the pen - stock for the

pump wheel,and at Q the flume in which the water is con

ducted from this pen - stock to the reversing wheel A ; bothfigures also illustrate at g, 91 the gates for both sections of thewheel

,at R the bell - crank

,and at S th e rod for operating the

gates .A side view of a hoist driven by a water - wheel through rod

conn ections is shown in Fig. 97. Here A is the reversingwheel

,and at BC and DE are seen‘ the tw o rods on one side

of the wheel,which connect the double return crank BD of

the latter with that of the hoisting drum CE . At G is shownthe guide - pulley over which the rope is carried from the drumto the working sh aft

,and at H the bucket suspended from the

rope . The brake KLK,and the arrangement MNM for operat

ing the gates,are identically the same as in the direct acting

hoist already described.

Hoisting machines Operated by tu rbin es always require theuse of one or more pairs of gears in order to reduce the largenumber o f revolutions of the turbine shaft to the small numbero f four to eight turns per minute required o f the hoisting drum ,

which is usually 2 g to 3 m . to ft.] in diameter,and moving at a surface velocity o f to 1 m . toft.] Fig . 98 gives an idea of how a machine of this class maybe arranged. Here a turbine hoist is illustrated

,as constructed

by Brau nsd orf at Freiberg. A is the turbine,on the shaft of

which is placed the cast - iron brake wheel B and the smallbevel - pinion C with 2 0 teeth

,which engages the large bevel



ne ighbouring mining districts,th e author has found that unde r th e

most favourable circumstance s,that is when no gears or conne ctions

are used,and th e hoisting is done in ve rtical shafts of an ave rage

depth of 3 00m. [984 this kind o f hoist give s a mean e fficiencyo f 77 and that unde r unfavourable conditions, that is, whenlong rod conne ctions are employe d

,and th e hoisting depth is very

great, an e fficiency of 77 only can b e e xpected.

2 5 . Hoisting Machine s operate d b y Water - Pre ssure

Engine s are rarely employed at the present day. In order toObtain the smoothest possible running

,machines of this type

are made with two double a- cting cylinders , and besides pi ovid e d with a large fly - wheel . An excellent example of thiskind of hoisting engine is that constructed by Ad riany atSch emn itz. The arrangement and working are clearly shownby Fig. 1 00. A is a four—way cock

,to yvh ich the inlet and

discharge pipes are connected at B and C respectively,and

at D and O the pipes leading to the driving cylinders . Thelatter pipes DE and NO branch o ff at E and N

,and lead

directly into the valve cylinders LMHland L1M1

H1at M and

M1 ,and then at F and F

1into other ,pipe connections which

lead to the valve cylinders at G and Q and at G1 and Q1 .On e o f the two valve cylinders HLM

,and one of the two driv

ing cylinders LKH,are shown Ou t open lengthwise . Short

pipes H,L

,H

1 ,and L

Iconnect the driving cylinders with

the valve cylinders . Each valve rod is provided with twopiston valves R and S

,and is operated by an eccentric T. .

Each driving piston K transmits its force through the pistonrods KU and the connecting rod UV to the crank V attachedto the drum shaft . The cross - heads are fitted with frictionrollers U

,UIand W

,W which travel in horse - shoe shaped

guides . The construction of the drums X and X1 ,as well as

the mode of connecting the cast - iron rim YY of the fly - wheelto the shaft by means o f wooden arms Z

,are plainly indicated

on the figure .

The operation o f th is engine is as follows . The stream of

water which is admitted to the regulating valve at B,and then

flows into the pipes DE,is divided at E

,and from this point

runs partly to F and partly to F1 .The portion of the water

which reaches F is conducted through the pipes FG into thevalve cylinder at G

,and hence arrives to th e driving cylinder

HO ISTING MACHINERY FOR MINES 1 89

through the short pipe H,and is there utilised to propel the

driving piston K. W hen this piston has reached the end o f


its stroke,the water flows back into the valve cylinder through

the short pipe L,and from here retu rns to the regul ating valve

or four - way cock A by the pipe MN0,and is here finally dis

charged through the pipe CP. At the latter part of the strokethe eccentric T

,through the action of the eccentric rod TW

,

and the valve rod WRS,pushes the piston valves R and S far

enough over to the Opposite side of the short pipes L and H tocut Off the admission of water from G

,and allow the latter to

enter at the other end from Q . Consequently the drivingwater now flows by the path FQLK ,

and forces the piston Ktowards the outer end

,while the di scharge water reaches the

outlet by the path KHMNOP. Shortly before the pistonarrives at the end o f this stroke

,the valves are pulled back by

the eccentric T,which reopens the communication between

Cr and H,as well as between L and M

, ,thu s allowing the‘

piston to start on a new stroke .The second engine LIMI

H1is driven in identically the same

manner as LMH,the two being similarly constructed

,and

having the inlet and outlet pipes BDE and NOP in common.

In order to make the resultant tangential effort as nearlyuniform as possible

,the cranks and eccentrics of the two

engines are set quartering, so that one engine is half a strokein advance of the other. If the four - w ay cock A is turnedthrough an angle of 45° by means of the lever Aa

,both admis

sion and discharge o f water are stopped,and if it is turned at a

right angle to the original position,the inlet is made into a

discharge and vice versa . When the hoisting machine is to bebrought to rest

,after the loaded bucket has reached the sur

face,it is then only necessary to turn the valve lever Aa at

an angle o f and when the load has been dumped and theempty bucket has been refilled

,the motion will be reversed if

the lever be turned through anotherIt is a matter of importance in water - pressure engines ,

which produce a rotating motion,as in the case at hand

,that

the length and height given to th e piston valves R and Sshould not exceed the diameter o f the pipes L and H, so as toprevent the water from being entirely shut Off from the drivingcylinder. This would cause very injurious shocks

,especially

at the points where the piston valves pass the inlets to thesepipes

,owing to the great resistance of water to

,

expansion and



possible ; by thi s arrangement, th e bend of the hoisting ropearound the guide - pulleys is reduced to a m inimum.

It is evidently necessary to build ‘

th e vertical engines in amore substantial manner

,and provide a firmer foundation than

is needed with horizontal engines,whereas the latter require

more floor space,which cannot always be spared . High

pressure steam is generally u sed together with expansion,while

condensers are nowadays rarely employed,although they were

formerly quite common in this class of engine. As absolutesafety is required

,however

,in the operation

,simplicity of con

struction is o f greater importance,and

,besides

,in many places

the necessary condensing water is wanting. To facilitate thereversing of the engine

,the latter is generally arranged with

two cylinders acting on cranks set at right angles . By th ismethod the objection s to a single - cylinder; engine , which canbe reversed only when the crank is at a sufficient distancefrom the dead centres

,are obviated. Single - cylinder engin es

also call for a heavier fly - wheel to ensure uniform motion,and

are therefore more difficult to reverse than the double - cylinderengines

,in which the inertia of the h oisting drum alone is

Often sufficient for this purpose.In older constructions the crank shaft of the engine was

arranged to drive the hoisting drum,with reduced velocity

,

through the medium of a pair of gears,but nowadays the

cranks are generally placed directly on the ends of the drumshaft ; in this manner greater hoisting Velocity is obtained ,provided that the pistons are made sufficiently powerful . In

good con structions a velocity of 6 to 8 m . toft.]

1 per second may thus be allowed,and below 2 an instance

is cited,where

,in an English mine

,the hoisting from a depth

o f 73 7 m. [2 4 1 8 ft.] is done in 55 seconds , which involves avelocity of 1 3 4 m . ft.]

Such great speed evidently necessitates that the wholehoisting plant should be constructed in the most substantialand satisfactory manner

,and that special safety appliances

should be provided to meet possible accidents , such as thebreaking of a rope

,etc. The drum shaft

,more particularly ,

must be fitted with a rel iable and powerful brake. A steam

1 Se e Serl o,Leitfad en d er B ergbau k

‘

u nd e , vo l . 1 1 .

2 Berg u nd Huttenmann isch e Zeitu ng, b y Ke rl and W imme r,1 876, p. 1 2 6.


brake is commonly made use of for this purpose,the pressure

of the steam on a piston working in a separate cylinder beingutilised for applying the brake blocks or strap (see vol. iii. 1 ,fig. 72 1 ,

W e isb . Mech .) The brake wheel is usuall y securedto the drum shaft between the two drums ; when a fly - wheelis used the rim of the latter also serves

.

as brake wheel.When only a small amount of power is needed, p ortabl e

Fig. 101 .

h oisting engin es are occasionally brought into servi ce . It isoften required to locate the hoisting engine in a shaft belowground, and it is then necessary to conduct the steam to itfrom the boilers which are placed above ground. As thisis accompanied with considerable loss from condensation

,and

besides it is difficult in such cases to get rid of the exhauststeam,

comp ressed- a ir engin es

1 have been introduced,Operating

in a manner similar to that of steam - engines. The air

1 Se e Hassl ach er, Zeitschr. f . Berg Hu tten u nd Sa l inenw esen , 1 869.

0


compressor is then placed above ground and driven by asteam - engine. The exhausting air may be used for ventilatingpurposes. By this indirect method o f

‘ driving a very smallfraction only of the driving force is utilised

,however

,and for

this reason the arrangement is justified only in special cases.A single - cylinder geared hoisting engine is illustrated in

Fig. 1 0 1 . The cylinder A is horizontal,and the piston rod

transmits motion through the connecting rod L to the crank

Fig. 1 02 .

C on the fly - wheel shaft B,which carries the smal ler gear

D,and by this drives the larger gear E on the drum shaft.

The ropes lead from the two drums F and G to the pulleysS and S

Ilocated above the shaft

,and from them vertically

downwards . The reversing is done by means of the twoe ccentrics e and e

1operating the link 0

,which may be raised

or lowered at will by the hand lever h . The under side o f

the fly- wheel rim is fitted with a brake strap operated by

placing the foot on the end o f the lever l .


1 96 MECHANICS OF HOISTING MACHINERY CRAP

connection with it by the aid of the clutch coupling G. Asbefore

,this arrangement admits of a change in the hoisting

d epth. The mode in which the piston o f the brake cylinderD acts on the brake blocks H by means of the lever combination h is plainly indi cated in the cut.Fig. 1 04 shows a small hoisting engine (w inch) 1 with two

oscillating cylin ders A and AI,as con structed at Sa lms’ works.

Fig. 1 03 .

Here the steam di stribution is effected by the oscillation o f

the cyl inders,the steam being admitted and discharged through

the central portion of the journal. The reverse motion isbrought about by turning the valve V

,which is so contrived

as to admit of the admission ports being turned into exhaustports

,and vice versa.

Finally,in Fig. 1 05 a tw o - cy l ind er geared steam w inch 2 is

represented. The gear Z is here rigidly connected with thetwo drums F and F

1 ,and the reversing is accomplished by a

1 Se e Excu rsionsbericht d . Maseh inen bau schu l e zu Wien ,u nd e r d ire ction o f

Rie d l e r, 1 876 , Sk etch 1 5.

2 Se e n ote ab o ve .


peculiar valve s,which likewise changes the fun ction of the

ports . (For further particulars w e refer to the paper mentionedin the note below.)

2 7. Balancing th e Rom We ight— When hoisting is

Fig. 104.

Fig 1 05.

being done from great depths,the weigh t o f the rope alone

forms quite an essential factor in the total resistance to beovercome by the motive power. It is evident that theresistance is continually growing smaller as the rope whichcarries the load is gradually wound on to the drum. At the


same time the rope from which the empty bucket is suspendedis uncoiled by the same amount, and thus furnishes a steadi lyincreasing extra driving force. Denoting by Q1 the resistanceOffered by the loaded bucket during the hoisting, and by Q2the addition to th e driving force furnished by the emptybucket

,then

,if S is the weight of a length of rope equal to

the hoisting depth 3, we obtain for the resistance to be over

come at the beginning of the hoisting operation the valueQI + S

— Q2 , and at th e end of the operation Q lwhile at the point during the motion of both buckets wherethe two ropes exactly balance each other

,the resistance is

expressed by Q 1 Q2 . The limits of the variable resistanceare thus found to be Q1 Q2 S in the lowest

,and Q1 Q2

— S

in the highest position,the two values differing by double the

weight of the hoisting rope. Consequently,the greater the

length 3 and the weight 7 per unit of length , the greater thevariation in the resistance

,the range being especially very

considerable when hemp ropes are used, which for the samestrength must be made twice as heavy as ‘wire ropes. In casethe weight S of the rope should exceed that of the load properQ l

— Q2 , which might happen when the shaft is very deep , itis apparent that at the latter portion o f the hoisting theresistance would change into a negative one which must becounteracted by the brake. This condition o f things wouldcause great waste of power

,and also make the driving arrange

ment very unsatisfactory,inasmuch as the motor must be

made powerful enough to overcome the maximum resistanceat the beginning o f the hoisting

,and then merely be required

to develop a gradually decreasing amount of power,which

would finally become negative.Several methods have been employed with a view to over

coming this d ifficu lty by balancing the weight of the ropes.The remedy nearest at hand is to apply counter - weights in

such a manner that they will assist the drum shaft by descending during the first part of the hoisting operation

,and oppose

its motion during the latter part by ascending again to theiroriginal position . To this end the two cages are connec tedfrom underneath by a second rope which passes around a guidepulley at the bottom o f the shaft

,the effect being practically

the same as if an endless rope were made use of,the two



that the tw o drums BD and BID1must be made Of the same

dimensions,as the same conditions pertain to the winding of

both ropes also it is clear that the part which holds the emptybucket leaves the drum at the largest radius

,in the highest

position,at the same moment as the loaded rope is wound on

at the smallest radius,when the loaded bucket is on the point

of starting from the bottom of the shaft. Further,the number

of coils n must be the same for both drums,and it is easily

seen that after half the total number of revolutions the tworopes touch the drums at the same distances from the centre

FG z F G = r

must be at the same height in the s haft, as the ascendingbucket has risen through a distance l

1equal to the length of

the coil s on the smaller half of the drum BD,while the empty

bucket has descended a distance Z2 ,which is equal to the length

of the coils on the larger half of the drum DG,and the two

lengths Z1and Z

2together equal the total hoisting depth 1.

Hence it follows that the point where the two buckets meetwill fall be l ow th e midd l e of the shaft

,because I

Iis smaller than

Z2

. Only in the case of cylindrical drums will the point of

meeting fall at the middle of the shaft.To determine the proportions of the conical drums

,let us

as above denote by Q 1 the resistance due to the ascendingbucket

,and by Q2 the auxiliary driving force derived from the

empty bucket. Further,let r

y be the weight per unit of lengthof the rope in case of vertica l shafts

,or its component in the

direction of the rope for the event that the shaft makes anangle a to the horizon , that is for the latter cond itionry= g sin a

,when 9 signifies the weight per un it of length

of the rope.The moment of the forces acting on the drum shaft through

the ropes,for the lowest position of the bucket about to b e

hoisted,will then be

M1 (Q1 17071 Q

and for its highest position

M2 e z (Q2 l7)7

'

1 (2 )

If these tw o moments are to be o f the same magnitude,

In this position the tw o buckets

HOISTING MACHINERY FOR M INES 201

and each equal to M,

'

w e obtain by adding together the tw oequations ( 1 ) and (2 )

2 M 2 (Q1 Q2)(71 7él

rr1

r2

2Q1 Q2

( 3 )

At the point above referred to where the buckets meet,

and where both ropes have the same lever arm r,the moment

MO e — Q2r

= (Q1— Q2 )r, as the ropes here balance each

other. Hence we find,by combining this equation with

that the moment of resistance MOat this point is also equal

to M. By using the assumed conical drum we thus obtainequal moments of resistance for three d ifle rent positions of thebuckets

,the h igh est, l ow est, and that where they meet in the

shaft.To determine r

1and r

2 ,when r is given

,we subtract (2 )

from thus getting

(Q1 Q2 2 1777 1 (Q1 s z0,

Q1 Q2 + Qty

By combining this equation with

r1+ r

2= 2 r

w e easily obtain from

2 l2 r = r + r r <2 +

71 1

1

1Q1 + Q2

Q1 + Q2 17fi )e aw a s h se c

t-t e

Q1 + Q2

lr = 2 r — r = r<l +

7 72 1

Q1 + Q2 + ly

The mean radius r is determined by the hoisting depth land the total number of coils n on each drum. From 2 7rrn = l

w e have


The point where the buckets meet is given by its distancefrom the bottom o f the shaft (measured in the direction of thelatter)

17

2 (Q1 Q2 17)“

fi n

and its distance from th e surface (grass) above

Ir +m

2717 0—

57 m

2

The length of each drum will be n b,when b denotes the

distance from centre to centre of two adjoining rope grooves,

which distance may be taken to b approximately,if 8

is the thickness o f the rope . It is evident that the equality‘

o f

moments just obtained for three different positions of thebuckets wil l only exist under the supposition that the "hoistingdepth is equal to l .The formulae above deduced are also applicable to the case

when flat ropes are u sed,wound spirally in coils on the top of

each other,around spool - shaped pulleys (see Fig . The

mean radius must then not be chosen arbitrarily, however,inasmuch as the difference in radu of two successive coils mustbe equal to the thickness 8 of the rope. Thus

,besides the

equations (4) and ( 2 ) w e Obtain,for n coils

r2

r1

n8

After introducing for r2and r

1the values from (7)and

w e get

from which equation follows

In practic e it is gene rally sufficient to balance th e rope s in th ethre e positions mentioned

,and for this reason th e drums are made '

in th e shape o f conic frusta . In all othe r positions during th ehoisting th e moments o f th e re sistance are variable . If it is de sired



place through th e angle w,w e apparently have , for an infinite ly

small angle Sw

6u =r6w ; o r x

6v=y6w ; o r y

and hence6u +av: (a:+y)6w =2 r . aw .

By integration w e the n obtain

u +v=2 rw,or v=2 rw — u (1 1 )

Th e constant o f integration is in this case zero, as for w 0 al so

8a.for a; and for g in th e

8111 Sw

equation w e get for th e moment of re sistance M (Q1— Q2)r

th e expre ssion

u v 0. By substituting th e value

Bu av(Q1 - u )7ga

— Q2§TZ— w % 1

and thus by integration

(Q1 Q2)rw =(Q1 by)u t } 7gAfte r substituting for v its value (2 rw u), we obtain

(Q1 -

r%°

Qazrw u )— 7

which e quation after some transformation give s

u 2 u (91:Q2 l 2 rw)

(Q12Q2V

w 2 72 10 2

If for the sake of brevity w e place

7‘

Y

and then solve th e e quation, w e find

2

_ Bw e ewz,

and hence finally by diffe rentiationl — 2 rw


Th e tw o signs always give th e two value s of a and g, wh ichbe long toge the r, and both diffe r from th e me an radius r by th efraction

l — 2 rw

VA2 4(l rw )rw

lFor w z

a,w e have x: g = r

,and for w 0, th e extreme radii r

1

and r2are found to b e

1ixki

as in th e case o f th e conical drum .

EXAMPLE — Let th e mean radius of a spiral drum b e r 2 m .

th e we ight of th e empty bucke t 2 00 kg . [44 1 andits load 500 kg. [ 1 1 02 l b s.] l et furthe r th e we ight o f th e rope pe rme tre b e y = 0

°5 kg. lb. per foot], and th e hoisting depth400 m . [1 3 1 2 then

,negle cting frictional re sistance s, w e have

Q1 700 kg. Q, 2 00 kg. ; ly‘= 2 00 kg.

,and hence w e obtain for

th e minimum radius

and for th e maximum radius2

0

r2 =2 ( 1 +fi) 2 3 63 m. [7 75 ft. ]

400Th e numbe r o f coils will b e found to b e

or x 2

3 1 8 , and thus

th e axial length o f th e drum,if th e distanc e from c entre to centre of

coils is taken about 40 mm. will b e 00 40 x 3 1 8 1 2 72

m. ft.] If th e drum is to b e shaped like a conoid,with a vi e w

to ge tting a constant moment of re sistance for all positions, it wouldb e ne ce ssary to calculate th e radii a:and g corre sponding to a numb er of angle s o f revolution w

,taken at inte rvals of every other coil

o f 2 7r, for instance . Afte r e ight revolutions, that is for w : 1 611

th e Corre sponding radii would thus b e

400— 2 x 2 x

x

henc e a: m . ft.]and g: m. ft.]F or a cone - shaped drum th e radii corre sponding to th e same

numbe r of eight revolutions would b e8 8

— 1 63 6+m 0 72 7— 1 82 0 m. [5 97

02 r1)=2°

3 6351350

-

72 7z 2-1 80 m. [71 5 ft.]


"Th e radu o f th e two style s of drum

,at th e assume d position

,

thus diffe r by th e amounts

cc m .

n1 . ft.]

By calculating in this manner a numbe r o f radu,and laying

th em o ff as ordinate s in Fig. 1 07, w e obtain as profile th e wavyline BJGKD,

which change s its curvature in th e central point G.

Evidently this profile is corre ct only unde r th e supposition that th eaxial distance be twe en th e rope groove s is eve rywhe re th e same .

We re this assumption to b e ignore d, it would b e possible to so

locate th e groove s on an ordinary cone , Fig. 1 06, as to accomplisha perfe ct balancing of the rope s. Such an arrangement, however,would cause an irregular side motion o f ,th e rope s, and make th eguiding o f th e latte r more difficult.If

,in plac e of a round rope

,a flat band of a thickne ss

mm. in .] is to b e use d, th e mean rad iu s°r o f th e coils will be

found to b e

and th e radius o f th e flange d pulleys

while that o f th e extreme coil will b e

gra -91 5 m . ft.]

Th e numbe r o f coils will in this case b e400

2 x x

and as a natu ral consequence w e havex 1

°

3 2 6 m.

o o ‘ o

5

The construction o f a conical spiral drum,designed by v.

Gerstn er, is sh ow n'

in Fig. 1 08 . Here A represents the lowerand B the upper drum o f a hoisting machine operated byhorse power

,the upright shaft being indicated b y CD . The tw o

‘

nearly horizontal ropes SIand S

2 ,leading to the rope - pulleys

above the Shaft, are guided automatically by the sheaves RI andR2mounted in the frame J

,which is suspended from a lever L.

‘

The frame~ is balanced by the counter - weight K

,and is given



in th e Case of cylindrical drums, is located in the middle ofthe shaft

, w e then have for the tensions in the ropes hangingdow n from the idler - pulleys

a + <i> cos aa)+ — <sin —2co s a)

for the driving rope,and

co s a) a6

for the rope descending with the empty bucket.If now 3 1 and s

’

l denote the resistances due to stiffness ofthe rope in passing over the idler - pulleys overhead,w hose radiimay be taken at r

3 ,and whose journals have a radi us $

3and

if R3and R'

3represent the pressures of these j ournals against

their bearings,resulting from the weight G o f the pulleys

,

together with the respective tensions i n the3

ropes ; then thetensions in the ropes between the idlers and the hoisting drumare found to be

Z = Z1 3 1 ¢R.

r

l

for the driving rope, and

Z!

Z/

l ¢R1

3_

for the descending rope.Denoting by R the pressure against the bearings of the

drum shaft,caused by the weight of the drum and the tensions

Z and Z’,and by s and s

’the resistances due to stiffness o f th e

rope in passing around the drum,which has a radius r and

journals of radii r,it will then be necessary to apply at the

circumference of the drum a moment of force

M Pr : (Z+ s)r (Z'

s'

)r + c t,

which equation gives for the force required in the circumference

P= Z

Without hurtfu l resistances,the same force for a useful

l oad Q woul d be P0 : Q sin a , and consequently we have,


exclusive of the prime -mover,an efficiency for the hoistingmachine of

Q

Z

The wasteful resistances which appear in the shape of

friction between the teeth and at the j ournals,whengearsare

employed,must be treated in accordance with 3 ; that is ,

the above value 77 shou ld be multipli ed by the eflic ie n cy o f thegearing

,in order to find the efficiency of the machine includ

ing the gearing. For determining the frictional resistancesconnected with the operation of the motor

, w e refer to thespecial deductions pertaining to prime - movers in vol. ii.To determine the value 3 for the resistances due to stiffness

of the ropes,the formulae given in vol. i. 1 99, We isb . Mech

,

may be made use o f in accordance with these,w e obtain in

th e case o f wire ropes and a tension Z

s 0 °000694g

In determining the pressure R against the journals of .th e

rope - pulleys and the drum shaft,the weight of these parts must

not be neglected ; on the contrary, the resul tant pressure mustbe calcul ated from these weights and the corresponding tensions. For this purpose w e can proceed in accordance withPonce l et

’

s Theorem (see vol. i. 1 8 6, W e isb . and resolve

all the forces in their vertical and horizontal components.If the respective sums of these are found to be V and H,

w e

shall have for the friction of the journals,approximately

R J vz R 2 v 1 0

°

96V o -4R .

EXAMPLE — Th e eflicie ncy of a hoisting apparatus ope rating ina shaft at 70

° inclination,and 500 m. [ 1 640 ft.] ve rtical d epth,

is to b e de te rmined, when th e load to b e hoiste d we ighs 800 kg.

[ 1 764 and th e empty cage G 3 00 kg. l b s.]500

Sin5 3 2 m . [ 1 745

and its we ight, fromth e we ight of 1 kg. per me tre of wire rope

Th e length of each rope is given by


in .] in thickne ss lb. to b e

S = 5 3 2 kg. [1 1 73 l b s.] Taking th e ratio”4 52 —

1 2 mm ’

02r1

r2

60 mm.

in.

in.

for th e rope,w e shall then obtain th e tensions in th e ropeshanging

d own from th e idle r- pulleys from

both for th e bucke t rollers and supporting rolle rs

Z1-940 0 - 1 x 02 x 03 42 ) 0 -

1 x 0-

2 x 0 3 42 )1 041

-

5+ 2 51-

8 1 2 93-

3 kg. l b s.]

2 3 : 3 00(o-

94o 0 -02 x o3 42 ) 2 66(o-94o 0

-

02 x 03 42 ) 2 800 2 48-

2

52 8 2 kg. [ 1 1 64-

7 l b s.]

Th e loss d u e to stiffne ss at th e idle rs o f ’

radn r3

1 m. ft.]will b e

3 1 5 0-57 0-000694 x 1 2 93 -

5 kg.

x 52 8 2 : kg. l b s.]

If each idle r—pu lley we ighs 600 kg. [ 1 3 2 3 and th e re ar endsof th e rope s form an angle o f

,8 1 5

°

w ith th e horizon,w e obtain

for th e idl er‘

of th e driving rope

V =600+ 1 2 93 (sin 1 5°

+ sin kg. [4443

H= 1 2 93 (cos 1 5°— cos kg. [1 779

and hence the pre ssure on th e Journals

R3 =0°

96 x 2 1 50 0-

4 x 807: 2 3 87 kg. [52 64 lb s.]

In like manne r w e get for th e idle r of th e de scending rope

V'600+ 52 8(sin 1 5

°

+ sin kg. [2 71 9

H’=52 8(cos 1 5°

co s kg. [72 8

and thus th e pre ssure on the journals4

R’

3=0 °

96 x 1 2 3 3 x kg. [2 902 l b s.]

Assuming a radius r3

40 mm . for th e journals o f th e idle r- pulleys,

w e then Obtain th e tensions in th e rope s at th e drum

Z=1 2 93 + x 2 3 87 1 3 04 kg. [2 876

x 1 3 1 6 53 4 kg. [ 1 177 l b s.]


2 1 2 MECHANICS OF HOISTING MACHINERY CRAP.

required to transport large gangs of men into and out of themine. Since so called man - engi nes (se e the following paragraph) are not in use everyw here, the hoisting machines arefrequently employed for the latter purpose. The lives andsafety of the miners are then m a large measure depende nt onthe prompt action of the safety appliances

,inasmuch as absolute

security against breakages can never be attained in spite of

daily inspection and the utmost care in the maintenance of theropes.These safety apparatus may be divided in safety - catch es

,

which cause a sudden stop at the cage by their locking actionat the instant a rope breaks , and safety - brakes

,which produce

a frictional resistance,sufficient n ot only to destroy the

momentum of the cage,but also to counteract the acceleration

due”to the force o f gravi ty

,and finally bring the sinking load

’

to rest. The latter kind can,therefore

,never bring about a

sudden stop,but must be in action for some length of time.

Itmustbe admitted,however

,that the brakes possess advantages

in the point of safety over the catches,irrthat the latter, when

they are instantaneously thrown into action in the manneroutlined

,are apt to generate such enormous shocks as to cause

the breaking of the locking parts.It makes considerable difference whether the break occurs

in the ascending or descend ing rope. In the former case,the

moving mass,which travels upwards at a velocity v

,is .

after the breakage carried a certain distance higher,like a body

thrown into the air ; for a hoisting velocity of 6 m . ft.]2

this height w ill be 1°

8 3 m. [6 if hurtful resistances2 9

are neglected. After covering this distance,the mass is for a

moment at rest,and when the catch is thrown into action

,it

will only have to resist the w eight of the cage,which load it

may easily be designed to withstand . On the other hand,if the

descending rope should break,it is evident that

,even for the

most favourable event,that is

,when the catch is immediately

thrown into gear,a shock will be caused by the living force

Gfi of the cage . As it is never possible,however

,to make

the action of the catches perfectly instantaneous,a certain

length of time t1 being always needed for effecting the engage

HOISTING MACHINERY FOR MINES 2 1 3

ment,the cage will have time to fall through a distance h

1

JQ—gtf , so that the shock which must be sustained by the catches

2

will be expressed by G6)

7h) It is clear from the above9

how much the danger from a breakage is increased by tardyaction o f the safety - catches

,sin ce even for a length of time t1

of only one second , we should have

h1 %g= 49 05 m. ft.]

Besides, the majority o f known apparatus of this class arevery unreliable

,from the fact that the catches are thrown . into

action by rubber or steel Springs, w hich may easily lose their

elasticity, thus causing the whole apparatus, which is usuallyinactive, to fail or operate too .

late in critical moments. It

must be noted that weights cannot be used for Operating thecatches, as they would take part in the motion of the cage, andtherefore would be unable to exert a pressure against it ; theforce o f gravity would be wholly spent in accelerating theseweights

,or, as it is sometimes expressed, falling bodies lose

their weight in their fall. The elastic action of compressedair has also been successfully used

,in place of springs, for

engaging the catches.In braking apparatus

,shocks from the above cause need not

be apprehended,at least not when the friction is generated to

such a degree only that the retardation of the moving masseswill cause no damage to the vital parts of the mechanism. In

reality all good safety - catch es are so arranged that the motionwill not be arrested instantaneously

,irons provided with sharp

edges or teeth being mostly employed and allowed to enter intothe wooden guides. By thi s method a certain amount of slipagainst the guides is not excluded at the beginning o f the fall

,

a fact which as a rule may be ascertained from the traces leftin the wooden guides . Safety - catches made of iron

,and e n

gaging an iron rack,are only applicable for slow speeds and

slight inclinations,as in the case of furnace - lifts (se e Fig.

A fe w of the more important safety appliances ,1 which havebeen devised and carried out into practice, will be describedbelow.

1 Ze itschr. d eu tsch . Ing. 1 868, page 3 53 ; v . Hau er, Die F '

o'

rd ermasch inen

Serl o,B ergbau ku nd e .


In Buttenbach’

s arrangement, Fig:1 09, the rope carries thecage by means o f the eye - bolt A

,the double elliptic Spring being

kept in tension by the weight o f the cage . In case the ropeshould break

,the action o f th e spring on the links C would

force the“latches R against the wooden guides F

,and allow

them to enter into pockets made in the timbers. This apparatu s can only be recommended for very small hoisting velocities.

Fontain e’

s construction has gained a more extensive appl i

cation . In place o f latches which enter into pockets , tw olevers are he re used which are moved on their centres by meansof springs when a rope happens to break. their sharp, claw

shaped ends being at thesame time forced intothe wooden guides.

‘Asafety - catch o f this kind

,

as built by Borgsmu l l er,is shown in Fig. 1 1 0.

The tw o chisel pointedcatch - levers A

,movable

about the fixed point Bin the framework of thecage

,are ordinarily held

at a distance away fromF ig- 102 the guide beams L by

the pull in the chains K,which connect the cage with the

rope S , the springs F being at the same time kept in a state Oftension. In case of a breakage o f the rope

,the springs cause

th e lever A to turn on B,thus allowing the claws H to - enter°

into the guide - beams L . As soon as the claws have takenhold

,the weight of the cage

,which wil l then be thrown on the

pins B,causes them to penetrate stil l farther into the woodwork.

The lever G serves as a means o f throwing the apparatus intoaction by hand

,when the machine is used for transport of

people . Many modifications of this arrangement have beenbrou ght into practice

,as

,for instance

,shaping the lever ends

like forks so as to make them enter the guide - beams at thesides in place of in the centre rubber springs have also bee ntried instead o f steel springs

,but have not proved quite reliable.

The apparatus shown in Fig. 1 1 1,of White and Grant’s

design,has been largely used in practice. The locking action



various forms. One of the most interesting designs is nu

doubtedly Hoh end ahl’

s arrangement, Fig. 1 1 2,the elastic action

of air enclosed in a cylin der C b eing here used in place ofSprings for operating the eccentric shafts . By two brackets orstandards E

,a cylinder C ,

Open at the bottom , is secured to th ecage D

,the piston F

,through the cross - pie ces G

‘

and H,and

the J,being suspended from the r mg N, to which the rope

Fig. 1 1 2 . Fig. 1 1 3 .

and chains K are attached. The lower cross - piece is besidesconnected to the eccentric shaft by the links M and the levers0 . The cylinder i s originally filled with a1r of atmosphericpressure, but before the cage itself is lifted, the piston F ispul led upward

,and by being thus forced into the cylinder

,a

certain dis‘ tance' raises the pressure of th e air to about five"

atmospheres. The eccentric shafts A are at the same timeturned sufficiently by the action of the links M to allow theguide - beams to pass freely between the eccentrics. Should therope

‘

happe n to break , the enclosed air will"operate in the same

manner as a spring, and b y_

pushing dow n the‘

piston bring th e


eccentrics into action. Thi s apparatus is considered verysatisfactory in its operation.

The resistance of the air to the cage in its fall h as also beenutilised for causing the eccentrics to lock themselves into the

guide - beams. In the apparatus constructed by Krau ss andK l ey,

l the eccentric shafts are for this purpose provided withparachutes made of sheet iron

,which act retarding on the

eccentric shaft,and thus bring about the turning

.

of the eccentric,on account of the greater acceleration of the lower part of th ecage.For throwing the catches into operati on a pecu liar method

has been employed by Lohmann . It is based on the principlethat a fall ing body

,whose weight is only employed for acc e l e rat

ing its own mass, is unab le to exert pressure againstsurrounding objects. In Fig. 1 1 3

,A and B are two movable

catches connected to the Springs F. The force exerted by thesprings is onl y equal to one - half of the weight of the catchesA which they carry

,so that under ordinary conditions th e

latter will hang sufficiently low down to clear the gui de - beams.At the instant a rope breaks

,however

,and the cage begins to

fall,the weight of the catches A will no longer Oppose the

tension in the springs , and as a result the latter will cause thecatches to enter the guide - beams . The weight of the retardedcage will assist in pre ssing them still farther into the wood.

The figu re also shows an attachment contrived by v. Sparre

for the purpose of rendering harmless the shock caused by themomentum of the cage when

”the catches take hold

,and which

frequently causes the destruction of the whole safety apparatus.To avoid or mitigate the shock

,the catches are not attached

directly to the cage G, being instead connected to a specialgi rder or framework Q ,

to the top of which a tube R,2 or 2 1

2

metres or feet] in length, is secured. A turned rodS, connected at the lower end with the cage G,

and at the topend to the rope

,passes through the stuffing box at the bottom

of the tube,and has secured to it a piston fitting tight in the

latter. The tube is partly filled with air and partly with somesoft material

,such as se a- grass or horse - hair. Wh en the safety

apparatus is thrown into action, the shock produced will bedue only to the slight momentum of the frame Q and th e tube

1 Se e Zeitschr. d eu tsch . Ing. 1 869,p. 499.

2 1 8 MECHANICS OF HOISTING MACHINERY CHAP. ‘

R,the cage being allowed to fall through a distance equal to

the length of the latter. In the meantime the air in the tub eis compressed

,and together with the elastic material acts lik e a

bunter,which absorbs the shock.

The most satisfactory apparatus,however

,for avoiding the

hurtful influences of the shock,are the safety - brakes

,of which

,

in conclusion of this subject, we will here describe one, as constructed by Hopp e ,

‘ and il lustrated in Fig. 1 1 4 . Two hardened

Fig. 1 1 4.

brake blocks B on each side are here used for producing thebraking action by being pressed against the guides A

,made o f

T- irons. The pressure is brought about by the torsion springF

,which is thrown into action when the rope breaks

,and

causes a slight movement o f the brake blocks B,the latter being

jammed against the guides A by the action of the arms Earranged in the manner of a toggle - joint. The frictionalresistance thus produced gradually brings the falling mass to astop

,and it is only necessary to regulate the retarding action

by means of an adjusting wedge,in order to prevent the“

pressure exerted on the brake blocks from exceeding a givenl imit, and thus avoid the danger of too severe strains in theframew ork of the cage .

Z e itschr. d eu tsch . Ing. 1 870, p . 619.


“2 2 0 MECHANICS OF HOISTING MACHINERY CHAP.

th e movable platform to the fixed one,and has thus

,in a single

stroke of the rod,been transported downward a distance equal

to the lift it BBI.

He now waits until the up stroke of therod has been completed

,and then steps on to a second plat

form T2 located on the rod at a distance h below the first one

,

and which by this time has arrived on a level with B1 . In

the following down stroke the traveller will be transportedanother distance it downward

,and wil l at this point be able to

step over to the next stationary platform B2

. By continuallyrepeating the above proceeding

,the workman will thus descend

from platform to platform,the distance travelled for each

double stroke of the rod being equal to the lift it. It ise vident that the same arrangement

]

can also be used for

ascending if the stepping is done from the fixed to the movable

p latform at the moment when the rod is in its low est position.

I t is readily seen that in a singl e - acting apparatus of this kind,the intervals at which both the fixed and the movable platforms are located must be exactly equal to the lift it

,and that.

n + 1 resting places are required, when“.n is the number o f

movable platforms communicating between them. As all thesen platforms may be occupied at once, it is also evident that 67.persons can travel e ith er up or d ow n at the same time . Therod may be utilised for trave l both up and down at the sametime

,on different levels

,but not to advantage in the same

sections,as the time at the traveller’s disposal at the turning

points hardly adm its of a transfer of two meeting parties .In the dou bl e - acting man - engines two rods of equal strokes

are placed side by side and arranged to move in oppositedirections

,the reversal of their motion taking place at the

same instant for both rods. If,therefore

,the machine is so

arranged that two platforms will always be alongside eachother on the same level at the turning points

,it is easily seen

that a person can by successively stepping from one rod to theother

,travel up or down according as the stepping is done to

the ascending or descending rod. The relative location of theplatforms is given by Fig. 1 1 5. Let A and B represent thetwo rods

,the former being shown in its highest and the latter

i n its lowest position . After stepping from the fixed point Cto the platform TI , the person is carried down a distance h to1 . Passing in this position from A to B

,b e

'

w il l in the next

HOISTING MACHINERY r ox MINES 2 2 1

down stroke b e transported from 1 to PI , which wil l then beopposite to the platform T2 on the rod A,

which platform’

accordingly must be located at a d istance2 h bel ow TI. As the same reasoningapplies to all remaining steps, it is apparentthat all platforms

.on each rod must b e

placed at intervals of 2 k,and that th e

travell er will be transported thi s di stance2 77. for each double stroke of the engine .

Letting 1 denote the total lift CD betweenthe fixed points C and D , the number oftimes a passing from one rod to the other

must take place is given by f n . Th is2 h

quantity also represents the number of

people w h o can ascend or descend at th esame time

,for the reason that a meeting

of two persons at the same platformswould not be practicable

,and consequently

it is only possible to occupy all platformson one rod or the other at the samemoment. Arranged in this manner therods may, of course, be utilised

_

for bothascent and descent at once at differentlevels

,but cannot be made to serve both purposes at the same

time and place.If

, however, a second set of steps if and p are introduced atintervals of 2 k

,and placed half- w ay between the platforms T

and P,then a second double - acting lift will be obtained

,whose

platforms will correspond to each other only,but not to T and

P,and wh ich can therefore be used independent of the latter

for either ascent or descent. This set of steps will then maintain the communication between the fixed points 0 and d

,

located at a distance it below C and D . The arrangement justdescribed is employed in order to enable the machine to beused for transport both up and down at the same time. Wh enutili sed in this manner by a full complement of men travellingin both directions

,it is possible to keep both rods equally

l oaded,which cannot be done when travelling takes place in

one direction only.

f

Fig. 1 15.


An interesting construction of the man - engine is presentedby that built at the mine Saar Longchamps,

1 which,as seen

by Fig. 1 1 6 , consists of a combination o f

one double - acting and two single - actingengines . Here A and B are the tworods carrying at a and b

,at intervals of

2 h,the platforms for the double - acting

engine,which serves for the ascent

,whil e

the platforms c and d placed at intervalsequal to h

,belong to the single - acting

engines which are used for descending intothe mine

,the fixed resting places being

shown at e and f. An ordinary ladderis frequently arranged between the tworods

,as is the practice“in several mines in

the Harz mountains,in order to provide

Fig- 1 16.means of leaving or returning to theman - engine at any point.

Motion is u sually given to the rods'

b y means of two bellcranks A and B

,Fig. 1 1 7, coupled together by a rod CD ,

andreceiving their reciprocating motion from a crank shaft

,which

Fig. 1 17. Fig. 1 18.

operates th e connecting rod DE. Although this arrangemen t,which is the usual method of drivmg when the prime mover isa water - wheel

,does

'

not admit of any period o f rest at theturning points

,the exchange o f platforms is nevertheless con

ne cte d with no danger, since the velocity of the rods near thedead centres of the crank is very slight.A clear idea of the reasons for this statement may be had

Serl o,Bergbauku nd e .



Oonform to each other. "TO attain this object a sO- calledhydrau l ic regul ator is commonly used. This contrivance con

Fig. 1 20.

sists essentiall y of tw o cylinders Aand B (Fig. 1 2 0) open at the topand filled with water

,the rods G and

H being connected to their pistons Kand L. The cylinders communicateat the bottom by the pipe CD

,

w hich allows the water from thecylinder B to pass over . into A whenthe plunger L descends by theaction of the steam engine

,thus

compelling the plunger K to rise,and

vi ce versa . The cylinders are also incommunication at the top throughEF

, in order to keep the plungersalways covered with water

,and thus

obtain a tight fit in a simple manner.When the rods are driven directlyby aa -steam engine

,it is evidently

possible to interrupt the recipro

cating motion at the end o f eachstroke for a suitable length of timeby the u se o f cataracts (se e volumeo n Steam - engin es).

In the earlier man - engines employed in the Harz

,the stroke o f the

rods was only 1 2 5 metres [41 f eet],while in modern constructions it ismade 3 m. [98 4 ft.] and more. Thenumber of double strokes can beassumed at 5 per minute, which for

a stroke of 3 m . ft.] gives an average velocity o f 3 0 m .

[98 4 ft.] when the stroke is longer, a mean velocity o f 4 8

m . [ 1 57 48 ft.] 1 8 occasionally reached. Wh en the apparatusis driven froma crank shaft

,the greatest velocity i s naturally

obtained 1n the middle positions,where it may be calculated to

be 5 x 3 x m . [ 1 545 3 ft.] per minute, for the casethat the stroke is 3 m . and that the machine makes5 double strokes per minute.

HOISTING MACHINERY FOR MINES 2 2 5.

From the assumed velocity of the rods and their load inascending

,the driving power required may be obtained in

conformity to known rules,if due attention be paid to the

frictional resistances between the rods and their guide - rollers .Itmay here be noted that the rod of a single - acting man - engineis only required to overcome the resisting forces in the ascent

,

while during the descent,the weight of the occupants tends to

accelerate the cranks, whi ch necessitates the application of. apowerful brake for this contingency. The weight of the rod isbalanced by means of a counter - weight

,in the case of single

acting machines,whi le in the double - acting apparatus the rods

balance each other. Perfect balance is also attained in thelatter case when both rods are equally occupied

,which is the

condition at hand when the machine is used for ascent anddescent at the same time. On all other occasions only one ofthe rods is loaded, namely, the ascending one when the travelling is done upwards

,and the descending one in downward

travelling.

'

In order to investigate the performance Of a man - engine,let

it denote the length of stroke,n the number of double strokes

or single revolutions of the crank per minute,and l the distance

between the top a nd bottom landings . Then,in the case of a

single - acting apparatus,the number of platforms w il l be

and . for a double - acting machine, on each rod

For each double stroke the traveller is , in the former case ,transported a distance it, and in the latter case a distance 2 k ,

and,consequently

,the time required for a complete lifting

operation is for the respective machines expressed by

minute s,

minute s.

2 2 6 MECHANICS OF HOISTING MACHINERY CHAR.

On e person is thus transported twice as quickly on thedouble - acting as compared with the single - acting machine. If

now we denote by N the number of persons to be forwarded,

then,since only one person can mount the lift for each revo l u

tion o f the crank , the platforms will be occupied at intervals of

l mi nutes,and thus the last person will mount the platform

7L

N 1minutes later than the first one. The total duration Of

77.

a complete hoisting or lowering operation will therefore b egiven by

N 1

for the single - acting,and

TN 1

2n

for the double - acting man - engine .FrOm these formulae it is evident that the greater the number

of persons to be forwarded , the more the greater despatch otherwise obtained from the double - acting machin e is placed in thebackground

,and for this reason, when a large number of miners

are to be transported,it may sometimes be more advantageous

to empl oy . two single - acting in place of one double - actingapparatus

,as indicated by the example shown in Fig. 1 1 6.

For this case the total duration of a complete hoisting Operationwould be only

gN — l l

n

+ah

Taking, for instance , a working gang o f N 500 men anda travelling depth of l .

- 3 00 metres [984 2 7 then,for

n : 5 revolutions per minute and a stroke o f h z 3 m.

w e obtain

TI

4

29

5

3

20

3998 2 0 cx:1 2 0 min . for a single - acting

,

499 3 00T2 5 1 0 x 3

99 8 1 0 m 1 1 0 m m. for a double - actmg, and

[machine sT

gig) 3 004 ‘8 2 0 m:70 min . for two single - acting

1 5 5 x 3


CHAPTER V I

CRANES AND SHEERS

3 1 . Crane s — A crane is a hoist with facili ties for movingthe load horizontally. Cranes are employed chiefly in warehouses

,workshops

,dockyards

,etc.

,and

,for the loads

Fig. 1 2 1 .

are p rovided w ith a Windlass , th e arrangement of which d oesnot differ from those already described . Various means

_ areemployed for giving a horizontal motion to the load. In theordinary rotary crane the framework is made in the shape ofa long projecting arm

,inclined or horizontal

,and may b e

CRAP. V I CRANES AND SHEERS 2 2 9

rotated about a vertical axis ; the long arm or j i b is providedwith a pulley at the extreme end

,over whi ch is carried from

the Windlass the rope or chain which supports the load.

For masting or dismantling ships,lifting the heavier parts

of marine engines,etc .

,large sl i cers

,Fig. 1 2 1

,are made u se of

,

having atriangular jib ABC hinged at the vertices, and carry :ing a pulley for the chain at the apex C ,

while the feet A andB rest on the foundation. After the load has been hoisted

,it

may be conveyed from Q to Q1 , either by moving the footB to B1 , or, keeping B fixed

,by shortening the side BC until

it has a length BCl . It is evident,of course

,that the strut

AC must be composed of two inclined pieces so as to allow th eload to pass between them.

Sometimes the rotary crane is moun ted on a four - wheeledcarriage travell ing on rails and is then called a p ortabl e crane ;this construction is chiefly employed for railways

,sh ipyards

,

and wharves. If,instead of being mounted on a carriage

,it is

supported by a float,it is known as a fl oating crane.

In so - called fou ndry cran es the load is suspended from asmall carriage or trolley which travels in and out on a trackplaced on the horizontal jib ; by turning the crane and moving the trolley the load can be conveyed to any point withinthe circle described by the outer end o f

,

the jib,whi le in an

ordinary swing crane,without trolley

,the horizontal motion

of the load is limi ted to the circumference described by theextremity of the jib.

Finally,w e have the various kinds of trave l l ing cran es

,in

which the Windlass is arranged in the form of a truck travellingupon a bridge ; the latter is mounted on wheels, so that thewhole may traverse a fixed railway placed at right angles tothe bridge ; with thi s arrangement, the suspended load maybe conveyed to any point within the rectangular area comprisedbetween the rails. Such cranes are especial ly adapted foruse in machine shops

,and for conveniently distributing the

materials in the erection of large and massive bridges . Wherecontinuous service is not desired

,cranes are operated by hand

,

whereas steam power is made use of in cases where a frequentor uninterrupted service is called for, as in warehouses, forinstance

,and in the erection of buil dings. The cran e

v

maythen have a steam - engine attached to it

,in which c ase it is


known as a steam cran e,or it

_may receive power from a

stationary engine which is also used for other purposes .Recently hydrau l ic cran es driven by accumu lators have been

employed to advantage ; this arrangement is well suited tocases where the power is used intermittently, and where a

means of transmitting power is needed. Such is the

Fig 1 2 3 ,Fig . 1 2 2 .

case at docks and other places,where a number of cranes at

various points are operated by the same engine. The size ofa crane and its capacity for hoisting must, of course , be adaptedto the work in hand. The heaviest designs are employed formarine purposes

,cranes having been constructed for lifting

1 00 tons and more.3 2 . Rotary Crane s

— In Figs. 1 2 2 and 1 2 3 is shown acrane made of wood and iron, and designed b y Care for the



imparted to the collar,the sliding friction of the lower plate T

I

upon its support is likewise transformed into rollin g frictionby employing a second set of roll ers

'

SI working on hori zontalpins. The object of this arrangement is to facilitate the swinging of the crane jib

,although this Operation is rarely effected

by the direct application of a lever ; a special mechanism is

Fig. 1 2 5.

generally required for this purpose,the arrangement of whi ch

will be described in the following.

In order to overcome the in conveniences attending the useo f a well for the crane - post

,and at the same time to gain easy

access to the footstep bearing,the construction shown in Fig.

1 2 5 o f the framework of the crane is frequently used. Thehollow cast - iron column S is firmly secured to the plate G,

Which is bedded in the foundation,and h eld down by long

anchor bolts A. The top Of the post is provided with a steel

v 1 CRANES AND SHEERS“ 2 3 3

pivot u,from which the movable framework is suspended by

means of a cross - piece V,while the collar R on the fixed crane

post serves as a bearing for the friction rollers s,carried

by the movable framework. The latter consists of two sideframes W which su pport th e Windlass ; these frames are conn e cte d above by the cross - piece V

,and below by cross - pieces

Fig. 1 26.

in which the friction rollers have their bearings. The j1b is awrought - iron tube T pivoted at H , while two w ro ugh t

Liron

ties connect the end L with the cross—piece V. The Windlass ,consisting of the barrel B ,

the gear shaft C,and the crank K

,

is of the ordinary arrangement. The roller J between thetension rods Z support the hoisting chain.

In order to swing the crane conveniently a spur - wheel Nis fixed to the pillar S

,and gears with a pin ion n on a shaft

which has its bearings in the movable framework, and is


driven by the crank handl e 7c through the medium of thebevel wheels a and b . a

In Fig. 1 2 6 is represented Fairbairn ’

s tubular crane . It

is mainl y distinguished from the preceding types by the formo f the jib T

,which is made . of wrought - iron plates and angle

i rons riveted together and arranged so as to give a body of

u niform strength . The jib is supported upon the crane - post

Fig. 1 27.

by means of the cross - piece V riveted to it , and is guidedat the base by friction rollers . For turning the crane thecast - iron foundation plate is fitted with a rim N havinginternal teeth .

When a crane is stationed within a buil ding,and is - not

intended for out - of- door u se the revolving crane - post may be supported at the top by a joist or beam. In this case the journalsmay be considerably reduced in size

,and the roller bearing



1 2 9, which depends upon the principle of Georges

’ platformscales. Here CDE, the jib proper, is connected with themovable crane - post AB by two pairs of iron links PQ andRS

, which prevent the crane - j ib from overturning ; the latterincluding the suspended load

,is supported upon the beam UC

at C . The upper pair o f links PQ pull on two knife edges ,while the lower pair RS press against two similar edges . The

Fig. 1 29.

mode of weighing the load,including ji b , by weights placed on

the scales at K,needs no fu rther explanation , and if the ratio

ML to MN of the lever arms be 1 0,a weight o f

116of the load

on the scales will suffice for weigh ing.

Rotary cranes for foundry use,Figs. 1 3 0 and 1 3 1

,are

provided with means o f altering the distance of load from thecrane - post. In Fig. 1 3 0 the load Q is suspended from thelower pulley- block N of a fourfold tackle; the upper block

v1 CRANES AND SHEERS 2 3 7

being arranged in the form of a small carriage DF,which

travels in and out onthe horizontal jib . Thelatter is made o f twoparallel beams betweenwhich the chain hangs .The manner of operating the latter by means

_of the Windl ass P0 isevident from the figure.

‘A rope S passing overthe fixed pul leys G

,H ,

J,and coiled round a

.barrel L,is employed

for moving the carriageo r trolley DE conv en iently from below

,

rotation being impartedto the barrel by means Fig - 1 3 9

of a crank M and apair of gears. Sinceboth ends of the ropeare attached to thecarriage

,it follows that

by turning the barrel Lto the right or left theload will travel towardor away from the cranepost.

In the crane,Fig.

. 1 3 1 , the travellin gmotion along the jibis obtained by means ofa pinion on the shaftG

,which engages a rack

EF,to which the pulley

ED is attached. Themanner of transmittingthe rotation of the crank L to this pinion by interposing th ebevel wheels K and H is evident from the figure.

Fig. 1 3 1 .


A defect of the two last mentioned cranes is the al terationin the height of the load as the trolley moves along the jib ,inasmuch as the arrangement of the hoisting chain causes theload Q to descend as it approaches the crane - post, and to riseas it recedes from it. This variation of height is considerablein the crane shown in Fig 1 3 1

,but is less in that given in

Fig. 1 3 0 on account of the great purchase of the tackle . Fig.

1 3 2 shows an arrangement for obviating this defect by attaching the chain at A

,and

allowing it to pass over thepulleys B

,D

,C and E

,thus

making the length Of thechain' constant between Fand A as the load travel salong the ; j ib .

g 3 3 . Cond ition of Equ i

l ib rium of Rotary Cranes.

For the purposes of thisinvestigation let ABC

,Fig.

1 3 3,re present the triangle

formed by the axes of thecrane - post

,strut

,and tie - rods

,

and let a, ,8 , and ,

8 1 be therespective inclinations to the

horizon of the strut AC,the tie - rods BC

,and the hoist

ing chain K . For the present the weight of the movable crane is neglected. Further

,let P denote the effort

applied to the chain to lift the load Q . This force acting inthe chain is given by the arrangement

,as when the load is

directly suspended from the chain,we may place P Q and

F ig. 1 3 2 .

when a movable pulley is employed we may put P if

the wasteful resistances of the pulleys are neglected . Toascertain the thrust T in the strut and the tension Z in thetie - rod

,w e may use the following equations expressing the

equilibrium of forces acting at C .

Q + P sin B1 + Z sin fl=T sin a,

co s a,



The action o f the force Z is to tear the tie BC,while that

of the force exerted along the axis of the strut is to crush it ;consequently, in calculating the dimensions o f the latter

,it

must be treated as a long column rounded at both ends,and

corresponding to case II.,vol. 1. 2 73 , Fig. 4 3 7

,W e isb . Mech .

Additional stresses are produced in the rods and strut by thebending action o f their ow n weight

,and these must be taken

into consideration in accordance w ith the rules laid down in

Fig. 1 3 4.

vol. i . 2 78 , W e isb . Mesh . The crane - postAB is subjected toa thrust Q ,

and also to the bending moment produced by theload Q and the weight of the structure combined. In orderto ascertain the stress to which the post is subjected, it isnecessary to consider the weight G o f the movable crane -

j1b ,

and the mode o f arranging the bearings . Let G be the weightof the rotating framework , acting at its centre of gravity E,

Fig. 1 3 4,at a distance 6 from the pillar

,let M denote the

resultant of the weight G and the load Q , so that M Q G,

and let FJ be the line of action of this resul tant. The j ib

CRANES AND SHEERS 2 41

bears against the crane - post at A,and AD normal to the

acting surface at this point,may be taken to represent the

d irection 1 of the reaction of the pillar. As this reaction R,

together with the reaction S of the pivot B,must keep the

load G + Q at FJ in equilib rium,it follows that the resistance

o ffered by the pivot B must be exerted in a di rection traversing the point of intersection D of the forces M and R— thatis

,in the direction DB . Let us therefore resolve the resultant

M Q + G = JD into components acting along DA and DB,

then DL will represent the thrust R of the strut at A,and

ND the pull S on the pivot B . Furthermore,let these two

forces be resolved into their horizontal and vertical componentsacting at A and B

,then CL KD will be the tw o horizontal

forces H forming a couple acting at A and B which tends tobreak the post. Le t h be the vertical distance between thepoints of application A and B,

and let I,b,and e be the

horizontal distances of the forces Q,M

,and G from the axis

of the crane - post,then the bending moment acting on the

p ost isHh =Mb =Ql + Ga

The vertical pressure on the post AB is expressed by

o f which NK = V1 is supported directly by the pivot B ,

andKL V

2by the conical bearing A. When the latter bearing

h as a cylindrical form ,which makes AD horizontal

,the whole

pressure V Q G falls upon the pivot B ; on the other hand ,when the inclination o f the conical bearing A is such as tobring the intersection D (of the reaction R,

and the loadQ G) on a hori zontal line passing through B ,

no part of thevertical load will fall on the pivot, nor on the crane - postb etween A and B. A further elevation of D would even giverise to an upward pull on B.

To ascertain the amount of pull W acting in the movableframework between A and B,

we must resolve the reactionR = LD along the directions o f the strut AC and connectingline AB

,which gives UD =W as the required force in the

frame,and LU as the thrust T in the strut. Al so resolving

1 Strictly speaking, th e d ire ction of th e reaction make s an angl e w ith th e

normal atA equal to th e angl e o f friction


the load Q = CQ along the directions CA and CB,will give

ZQ Z as the stress in the tension rods and chain.

To prevent the crane from overturning,the anchor bolts

AIAImust be sufficiently strong to resist the force X deduced

from the equation where f is the horizontaldistance between the anchor bolts AI and B1 . The weight ofth e masonry in which the foundation bolts are secured mustbe proportional to this value of X

,in order to give the crane

the necessary stability .

As a rule , graphical methods give the simplest solution of

crane problems,owing to the fact that the analytical formulas

differ for each individual case,and generally are very incon

ve nie nt for use.The steps fordetermining the effort P required at the crank

for lifting the load Q are exactly the same as those followedin 8 and 1 1 .

Let 771 denote the efficiency of the pulley in the j1b head

(the efficiency o f the hoisting tackle,if such is used

,being

included in this symbol), let 772denote .the efficiency of the

drum,and 773 ,

774 represent th e efficiencies of thesuccessive pairs of gears ; then the efficiency of the entiremachine is

7? 7

The resistances due to friction o f the rollers supporting thechain may

,in most cases

,be neglected as inappreciable. If

w e wish to include them in the calculation, it is only necessaryto increase the tension S in the portion of chain which passesfrom the drum to the pulley 1n the jib head by an amount

(pi—G 1 ,where G 1 is the weight o f this chain , and 5:the ratio o f

the radu of the pin and rollers,so that

r

expresses the

efficiency of the supporting rollers,and may be entered in the

formulas as such ; this term will generally differ but littlefrom unity. Let n represent the ratio between the velocity o f

the crank h andle and load Q, then the effort will again beexpressed by


b1 + c

shaft FG is expressed by P32 P

1 P2

P If now thisbl

bearing pressure P3, acting at a distance a

1 blfrom the

Fig. 1 3 5.

of the cran e - post is to be sufficient to swing the crane, w e

must6

have M P3 (a 1 b

l ) P2

1

;c

(a 1 Hence in the absence1

V I CRANES AND SHEERS 2 45

where M denotes the above moment of friction,

Taking into consideration the wasteful resistances of the teethand journals in accordance with 3

,would necessitate an

increase in the dri ving force at the crank of about 1 0 or 1 5per cent.

EXAMPLE — It is required to de te rmine th e dim ensions o f a cranefor lifting a maximum load of 6000 kg. l b s.]at a radius of

6 me tre s [1 9 7 th e inclination Of th e strut to th e horizon be ingand th e he ight o f th e crane - post h 2 m. ft.]Th e re spe ctive stre sse s Z and“T along th e tie s and strut are pro

portional to th e corre sponding side s of th e triangular frame o f th e

crane the lengths o f th e tie s are found to b e J 42 62 m e tre sand th e length of th e strut isJ 2 x 62 m. [2 78

ft.] Hence w e have

z: 6000 kg. l b s.1,

T: eooof

gsz kg. l b s.]

If. w e assume that th e whole strain Z is to come upon th e tensionrods

,and none upon th e chain

,then for a tensile stre ss of k 6 kg.

[8500 l b s.]th e se ctional are a o f each tie is2

2

1

610

sq. which corre sponds to a diame te r of 48 mm . in .]Th e strut is to b e regard e d as a long column rounde d at both

ends ; its area of se ction F is compute d according to vol. i. 2 74,

We isb . Mech,which give s

P=F

1 803 sq. mm.

He re l de signate s th e length, KI I th e ultimate re sistance to crushing,w h ich

’

for w rought iron is Kn: 2 2 kg. l b s. pe r sq. in .]

Efurthe r 1) expre sse s th e w h o

K 3 whe re E i s

1 1

the modulus of e lasticity, andW Moment o f In ertia o f Cro ss Se ctionF Se ctional Area

In the pre sent case r 9 1 0 for an annular cross- se ction

2 46, MECHANICS OF HOISTING MACHINERY CRAP.

w ith external diame ter cl and inte rnal diame ter d109 6d

,w e have

0112) 34

5g O°963)d2=00 615012 ,

(1 0 '962)d 2 0‘1 2 0d 2 .

Introducing this value in th e above formula,and assuming a factor

of safe ty of 6,w e have

6 x =0‘

061 5d 2

Follow ing th e m e thod of solution proposed for th e example in

2 74,vol. 1. We isb . Mech

,w e find

d = 3 3 6 mm . [1 3-

2 3 h e n c e d 1 =0°

96 x 3 3 64 3 2 2 mm .

so that th e thickne ss of th e mate rial of th e strut w ill b e

d — d l

27mm. in .]

In orde r to de te rmine th e d ime nsionswo f th e crane - post w e musttake into conside ration th e we ight G of th e movable jib. Let u s

,

as a rough e stimate , call this we ight 1 500 kg . [3 3 00suppose its centre of gravity to b e at a distance of m. ft.]from th e axis of th e crane - post then for th e ve rtical pre ssureupon th e latte r w e have

V :Q G 6000 1 500 7500 kg. l b s.

and for th e horizontal force H of th e couple , which tends to breakit off, w e have

6000 x x

hkg. l b s.]

Suppose D and D1

0°7D to repre sent th e exte rnal and inte rnal

diame te rs of this hollow crane - post at th e point of attachment toth e foundation plate then for a permissible stre ss h 3 kg. [42 70l b s. pe r sq. th e diame ter D is given by

0

3 2 D ( 3 2(1 0 °74)3D

3,

from which w e get D about 560 mm. [about 2 2 in .] This give sfor th e inte rnal diame te r 0 7 x 560 3 92 mm. [1 54 and thus

2.



and the ir pins. Introdu cing th e numerical value s

75

3

00x 0 1 00+ 0 1 x x x

—[1 s40

~

s ft. l b s.]

mhg.

Now l et th e spur whe e l attach ed to th e crane - post have a radiusa m. 8 and th e radius of th e pinion gearing withit b e 6 m. in .] furthe r, assume th e radii o f th e beve lwhe e ls to b e 6 m. in .]and d : m. andthe length of th e crank arm m. in .] If w e take th e

e fficiency of the turning ge ar at th e e ffort required at th e crankfor sw inging th e jib will b e

1 d M b 1 00 5

This force can be easily applied by two workmen.

3 4 . Sh e ers.—This type of hoisting apparatus is used

Fig. 1 3 6.

masting ships,for lifting boilers and engines on board steam

ships , etc . It consists of two long spars AC reaching out from

v1 CRANES AND SHEERS 2 49

th e wharf wall M,Fig. 1 3 6 ; the spars lean towards each other

and are joined at the top C by a cross - piece ; from this piecea chain or stay (or a pair of stays) CB is carried to an anchorat B.

A hoisting chain K,worked by a Windl ass W

,is carried to

the fixed pulley or hoisting tackle suspended at C . Thisarrangement allows the load to be moved in the verticaldirection only

,as the spars AC are exposed to a thrust

, and

the stay BC to a pull. More recently, however, this frameworkhas been so constructed as to admit of the load being movedhorizontall y. This is accompl ished either by making the footB of the third leg BC movable in the direction BBl , by whichmeans the apex C can reach C l , and the load Q may be broughtinto the position Q1 , or by keeping the foot B stationary, andshortening the third leg to a length BC

l. In both cases this

leg must be a rigid member, since at the moment it passes th evertical position it w ill be subjected to a thrust.Let a denote the inclination to the horizon of the plane of

the legs AC in the extreme position,and let

,8 represent the

inclin ation of the tie - rod BC,then, if the

.

pull along the chainK is neglected, the stresses produced by the load Q, whenresolved along CA and CB

,are expressed by

CE T along th e strut AC,

The same formulas hold for the position AClBl ,and the

corresponding forces TIand Z

1are obtained by merely intro

du c ing aland

,8 1 to represent the inclinations o f AC1 and BIC] .

We see that Z changes its sign when a exceeds that is Zchanges from a pull to a thrust. Hence the spar BC is to betreated as a strut

,and its dimensions must be proportioned to

sustain the thrust

sin (a 1 ,81)

for the stress produced by a thrust in such a long member ismore unfavourable than the tensile stress due to the force


acting when the sheers are in the extreme position,although Z

is greater than Z1 . The thrust T,

.o n the other hand,has its

greatest value for the extreme position, and if denotes theangle between the legs AC at C

,th e sectional area of each

sheer must be able to bear the thrust

T Q co s B2 cos y 2 co s y sin (ct — B)

In this calculation w e must make use of the formulas forcompound stress (vol. i. 2 78 and the following), as , on accounto f the great length o f the spars

,the bending strain due to their

weight must not be n eglected.

The manner of transporting the]

load horizontally is seenfrom the two following figures.Fig. 1 3 7 shows the earlier form of

’ a sheers at F ol d,in

w h ich

b

the forked end B of the spar CB 1s jointed to the nut ofa powerful screw S by means of two gudgeons. The nut Mslides in a rectangular guide G,

which prevents the nut fromturning

,while it moves from B to B1 , thus carrying the load

from Q to Q1 . The screw receives its motion from a steamengine N by means of the bevel gearing H the engine alsodrives two winches W

,whose chains K are passed over the

fixed guide - pulleys R to the hoisting tackle suspended from C .

Ow ing to the great length of chain,each winch is provided

with two drums similar to those in Fig. 5 3,and the wells J

receive the free portion of the hoisting chain.

In order that the screw S may not be exposed to a lateralstress

,the guide G must be suitably constructed and Secured

to the foundation,so as to resist the vertical upward pu ll V:

Z sin B which acts in the extreme position of the sheers.‘

In

this position a direct pull H: Z cos B is exerted along thescrew

,and in proportioning the screw

,this pulling action must

be considered. From what precedes,it follows that this force

gradually diminishes to zero in the vertical position of thesheers AC ; any furthermotion in the same direction changesZ to a thrust

,so that the nut is now pressed downward with a

force V : Z sin B,while the screw is likewise subjected to a

thrust H: Z cos B. The screw is therefore under the actionof a variable force whose initial intensity is Z cos B,

thenbecomes zero

,and finally increases to the value Z1 cos B1 .



by subtraction,which gives

f 2 (co s B1 co s B) t(p os 0t1

cos a).

The great sweep required for this kind of hoistin g apparatusgenerally makes f very large , and as it is impossible to supportthe screw except at its ends

,it follows that the screw must be

made very heavy,which greatly increases the frictional resist

anc e s. This evil is less noticeable in the construction,

1 Fig.

F ig. 1 3 8.

1 3 8,which w as used for a large masting sheers designed at

the machine works at Wa lty'

en,in Bremen

,for Wi lh e lmshaven .

Here the screw S for movi ng the load toward the wharf ispivoted at the fixed bearing B

,and works in a nut attached

to the lower end of the leg CF. If now the motion of theengine is communicated to the screw S by means of a bevelwheel H

,the nut advances toward B

,which is equivalent to a

shortening of the spar BC . It is evident that the length of

screw required is considerably less than in the form given inFig. 1 3 7, other things being equal ; for drawing in Fig. 1 3 6

1 Se e Ruh lmann,A l lgemeine Masch inen l ehre, vo l . iv.


the horizontal line BB1 through the centre at B,and making

CIB1CB = z

,then the nut M in the former case advances

through a distance f BB] ,wh ile in the present form of

arrangement the advance only amounts to f’ CB C

lB

ClBl— C

IB

,which value

,representin g the di fference between

two sides of a triangle,is always less than the third side.

The resistance to be overcome by the screw in the present

Fig. 1 3 9.

case is represented by the force Z exerted along the spar,whi ch

force as before acts as a pul l until the sheers reach the verticalposition

,when it changes to a thrust.

It is with reference to this last stress that the end F of thespar is guided by a link FE pivoted at E

,the link being so

arranged as to cause the arc FFo described by the pin F,to

coincide as nearly as possible with the path FGF1 in which the


end of th e spar CD moves. Since the path of the latter pointdoes not, however, coincide exactly with an arc of a circle

,it is

necessary to provide the link EF at F with a sliding piece,which is capable of a slight motion in a slotted head attachedto the spar CD .



o f a valve gear worked by hand . Fig. 1 4 1 illustrates thevalve chest of the lifting cylinder

,and Fig. 1 4 2 that of the

cylinder for swinging the crane . Wh en the slide valve S ismoved into the position shown in Fig. 1 4 1

,the pipe A opens

communication with the supply pipe from the accumulator,

and allows th e water to enter the lifting cyl inder through thepipe B . If

,however

,the valve is brought into the position SI ,

the water in the cylinder can escape from B through the cavityo f the valve into the discharge pipe V. “Then lowering theload the descent can be controlled by throttling the passage S

1 ;

so that in this case, as in all hydraulic hoisting apparatus , abrake is unnecessary. It is also unnecessary to use a ratchet


wheel and paul for sustaining the load at any elevation,since

for this purpose the valve S can be brought into its mi ddleposition

,where the lower edge of the valve just covers the post

SI ,thus cutting o ff communication with the cylin der by either

A or V.

The arrangement of the distributing valves of the waterpressure engine for swinging the jib is understood from Fig.

1 4 2 without further explanation , if it be noticed that thedriving water enters through C

,and is discharged through W

,

whereas the two pipes P and O are in communication with theends of the double - acting cylinder. It is evident that thesevalves are simil ar to those of the single and double - actingsteam - engines .The force required to move the valve is considerable

,since

the frictional resistance between the face and seat arising fromthe pressure of the driving water upon the back of the valvemust be overcome. For this reason it is impossible to movethe valves simply by means of levers

,as is the case in the

hydraulic hoisting apparatus,Figs . 73 and 77, but some con

ve n ient mechanism must be introduced with a V iew to in creasing the force exerted by hand. Fig. 1 4 3 shows how the valveis moved by the rods E and E ,

which terminate in screws fittingin the hollow heads of the valve rods T and T

I. In order to

ascertain the positions of the valve from the outside,the hands

Z and Z1are employed, which turn above two horizontal dials ,

an d the apparatus is so arranged that each of these b andswill make less than one revolution while the correspondingvalve traverses the distance between its extreme positions.For this purpose the cranks K are fastened to the rods E andE1 ,whereas the hands Z are attached to sleeves which are

placed loosely on the rods . By means of the toothed wheelsa,b,c,d,of which a is attached to the rod E

,d to the sleeve

of~

the pointer, and b c on a separate stud, the rotation of thecranks is reduced to that Of the pointer

,as in the so - cal led

back—gearing of lathes.In order to avoid the hurtful effects of the shocks 1 8)

whi ch occur when the water is suddenly shut off,and whi ch

are especially great in th e turning apparatus, on account o f thecomparatively great horizontal velocity of the jib and its load

,

special relief valves are introduced in the pipe connections 0


and P between the turning cylinder and its valve chest. Apair o f these valves

,X and X

1 ,Fig. 1 44

,are placed in each of

the valve chambers represented b and Y,Fig. 1 4 3 . Of

these two clacks X acts as a safety - valve,being held down b y

the weight of the water in the supply pipe AI ,while X

1~ acts as

a suction - valve,inasmuch as it communicates with the dis

charge pipe W (Fig. 1 4 3 ) by means of W1. It is evident

from what was said in 1 8,that

by suddenly closing the slide - valveo f the turning apparatus the water‘

which is being discharged from thecylinder

,through the pipe 0

"

for

in stance,Opens X by virtue of the

living force of the ji b . The result isthat a small quantity of water isforced back from the cylinder to th eaccumulator

,while in consequence

of the vacuum occurring in the pipeP

,the clack ‘X

1is lifted

,and

water is sucked up through W from the waste - water cistern.

In addition to the cranks for working th e slide - valves,a third

crank is frequently employed to move a throttle valve in thesupply pipe.

Plungers which are only packed at the stuffing - boxes,as in

hydraulic presses,are generally used in hydraul ic cranes instead

of pistons,Fig. 1 40

,which are packed at both cylinder and

stu ffing—box

,as in steam - engines. Plungers are also employed

for the turning - gear,and as they are single - acting

,it is n e c e s

sary to combine two such cylinders in order to turn the cranejib in both directions.

Such an arrangement is shown in the ten cranes constructed for the harbours of Gu stemii nd e} Fig. 1 45. Thecrane jib B is constructed according to Fairbairn ’

s system ,

and turns with the cross - piece C on the hollow pivot o f thefixed crane - post A

,through the centre of which the chain K

ascends . The latter is carried over the guide - pulleys LIand

L2to the end o f the jib

,and is provided with a hook for the

load Q and a counter - weight G,which serves to keep the

chain tight when the hook descends . empty. The horizontal1 Zeitschr. at. B ann er. Arch . u . Ing.

- Vere ins; 1 866.

F ig. 1 44.



vid e d w ith three pulleys , and is represented by H. Thus themotion of the piston is multiplied sixfold. For the purpose ofbringing the plungers to their original position when the emptyhook descends

,the cross - bar E is connected with the piston of a

counter- cylinder D1 ,which is always in communication with the

supply pipe. By this means the pressure of the water in thiscylin der causes the return of the plunger whenever the water

,

after use in the working cylin der,is allowed to escape

,w ithout

the need of a special valve gear for the auxiliary cylinder.Of course

,the effective pressure in the lifting cylinder is only

equal to the difference between the pressure i n this cylinderand that in the counter - cylinder. For swinging the crane thej ib is provided with a chain pulley M

,whose acting surface is

adapted to th e shape of the chain K 1. The ends o f this chain

are attached to the cylinders J and J1of the turning appa

ratus,after being carried over the movable pulleys N and N

1 ,

which are fixed to the cross - heads of the plungers O and or

Let us suppose a slide valve similar to the one in Fig. 1 4 2 to

be so connected with these tw o cylinders that one of them isalways in communication with the discharge pipe while thedriving water is being admitted to the other. Then as one o fthe plungers O is driven out o f its cylinder J

,the other plunger

0 1 is pushed into its cylinder J thus turning the crane j ib.

The combined action o f the tw o single- acting cy l ind ers J and

J1is therefore equivalent to a d ou bl e - acting water - pressure

engin e,and allows the jib to swing in either direction . The

effect of interposing movable pulleys N and N1is that the

velocity o f the chain K is twice that of each plunger,and

thus the crane jib revolves through an angle

corresponding to the length of stroke 3,where r represents th e

radius of the chain - pulley M.

The stroke of the turning piston is calculated to give the

ji b a circular motion of 06 of a turn to each side of the middleposition in which the jib - head is farthest from the wharf, s0 °

that the total range of motion is 1 2 of a complete revolution.

Accordingly,for a radius r = metre in .] of the

vx CRANES AND SHEERS 2 61

chain - pulley,the length of stroke of each working plunger is

estimated at

% x x 2 71-7 : x m . ft.]

In order to keep the chain K 1 always taut , th e cross - h eads o fthe plungers O and 0

1are connected by an additional chain

Fig. 1 46.

K2 ,which passes over the fixed pulley N

2. This chain comes

into action when the swinging o f the jib is stopped by suddenlyshutting o ff the driving water. In this case the inertia of thejib carries it a little further

,the result being that

,although one

of the plungers is forced into its cylinder by the chain K1 ,the

other plunger wou ld not move unless the chain K2exerted a

pull upon it. The valve gear for the turning cylinder is a


slide - valve of the form shown in Fig. 1 4 2,whi le lift valves

are employed to work the hoisting apparatus .A peculiar arrangement of a hydraulic crane is that

designed by Ritter o f A ltona . Here the crane - post A is alsothe hoist cylinder, and the cross - head B is provided w i th threepulleys C which make angles o f 1 2 0

° with each other. Thedriving- chain K is carried over these pulleys and the threefixed pulleys D , so that the motion Of the plunger is multipliedsixfold. The water is drawn from a reservoir W by means ofa hand - pump P

,and forced into the hoist cylinder. The reser

voir is closed at the top,an d answers the purp ose of an air

chamber. During the descent o f the load Q the water passesfrom the hoist cylinder back into th e air - chamber

,thus com

pressing the air, and at the same time lifting a counter - weigh tG which swings with th e lever E. Through the action of thecounter - weight and the compressed air

,the hook for attaching

the load and the working plunger ascend after the load isremoved. This arrangement offers special advantages forunloading and lowering loads . V is a 'valve for drawing thewater from the cylinder A and forcing 1it into the reservoir Wor the reverse. This crane is of the portable type, which classo f machines w ill be more fully described in the followingparagraph.

EXAMPLE — A hydraulic crane,Fig. 1 45

,is to lift a load of

2 000 kilograms [441 0 th e pre ssure of wate r in th e accumu

lator corre sponding to a head of 500 me tre s [1 640 It is

required to de termine its dimensions.

Let F denote th e area of th e working plunge r, andf that Of th ecounter plunger

,and l et u s suppose that th e motion of th e plunge r

is mul tiplie d sixfold by interposing a chain- and - pulley tackle b etwe en th e piston and th e hoisting chain. Then assuming ane fficiency of 77 for th e hoisting apparatus, w e have

(F —f )x 500 x 1 000 kil ograms x 6 x 2 000,

[ (r - f )x 1 640 x 62-5

from which w e find th e diffe rence be twe en th e area of th e workingplunge r above that of th e counte r- plunge r to b e

F —f=0°

03 2 sq. m . sq. ft. ]



and‘

e ach plunge r,ow ing to th e inte rposition

'

o i th e movable pulley,

must have a length of stroke of 1 0 47 me tre s ft.]

3 6. Portab le Crane s — For building purposes,railway

yard s; and docks, portable cranes are often employed. In thisclass of cranes the post and jib

,instead of being permanently

secured in o n e place , are mounted upon a low carriage whichtravels upon rails. It is

,of course

,understood that the load

may. also be transported along the railway,in which case the

crane takes the place o f a car. But this use of cranes is theexception

,as

,for instance

,when the crane is used to transport

the heavier parts o f machinery in large erecting shops .Portable cranes are constru cted to work both by hand and

steam power. The hydraulic crane Of B itter,Fig. 1 46, which

comes under the head o f hand cranes,is an exceptional case.

The steam cran es proper,Which have their“ own engine and

boiler mounted upon the carriage,must be distinguished from

pow er cranes,which are driven by a stationary engine, which

may also be used for other purposes. At th e present day thelatter kind of portable cranes are operated to advantage bymeans of cotton rop es.

To the two mechanisms which affect the raising or loweringof the load

,and the turning o f the crane jib

,must now be

added a third for transporting the crane al ong the railway.

In the lighter hand cranes this travelling motion is Obtainedby direct hauling on the part of the workmen, or by theemployment of horse - power. In the heavier designs a commonarrangement is to provide one or both carriage axles with atoothed wheel

,which receives its motion through the medium

of gearing worked by a crank shaft. In steam cranes motion isoccasionally imparted to the crank shaft by hand

,as connecting

the latter with the engine which revolves with the crane givesri se to many constructional inconveniences. At times theWindlass of the crane is utilised for propelling the car ; this

’ isdone by paying out the hoisting chain and attaching its hookto some fixed point of the railway

,so that the winding o f the

inclined chain upon the drum will cause the desired motion .

This means,however

,should be employed with care, as there

is danger of upsetting or breaking the jib,which is usually not

designed to resist such a stress . Portable ‘cranes for railroad


u se may be best conveyed from place to place by attachingal ocomotive.

In all portable cranes particular attention must be paid to

the question of stabil ity ; this may be obtained by a properdistribution of the weights . When the fulfilment of thiscondition gives rise to great difficulties the crane may besecured to fixed points o f the railway

,as

,for instance

,by


h o l d irig- d ow n

’

c l ips which are attached to the top o f the rails;This plan is only to be used in case o f necessity

,and is of

course impracticable when th e crane is to be transported withthe jib and suspended load standing at right angles to therailway. In order to prevent the overturning of the craneunder the action of the suspended load

,counter - weights are

generally used. For this purpose either actual weights,or

,in

the case of steam cranes,the weight of the boiler and engine,

Fig 1 48.

may be advantageously employed. Since these balance - weightsand the load Q must always be placed on Opposite sides of thecrane - post

,it follows that the former must be connected with

the movable jib,and not with the carriage.

For certain kinds o f work the crane is made double, havingtwo jibs and cranks

,in which case su fficient stability is secured.

Such a cran e is sh own in Fig. 1 47. Here AA is a hollowcrane - post fixed to th e fo u r- wheeled carriage W

,while B is

a vertical spindle which is free to rotate within the post.The tw o braces E,

united by the wooden ties D,are con

n e cte d with the spindl e B by tension rods G and H , and rest



and from ( 3 )

EXAMPLE — Suppose 2 500 kilograms [5500 l b s.]to repre sent th emaximum load to b e lifted by a portable crane ; l et th e radius of

th e jib b e a me tre s [1 1 5 ft.] th e weight o f th e movable jibG1

1 500 kg. [3 3 00 l b s.] th e distanc e of its centre of gravityfrom th e crane - post c m. and th e we ight of th e

carriage G2 1 2 00 kg. [2 65 1 how large must th e counterwe ight G be

,and what must be its distance d from th e crane - post

,

assuming the distance be twe en th e rails to b e 2 6 1 4 4 m. [47 2and th e distance of th e centre of gravity of th e crane from th e

cranepost not more than 0 °

85b l

Th e we ight G is

and th e distance of its c entre o f gravity from th e axis of th e cranepost is

2 500 x 0°72 1 500

3 2 00 2+m x 0 3 — 1 2 7metre 1 6 ft.]

Instead of connecting the counterweight rigidly with the

ji b , it is sometimes constructed in th e form of a small carriage,

Fig. 1 49.

travels upon a horizontal railway fixed to the ji b , sothe di stance o f the counter - weight from the crane - post may bealte red to correspond to any variation in the weight of the load.

The railway and balance - carriage have also been so arranged

VI CRANES ~

AND SHEERS 1269

that the action of the load itself causes th e necessary movemento f the carriage. The manner in which this is accomplished isshown in the sketch

,Fig. 1 49.

The hoisting chain is carried from the drum W over thefixed pulley R

I,and hangs down in a bight which supports

'

a

movable pulley with load Q . It is then passed over the fixedpulleys R2 and R3 , and .final l y attached to th e counter- weightG

,which is mounted on wheels

, so as to travel along thecurved rail way L. Let Q represent any load to be lifted, andG the counter - weight ; further, let P be the tension in thechain K which tension

,in the present case

,must be taken

equal to % Q in the absence of friction at the pulleys. Thenthe . action of the force P is to draw the weight G up the curvedtrack until it reaches the point at which

81 11 a

B

where a denotes the inclination to the horizon of the pathdescribed by the centre o f gravity of the counter - weight at theinstant mentioned

,and B the angle included between the d ire c

tion of the pull and this path.

The form of the railway is therefore fixed by the conditionthat the moment o f the counter - weight G for every positionmust be in equilibrium with the moments of the load and jib.

This mode o f arrangement,however

,has never been extensively

used,owing to the great length of chain required and other

inconveniences.A portable steam crane is shown in Fig. 1 50. As hereto

fore,the movable crane jib is supported by a cross - piece B upon

the pivot of the crane - post A,which is fixed to the carriage

W. The two side frames D‘

extend back of the jib,and carry

the vertical boiler K and the tank V,which at the same time

serve as"counter - weight.’ The small (4 to 6 horse - power)steam - engine E is provided with a link - reversing gear, andtransmits its motion by means of the

,pinion F to the toothed

wheel G attached to the winding - drum W. Motion is impartedto a vertical shaft through an intermediate pair o f bevels notrepresented in the figure

,whi ch turn the crane as described in

Fig. 1 3 5. Th e travelling motion is obtained from the engineby means of an endless chain N

,which connects the chain


pulley on the shaft of the engine with another on the rear axleL of the carri age. It. is obvious that this chain .gearing cannotbe employed unless the two shafts connected are parallel

,that is

to say , unless theCrane jib stands in the vertical plane throughthe centre line o f the track . In order to transport th e crane

,

whatever the position of the jib,a shaft may be arranged to

coincide with the axis of the crane - post. This shaft may receive

Fig. 1 50.

motion from the engine through a pair o f bevels at its upperend

,and impart it to one of the car axles by means of a pair

o f bevels at its lower end. Z are holding down clips for clamping the crane to the rails, should the weight of the boiler ande ngine be insufficient to

'

b alanc e the heavier loads.The direct action of steam has also been advantageously

applied to steam cranes, as,for instance , in the excellent steamcrane constructed by Brow n of London

,which is distingu ished



head represents the movable block of a six -

pu l l ey tack l e, thefixed pulleys being placed at R

2 ;thus the height of lift o f the

load is six times the stroke of the piston. To prevent theload from running down (in consequence o f the gradual cond ensation o f the steam below the piston), the cross - head E isprovided ,with two vertical plungers F, which during the u p

stroke of the main piston are lifted out of their cylinders F1 ,

and draw i n water from the reservoir H through a suctionvalve. As this val i e closes when the plungers are presseddown by the action of the load Q ,

the water checks thedescent until the valve is again opened ; thus , by adjusting thearea through which the water in the cylinder F i s forced intothe reservoi r H, w e may create any required resistance andall ow the load to descend uniformly.

For turning the crane jib the direct motion of a pistonworking in a doub le - acting cylinder G is employed ; for thispurpose the head J of the piston - rod has attached to it bothends of a chain K ,

which,after passing over the fix ed pulleys

r1 , 2 ,

and rs, is ca

l

rrie d around the pulley r attached to thefil

xe pivot A . From this it is evident how the motion o f thehead J causes

1

the chain to be unwound from the pulley r4,and

as the latter cannot turn,and th e slipping of the chain is made

impossible, it follows that th e crane jib A with platform P is

turned round the pivot AI ; the motion is to the left or right,

according as the piston in the cylinder G moves up or down.

In this apparatus there is no special arrangement for obtainingthe travelling motion ; as a rule, a method already mentionedis used

,which consists in securing the hoisting chain to some

fixed point on the railway,and then giving an upward motion

to the lifting piston.

The relations between the forces and motions o f this craneare to be determined as in hydraulic rotary cranes . Inasmuchas the tackle used has a sixfold purchase

,the length o f stroke

o f the lifting pistons must be made equal to one - sixth o f themaximum height o f lift o f the load , and th e areaso ffth

'

e pistonsmust be so proportioned that the total pressure of the steam

upon both surfaces shall exceedm6Q after deducting thel

friction of the piston and stu ffing box , where (77) representsth e efficiency corresponding to the reverse motion of - the tackle


(See table, The stroke of the piston for the turningapparatus is to be estimated

,as in the hydraulic crane 3 5

,

Fig. from the radius of the chain - pulley r4 ,and the angle

through which the crane - jib is to swing. The present crane ismade to sw ing one and a half times round

,namely

,th ree - quarte rs

o f a circle to each side of the middle position. In the cranesused at Hamburg with capacity to lift 40 cwt . each hoist - cylinderhas a diameter of metres ins ]; and a stroke ofmetres [5 9 ft.] The pressure of the steam in the boiler variesfrom 6 to 8 atmospheres

,according to the load. To adapt the

crane to the work in hand,the radius is made to vary by the

following arrangement. The chain for the derrick motion,

after passing over the movable pulley z1at the end of the

tension - rod Z,has one of its ends made fast to the Windl ass

frame,while the other is attached to the derrick barrel z

z,so

that by turn ing the latter by the aid o f a worm - shaft S,the

radius is altered ; the maximum radius of the jib is 1 1 metres

[ 3 6 ft.]The derrick motion requi res that the strut T be pivoted

at the base of the movable frame. When in consequence ofhigh water in the harbo ur the total lift is small, it is evidentthat for the lowest position of the load the l ifting piston wouldbe a considerable distance from the cylinder bottom

,and that

the clearance spaces below the piston, whi ch must be filledwith steam at each lift

,woul d b e very great. To preven t the

consequent waste o f steam it is onl y necessary to shorten th ehoisting chain by taking in the end attached to the frame

, so

as to bring the pistons nearly to the bottom of the cyl in derw hen the hook is in its lowest position ; that is, the strokeshould always begin at the lower end of the cylinder

,the

l ength of stroke, of course , corresponding to the smaller lift.3 7. Trave lling Crane s — This term applies to the class

o f hoisting machines whi ch , lik e portable cran es, travel upon apair of rails

,and in which the load , be sides be ing lifted ,

has a"

horizontal motion at right angles to the motion of the entireapparatus . As regards construction , this kind of hoistingm achine is chiefly distingui shed from the portable cran e byth e absence of the rotating jib ;

‘

for this reason the term crane,

strictly speaking,is less applicable to it, but takin g into con

s ideration its general usage,w e shall retain the word. Also as

T

2 74 MECHANICS OF HOISTING MACHINERY CRAP .

regards its application,the travelling crane .differs from the

portable crane,inasmuch as the object of the former always is to

convey the load lifted in horizontal directions at right anglesto each other

,while in the latter class the travelling motion is

used merely for shifting the position of the crane,an d rarely

to transport the load. Accordingly, the travelling motion of

the entire machine is always Obtained by means of a suitablemechanism

,whose e mployment for portable cranes

,as before

mention ed,is the exception

,and not the rule. Travelling cranes

are principally . employed in foundries,machin e and erecting

shops,and in the construction o f large engineering works

,as

,

for instance, for distributing the tools and materials in buildingpiers and massive bridges . It is evident that with the travelling cranes the load may be conveyed to any point within therectangle formed by the total travel in each direction . In th e

smal ler cranes,and for transferring light loads

,the motion of

the bridge and winding gear,as also the raising of the load

,is

effected by hand - power,w hile for heavy work engine - power is

applied either directly or by means(of rope transmissions

,

electric motors,etc .

A requisite o f every travelling crane i s a strong bridge , whichis fitted with rails for a truck or trolley

,and which h as a motion

o f its own along a track perpendicular to its length. According to the location of the, track along which the bridge travels

,

w e may distinguish two forms of travelling cranes . Wh encircumstances permit the track to be placed at the same levelto which the load is to be lifted

,as

,for instance

,in workshops

and buildings,and in high scaffoldings

,a bridge constructed of

two parallel frames of timber bolted together,and mounted at

each end upon two wheels,is all that is required. In cases

where a firnr scaffolding is impossible to obtain,as in many

building Operations and in railroad yards , the tracks are laidupon the ground

,and the wheels are fixed to the base of two

high frames or trestles,which support the bridge. The travel

ling crane is then known as a gantry.

Fig. 1 5 2 shows such a gantry as used at freight depots,and for distributing the materials in building piers. The twoframes or trestles ABC

,which travel upon the rails DE

,su p

port the two timbers SSl ,fitted in turn with a pair of rails ,

upon which - th e _ tro l l ey . with winding- gear WW1moves . Thi s .


MECHANICS OF HOISTING MACHINERY CRAP.

heavier weights the load Q may be raised by the applicationo f two movable pulleys, one for each rope, the ends o f th e

latter being secured to the trolley W,or the single pulleys R-

lR

may be replaced by two or three pulleys mounted side by sideon the same shaft.From the figure w e se e how the crane can b e '

mad e to travel‘

Fig:1 53 .

along the rails H by turning the w inch - handl es FF w hichdrive a pair of toothed wheels GG

I.

In order to prevent the bridge from binding during thelongitudinal motion o f the crane

,motion must be given at the

same time to one of th e wheels at each end of th e bridge.Fig. 1 5 3 represents a travelling crane e mployed in shops.

The bridge, which is made o f two wrought - iron girders A conn e cte d at each end, travels along the rails B,

the latter eitherresting upon an offset in the masonry or supported from below

v1 CRANES AND SHEERS 2 77

by iron columns. The crab W carries the chain barrel1

T,

which receives its motion in the usual manner from the winchhandle K and the double Windlass CC

1and DD

l. The friction

wheel F and ratchet wheel E require no further explanation .

Th e longitudinal and transverse travelling motions are obtainedfrom a second winch - shaft h , which may be shifted in itsbearings. Thus the pinion a can be made to engage with thespur wheel b on the shaft 0, which in turn drives the wheelsof the

,

truck W through the intermediate pair o f gears d ande or by throwing into action the bevel gears f and g, motionmay be given to the shaft h connected with the bridge. Thisshaft is provided at each end with a pinion i

,which gives

motion to the bridge - axles n by means of intermediates 0 and Z.In the former case the crab moves, in the latter the bridge.As the shaft h is too long to be without support between theextreme bearings

,supporting levers are introduced

,which are

pivoted at m,and always tend to assume a vertical position by

the action of the weight n . In travelling back and forth thebevel g pushes the lever far enough aside to allow it to pass.This gear is provided with a feather

,w hich slides in a key - way

running the whole length of the shaft h,and consequently can

be made to rotate this shaft in any position of the truck. H

represents a platform for the workmen,supported by the

brackets G. Wh en , as in foundries , the motions o f the trolleyand bridge must be obtained from below, the cranks K and 16are generally replaced by chain - pulleys and endless chains

,the

loops of which can be conveniently grasped by the workmen.

Little is to be added concerning the formulas applicable tothese cranes. The proportions of the hoisting apparatus areto be determined from the rules laid down for windlasses.The force required to transport the load horizontall y is obtainedas follows:Let G represent the total weight of the crab

,

including the suspended load , or th e weight of the bridge,

including the workmen,crab

,and load ; further, l et R denote

the radius of the wheels carrying the crab or bridge, and r theradius o f the journals. Since w e may suppose the entireweight to be concentrated upon one axle

,the resistance to be

overcome at the circumference of the carrying w heel w ill beexpressed by


where (j) i s th e co - e ffic ient of journal fri ction and f th ec o - e fficie nt of rolling friction

,which

,according to I

, g 1 97;W e isb . Mech

,may be taken at f = 01 5, when R is expressed in

mi ll imetres [j =°0 1 968 When R is e xpressed in inches]. In

order to overcome this resistance W acting with a lever - armR, the toothed gearing required for transporting th e apparatusmust be arranged as in a Windlass

,which has a load W hang

ing from the winding barrel of radius R.

The girders of the bridge are to be considered as in thecondition of a beam supported at both ends

,which

,in addition

to its own weight,is to support a movable load

,consisting of

the useful load and the weight of the crab.

r '

Th e applicationof graphical statics to this problem is explained in vol. i.Appendix

,4 5

,W e isb .

‘

Mech .

§ 3 8 . Pow e r Crane s — The necessity of givmg a morerapid motion to the load th an can be Obtained by musculareffort has caused the introduction of other motive power.Although the pow er derived from a stationary motor maybe easily transmitted by means of rope or toothed gearingto a fixed win ch or tackle

,special

\arrangements must be

employed to adapt the driving gear to cranes . In rotarycranes the pow er must be communicated through the axiso f the movable j ib

,while in travelling cranes the mechanism

must be so arranged that the crane shall not be thrown outof connection with the prime mover by the shifting of thetruck and - bridge .Fig. 1 54 illustrates a crane in use at the railway station

at Liverpool,and driven by a continu ally running shaft. The

winding barrel E is supported by fixed standards,and the

rope,after passing over the pulley F

,located Opposite the

axis o f the crane j ib FL,is carried down through the centre o f the

latter,and over the two pulleys G and H . The shaft B

,which

receives its motion by means of frictional gearing from thecontinuouslyrunning shaft A

,transmits it through the medium

of the toothed gearing DC to the winding barrel . For thispurpose the bearing R of th e shaft A is arranged upon thelever U ; by pulling upon the cord X ,

attached to the lever,

a small friction - wheel at the end of A is caused to pressagainst the inner surface of the pulley T

,by which the shaft

B is driven . By releasing the cord,contact between the


2 80 MECHANICS OF HOISTING MACHINERY CRAP. V I:

th e longitudinal track. Each shaft was provided with a keyw ay receiving a feather set in the hub of a pinion

,by which .

the latter w as made to take part in the rotation of the shafts.In this case

,if the wheel on the shaft B is a bevel b

,which

gears with another bevel d on the shaft A,then in any posi - f

tion of the bridge the shaft A will receive motion from . B.

By employing a reversin g gear,it is a simple matter to obtain

the longitudinal travell ing motion .

Similarly, the right or left - handed rotation of the cranebarrel

,and of the shaft for shifting the position o f the truck

,

is obtained from A by the shifting spu riw h e e l s a

,and d

, ,and

the two reversing gears c1and o

z,which are connected with the

truck . This makes quite a complicated and aw kw ard,arrange

ment,

- however,for th e reason that the two shafts A and B

are too lOng to be without support between the end bearings .It is therefore necessary to employ a series of intermedi atebearings , which, however, cannot be stationary, as the passageof the traversing wheels a and 6 must not be interfered wi th.

The plan adopted w as the lever arrangement described inFig. 1 54 .

These inconveniences are avoided by the use of suitablerope - driving

,concerning the general arrangement of which a

detailed account may be found in iii . 1,58

,W e isb . Mech .

In the following we will only mention an application of ropedriving to travelling and portable cranes as made by Ramsbottorn

,

1 and used to advantage in the locomotive works atCrewe .Fig. 1 55 shows the plan and side view of the travelling

crane. Here AA are the girders of the bridge,constructed of

wood and iron,and mounted on wheels a

1for travelling along

the rails a while the truck B,mounted on wheels b

,rolls o n

the bridge . The latter carries the four vertical pulleys cl ,02 ,

03, 0

4,ab out which the endless rope s

134runs in th e direction indi

cate d by the arrows. This rope is carried over two“pulleys

o f 1 2 metre ft.] diameter, at each end of the building,

one of which is driven by a steam - engine,while the other

,

which is weighted and movable horizontally,acts as a tightener,

so as to keep the endless rope at the necessary degree of

1 For furth er d etail s on th is point se e th e artic l e b y G. Lentz, Zeitschr.

de u tsch . Ing. 1 868, page 2 89.


tension . The rope - pulleys 0 therefore turn continually,and

th e pulley cl ,owing to the connection established between the

friction - wheels d1d2and c

l ,serves to shift the crane when

,by

means of a hand - lever,either the upper wheel d

1or the lower

d2is brought in contact with a friction - wheel e

,carried on

a horizontal shaft. Thus the latter shaft can be turned to th eright or left, and being connected by gears with the shaft fon the bridge and the wheels a

l ,it may be made to communi

cate the corre spond ing motion to the bridge .The crane - barrel T is driven by a pulley g on a short upright

shaft G,with a worm engaging a worm - wheel t on the barrel

shaft . Ordinarily the pulley g does not touch the drivingrope s ; it is only when, by means of the roller g2 , the rope32or

,by means o f the roller gs, the rope 3

3are forced into

grooves in the pulley g that motion is'

communicated to theshaft G ; it is obvious that these motions will be in oppositedi rections

,and they are therefore adapted for raising or lower

ing the load. The grooves in the pulley g are of differentradii

,the smaller being utilised for lowering the load rapidly,

while th e larger is used for hoisting.

Motion can be imparted to the truck B through the pulleyh on the vertical spindle H ; this is effected by pressing eitherof the ropes s

2or 3

3into the single groove of the pulley h by

means of the respective rollers h2or h

3. The spindle H

,by

means of a worm and worm - wheel,drives one of the axles of

the truck B . The driving - rope is made of cotton,and is

1 6 millimetres in .) in diameter, and by the action of thetightener - pulley it is subjected to a tension of 50 kilograms

[ 1 1 0 It travels at the high velocity of 2 5 metres

[8 2 ft.] per second. In order to diminish as much as possiblethe w e ar

,o f the rope and the resistances due to bending the latter

around the pulleys,the diameter [0 4 55 metres] of the pulleys

is about thirty times that of the rope,which gives to them

a velocity o f 1 000 revolutions per minute . This high speedrequires carefu l balancing and good lubrication for the journals .The velocity ratio o f the hoisting - gear is likewise very large ,and has a value of for a maximum load of 2 5 tons

,

so that the rate at which the load is lifted is 0 495 m.

ft.] per minute ; while for smaller loads and a velocity ratio of about 1 800 the ratio is

,say

,four times as



to.

the vertical shaft a,whatever the position of the crane

,

and this motion may be at will imparted to the crane - barrelT or the carrying - wheels C . For driving the barrel the wormshaft is provided with a conical friction - wheel e

,while the

shaft a carries a pair of similar bevels e e which may be1 2 ’

shifted on a feather in the shaft. A hand - lever“

h serves to

Fig. 1 56.

raise or lower this pair of bevels , and in this manner motionin either di rection may be given to the worm c.

In a similar manner motion is transmitted to th e carw h e e l s ~C through the worm - wheels d

land d

2 ,and the inter

mediate shaft d for this purpose a reversing gear is employed,consisting of the three friction cones e , 61 ,

and e2, which are

operated by means o f a lever p . The sw inging of the jib is


accomplished by hand - power. This crane has a motion longitu dinal ly of 3 6 metres [ 1 1 8 and is capable o f lifting80 cwt. at a radius o f metres [8 5 ft.] The speed atwhich the load is lifted is metres ft.] per minute,corresponding to a velocity ratio of about The diameterof the driving - rope is also 1 6 mm. [2 ins]

Such cranes are suitable onl y where a amount of

work is to be done,as otherwise there woul d be an unnecessary

waste of power for driving the rope alone.

CHAPTER V II

EXCAVATORS AND DREDGES

g 3 9. Excavators — These hoisting , arrangements, which aresim ilar to cranes in their construction and mode o f action

,

‘arelargely used at the present day

,especially in America, b oth

as dredging mach in es in excavating canals and building - grounds,

and also for similar purposes in railroad building. In theirmain features they agree with the hand l e or scoop dredges,

which have been in u se for a long time. Like the latterapparatus

,they carry as their essential constituent a scoop

or d ipp er provided with a handle, the combination beingOperated by the drivmg motor in such a manner that forevery revolution the scoop cuts out a fixed quantity o f material

,

which,after being lifted

,is delivered to a vessel for further

transportation. The work to be done by these machines,

therefore,consists not only in a hoisting operation,but also

in a d igging or cu tting process, which requires that a suitableshape and movement be given to the bucket.When actual d redging, that is, increasing the depth o f a

waterway,is to be done, the excavator is placed on a barge or

vessel,whereas for excavating purposes on land

,it is placed on

a car travelling along a special temporary track in the mannerof portable cranes. In the latter manner these machineswere u sed on a large scale in the Construction of the PacificRai lroads.

In Fig. 1 57 the arrangement of a handle dredge, as builtby Otis in New York, is shown in its essential features. Thebarge A

,which is made o f wood or iron

,and is of rectangul ar

plan and cross - section,carries the steam - engine with its tubular

boiler,and h as one end arranged to receive a movable crane


MECHANICS OF HOISTING MACHINERY .CHAP.

handle F,besides having a sliding moti on, may obtain a

simul taneous rotary movement about the shaft fr The ji bis revolved horizontally by mean s’ of a chain - pulley W

,

“ at. the circumference o f which the two ends of a chain ls

,are

fastened,the latter being operated by a Windlass mounted

on the deck of the barge, and arranged to be turned in eitherdirection.

As will be seen from the following considerations,the

scoop G can, by the mechanism just described, be given thesame kind o f motion which is required for digging by hand.

Let us assume that, by the action of the hand - lever H,the

connection between the chain - whee l f2 and the pinion on theshaftfr is interrupted , so that the former will run loose on theshaft

,then the scoop with its hand le will assume a position

such as to bring its centre of gravity in th e vertical tangentof the pulley c

l. By paying out the chain 13 th is centre of

gravity will sink in the same vertical V V,the handle F at

the same time moving downwards a corresponding distance.Haul ing in the ch ain It will naturally cause a vertical rise o f

the centre of gravity, and a corresponding upward movemento f the handle F. By this means the scoop may thus bebrough t to any height that may be required in the dredgingoperation. If now th e ch ain - wheel f 2 by the lever H isrigidly connected to the pinion - shaft f l , then paying out thechain 76 will cause the pulley c

1and the chain - wh eel f2 to

revolve to the left, and thus bring about an upw ard movementof the handle F. The extent of this movement will beexpressed by v h , if h denotes the increased length of theportion 0

1G o f the ch ain and v the velocity ratio of the pulley

c1and the pinion fr Likewise

,by hauling in the chain

,a

d ow nw ard motion of the handle F will take place . In consequence of this combination

,the scoop will describe a certain

curved path , depending on the velocity ratio v, and indicatedin the figure at Gl G G 3 for the point G,

under the assumptiono f a ratio v= ;

1f . From the figure is evident how excavating

as well above as below the waterlevel can be done by amotion o f this kind at any height of the dipper. Itmay herebe noted that, since the h andle is lowered by the action of

gravity,the extreme position of the dipper will be at the

point G2, which is the lowest position of its centre of gravity.

.v1 1 EXCAVATORS AND DREDGES 2 89

If it is required to pull the dipper further backwards, as, for

instance,to G

1 ,this may be done by a special chain k

sattached

to its rear end,and operated by a winch ; such was also the

original arrangement in this kind o f machines.1 The sameresult may also be accomplished by deriving the motion of

the shaft f1 d irectly from the motor, and not from the pulley cl

.

This is the method employed on the dredges built by thePh i lad e lph ia Dredging Company. It is possible in this caseto continue the backward motion of the dipper close to thebarge at G

1by the simultaneous movement of the chain 76 and

the pinion at frAfter the dipper has

'

been lowered and pulled back to itsextreme position

,it is filled by cutting out a quantity of material

in the above described manner,and is then

,by the continued

motion,raised to a certain height. The j ib is subsequently

swung around by throwing into action the winch for the chain162,and a pull on the latch - rope allows the bottom door to fly

open,thus causing the contents o f the dipper to drop into a

special barge or car. The operation is repeated after the j ibhas been pulled back and the handle again lowered.

These machines work very rapidly,the whole operation in

many cases requiring but one minute,provided that the person

in charge is in possession of the necessary experience. In anapparatus of this kind used for improvements of the Drau ,

2 thecubic contents of the dipper w as about 06 cub. m. [2 1 cub .

the swing o f the jib w as m . [2 4 th e length o f

the barge was m. [61 and its width m . [ 2 4 ft.]A steam - engine of 1 4 h . p. w as used, and the earth excavatedwas 3 1 0 cub . m. [4055 cub. yds ] in ten hours for a greatestdredging depth of m . [ 1 6 ft.] below the water - level, anda maximum discharging height o f m. [ 1 4 ft.] above it.Another kind o f excavator is that in which the receptacle

for the masses to be removed is simply lowered to the bottomby means o f a w in ch

'

and chains,and then , after being filled ,

hoisted again above the surface to the desired height for discharge of the material. To this end the receptacle con sistsof two scoop - shaped parts (clam sh e l ls), which are so connectedby hinges that they can come together or move apart in the

1 Se e Zeitschr. d eutsch . Ing. 1 872 , page 2 69.

2 Se e Zeitschr. d . esterr. Ing. u . Arch .- Ver. page 1 81 .


same manner as the jaws of a pair of tongs. This principle isillustrated in Fig. 1 58 . The two shel ls A

1A2are at a

la2

hinged to an iron frame B,in which. the shaft ' C h as its bear

ings. On this shaft C is secured a large chain - wheel D,from

the circumference o f which a chain K is carried upwards to a

Fig 1 58.

guide - pulley,and thence to a winding - drum

,which may be

revolved at will . Besides this larger chain - pulley D twosmaller pulleys E are also placed on the shaft C, a chain fleading from each to a cross - shaft F higher up. When theshaft C

,by hauling in the chain K

,is revolved in the direction

o f the arrow,the cross - shaft F

,being guided at each e nd by

slots in the framework B,will therefore be approached to the



and in its direction a tension Z,which must intersect the former

in C . These two forces P and Z will be in equilibrium withthe reaction R produced by the frame G on the journals of th eshaft C

,and for this reason this reaction must have a direction

OC. Making,therefore

,to any scal e 0 1 equal to P,

'

w e obtainth e tension Z in 1 2 ,

and the reaction R at the journals i n ,

O 2 , if 1 2 is drawn parallel to the chain f . Now resolvingthe ten sion Z 1 2 along the directions of the push - rods Fb

1

and Fb2,w e obtain the pressures acting in these rods, namely ,

L2in 1 3

,and L

Iin 3 2 . Now ,

to determine the resistance o fthe bottom

,let us recollect that the cutting edges H

1an d H

2

have a tendency to revolve about a1and a

2 ,and for this reason

th e’

re sistance o f the bottom must be assumed perpendicular tothe respective radii H

laland H

2a2,that

,

is,in the directions

HIW

1and H

2W

2. As these resistancesW

1andW

2intersect the

forces LIand L

2in 0

1and 0

2 ,w e further obtain in O

la1and 0

za2

the reactionsRIand R

2of the frame on the jou rnals a

1and a

2.

Resolving,therefore

,the force L

I: 3 2

_ acting in the push - rod ;

along 3 4 parallel to WlH1and 4 2 parallel to a 0 w e shall

have in 4 3 the resistance offered by the bottom atI

H and in2 4 the reaction R

Iof the frame on the journal“

1° In th e

“

same manner w e resolve the force L2: 1 3 along directions

paral lel to "W2H2and a

2O2 ,and thus obtain in 5 1 the resist

ance of the bottom at H2,and in 3 5 the reaction of th e frame

on the j ournal a2. We have thus constructed the polygon of

forces 1 O 2 4 3 5 1 , and if for easier survey w e removeW

1: 4 3 to 6 5

,and R

2: 3 5 to 4 6

,that is

,if w e draw the

parallelogram 4 3 5 6, the pol ygon 6 5 1 O 2 4 6 will give aclear view of al l the forces acting on the apparatus . Th e

external forces W1 ,W

2, and P are here represented by 6 5 1 O,

and the reactions R,RI ,and R

2o f the frame at the journals .

C,a1and a

2by O 2 4 6. It will therefore be seen that for a

resistance at the bottom expressed by W1: 6 5

,the driving

force P in th e chain K must have the value 1 O,and that the

resultant reaction which the frame must exert on the journal sis given by the line 0 6. This line thus represents the weight .°

G required.

In the figure the two forces W1and W

2are made of

different size , and it is therefore evident that in the positionassumed onl y the edge H

1 ,at which the greater force acts, will

V II EXCAVATORS AND DREDGES 2 93

enter the bottom. A change in the position o f the apparatus ishereby brought about

,together with a change in the ratio of th e

resistances W1and W

2, in consequence whereof the second edge

H2is also made to enter. It is also apparent that the mach ine

will always so adjust its position that the resultant reaction0 6 o f the frame at the journals will always be vertical

,since

this reaction is due to the weight of the frame, and thus is

Fig. 1 59.

able to act in a vertical direction only. In the above presentation the hurtful resistances

,such as journal friction, etc.

,are

neglected. Were these to be taken into consideration , the.only ch ange necessary in the above construction would be todraw the reactions R

,RI ,and R

2tangential to the corresponding

friction - circles,in place o f drawing them th rough the centres,

as h as been previously explained. (See vol . iii. 1 , Appendix,W e isb . Mech .)While for d redging in soft bottoms , which only slightly


oppose the pressure o f the cutting edges,the weight of the

machine itself is sufficient to bring about the desired result, itis necessary, when excavating h ard clay bottoms, to add con ;sid e rab l e extra weight, amounting to several tons for the largerapparatus. Owing to this circumstance

,the efficiency of the

machine in such cases is very slight. For,letting Q denote

the weight of the detached mass,and G. the - weight of the

machine with its bal last,then th e final pulling force in the

ch ain must be equal to G + Q, and thus w e obtain for theactual hoisting operation

,neglecting all wasteful resistances

,

QQ G

When the total weight G o f the apparatus is insufficient,

an imperfect action of the excavator results, inasmuch as thej aws then continue to enter the bottom only until th e tensionin the chain becomes equal to the weight o f th e machine plusthe resistance wh ich the bottom offers to tearing off the

,under

cut mass. In such cases the bucket is n ever completely filled,

the contents being tw o lumps o f earth only. In order toovercome this difficulty the machine has been constructed invarious ways

,on e of these

,as originated by Both

,

1 and illustrate d in Fig. 1 59, is here given. Here a n early con stan tcutting resistance is obtained by the use o f the two guide - linksCb and da on each sid e, in place of the fixed gudgeons forswinging the shel ls A

Iand A

2 ,the closing of the jaws being

as before accomplished by the push - rods Fb . The drums Hfor the chains f are not placed directly on the shaft operatedby the chain K, being instead attached to another shaft d z,and revolved from C by the gears cc and DD on each side.On account of this arrangement the motion o f each sh ellmay in every moment be considered as an infinitely smallrotation around th e corresponding pole or instantaneous centreP

,which will be located at the point of intersection of the

links Cb and da .

When the bottom is rocky,and for raising the stone frag

ments after blasting under water,the jaws o f the excavator are

given the form shown in Fig. 1 60,which represents the apparatus

designed by Holroyd , and used by th e American Dredging Company. When the mach ine is lowered (I) it is suspended from

1 Ze itschr. d e u tsch . Ing. 1 874, page 3 5.

an effi ciency o f 77 only.


2 96 MECHANICS OF ROISTING‘

MACRINFRY CRAP.

sponding to th e number of its sides'

The w idth’

of th e lattermust evidently be exactly equal to the length of the links.These . dredging machines are of tw o kinds:those havingvertica l and those having incl in ed bucket - chains. The formerare chiefly employed for dredging at building grounds

,the

upper drum i n this case being movable on the fixed pileplanking in the manner of a travelling“ crane. For dredging:in canals

,rivers

,and harbours , on the other hand , th e inclined

chains are mostly u sed. In this case the w hole apparatus isplaced in a hull

,which may easily be moved to any point where

dredging is to be done. Only in small dredging machines usedfor Slight depths is the upper chain - drum revolved by handpower, whereas for h eavy service and great depths steam isalways the motive power. The lower drum is never operateddirectly

,but derives its rotation from th e tmotion of the chain.

The h orse d redge , formerly used in Holland, is rarely employedat the present day

,and the same thing can be said of the

machines used at an earlier period for dredging in large riversand operated by ship

- mil l w h ee ls,the principal objection to the

latter being that the dredging,as a rule , w as desired in places

where the current w as of slight force.Along with the movement of the bucket - chain a simultane

ous advancing o f the whole apparatus is evidently necessary,which movement in steam - dredging machines is also aecom

pl ish e d by steam - power. As it is not always possible,where

excavating is to be done to any greater depth,to accomplish

the desired result by passing over the ground only once,it is

necessary to make the apparatus adjustable vertically withincertain limits. In vertical machin es this is accomplished byincreasing the length of the bucket - chain and frame, while ininclined machines the pitching of the chain to the horizon maybe varied

,whereby the same result is produced.

The bucket is filled simply by being forced against thebottom by the advancing motion of the whole machine, andupon reaching the drum at the summit

,discharges its contents

by overturning,the latter action being occasionally assisted,

when the material is excavated from tough clay bottoms, bylight blows on the bucket. The material is discharged into anin clined chute leading to the transporting - scow or barge. TheSlope of the chute must be greater than what w ould correspond

vri EXCAVATORS AND DREDGES 2 97

to th e natural point of sliding for the e xcavated'

mass. Forsand an inclination of not less than and for clay as muchas 4 5

° to the horizon is chosen. It is thus evident that thematter must be li fted considerably above the actual hoistingh eight

,and the more so the longer the chute, that is, the farther

the receiving vessel is removed from the upper drum. In

some cases, when the inclination of the chute is slight, it isnecessary to facilitate the removal of the masses by addingwater

,which is carried along in the bucket, while ordinarily

the useless lifting of the water is avoided by allowing thelatter to run out through holes in the bottom of the buckets.In the buil ding o f the Suez Canal 1 water w as

.

employed on alarge scale for washing away the excavated material, which w asdischarged into troughs measuring about 70 m . [2 3 0 ft.] inl ength

,and having only a slight inclination. The latter w as

provided at each end with a drum,over which moved slowly

an endless chain,whose links carried transporting plates

,dished

ou t for the reception of the material,which w as further assisted

in its motion by a simultaneous supply of w ater. With thisarrangement an inclination of the troughs of 4 to 5 per centproved sufficient when sand w as removed, and 6 to 8 per centwhen clay was carried. The quantity o f water requiredequall ed about one - hal f of the excavated volume for sand

,and

less for clay.

In order to prevent the mass which is being dischargedfrom the bucket from falling back to the building - ground whenvertical dredging - chains are used, it is necessary to Slide thechute close up to the chain, so that it wil l come in the w ay of

the bu cket for a Short period of time. After the discharge thetrough must b e pulled aside

,so as to allow the bucket to pass

,

and then be pushed back again to the former position. Forsmall machines this operation is performed by a workman

,

whil e in larger machines an automatic contrivance is introducedfor the purpose. Each bucket is then provided with a pro

je cting stud, which at the proper moment engages a lever,which communicates the desired motion to the chute. Whenth e chain is inclined , n o mechanism of th is kind is required

,

Since a fixed chute in this case offers no hindrance to thereturning bucket.

Se e Oppe rmann , Portfeu i l le c’

conomiqu e , 1 869, Pl s. 1 5, 1 6.


AS the principle embodied in these machines can be utilisedfor excavating on land as wel l as for dredging below the waterlevel

,it has more recently been carried out to advantage in so

c alled land dredges, which were in Operation at the constructiono f the Suez Canal, and also at the works carried on for improving the course of the Danube near Vienna. A land machineo f this kind, as first employed by Cou vreu oc at the Suez Canal ,

Fig. 1 61 .

may in the main be designated as a p ortabl e steam cran e , inwhich the hoisting drum is repl aced by the upper drum o f aninclined bucket - chain

,the framework of the latter being at its

;

lower end attached to a tackle suspended from the crane j ib.

A vertical hand dredge,as used in excavating for bridge

piers,is Shown in Fig. The platform B , resting on th e

surrounding piles A,is movable on the stringers a in the

1 Se e Hage n , Wasserbau kunst, vol . iii . part iv.


3 00 MECHANICS or HOISTING MACHINERY CHAP.’

tion of the arrow ,or the lower drum B may, as in (II), be

placed at the end of th e vessel, the material raised being in.

this case precipitated at A into th e ' tw o chutes R and RIalter

n ate l y . Hence it falls either into the scowM orM1 ,the direction

being gov erned by the movable trap—door K. With the latterarrangement no loss o f time occurs, as in arrangement (I)whenan empty scow M is substituted for a loaded one, S ince i n ( 1 1)it is always po ssible to keep an empty scow in waiting on oneside of the vessel, while another is being filled on the otherSide. This circumstance is of great advantage, especially inheavy surf or rough sea, as an exchange of scows is then verydifficult

,and connected with great loss of time. A further

advantage of style (II) is that it can/ be u tilised for procuringthe necessary depth ‘

Of

water required for its

operation . This is owingto th e fact that the lowere nd B of the bucketchain protrudes “beyondthe end o f the hull, acircumstance w hich em

ables the machine to beemployed for excavatinglow shores or projectingnecks of land

,that is, to

act in a measure as a land dredge , which is not possiblewith construction On the other hand

,style No. II

suffers from the disadvantage that the excavated matter heremust be raised to a greater height than is the case in No. I,on account of having to cross half the width of the vessel uponleaving the buckets

,which requires a corresponding inclined

piece to be added to the chutes R and RI. For this reason

more power is absorbed in lifting the material . AS, however, byfar the greater amount of power is in this class of machinesrequired for th e process of excavating and not for lifting, thedisadvantage just mentioned is o f small consequence (see below).The bucket - chain is occasionally placed crosswise at one

end o f the dredge - boat,as w as the arrangement in the earlier

horse dredges at the ports of the Baltic.1 This construction1 Hagen , Hand buch d er Wasserbau kwnst, vol . i ii. part

'

F ig. 1 62 .

3 01V II EXCAVATORS AND DREDGES

may under some conditions be recommended foru se in dredging for bridgepiers1

Finally,steam d re dg

ing machines w ith twob ucket - ch ains 1 have beenc onstructed , h aving thelatter placed lengthwiseat each side of the vessel,and intended to fill twoscows at the same time.This arrangement has notproved very satisfactory ,however, the resultsObtained from a doubledredge never equal lingthose derived from twosingle dredges o f the sameproportions. The reasonmay be traced to thefrequent interruptions inthe working o f the machinedue to the fact that th etwo receiving scows arenever fu ll at exactly thesame time ; it is therefore necessary to stop thewhole machine at frequentintervals for the sake o f

replacing one of the scows.Double dredges are on thisaccount passing out o f

use.In Fig. 1 63 a Sketch

1 For draw ings of a d ou b l e

d re dge as u sed on th e Clyd e se e

Procee d ings of th e British Institu

tion of Ci vi l Engineers, 1 864, and

Riih lmann’s A l lgem. Masch inen

l ehre, vo l . iv.


taken from Hagen’

s work is shown, representing the steamdredging machine Greif”used on the River Oder. Thechain frame L,

consisting of tw o strong iron girders”con

ne cte d by braces, is hinged on the u pper drum - shaft at A .

By the tackle F, which is attached by means of a chain tothe lower end o f the frame w o rk

,th e latter may be given a

greater or less inclination according to the depth required.

The lower ends o f the girders carry the bearings for th e lowerdrum B

,the former being so contrived that the chain may be

given any degree of tension by means o f an adjusting screw.

The upper half of the chain which carries th e loadedbuckets is supported by a number o f rollers w introducedbetween the girders, while the lower , slack half of the chainhangs freely in an arc. The tightening of the chain is done inorder to prevent the slack portion from dragging on the bottomb1before the working bucket reaches the point of excavation

at b2. Care must be taken

,however

,not to make the verse

sin e of the lower chain so small that undue strain is broughton the links by the influence o f the w eight of the buckets andchain. 1

The motion of the chain - drum A is derived from the gearsC attached to its Shaft

,and driven by additional gearing from

the vertical steam - engine D provided with two cylinders. Theconnection between the steam - engine and the u pper drum ismade in such a manner as to yield when the power transmittedexceeds a certain limit. For this purpose either a frictioncoupling is introduced, or the gears C are secured to the Shafta by means o f wooden keys

,the dimensions being so chosen

that for a given maximum strain the keys are Shorn o ff,whereby

the motion o f the drum is discontinued,although the gears

continue to revolve. This feature is necessary in order toprevent break - downs

,which w ould inevitably result at times

were the connection made rigid. If,for instance

,a bucket

should strike a large boulder or a piece of driftwood too longto pass crosswise into the opening of the hull

,etc.

,the e xc ep

tional ly great resistance offered to th e momentum o f the rotatingmasses would of necessity cause a breakage at some point.From the figure it is evident how; by turning the trap - door

from the position K1to K

2and vice versa, it is possible to

conduct the discharging material to one side or the other. The


.3 04 MECHANICS OF HOISTING MACHINERY CRAP.

upon the winches T are reversed and made to move the vesselback in the direction of the arrow B, a new furrow concentricto the preceding one being now excavated. When the chain lohas been redu ced in length to about 1 50 or 2 00 metres (yards),the main anchor A is removed to a point farther up the rive r.This modern method o f transverse or rad ia l dredging offers

many advantages over l ongitud ina l dredging, one of these beingthat the loss of time incident with the latter method

,when the

vessel is returned to start a new furrow,does not occur in the

empl oymen t o f the former method. Besides, the one - Sidedresistance during the longitudinal dredging w as very apt tocause the bucket to return into an already excavated furrow

,

and if an attempt w as made to overcome this difficul ty byapplying a Sidewise pressure to the vessel

,the furrows w ere

liable to become separated by remaining ridges of ground.

The inclination o f the bucket- ladder to the horizon rangesfrom 45

°

for great depths to 1 5° when the buckets are notintended to operate, as during transportation o f the machine.The length of the ladder therefore depends entirely on the ‘

depth at which dredging is to be done,and amounts in themachine Shown in Fig. 1 64 to 1 8 4 m. ft.] In thiscase the upper drum

,which is generally made four- sided

,makes

from 5 to 8 revolutions per mi nute,according to the quality

Of the bottom,thus allowing in this time 2 0 to 3 0 chain

links to pass, or half thi s number of buckets,if the latter are

attached to every other pair o f links. The velocity o f thebucket - chain may, on an average, be taken at m . [ 1 ft.]per second

,and the side motion of the vessel for each advancing

bucket may be assumed to be to m. [4 to 51

ins.]The latter velocity largely depends on the nature of the bottom,

however,as w ell as on the depth of cut to be taken . For hard

clay bottoms the depth o f cut is about m . whiledredging in loose sand is often done with a cut of 2 m. [6 ft.]in depth, and more.

The size of bucket required naturally depends on the workto be done by the machine in a given time and for a certainvelocity of the chain. It may be assumed that the bucketsare never filled to more than or g of their cubic contents .As regards

'

th e power required for a dredging machine, a caloulation for determining it, based on the w ork to be performed

V II EXCAVATORS AND DREDGES 3 05

during the lifting process , would not give a sufficiently largeresult

,even though all wasteful resistances in chains

,rollers

,

gears , etc.,which here are very considerable

,were to be taken

into account. The greater portion o f the power is insteadabsorbed in the work o f detaching the material

,and it is

e vident that this amount may easily be estimated from empiricalresults.According to Hagen ,

the best steam dredging machines rarely

give a performance exceeding cub. m. [58 2 cub. yds ]perhorse - power per h our. Assuming a dredging depth of 6 m .

ft.]below,and an additional lift o f 5 m . [ 1 6 4 ft.]above

the waterlevel,the specific gravity o f the raised material being

2,we can calculate the work per second corresponding to th e

hoisting operation,taking also into consideration the reduction

o f w eight below the surface , to be

60 x 60

02 64 horse - powe r.

Hence w e conclude that more than 73 per cent of the totalpower absorbed are required for detaching the material ando vercoming wastefu l resistances. It may be noted

,however

,

that according to other authorities the performance of steamd redging machines falls considerably short of that cited above .For further information on this subject we refer to Rii h lmann

’

s

A l lgemein e Masch in en l ehre,vol. iv.

According to Hagen ,4; o f the total driving - power are required

for the actual lifting, 1 for overcoming wasteful resistances, andth e remainder for excavating the material , when the latterc onsists o f sand . At any rate

,it is evident from these figures

that an increase in the lift above the surface, with a view toattaining a quicker and surer precipitation of the excavatedmatter into the scow

,will but slightly influence the efficiency

o f the apparatus. It is therefore always advisable to provideample lift, more especially as the expense connected with th eO peration of the dredging machine is generally greatly exceeded‘

by that incurred for removal of the excavated matter.In conclusion , a land dredge , as employed by 00u vreu oc

1 in

th e building o f the Suez Canal, is shown in Fig. 1 65. Here1 Se e Oppermann ,

Portef . e'

conomiqu e d . Mach . 1865, and Riih lmann, Al lgem.

Masch inen l ehre , vol . iv.

3 06 MECHANICS OF HOISTING MACHINERY CHAP. V II

a frame attached to a car W carries the u pper chain - drumwith its shaft A

,around which the ladder AB is movabl e

,the

lower end o f the latter being suspended from the crane jib CDby means o f the tackle F. As in a portable crane, a verticaltubular boiler K and a steam - engine E are placed on the carW for the purpose of operating the chain prism by the aid o f

Fig. 1 65 .

suitable gearing. The buckets ou t the material from the slopeG

,and discharge it through the chute B into the transporting

car T. From the figure it is evident how the whole apparatusmay be moved along the track S, and al so how the pitch of

the bucket - ladder may be varied by means of the tackle. Thedaily performance of a machine of this kind driven by a 2 0horse - power engine is claimed to be 1 000 cub. m. [ 1 3 08 cub.

yds ] in 1 0 hours.



from splitting. The ram is either raised directly by hand,or

by means of a rope passing over a pu lley. In the former caseit is known as the simple rammer, in the latter as the ringingp i l e

- engine . In the ringing engine the hauling part of the ropebranches out in to a number of ropes held by men

,w h o pull

together Whenever the ram is to be l ifted. In the so - calledmonkey engin e the ram is lifted by suitable mechanisms, as, forinstance

,toothed gearing, etc.

The rammer i s but an imperfect contrivance for drivingpiles. It consists of a block AB

,Fig. 1 67, of oak, provided

with four long handles,by which four workmen

”A grasp and lift it. Such a ram should not weigh

more than 60 kg. [ 1 3 2 since 1 5 kg. [ 3 3 lbs .]is all that should b e al l otte d to each man. Theyare therefore only adapted for driving small piles.

In the ringing engin e,Fig. 1 68, the ram R is

provided with arms, which embrace the uprighttimbers, and serve to guide it w hen rising and

Fig. 1 67. falling. The framework ABC rests upon a portable base ADE,

which may be provided with planking for the workmen to stand upon. A pulley H at the topof the upright serves to carry the“rope REK from th e ramto the platform . The winch LM is used to place the pile inposition .

Fig. 1 69 shows a very simple and efficient pile - engineu sed in Holl and. The frame is composed of three timbersAD

, BD ,and CD

,secured at the top by a bolt

,its feet are

fitted with iron pins,resting on tw o planks

,as shown i n the

figure. The ram Q is provided with eight lugs, which embrace the light uprights EF, whose iron feet are either set intothe ground or into planks . The frame is made steadier by aguy DC , which passes

‘

from the apex of° the frame to a post

G driven into the ground. The employment of muscularforce to work a ringing pile - engine is a very unsatisfactorymode of driving, as after only a short period of such severeexertion the w orkmen are obliged to take an equal intervalo f rest.

The efficiency of the pile - driver increases with the weighto f th e ram,

and the height to which it is raised,and therefore,

since a large number of men cannot work to advantage at the

vm FILE - DRIVERS 3 09

same time, and the greatest height to which a ram can beraised is only 1 metres [5 it follows that the ringi ngengine is a very imperfect means o f performing the work o f

pile - driving. These i 11 1pe rfe ction s are , in a great measure,

Fig. 1 68.

avoided in the monkey - engine,as here the workmen can be

employed to better advantage in th e work o f turning cranks,and it is also possible to in crease the weight and fall of theram at wil l by interposing suitable gearing. Consequently,


thi s type of pile - driver is decidedly to be preferred to theringing pile - engine.The arrangement of a simple monkey- engine is seen from1 70. By means of two winch handles , motion is com

Fig. 1 69.

mu n icate d to theshaft B

,and in

turn impartedthrough E and Fto the barrel G.

Let us supposethe ram Q tohave been liftedto a certainheight the crankB is then shiftede ndwise bymeans of thelever CDE

,the

toothed wheel Ebeing therebythrown out o f

gear w ith thewheel F, so thatthe ram Q canfreely fall uponthe pile P. A

d isadvantage o f

this contrivanceis that the rope

which sustains the ram rapidly unwinds from the barrelduring the fall

,and consequently the arrangement is not

only liable to get out o f order,but the moving parts are

besides subjected to great wear. The effect of the blowis also considerably diminished by the frictional resistances o fthe rapidly - revolving barrel. For this reason it is preferableto attach the rope to the ram by means of a hook, which isautomatically detached

,and allows the ram alone to fall

after it has reached a certain h eight. The use of a pair ofnippers

,as

- shown in Fig. 1 71 , is very expedient. Theram Q is held by a staple in a pair of tongs HOK, which are



head of the pile. At this moment the lever CDE throws thetoothed wheels out o f gear

,freeing the block F

,which fall s

,

and as it strikes the ram, causes th e jaws to open and engagethe staple .With the monkey - engine here described

,three to six men

are capable of lifting rams weighing from 3 00 to 800 kg.

[660 to 1 760 lbs.] to a height ranging from 5 to 1 0 metres

[ 1 6 to 3 3 ft.]Monkey engines were formerly driven by tread - wheel s

,

whi ns,or water wheels, but at the present day are more

generally worked by steam - power. In theclassification o f steam - pile drivers w e mustdistinguish those that are d irect- acting,

th e ram being lifted by the piston - rod asin the steam hammer

,from th ose which

are ordinary monkey p i l e - d rivers operatedby steam - engines.

4 2 . Dire ct acting Ste am PileDrivers.

— This type of engine,first con

structed by Nasmyth ,has demonstrated

its usefulness and efficiency in heavyservice. It is distinguished from themonkey - engine chiefly by the feature thata ram of great weight is lifted to a smallheight

,and that ‘ the blows are allowed

to follow each other in quick succession.

Since the energy of the blow dependsupon the product Q h of the weight

Q of the ram and the height h from which it falls,

it follows that no loss o f energy is incurred by diminishing kif Q is increased in the same ratio. The arrangement

,on the

contrary,offers the decided advantage that it admits o f making

the engine direct - acting,that is

,so as to have the ram lifted

directly by the piston - rod,an impracticable construction in

monkey - engines,owing to the great height to which the rams

must be hoisted. The chief benefit derived from the directacting pile - driver is due to its rapid action , experience havingproved that the piles enter more readily when the blowsfol low each other in quick succession. The hammer sometimes weighs as much as 50 cwt and makes from 70 to 80

Fig. 171 .

FILE- DRIVERS 3 1 3

blows per minute,with a fall of one metre [3 -i ft.] In the

monkey- engine,on the other h and

,where only a small num

ber o f men can work atthe same time

,the operation

is very slow,such machines

,

in fact,giving no more than

1 0 to 40 blows per hour.The platform A of

I

asmgth’

s direct actingengine, Fig. 1 72 ,

ismounted on four w heels

,

and arranged to travelalong a railway. Thevertical guide - post C isbolted to the platform A,

and is further stiffened bya stay E and a gu y D .

The driving apparatusT

,consisting o f the hammer

and steam cylinder, issuspended from a chainK

,which passes over the

pulley R to the barrel of

a Windlass W. The lowerpart o f T is provided w itha conical enl argement resting on the head o f the pileP ; by turning the winchW

,the driving apparatus

is enabled to follow thepile in its downward course. A second winch W

1 ,with chain

K1 ,is employed to lift the pile in place ; both windlasses are

operated by a small steam - engine M,which also serves to

move the pile - driver along the railway when a new pileis to be driven. A jointed pipe Q supplies the steam tothe cylinder of the driving apparatus, and follows the latterduring its downward movement.The driving apparatus, illustrated in Fig. 1 73 , I and II,

consists o f the steam‘

cylinder A and the wrought - iron pilecase D

,which serves as a guide for th e hammer Q, weighing

Fig. 1 72 .

.3 1 4 MECHANICS OF HOISTING MACHINERY CHAP.

about 50 cwt. , and hung from the end of the piston - rod C.

At F steam enters through the jointed pipe above mentioned

Fig. 1 73 .

to the valve - chamber,in which a slide - valve S effects the

distribution o f the steam. As it is only proposed to l ift thepiston by the pressure o f th e steam

,the cylinder is made

single - acting. In position I the steam is admitted from thevalve - chamber to the space below the piston B

,thus raising


3 1 6 MECHANICS OF HOISTING MACHINERY CRAP. vn r

.up- stroke, so that the steam acts on b oth“sid e s of the piston

during the fall of the hammer. Since the upper surface is2 2

expressed by F7

21

3 and the lower by f = 7r

D — d2

wh ere

D and d represent the diameters o f the cylinder”and piston

rod , it follows that the excess of pressure 0 11 the upper surfaceabove that on the lower surface adds its force to the weight o fth e fall ing hammer

,and allows the blow s to fo llow each other

i ncre rapidly. Moreover,steam is economised

,for during the

above - mentioned process the steam which was suppl ied below2

the piston works expansivelyin the ratio o fJ?

D2

1

? d 2 whenever communication is o

'

pened with the upper portion of thecylinder. This is th e prin c ipl e adopted in Schw artzkopf s steampile - drive r.

l

Another construction depends upon the principle o f th e

Cond i e’ steam hammer. Here the steam cyl ind er is the hammer

,

be ing guided by the stationary piston - rod suspended fromabove. The rod is made hol low, and conducts the steam tothe upper portion o f the cylinder through holes in the piston ;when the cylinder has been lifted to a certain height an opening in the hollow rod forms an outlet for the steam. At thisinstant th e cylinder falls, and the air, which w as previouslycompressed in the bottom of it

,expands

,and increases the

force of the blow. Owing to this pneumatic action the guideframe for the cylinder

,from which the piston - rod is suspended,

must be firmly secu red to the head of the pile. This is th earrangement o f the steam pile - driver which Riggenbach employedin bui lding the railway stations at Biel .2

A somewhat different construction, in which , by dispensingwith the air - cushion

,the necessity of securing the guides to

the head o f the pile is obviated,w as designed by Lew /l ake 3 for

the improvement o f the Diina near Riga. The details o f thismachine are here given. Fig. 1 74 illustrates the drivingapparatus

,the essential part o f wh ich is the heavy hammer or

steam cylinder A,which slides on the hollow piston - rod

,

B

1 Ze itschr. d . Ver. d eu tsch . Ing. 1 860, page 2 2 4 ; Mitthe i lnngen d . B annov.

Gew erbe - Verez’

ns,1 863 , page 2 43 .

2 Pol ytech . Centra l b l atl,1 865, page 2 1 9.

3 Se e Civi l - Ingen i eu r, vo l . xxi. part i.


suspended from the cross - piece C. The frame for guiding thecylinder consists of the two cross - pieces C and D boltedtogether by two wrought - iron rods E. This frame is guidedby the two uprights F belonging to the usual form o f piledriver, and, before the pile - driving begins

,is lowered by a

Windlass,until the lower cross - piece D rests upon the head of

the pile P. By means of a jointed pipe a communicating witha tubular boiler, steam first enters the valve - chamber Cr

,and

from here is admitted through the hollow piston - rod B andholes 6 to the annular space above the piston. In consequence

,

the cylinder is lifted,inasmuch as the air below the piston is

driven out through the openings e . If now in the highestposition o f the cylinder the steam is allowed to escape into theatmosphere through 6 and the piston - rod

,the cylinder falls and

drives in the pile P, the driving apparatus following its downward movement.The peculiar action o f the valve - gear is shown in Fig. 1 75

,

I and II. The steam enters,as above mentioned

,through the

pipe a into the valve - chamber Cr,in which a double piston - valve

Hl works. The lower surface o f H1is always acted upon

by the steam - pressure in a,while the upper surface o f the

somewhat larger piston H2is not influenced by th e steam in

a,unless the small piston - valve J in position II allows the

steam to enter through 752

. Suppose,on the other hand

,the

valve J to have the position I,the space above H

2is then

in communication with the atmosphere through the Opening 731.

From this it is evident that the valve H in position I is liftedby the steam acting on H

1 ,so that now the steam from the

boilers enters at a through the annular passage bland the

piston - rod B to the cylinder,thus lifting the hammer. If

,

when the latter is in its highest position,the valve J is brought

into position II, the valve H will be depressed, owing to theexcess o f pressure o n the larger area H

2. No steam will then

enter from a to B along th e above -mentioned route,whereas

that in the cylinder can escape into the atmosphere throughB

,b l , and 62 , thus liberating the hammer. To obtain an u n inte r

rupte d action o f the hammer an automatic device for movingthe valve J must be employed

,so arranged that when the

hammer is at the bottom of its stroke the valve must occupyposition I, and w hen the former is at the t0p of its stroke th e



ButWith rapid firing the cap b ecomes so h ot as to ignitethe cartridge before the descent of the hammer. For thisreason the hammer is held at its highest point by the abovementioned trigger until the release o f the latter allows thehammer again to fall . A piston at the top o f the uprightsente rs a cavity in the hammer during its upward motion

,and

acts as a buffer. These pile - drivers,which were exhibited at

the Centennial Exh ibition at Philadelphia,1 876, are extensively

used in the United States. Besides their simplicity andcapacity, it is further stated of these pile - drivers that theh eads o f the piles are not injured b y the blows, and need noprotection against splitting.

According to Kn ight,1 the weight o f the cartridge is only

one - third of an ounce (95 g.) for a hammer weighing 675 lbs .( 3 08 kg.) It is stated in a report made to the FranklinInstitute by Prind l e that experiments were made in drivingpiles with the cartridge and withou t it, the fall being thesame ( 1 5 ft.) in both cases, and the penetration of the pilerecorded . Results showed th at when a cartridge w as employedth e penetration of the pile w as always considerably greater

,

sometimes four, and even eight times as great as w hen thehammer worked

,as in the ordinary monkey - engine without the

cartridge.§ 4 3 . Pil e - Drivers With Ste am- Engine s.

— The frequentinterruptions to w hich direct acting steam pile - drivers aresubject when at work are probably th e principal reason w hyo f late there has been a return to monkey—engines driven bysteam

,i .e . ,drivers in which the hammer or monkey is raised

to a great height by hoisting apparatus. In certain cases, e spe c i

ally for very heavy piles,this form of driver is indispensable

,

because then very powerful blows are needed,which cannot

be obtained by the direct - acting steam pile - drivers,on account

of their short strokes . The stroke of the hammer in thesedrivers must always be small

,for constructive reasons

,and

seldom exceeds 1 metre [3 2 8 ft.] On the other hand,the

stroke or fall in the monkey - engine is limited only by theheight and strength of the frame. Of course

,th e blows o f

the monkey - engine are delivered much less rapidly than thoseof the steam - drivers

,which can deliver u p to 1 2 0 blows per

1 Ameri can Mechan ica l D icti onary , p . 1 041 .

V 1 1 1 PILE- DRIVERS 3 2 1

minute . Under certain circumstances,depending upon the

nature of the ground,the rapid succession o f blows o f the

steam pile - driver is very advantageous,and experience has

shown that fo r driving small piles this rapid delivery isbetter suited than themonkey - engine. On

the other hand,for long

and heavy piles,the

powerful blows of themonkey engine arebetter.Another reason why

pile - drivers driven bysteam - engines are b ecoming more popular isthat their arrangementis simple

,the hammer

being l ifted by a h oistthat is worked by anengine

,say a .portable

one,perhaps already

in use for other purposes. For transferringthe motion from engineto hoist

,belts or chains

are usedSuch an arrange

ment is employed inSchw artzlcopf

’

s piledriver

,Fig. 1 76. Here

a Ol issol d chain K (seevol. iii. 1 , g 65, W e isb .

Mech .) transmits themotion from a portableengine M to a hoistW

,which raises the hammer by means of the rope t. This

h oist is composed o f tw o drums B and C,turning loosely

on the shaft A ; one drum B serves to lift the hammer, andthe other C to place the pile in position for driving. Thedrums are turned by means o f two friction - couplings

,whi ch

Fifi . 1 76.O


Fig. 177.

receive their motion from a d riving- pulley D fastened to the shaftA,

and'

re c e iving continuous rotation from the portable engine bymeans o f a chain with wedgeshaped links . By shifting thedriving - pulley D and its shaft inone or the other direction bymeans o f the screw S and handwheel R

,su fficie nt friction arises

at the conical surface of contactbetween D and the drum to windup the rope that carries the load.

When the hammer h as been raisedto the desired height, a slightreversing o f the hand - wheel Rwill remove the friction betweenD and B

,and the hammer will

at once fall,causing the drum B

to turn backward. As statedabove

,this action always weaken s

the force o f the blow to someextent.To avoid the last - mentioned

defect and render the pile - driverautomatic

,an endless l ink - chain

is sometimes employed. Thischain is constantly moving u p

ward between the guides,one o f

the chain - bolts taking hold o f aclaw on the hammer when thelatter is in its lowest position,and then lifting it till the selfacting disengaging device releasesthe claw and allows the hammer to fall. During the fall thechain is continually moving, andafter the blow has been deliveredit again li fts the hammer. Thispile - driver w as applied by Sisson



( twenty - five to forty) simultaneously pulling on the main rope,the individual hauling lines make a considerable angle a withthe vertical di rection, thus util ising only the component P cos aof the pul ling force P of a labourer. The latter disadvantagecan

,in a large measure

,be overcome by attaching a horizontal

ring to the main rope,and conne cting with it the hauling

lines,which will then hang verticall y.

The hurtful resistances in the ringing engine are comparative l y smaller than in the monkey - engine. In the formerthe resistances are principally due to the stiffness o f the mainrope and the journal friction o f the pulley over which therope passes. Moreover

,when the rope acts on the hammer

to one side o f the centre o f gravity,friction is d eveloped in

the guides,the lifting is rendered more difficult, and the efle ct

of the blow is diminished. As th e diameter of the main ropeof the pile - driver is not usually more than 50 millimetres

( 2 ins ), these resistances may, ac cording to 7, be taken asat least equal to 5 per cent o f the effective work.

In the monkey - engine we must first deduct the resistances .

of the hoist or Windlass. As the Windlass works with achain

,and usually employs a single purchase

,about 1 5 to 1 6

per cent must be deducted for these resistance s . But besidesthe ram o f weight G

,the nipper block with a ppendages must

be lifted,the weight o f which may be assumed at about 8 to

1 0 per cent of that of the ram ; as this, how ever, addsnothing to th e weight of the fall

,no essential error will

occur in taking the efficiency of the monkey - engine between75 and 80.

According to the observations o f Ko'

pke in building s theCustom - house at Harburg

,the average work performed by a

labourer in ten workin g hours per day w as, with the ringingengine

,

ft. l b s. me tre kilograms ;

and with the monkey—engine,

ft.

’

l b s. me tre kilograms.

Lahmeyer gives the network, after deducting the wasteful:

resistances,at

ft. l b s. me tre kilograms

V III FILE - DRIVERS

for the ringingengine,and

ft. l b s. me tre kilograms

for the monkey - engine ; so that the work obtained from thelatter may be assumed to be from tw o to two and a hal f timesas much as from the former.

In the direct - acting steam pile - driver the pressure o f thesteam upon the piston

,after deducting the friction of the latter,

and in the stu ffing- box must exceed the weight of the hammerin order to

i

ove rcome the friction in the uprights, and impartto the hammer the acceleration necessary to give th e desirednumber of blows per minute. Owing to this acceleration, thehammer

,at the instant at which the steam escapes into the

atmosphere"

,has attained a certain velocity v. The energy thus

stored in the hammer is expended in lifting it to an additionalheight before falling. In o rder to determine th e formulasapplicable to this case

,let F denote the area o f the piston o f a

Nasmyth machine, G the weight o f the hammer, including th episton and its rod

,and h the length of stroke. Further let p

represent the effective pressure per unit o f area of the steam inthe cylinder, and 170 the atmospheric pressure, and let us reduceall the hurtful resistances, consisting o f th e friction of thepiston

,the stu ffing

- box,and the ram in the uprights

,to an

equi valent pressure f per square inch, acting on the piston .

Let us conce ive the piston to have passed upward a distance31 ,then the effective energy exerted by the steam on the

piston will beA F0? 5

this is expended in lifting the ram to a height Srin overcoming

the wasteful resistances through the same path 31,and in

accelerating the hammer of weight Cr. Supposing the hammerto have attained the velocity v,we deduce the equation

F (p —p0

— f)s1 G 31: G

from which we obtain the velocity 1) of the ram at the momentat which the steam escapes from the cylinder:


(g = 9 8087 in metres and 3 2 1 87 .ih feet).By virtue o f this velocity v the hammer is able to lift itself

to an additional height 32,wh ich follows from

7,a

to

sG o

2

2“

G + Ff 2 g

If in this formul a we substitute the value given in ( 1 )we obtain

F(p —no

— f)— G

G + Ffsl— les

1

F(r —

ro— f> G

G + Ff

Therefore the total lift o f the hammer will be

G + Ff + F(p —p 0

— f)G + Ff G + bf

s

where

h = sl+ s

2

If now for a given lift h the hammer is to make n strokesper minute

,so that the time occupied by each up and down

60stroke is given by t

n

seconds,w e can determine the rela

tions in the following manner. The whole period t for eachdouble stroke is composed o f four intervals of time, 151 15

2+ t

3

+ 154,where t

]represents the time during which the piston is

driven by the steam,and rises through the distance 3

1 >and 152

is the time required by the hammer to lift itself to the height32by virtue of its living force ; t3 is the time required for the

fall,and 15

4an interval needed for the blow to exert its effect.

The latter interval must be assumed according to circumstances ,but the val ues and t

3can be calculated . The constant

pressure F(p —p 0) exerted during the time tl gives a uniformly

accelerating motion to the piston,the acceleration being ex

pressed byFf}? "PO ‘ f l G


3 2 8 MECHANICS or HOISTING MACHINERY can ».

We‘

may also follow th e method given by,L ew iclei l in the

article already referred to . Al though the application of steamto the direct - acting m achine is not very economical on accounto f th e absence o f expansion, still th is is generally o f littleimportance when compared with the greater expense attendingthe hand - power pile - driver. Moreover

,as all interruptions in

the w ork are attended with drawbacks , it is best in pile - drivers,

and in all machines employed for building purposes,to ‘lay

more stress upon the simplicity of the construction than uponthe efficiency of the machine.

In the preceding remarks attention - has on l y b e e n given to‘

the amount o f en ergy required for lifting the ram,and the

corresponding efficiency, o f course, applies only so far as thepile - driver is considered a h oisting ma

’

ch in e . The action of thefalling ram upon the pile, the forcing of the latter into theground

,and the compre ssIon of the ground

,are effects which

can be ascertained only by practical experience. We musttherefore refer to technical journals for information upon thesesubj ects .We will note here

,however, a fact concerning the compara

tive action of the d ifferent types of pile - drivers and theinfluence of the height o f stroke or fall. When th e ram of

weight G1fall s from a height h ,

th ismotion repre se nts me ch an ical

work to the amount of A : Clh , w hich, leaving frictional

resistances out of account, will produce a velocity 73 J 2ghin th e hammer at th e moment of impact. Now let G

2denote

the weight of th e pile ; then, if the bodies be consideredinelastic

,the amount o f energy which disappears after the blow

is determined from 3 3 5,vol . i.

,W e isb . Mech . ,

and is given by

GIG2

G

G1+ G

2

h AG1+ C

,

’

while the remaining actual energy imparted to the pile is

Al

A =A AG2

,

the latter being utilised in driving ; that is, in giving motion

to the pile . Th e lost energy A’ is essentially employed indoing molecul ar w ork, for example, In 1nju r1ng th e pile, which

‘

1 Civi l - Ingen ieu r, vo l . xxi. part i .

v III FILE - DRIVERS 3 2 9

represents work foreign to the purposes o f the machine, and w e

must therefore seek to make this loss as small as possible. It

is obvious that this value

G2

1AGI+ G

2G1+ 1

2

expresses a smaller fractional part o f A,the greater the ratio of

the weight of the ram to the weight o f the pile. Were w e to

assume G1

G2 ,the loss w ould become A’

-%A, while inordinary cases where a value from G

12 G

2to 2 —G

2is chosen,

the value of A’ varies from O'

S3 A to 0 2 68 A. If now acertain amount of work A has to be expended in lifting thehammer G

1to the height h

,it follows that the l oss du e to

imp actw i l l be a larger fraction of th is w ork,th e greater th e l ift

h ,i .e . th e smal l er G

1 ,and consequently

,for the same e xpe ndi

ture of work A, the percentage of loss due to impact in themonkey pile - driver is greater than in the steam pile - driver

,

w here the lift h is smaller, and accordingly the weight G 1

greater. This result agrees with the fact observed in practicethat considerable injury is done to the piles when monkeypile - drivers are used.

Now,although the impact of the hammer on the pile is not

perfectly inelastic,and consequently the amount A’ is not

wholly lost,yet the loss due to impact will be greater the

smaller the ratio of G1to G

2.

Concerning the load which a driven pile will sustain, w e

must refer to W e isb . Mech .,vol . i . 3 71 , Ger. cd .,

for moreexplicit information. For practical purposes it is advisable

,

however,to base such estimates upon empirical results rather

than upon theoretical deductions. (See Hagen , Hand bu ch d er

Wasserbau ku nst, vol. 1. page


3 3 2 MECHANICS OF HOISTING MACHINERY

Hydrau l ic crane s, 2 55

h o ists,1 1 4

jacks,1 1 6

lifts,1 3 2

regu l ator, 2 2 4

INCLINED l ifts,1 05

, 1 09

plane s,1 67

JACKS, 7, 1 8

Jack scre w s,2 5

KOPKE’

S experime nts,3 2 4

Krau ss and Kl ey’

s safety catch,2 17

LARMEYRR’

S experime nts, 3 2 4Land d redges, 2 98Le ver

,6

jacks, 7Le w ick i

’

s ste am pil e - d river, 3 1 6

Life - saving apparatu s, 1 60Lifts

,1 02

Loc omotive l ift,1 2 2

Lohmann’

s safety catch,

. 2 1 7'

Longitu d inal dre dging, 3 04Long

’

s h o ist,92

Lo w e ring crane,2 62

MAN - ENGINES, 2 1 9Masting sh e e rs

,2 52

Min e h o ists,1 69

w in ch,1 70, 173

Monk e y pil e - d river,3 1 0

Movab le pu ll eys, 42

NASMY'I‘R

’

S pil e - d river,3 1 2

Ne ustadt’

s crane,99

Nippe rs,3 1 2

OTHER forms of h o ists, 89o f tack l e

,67

FILE - DRIVERS, 3 07w ith steam - engin e s, 3 2 0

Pl unge r friction ,1 49

Pneumatic h o ists, 1 53

Portab l e crane s,2 64

h oisting e ngine s, 1 93

ste am cran e , 2 69, 2 70

Pow er crane s,2 78

Pre ssu re re se rvo irs, 1 2 0

Prind l e’

s experiments,3 20

Pu l l eys, 3 8

TACKLE, 46Transve rse dre dging, 3 02Trave l ling cran e s

,2 73

Turb in e h o ist, 1 84

V ERTICAL drums, 1 74h o isting engin e s, 1 95

RACK and pin ion jacks,1 8

Rad ial dre dging, 3 02

Rail road crane,2 3 4

,2 79

Ram,3 07

Rammer,3 08

Ramsb ottom’

s crane s, 2 80

Re l ie f- val ve s, 1 3 7, 2 58

Re versing w h e e l , 1 81

Riggen b ach’

s ste am pil e - drive r,3 1 6

Ringing pil e - engine , 3 08

B ittou

r’

s h ydrau lic cran e, 2 62

Roll er- b e aring for cran e- post, 2 3 1

ROtai '

y crane s,2 3 0

SAFETY apparatu s,2 1 1

b rak e s,2 1 2 , 2 1 8

catch e s, 2 1 2'

Saxon h orse -

gin , 1 77Schw artzk opf’s pil e - drivers

,3 1 6, 3 2 1

Scoop d redge , 2 86Scre w - jack

,2 5

Shaw ’

s pile - driver, 3 1 9

Sh e ers,2 48

Sisson and Wh ite ’s pile - d river, 3 2 2

Sparre ’s safety catch , 2 17Spiral d rums, 1 99, 2 06Stab ility o f portab l e c

'

rane s,2 67

Stau ffe r’

s Win d lass,1 01

Steam h o ists, 88

h o isting e ngine s, 1 91

Sw e d ish l eve r-jack , 8

WAREHOUSE cran e,2 3 5

l ifts,1 3 4

Water- pow er h o ists, 1 80pre ssu re h o ists

,1 88

We igh ing crane,2 3 6

We ston b l o cks,59

Wh ite and Grant’s safety catch , 2 1 4

Wh ite ’s tack l e , 55Wind l asses, 1 2 , 74Work of pil e - drive rs, 3 2 3

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