Gear Speed Reducer

NEW ERA UNIVERSITY

COLLEGE OF ENGINEERING AND TECHNOLOGY

MECHANICAL ENGINEERING DEPARTMENT

ME 484

MACHINE DESIGN II

GEAR REDUCER DESIGN

Submitted by:

Vallejos, Dario Jr. C.

IV-BSME

Submitted to:

Engr. Nelio S. Gesmundo, Jr

Course Instructor

ACKNOWLEDGMENT

This work, though amateur at best, would not have been possible without the help of the

people within my immediate surroundings, that is, my family, professors, friends, and

acquaintances. Of special mention are the following individuals/persons:

My parents, without whose support this endeavor would surely fall apart in terms of

logistics and moral support,

My professors and instructors, without whom the knowledge and information taxed by this

task would not have been met,

My classmates/colleagues, without whom the ideas developed here would not have an

environment to thrive, improve, and grow,

My paramour, who kept me going, without whom this project would not have been rebuilt

each time it fell apart,

And to God, without whom all of these are otherwise physically void, intellectually

impossible, and mentally hopeless.

TABLE OF CONTENTS

I. DESIGN PROBLEM AND DESIGN SPECIFICATIONS

A. DESIGN PROBLEM

B. DESIGN SPECIFICATIONS

1. GEAR PAIR

2. SHAFTING

3. RIMS AND ARMS

4. GEAR HOUSING

II. DESIGN SKETCH/ILLUSTRATION

III. COMPUTATIONS

A. GEAR PAIR

1. PRELIMINARY GEAR DIMENSIONS, CONTACT RATIO, AND INTERFERENCE

2. TORQUE AND FORCES

3. BENDING STRENGTH

4. PITTING STRENGTH

5. MATERIAL SELECTION

B. SHAFTING

1. SHAFT

2. GEAR HUB

3. BEARING SELECTION

4. TOLERANCES AND FITS

5. KEYS AND COUPLINGS

C. RIMS AND ARMS

1. INITIAL DIMENSIONS

2. ARM GEOMETRY

D. HOUSING

1. INITIAL ILLUSTRATION

2. GEARBOX DIMENSIONS

IV. RECOMMENDATIONS

V. APPENDIX

I. DESIGN PROBLEM AND DESIGN SPECIFICATIONS

A. DESIGN PROBLEM

A gear-reduction unit is to be designed according to the data in the table and the

following specifications. The velocity ratio may be varied by an amount necessary to have

whole tooth numbers. The given center distance is the permissible maximum (but this

does not preclude asking the engineer in charge if a slightly larger one can be tolerated, in

case it looks impossible to satisfy this condition. The teeth are to be 20ᵒ F.D. with Np≥ 18

teeth, with 17 as the minimum acceptable. The service is continuous, with indefinite life.

Use Bucking ham’s dynamic load for average gears.

(a) Decide upon the material with its treatment, pitch, and face with. Start out being

orderly with your calculations so that you do not need to copy all of them for your report.

The report should show calculations for the final decisions first, but all significant

calculation should be in the appendix. These latter calculations should show: that a cheap

material (as cat iron) cannot be used; that through-hardened steel (minimum permissible

tempering temperature is 880ᵒF), flame or induction-hardened steel, and carburized

case-hardened teeth have all been considered in detail.

(b) To complete the design of the gears, a shaft size is needed. At the option of the

instructor: (i) compute shaft diameters for pure torsion only using a conservative design

stress, as Ss= 6 ksi (to cover stress concentration, minor bending, on the assumption that

the bearings will be quite close to the gears, etc.); or (ii) make a tentative assumption of

the distance between bearings, and design the shafts by a rational procedure. It would be

logical for the input and output to be via flexible couplings. Let the shaft material be cold-

finished AISI 1137. Design the keys for cold-drawn AISI C1118. Use better materials than

these only for good reason.

(c) Determine the dimensions of the hub, arms or webs, and rims and beads of both

gears.

(d) Make a sketch of each gear (on separate sheets of paper) including on it all

dimensions and information for its manufacture.

(e) At the instructor’s option (i) choose rolling type bearings, or (ii) design sleeve

bearings.

(f) Decide upon all details of the housing to enclose the gears, with sketches depicting

them.

(g) Your final report should be arranged as follows: (1) title page; (2) a summary of final

design decisions, and material specifications; (3) sketches; (4) final calculation; (5) other

calculations.

B. DESIGN SPECIFICATIONS

1. GEAR PAIR

MATERIAL

TABLE I.B.1-1

MATERIAL

Pinion AISI 6150 OQT 400

Gear AISI 6150 OQT 400

YIELD STRENGTH 270 ksi

HARDNESS

Pinion Approx 634 HB or 59 HRC

Gear Approx 670 HB or 61 HRC

CASE DEPTH .023 in

ALLOWABLE STRESS NUMBERS:

TABLE I.B.1-2.a

RATING METHOD ANSI/AGMA 2001-D04

ALLOWABLE BENDING STRESS NUMBER

Pinion ≳ 74.79 ksi

Gear ≳ 58.51 ksi

STRESS CYCLE FACTOR

Pinion .94

Gear .97

TEMPERATURE FACTOR 1.0

RELIABILITY FACTOR 1.0

BENDING STRESS NUMBER

Pinion 81614.24 psi

Gear 65881.37 psi

GEOMETRY FACTOR

Pinion .335

Gear .415

OVERLOAD FACTOR 1.75

DYNAMIC FACTOR 1.275

SIZE FACTOR 1.0

LOAD DISTRIBUTION FACTOR 1.181

RIM FACTOR 1.0

TABLE I.B.1-2.b

ALLOWABLE CONTACT STRESS NUMBER


Gear ≳ 252.79 ksi

STRESS CYCLE FACTOR

Pinion .91

Gear .94


Pinion 237617.65 psi

Gear 237617.65 psi

GEOMETRY FACTOR

Pinion .109

Gear .109

GEOMETRY

TABLE I.B.1-3

PROFILE TYPE INVOLUTE

PRESSURE ANGLE 20°

DIAMETRAL PITCH, Pd 6

FACE WIDTH, F 2.67 in

CENTER DISTANCE, c 9.583 in

GEAR RATIO, mg 5.053

NUMBER OF PINION TEETH, Np 19

NUMBER OF GEAR TEETH, Ng 91

PINION SPEED, np 900 rpm

GEAR SPEED, ng 178.125 rpm

PINION DIAMETER, Dp 3.167 in

GEAR DIAMETER, Dg 8.00 in

PITCH LINE VELOCITY, v 776.44 rpm

DEDENDUM, b .2083 in

CLEARANCE, c .0413 in

WHOLE DEPTH, ht .334 in

WORKING DEPTH, hk .50 in

TOOTH THICKNESS, t .262 in

BASE CIRCLE DIAMETER (PINION) 2.976 in

BASE CIRCLE DIAMETER (GEAR) 7.516 in

CIRCULAR PITCH .5234 in

BACKLASH .015 in

2. SHAFTING

SHAFT MATERIAL

TABLE I.B.2-1

MATERIAL AISI 1137 CD

ULTIMATE TENSILE STRENGTH 98 ksi


MODULUS OF ELASTICITY 30E6 psi

MODULUS OF RIGIDITY 11.5E6 psi

DESIGN STRESS 6 ksi

SHAFT DIMENSIONS

Pinion

TABLE I.B.2-2.a

D1 D1s D2 D3

DIMENSION 1.5475 in 1.8504 in 1.80 in 1.5475 in

HOLE + 0 No Adjustment + 0 + 0

SHAFT +.0024 in No Adjustment -.0030 in +.0024 in

Gear

TABLE I.B.2-2.b

D1 D1s D2 D3

DIMENSION 2.7559 in 3.0709 in 3.00 in 2.7559 in

HOLE + 0 No Adjustment + 0 + 0

SHAFT +.0029 in No Adjustment -.0037 in +.0029 in

GEAR HOB

TABLE I.B.2-3

DIAMETER LENGTH

PINION 2.70 in 2.25 in

GEAR 4.50 in 3.75 in

BEARINGS

TABLE I.B.2-4

MANUFACTURER/

MODEL NAME

DYNAMIC LOAD

CAPACITY

INNER

DIAMETER

OUTER

DIAMETER

BEARING

WIDTH

PINION SKF

NUP 2208 ECP

18300 lbsf 1.5748 in 3.1496 in .9055 in

GEAR SKF

NU 1014 ML

12600 lbsf 2.7559 in 4.3307 in .7874 in

COUPLINGS

TABLE I.B.2-5

MANUFACTURER/

MODEL NAME

TORQUE

CAPACITY

MINIMUM

DIAMETER

MAXIMUM

DIAMETER

COUPLING

WIDTH

PINION SKF

KD2-153

7884 lbs-in .748 in 2.874 in 2.008 in

GEAR SKF

KD2-303

37812 lbs-IN 1.4961 in 6.7323 in 3.386 in

KEYS MATERIAL

TABLE I.B.2-6






KEYS DIMENSIONS

TABLE I.B.2-7

PINION KEY GEAR KEY PINION

COUPLER KEY

GEAR

COUPLER KEY

ORIGINAL 1.12 in 2.26 in 2.084 in 2.46 in

ADJUSTED 2.00 in 3.50 in 2.00 in 3.25 in

3. RIM AND ARMS

Data for the rims and arms are summarized as follows:

TABLE I.B.3-1

MATERIAL AISI 6150 OQT 400

RIM THICKNESS .5864 in

RIM BEAD INCORPORATED IN RIM

HUB BEAD NONE

NUMBER OF ARMS 5

ARM LEGNTH 4.955 in

ARM GEOMETRY ELLIPTICAL (h = 1.06 in)

4. HOUSING

Summary of gearbox dimensions is as follows:

TABLE I.B.4-1

MATERIAL Cast iron

WALL THICKNESS .45 in

TOP COVER THICKNESS .36 in

COVER FLANGE THICKNESS .90 in

COVER FLANGE BOLT DIAMETER .75 in

COVER FLANGE WIDTH 1.875 in

COVER FLANGE BOLT SPACING 4.5 in

FOUNDATION FLANGE BOLT DIAMETER .875 in

FOUNDATION FLANGE THICKNESS 1.3125 in

FOUNDATION FLANGE WIDTH 2.1875 in

PINION BEARING HOUSING DIAMETER 3.80 in

GEAR BEARING HOUSING DIAMETER 5.20 in

II. DESIGN SKETCH/ILLUSTRATION

III. CALCULATIONS

A. GEAR PAIR

1. PRELIMINARY GEAR DIMENSIONS, CONTACT RATIO, AND INTERFERENCE

INITIAL CALCULATIONS FROM THE ORIGINAL PROBLEM SPECIFICATIONS

Original specifications given by the problem are as follows:

TABLE III.A.1-1

POWER 90 hp

GEAR RATIO 5

MAX CENTER DISTANCE 9.5 in

PINION RPM 900

LOAD TYPE Shock load

SAFETY FACTOR 1.4

PRESSURE ANGLE ϕ 20°

PINION TEETH ≥ 18

Using the tabulated values, we may assign initial values to the center distance, number

of gear teeth, diametral pitch, and the pinion and gear diameters using the following

equations and correlations, respectively:

C = (Dp + Dg)/2 Eqn III.A.1-1

mg = Ng/Np ∝ Dg/Dp Eqn III.A.1-2

∴ mg = Dg/Dp

5 = Dg/Dp = Ng/Np

5Dp = Dg

C = (Dp + 5Dp)/2 = (6Dp)/2

9.5 in = (6Dp)/2

Dp = 3.167 in (initial)

Ng = 5Np = 5 × 18

Ng = 90 (initial)

Dg = 5Dp = 5 × 3.167

Dg = 15.835 in (initial)

DIAMETRAL PITCH Pd

The diametral pitch is given by the formula:

Pd = N/D Eqn III.A.1-3

For this design, any value derived from Eqn III.A.1-3 will be rounded up in order to

meet a value for the center distance that is below the minimum. Hence:

Pd = ⌈N/D⌉ = ⌈18/3.167⌉ = ⌈5.684⌉

Pd = 6

CENTER DISTANCE C

The original maximum center distance C = 9.5 in will have to be adjusted with respect

to the adjusted diametral pitch. Modifying Eqn III.A.1-1:

C = (Dp + Dg)/2 = (Np + Ng)/2Pd = (18 + 90)/(2 × 6)

C = 9.00 in

DIAMETER ADJUSTMENT

Using Eqn III.A.1-3, the diameters for the gear pair may be derived as follows:

Dp = Np/Pd = 18/6

Dp = 3.00 in

Dg = Ng/Pd = 90/6

Dg = 15.00 in

Since the value for the center distance has not yet reached the maximum, these values

may still be increased without compromising the initial specifications.

The relations below logically follow if adjustments from the original gear pair diameters

are incrementally iterated in terms of the number of teeth:

Dp = (Np + ∆N)/Pd = (18 + ∆N)/(6) = (18 + ∆N)/6 Eqn III.A.1-4

Dg = 5Np = 5(18 + ∆N)/6 Eqn III.A.1-5

Np’ = (Np + ∆N) = 18 + ∆N Eqn III.A.1-6

Ng’ = 5Np = (Ng + ∆N) Eqn III.A.1-7

C = (Dp+Dg)/2=(Dp+5Dp)/2=6(18+∆N)/(2×6)=(18+∆N)/2 Eqn III.A.1-8

Summarizing the values for ∆N until C ≅ 9.50 in

TABLE III.A.1-1

∆N Dp (in) Dg (in) Np’ Ng’ C (in)

0 3.00 15.00 18 90 9

1 3.167 15.833 19 95 9.5

Only a single tooth can be added to the pinion, otherwise, the center distance limit will

be exceeded. This value will be checked if the resulting contact ratio has a range of 1.0

≤ mp ≤2.01, and no interference exists.

CONTACT RATIO

The contact ratio is given by the formula:

CR = AB/Pb Eqn III.A.1-9

Where:

AB = Line of contact = AP + BP

1 . ANSI/AGMA 2001-D04, Clause 1.2

Pb = (πD/N)cosϕ = (π/Pd)cosϕ

CR = (AP + PB)/(π/Pd)cosϕ Eqn III.A.1-10

To find the length of lines AP and BP, consider Fig III.A.1-12. An examination of the

figure yields the following relations:

Fig III.A.1-1

α = 90 + ϕ Eqn III.A.1-11

β3 = arcsin [(PO3sinα)/AO3] Eqn III.A.1-12

θ3 = 180 - (α - β3) Eqn III.A.1-13

AP = (AO3sinθ3)/sinα Eqn III.A.1-14

β2 = arcsin [(PO2sinα)/BO2] Eqn III.A.1-15

2 Kinematics and Dynamics of Machines, Martin, 2 ed., p. 251

θ2 = 180 - (α – β2) Eqn III.A.1-16

BP = (BO2sinθ2)/sinα Eqn III.A.1-17

The length of PO3, AO3, PO2, and BO2 can be expressed in term of the radii of the pinion

and the gear, and the addendum circle.

PO3 = Rg Eqn III.A.1-18

AO3 = Rg + 1/Pd Eqn III.A.1-19

PO2 = Rp Eqn III.A.1-20

BO2 = Rp + 1/Pd Eqn III.A.1-21

Considering the sum of the pinion and gear radii, the center distance, equals 9.00”, i.e.

Rg + Rp = 9.50 in Eqn III.A.1-22

Eqn III.A.1-22 has to be modified in anticipation of a hunting tooth. Considering the

length that a single tooth of the gear adds on the center distance:

(Rg + 1/2Pd) + Rp = 9.5 in +1/2Pd = 9.5 + 1/(2×6)

(Rg + 1/2Pd) + Rp = 9.583 in

let Rg’ = (Rg + 1/2Pd)

∴ C = Rg’ + Rp = 9.583 in Eqn III.A-1-23

Combining Eqn’s III.A.1-10~23, the final equation for the contact ratio of the gear pair

in term of the gear radius is given by Eqn III.A.-1-23. For the full derivation, see

Appendix A.

CR = ((Rg’+1/6) sin(70-arcsin(xsin110/( Rg’+1/6))) +

(9.75-Rg’)sin(70-arcsin((9.583-Rg’)sin110/(9.75-Rg’))))/ ((sin110)(cos20)(π/6))

Eqn III.A.1-24

Using Microsoft Mathematics confirms that valid values for Rg include {0 <mp < 9.0”}.

Fig III.A.1-2

Plotting the value of the contact ratio (y-axis) with respect to the gear radius (x-axis) =

(Rg + 1/2Pd) = (15.833 + 1/(2×6)) ≅ 8.00 in, a value of contact ratio mp ≅ 1.70 is

obtained. Therefore, the diameters of the gear and the pinion are valid values for the

design.

HUNTING TOOTH

The addition of a hunting tooth in the gear modified the gear ratio mg = 95/19 = 5, a

relatively poor distribution of load amongst the teeth, to mg = 96/19 = 5.053. This

means that for the same tooth from the gear and the pinion will mesh again for every 96

revolutions from the gear and 19 revolutions the pinion.

The angular speed of the gear also changes in correspondence with the hunting tooth.

From 180 rpm, the value changes to ng = 178.125 rpm.

ADDENDUM a

The addendum is identified early on because it will be used to find whether or not

interference exists. It is given by the formula:

a = 1/Pd = 1/6 Eqn III.A.1-25

a = .167 in.

INTERFERENCE

Using SolidWorks, interference with Rp = Dp/2 = 3.167/2 = 1.584 in and Rg = 8.00 in is

determined graphically. Looking at Fig III.A.1-3, points A and B do not exceed either

points E and F. Hence, no interference occurs.

Fig III.A.1-4

PITCH LINE VELOCITY

After finalizing both the diameters of the pinion and the gear, the pitch line velocity v

may now be determined.

v = 2πRpnp = 2π × 1.584 in × 900 rpm Eqn III.A.1-26

v = 8957.31 in/min = 776.44 fpm

FACE WIDTH

After finalizing the diametral pitch, the face width can now be determined. Using the

formula

F = (8 ~ 16)/Pd, say 16/Pd Eqn III.A.1-27

= 16/6

F = 2.67 in

Other geometric dimensions of particular concern are solved as follows:

DEDENDUM, b Eqn III.A.1-28

b = 1.25/Pd = 1.25/6

b = .2083 in

CLEARANCE, c Eqn III.A.1-29

c = b - a = .2083 - .167

c = .0413 in

WHOLE DEPTH, ht Eqn III.A.1-30

ht = a + b = .167 + .2083

ht = .3753 in

WORKING DEPTH, hk Eqn III.A.1-31

hk = 2a = 2 × .167

hk = .334 in.

TOOTH THICKNESS, t Eqn III.A.1-32

t = π/2 Pd =π/(2 × 6)

t = .262 in

BASE CIRCLE DIAMETER

Db = Dcosϕ Eqn III.A.1-34

Pinion

Dbp = 3.167cos(20)

Dbp = 2.976 in

Gear

Dbp = 8.00cos(20)

Dbp = 7.516 in

CIRCULAR PITCH

Pc = πD/N = π/Pd = π/6 Eqn III.A.1-35

Pc = .5234 in

BACKLASH

The 26th edition of Machinery’s Handbook provides a table to serve as a guide in

determining the amount of backlash of the gear:

TABLE III.A.1-2

For this design, an average between the two limits of the recommended gear backlash

value for gear pairs with diametral pitch Pd = 6~9.99, i.e., backlash bl = .015 in.

SAFETY FACTOR SF

The original specified safety factor SF = 1.4 will be reduced to unity. This is because the

design will use the rating method employed by the American Gear Manufacturer’s

Association (AGMA), an empirical approach to determine factors to be applied in the

design rating, i.e., uncertainties from which the safety factor was deemed fit to be

employed are now evaluated by empirical means.

UPDATED DIMENSIONAL SUMMARY

Preliminary dimensions for the involute spur gears are re-evaluated as follows:

TABLE III.A.1-3

POWER, P 90 hp

DIAMETRAL PITCH, Pd 6

FACE WIDTH, F 2.67 in

CENTER DISTANCE, c 9.583 in

GEAR RATIO, mg 5.053

NUMBER OF PINION TEETH, Np 19

NUMBER OF GEAR TEETH, Ng 91

PINION SPEED, np 900 rpm

GEAR SPEED, ng 178.125 rpm

PINION DIAMETER, Dp 3.167 in

GEAR DIAMETER, Dg 8.00 in

PITCH LINE VELOCITY, v 776.44 rpm

DEDENDUM, b .2083 in

CLEARANCE, c .0413 in

WHOLE DEPTH, ht .334 in

WORKING DEPTH, hk .50 in

TOOTH THICKNESS, t .262 in

BASE CIRCLE DIAMETER (PINION) 2.976 in

BASE CIRCLE DIAMETER (GEAR) 7.516 in

CIRCULAR PITCH .5234 in

SAFETY FACTOR, SF 1.0

DRIVEN LOAD Shock load

2. TORQUE AND FORCES

In order to proceed with the design, it will be necessary to find the value of the torque,

tangential force, radial force, and normal force acting on the gear pair assembly. These

are calculated by the following formulae, respectively:

T = 63000P/n; lbs-in Eqn III.A.2-1

Where

P = power in horsepower

n = angular speed in rpm

Wt = T/R; lbs Eqn III.A.2-2

Where

R = radius in inches

Wr = Wttanϕ; lbs Eqn III.A.2-2

Wn = Wt/cosϕ; lbs Eqn III.A.2-2

Applying the formulas for both the pinion and the gear:

PINION

T = 63000 × 90/900

T = 6300 lbs-in

Wt = 6300/1.584

Wt = 3977.27 lbs

Wr = 3977.27 × tan20

Wr = 1477.61 lbs

Wn = 3977.27/cos20

Wn = 4232.52 lbs

GEAR

T = 63000 × 90/178.125

T = 31831.58 lbs-in

Value for Wt, Wr, and Wn for the gear is the same with the pinion.

TABULAR SUMMARY

Summarizing the computed values on a table:

TABLE III.A.2-1

PINION GEAR

TORQUE, T 6300 lbs-in 31809.26 lbs-in

TANGENTIAL FORCE, Wt 3977.27 lbs 3977.27 lbs

RADIAL FORCE, Wr 1477.61 lbs 1477.61 lbs

NORMAL FORCE, Wn 4232.52 lbs 4232.52 lbs

3. BENDING STRENGTH

The bending strength is determined by the allowable bending stress number Sat, which,

in turn, is determined by the bending stress number St. The formula for the two are as

follows:

St = WtKOKVKS(Pd/F)(KmKB/J) Eqn III.A.3-1

Sat ≥ St × (SFKTKR/YN) Eqn III.A.3-2

Where

KO = Overload factor

KV = Dynamic factor

KS = Size factor

Km = Load distribution factor

KB = Rim factor

KT = Temperature factor

KR = Reliability factor

YN = Stress cycle factor

To proceed with the design, St is determined first. The factors are calculated next.

OVERLOAD FACTOR KO

The overload factor is determined by the use of the table below:3

TABLE III.A.3-1

3 Machine Elements in Mechanical Design, Mott, 4

th ed., p. 389

The given design problem specifi.e.s that the driven load is shock load. However, the

power source is not specified. The design will limit its application to uniform shock

power source, eg, electric motor. Therefore, KO =1.75.

DYNAMIC FACTOR KV

The dynamic factor is determined using the figure below4:

Fig III.A.3-1

Since the transmission grade QV is not specified, assumption will be made according to

the type of load and pitch line velocity. From TABLE III.A.3-25, shock load applications

usually fall under QV = 7 or below; by the pitch line velocity method, it is suggested to

have QV = {6, 7, 8} for pitch line velocity v < 800 fpm.

4 ANSI/AGMA 2001-D04, Appendix A

5 Machine Elements in Mechanical Design, Mott, 4

th ed., p. 389

TABLE III.A.3-2

For a high grade rating, QV = 8 will be used. Applying the formula for curves 5≤ QV ≤ 11

from Fig III.A.3-1:

KV = ((A + v.5)/A)B Eqn III.A.3-3

Where

B = .25 × (12 - QV).667 = .25 × (12 - 8).667 Eqn III.A.3-4

B = .6303

A = 50 + 56(1.0 - B) = 50 + 56(1.0 - .6306) Eqn III.A.3-4

A = 70.6864

KV = ((70.6864 + 776.44.5)/70.6864).7314

KV = 1.275

SIZE FACTOR, KS

The size factor may be taken as unity for most gears provided that the materials are

properly selected for the size.6 For this design, KS = 1.00.

6 ANSI/AGMA 2001-D04, clause 20.2

LOAD DISTRIBUTION FACTOR Km

ANSI/AGMA 2001-D04 defines the laod distribution factor as “...the peak load intensity

divided by the average, or uniformly distributed, load intensity; i.e., the ratio of peak to

mean loading.” It is affected by two components, namely the face load distribution

factor Cmf, which accounts for the distribution of load along the face width, and the

transverse load distribution factor Cmt, which accounts for the distribution of load

among the teeth that share the transmitted load instantaneously. I.e.,

Km = Cmf + Cmt Eqn III.A.3-5

Since there is no standard rating method for the transverse load distribution factor, it

can be assumed that Cmt = 1.00.

The empirical method of calculating for the Cmf may be used provided the design meets

certain criteria that are explained in Appendix C. Its formula is given as:

Cmf = Cmc(CpcCpm + CmaCe) Eqn III.A.3-6

Where

Cmc = lead correction factor

Cpf = pinion proportion factor

Cp = is pinion proportion modifi.e.r

Cma = mesh alignment factor

Ce = mesh alignment correction factor

The value of Cmc is rated either as 1.00 for unmodified loads or .8 for crowned leads. For

this design, with uncrowned leads, Cmc = 1.00.

For Cpf, Fig III.A.3-27 is used.

7 ANSI/AGMA 2001-D04, Fig 5

Fig III.A.3-2

For face width 1.0 < F ≤ 17, the curves from the table is defined by the formula:

Cpf = F/10Dp - .0375 +.0125F = 2.67/(10×3.167) -.0375 +.0125(2.67)

Cpf = .08 Eqn III.A.3-6

Cpm is based on the location of the gear pair from their respective distances from their

bearing centrelines. Consider the figure8:

Fig III.A.3-3


Cpm is 1.0 for straddle mounted pinions with (S1/S) < 0.175; Cpm is 1.1 for straddle

mounted pinions with (S1/S) ≥ 0.175. For this design, the pinions will be located at the

center of the bearing line, hence (S1/S) < 0.175. ∴ Cpm = 1.00.

The mesh alignment factor, Cma, can be obtained from the figure9 and table10 below:

Fig III.A.3-4

TABLE III.A.3-3

For this design, precision enclosed gear units will be used. Using the graph and the

empirical values above, the mesh alignment factor is computed with the formula:

Cma = A + BF +CF2 = .675E-1 +. 128E-1×2.67 - .822E-4 ×2.672 Eqn III.A.3-7

Cma = .101


10 ANSI/AGMA 2001-D04, Table 2

The mesh alignment correction factor Ce is used to modify the mesh alignment factor. It

is rated as either .8 if alignment is improved upon assembly, etc, or 1.00 if no further

improvement with the alignment is made. For this design, the latter scenario is

assumed, hence Ce = 1.00.

Substituting the obtained values for the factors in Eqn III.A.3-5 yields:

Km =1.0 + 1.0(.08×1.0+ .101×1.0)

Km = 1.181

RIM FACTOR KB

This factor is only modified for thin rimmed gears. Current information is insufficient to

find out whether or not rimmed gear is more appropriate for the design. However, the

graph11 shows that for a certain range of backup ratio mb = ht/tR ≥ 1.2 the rim factor is

at unity. Rimmed or not, this limit shall be observed so that KB = 1.0.

Fig III.A.3-5

11

ANSI/AGMA 2001/D04, Fig B.1

GEOMETRY FACTOR J

Calculation for the geometry factor for the bending stress of spur gears is relatively

complex. It is simplified, however, with the aid of the table12 below.

Fig III.A.3-6

It logically follows then that the pinion and the gear will each have a different geometry

factor J. Thru inspection:

Jp ≅ .335

Jg ≅ .415

Substituting all the calculated values of the factors from Eqn III.A.3-1 for the pinion

yields

Stp = WtKOKVKS(Pd/F)(KmKB/Jp) = 3977.27 × 1.75× 1.275× 1.0 × (6/2.67) ×

(1.181 × 1.0/.335)

Stp = 70303.20 psi

12

Machine Elements in Mechanical Design, Mott, 4th

ed., p. 389

For the gear, Stp is multiplied to Jp to cancel its value and divide the new value with Jg.

Stg = Stp (Jp/Jg) = 81614.24 (.335/.415) Eqn III.A.3-7

Stg = 56750.78 psi

RELIABILITY FACTOR KR

The reliability factor accounts for the normal statistical distribution of failure amongst

gear units. Refer to the TABLE III.A.3-213. For this design, a .99 reliability will be used,

i.e., one failure in 10000, hence, KR = 1.00.

TABLE III.A.3-4

TEMPERATURE FACTOR KT

The temperature factor is usually taken as unity for temperature range 32< °F <250 (0

< °C < 121). For this design, it will be assumed that the normal operating conditions

will observe this limit; hence, KT = 1.00.

STRESS CYCLE FACTOR YN

The bending stress number adjusts the allowable stress numbers for the required

cycles of operation. It is given Fig III.A.3-714:

For number of cycles N exceeding 107, the upper limit of the shaded region in the graph

will be used.

13

ANSI/AGMA 2001-D04, clause 18 14

ANSI/AGMA 2001-D04, Fig 18

Fig III.A.3-7

YN = 1.3558Nc-.0178 Eqn III.A.3-8

In which N shall be determined by the formula

Nc = 60Lnq Eqn III.A.3-9

Where

L = Number of life hours

q = Number of contacts per revolution

From Eqn III.A.3-9, it is obvious that different values of YN For this design, the number

of life hours will be designated as the upper limit of the design life of multi-purpose

gearing application (15000 hrs, or approx 5 years for 8-hour continuous, daily

operation) given by the TABLE III.A.3-515.

For q, a value of unity is designated because the gear pair only mesh with one another

in each revolution, i.e., q = 1.0 15


ed., p. 396

TABLE III.A.3-5

Evaluating Eqn III.A.3-9 for both the gear and the pinion

Ncp = 60 × 15000 × 900 × 1

Ncp = 8.10E8

Ncg = 60 × 15000 × 178.125 × 1

Ncg = 1.60E8

Substituting the values of Np and Ng to Eqn III.A.3-8

YNp = 1.3558 × (8.10E8)-.0178

YNp = .94

YNg = 1.3558 × (1.60)-.0178

YNg = .97

Substituting the values of St, SF, KT, KR, and YN to Eqn III.A.3-2 for both the gear and the

pinion yields:

Satp ≥ 70303.20 × (1.0 × 1.0 × 1.00/.94)

Satp ≥ 74790.64 psi ≳ 74.79 ksi

Satg ≥ 56750.78 × (1.0 × 1.0 × 1.00/.97)

Satg ≥ 58505.96 psi ≳ 58.51 ksi

TABULAR SUMMARY

Summarizing the values for the bending strength in a table:

TABLE III.A.3-6

ALLOWABLE BENDING STRESS NUMBER


Gear ≳ 58.51 ksi

STRESS CYCLE FACTOR

Pinion .94

Gear .97

TEMPERATURE FACTOR 1.0

RELIABILITY FACTOR 1.0


Pinion 81614.24 psi

Gear 65881.37 psi

GEOMETRY FACTOR

Pinion .335

Gear .415

OVERLOAD FACTOR 1.75

DYNAMIC FACTOR 1.275

SIZE FACTOR 1.0

LOAD DISTRIBUTION FACTOR 1.181

RIM FACTOR 1.0

4. PITTING STRENGTH

The pitting strength is determined by the allowable contact stress number Sac, which, in

turn, is determined by the contact stress number Sc. The formulae for the two are as

follows:

Sc = CP × (WtKOKVKS(Km/DpF)(Cf/I)).5 Eqn III.A.4-1

Sac ≥ Sc × (SFKTKR)/(ZNCH) Eqn III.A.4-2

Where

CP = elastic coeffici.e.nt

Cf = surface condition factor

I = pitting geometry factor

ZN = pitting resistance stress cycle factor

CH = hardness ratio factor.

All other variables have been previously identified. The remaining unknown factors

shall be accordingly identified.

ELASTIC COEFFICI.E.NT CP

The elastic coeffici.e.nt is defined by the equation16:

CP = (1/(π((1 - μp2)/Ep) + ((1 - μg2)/Eg))).5 Eqn III.A.4-3

Where

μp = Poisson’s ratio of the pinion

μg = Poisson’s ratio of the gear

Ep = Modulus of elasticity of the pinion

Eg = Modulus of elasticity of the gear

For steel, the design material, μ = .3 and E = 30000 ksi, CP = 2300.

16

ANSI/AGMA 2001-D04, Eqn 31

SURFACE CONDITION FACTOR Cf

This design assumes that the manufacturing of the gear allows for appropriate surface

finish. Hence, surface condition factor can be taken as Cf = 1.0.

PITTING GEOMETRY FACTOR I

Likewise with the bending geometry factor J, the pitting geometry factor I requires a

relatively complex procedure to identify. For this design, a simplified approach will be

taken based from the pressure angle and the number of teeth of the pinion and the gear

ratio. Consider the figure17:

Fig III.A.4-1

Plotting the corresponding value of I for Np = 20 and gear ratio 4.45, I ≅ .109

Substituting the unknown variables from Eqn III.A.4-1 with the values from TABLE

III.A.3-6 and the new calculated values yields:

Sc = 2300 × (3733.27 × 1.75 × 1.275 × 1.0 × (1.181/2.67 × 3.167)(1.0/.109)).5

Sc = 237617.65 psi

17


ed., p. 402

STRESS CYCLE FACTOR ZN

The contact stress number also adjusts the allowable stress numbers for the required

cycles of operation. It is given by the graph18:

Fig III.A.4-2

For a number of load cycles greater than 107, the shaded region shall be used to identify

ZN. Using the formula for the upper region:

ZN = 1.4488Nc-.023 Eqn III.A.4-5

The values of Nc for the gear and the pinion have been previously identified, namely Ncp

= 8.10E8, and Ncg = 1.60E8. Substituting these values to Eqn III.A.4-5 yields:

ZNp = 1.4488(8.10E8)-.023

ZNp = .90

ZNg = 1.4488(1.60E8)-.023

ZNg = .94 18


HARDNESS RATIO FACTOR CH

The value of CH for the pinion is set at 1.0. The value of CH for the gear is either set at 1.0

or otherwise depending upon the gear ratio, surface finish of the pinion, and/or

hardness of the pinion and the gear.

For this design, it is initially assumed that the hardness ratio factor for the gear CH = 1.0

until further information regarding the material of the gear is decided.

Substituting the values for the variables in Eqn III.A.4-2:

Sacp ≥ 237617.65× (1.0 × 1.0 × 1.00)/(.90 × 1.0)

Sacp ≥ 264019.61 ≳ 264.02 ksi

Sacg ≥ 237617.65× (1.0 × 1.0 × 1.00)/(.94 × 1.0)

Sacg ≥ 252784.73 psi ≳ 252.79 ksi

TABULAR SUMMARY

TABLE III.A.4-1

ALLOWABLE CONTACT STRESS NUMBER


Gear ≳ 252.79 ksi

STRESS CYCLE FACTOR

Pinion .91

Gear .94


Pinion 237617.65 psi

Gear 237617.65 psi

GEOMETRY FACTOR

Pinion .109

Gear .109

5. MATERIAL SELECTION

Given the allowable contact stress number and the allowable bending stress number

previously calculated, it will be necessary to select a relatively stronger type of steel.

With the contact stress as the governing stress for this design, consider the figure19

below:

Fig III.A.5-1

Required Brinell hardness number is calculated for both the gear and the pinion for

both Grades 1 and 2.

Grade 1

HB = (Sacp - 29100)/322 Eqn III.A.5-1

Pinion

HB = (264019.61 - 29100)/322

HB = 729.56

Gear

HB = (252784.73 - 29100)/322

19


HB = 694.67

Grade 2

HB = (Sacp - 34300)/349 Eqn III.A.5-2

Pinion

HB = (264019.61 - 34300)/349

HB = 658.22

Gear

HB = (252784.73 - 34300)/349

HB = 626.03

The Brinell hardness numbers, all well above 400, suggest that through hardening will

not be sufficient. Heat treatment case hardening will be required. In order to select the

appropriate heat treatment, consider the table20:

TABLE III.A.5-1

Only carburization hardening meets the requirement for the allowable contact stress,

namely Gear 3 for both the pinion and the gear. In this regard, a material with good heat

treatment hardening property and yield strength will be required for the gear pair.

20

ANSI/AGMA 2001-D04, TABLE 3

Upon inspection of the properties of AISI 6150 (tempered at 400 °F)21, it is conclusive

that it should serve well as the material for the gear pair.

Fig III.A.5-2

CASE DEPTH

ANSI-AGMA provides suggested case depth for carburized gear teeth. Consider Fig

III.A.5-322. For this design, normal case depth is selected for economy. Using the

equation for the normal case depth curve, the normal case depth is evaluated as

he = .119935Pd -.86105 = .119935 × (6 -.86105) Eqn III.A.5-2

he = .023 in

21


ed., p. A-10 22


Fig III.A.5-3

TABULAR SUMMARY

Tabulating the new data23 for summary:

TABLE III.A.5-2

MATERIAL

Pinion AISI 6150 OQT 400

Gear AISI 6150 OQT 400


HARDNESS24

Pinion Approx 634 HB or 59 HRC

Gear Approx 670 HB or 61 HRC

CASE DEPTH .023 in

23

See Appendix C for more details on metallurgical factors 24

See Appendix D for hardness conversion chart

B. SHAFTING

1. SHAFT

ORIGINAL SPECIFICATION FOR THE SHAFTS

The shaft material and the allowable design stress are given by the design problem. The

data are tabulated as follows:

TABLE III.B.1-1






DESIGN STRESS 6 ksi

INITIAL SHAFT DIAMETER

The design problem specifies that the design stress be limited to 6 ksi, only for pure

torsion, with the value covering for the stress concentration, minor bending, etc. Using

the torsion equation, initial shaft diameter is evaluated:

τd = 16T/(πd3) Eqn III.B.1-1

∴ d = (16T/(π τd))1/3

Evaluating d for the pinion and the gear:

dp = (16Tp/(π τd))1/3 = (16 × 6300/(π × 6000))1/3

dp = 1.749 in ≅ 1.75 in

dg = (16Tg/(π τd))1/3 = (16 × 31831.16/(π × 6000))1/3

dg = 3.00 in

INITIAL SHAFT LENGTH

The problem does not specify the length of the shaft. However, it does suggest keeping

the distance of the gear pair from each of their respective bearing as little as possible.

For this design, the distance of the gear pair from the bearing will be determined by

angular deflection, and synchronous vibration and transverse deflection.

The website roymech.co.uk provides data sheet for engineering application, including

recommended shaft deflection. From the table:25

TABLE III.B.1-2

The design specified the use of roller bearings. For this design, cylindrical roller

bearings will be used for economy, hence, the maximum angular deflection of .06°.

TORSIONAL DEFLECTION

Using the torsional deflection formula:

Θ = TL/JG Eqn III.B.1-2

∴ L = ΘJG/(T)

Where

L = Distance of gear pair from the bearing

J = Polar moment of inertia

25

http://www.roymech.co.uk/Useful_Tables/Drive/Shaft_design.html#Deflections

http://www.roymech.co.uk/Useful_Tables/Drive/Shaft_design.html#Deflections

Θ = angular deflection in rads

Evaluating for the gear and the pinion shafts:

Pinion

L = ΘJG/(T) = (.06° × π/180°)(π(1.754/32))(30E6))/(6300)

= (.00105)(.9208)(30E6)/6300

L = 4.59 in

Gear

L = ΘJG/(T) = (.06° × π/180°)(π(3.004/32))(30E6))/(31831.16)

= (.00105)(7.9522)(30E/6)/6300

L = 7.85 in

SYNCHRONOUS VIBRATION

In order to design the shafts against critical speed, they must be designed such that

resonance starts to occur at about each of their fifth harmonics26, in which the impulses

are negligible, i.e.:

ns ≥ fn /2n-1 Eqn III.B.1-3

Where

ns = angular speed of the shaft

fn = natural frequency

n = nth harmonic (5th harmonic for this design)

∴fn ≥ ns × 25-1

For the pinion

fnp ≥ (900) × 25-1

fnp ≥ 14400 vib/min ≥ 240 vib/sec

26

Internal Combustion Engine, Maleev, 2 ed., p. 447

For the gear

fng ≥ (178.125) × 25-1

fng ≥ 2850 vib/min ≥ 47.5 vib/sec

The design natural frequencies of the pinion and the gear shafts are substituted to Eqn

III.B.1-4 in order to find the allowable transverse deflection.

fn = (12g/y).5/2π Eqn III.B.1-427

Where

g = 32.2 ft/s2

y = transverse deflection

∴ y = (12g)/(2πfn)2

For the pinion

yp = (12 × 32.2)/(2π × 240)2

yp = .00017 in

For the gear

yg = (12 × 32.2)/(2π × 47.5)2

yg = .00434 in

Using the acquired values of deflection, the distance of the gear pair from the bearings

may be obtained by the beam deflection formula for simply supported beams:

y = WnL3/48EI Eqn III.B.1-5

E = Modulus of elasticity

I = Moment of inertia

∴L = (48EIy/Wn)1/3

27

Internal Combustion Engine, Maleev, 2 ed., p. 460

Calculating the moment of inertia for both the pinion and the gear shaft using the

formula:

I = (πD4/64) Eqn III.B.1-6

Pinion

Ip = (π ×1.754/64)

Ip = .4604 in4

Gear

Ig = (π ×3.004/64)

Ip = 3.9761 in4

Substituting the values to Eqn III.B.1-5

Pinion

Lp = (48 × 30E6 × .4604 × .00017/4232.52)1/3

Lp = 2.99 in ≅ 3.00 in

Gear

Lg = (48 × 30E6 × 3.9761 × .00434/4232.52)1/3

Lg = 18.04 in

The evaluated distance of the pinion shaft from the bearing is also safe for the gear

shaft. For housing convenience, the same value will be used for both the pinion and the

gear shafts. Therefore, tentative shaft length = 2L = 6.00 in.

BEARING REACTION

To illustrate the initial set-up of the gear and shaft assembly, consider Fig III.B.1-1. The

combined radial and tangential forces are combined and are represented as the normal

force. The bearing reactions from the gear and the pinion will be the same since the

same amount of force acts on the shafts.

Using static moment equation to evaluate bearing reactions, with clockwise set as

positive:

MA = 3Wn - 6RB = 0

∴ RB = (3 × 4232.52)/6

Fig III.B.1-1

RB = 2116.26 lbs

MB = 6RA - 3Wn = 0

∴ RA = (3 × 4232.52)/6

RA = 2116.26 lbs

SHEAR AND MOMENT DIAGRAM

With the forces acting on the shaft already known, the shear and moment diagram may

now be determined. Using the shear and moment equation:

V = ΣFy Eqn III.B.1-7

Where

V = Shear force

Fy =Vertical forces

M = ΣM = ∫f(V) Eqn III.B.1-8

Evaluating the two equations:

V = 2116.26 - (4232.52) + 2116.26

V = 0

M = ∫f(V) = (∫ 2116.26

) - (∫ 4232.52

) = 2116.26(6) - 4232.52(6-3)

M = 0

Using Microsoft Mathematics, the shear and moment diagram are graphed as follows:

Fig III.B.1-2a

Shear diagram

Fig III.B.1-2b

Moment diagram

ACTUAL ENDURANCE STRENGTH Sn’

The actual endurance strength of the material must be evaluated in order to proceed

with the shaft design. Its value is evaluated as:

Sn’ = SnCmCstCRCs 28 Eqn III.B.1-9

Where

Sn = Endurance strength

Cm = Material factor

Cst = Stress type factor

CR = Reliability factor

Cs = Size factor

These variables are evaluated accordingly.

28


ed., p. 174

ENDURANCE STRENGTH Sn

The endurance strength may be derived from Fig III.B.1-329

Fig III.B.1-330

Plotting the tensile strength of AISI 1137 CD against the surface finish condition,

endurance strength Sn = 38 ksi.

MATERIAL FACTOR Cm

According to its density and general characteristics, AISI 1137 CD can be classified as

wrought steel31. Hence, from TABLE III.B.1-3, its material factor Cm = 1.00.

TABLE III.B.1-3

29


ed., p. 175 30


ed., p. 175 31

http://www.steelforge.com/literature/ferrousnon-ferrous-materials-textbook/ferrous-metals/carbon-steel/

http://www.steelforge.com/literature/ferrousnon-ferrous-materials-textbook/ferrous-metals/carbon-steel/

STRESS TYPE FACTOR Cst

Stress type factor is either evaluated 1.0 for bending or .80 for axial tension. For this

design, Cst = 1.0032.

RELIABILITY FACTOR CR

The same reliability from the gear pair shall be applied for the shafts. Hence, from the

table33 below, reliability factor CR = .81.

TABLE III.B.1-4

SIZE FACTOR CS

The size factor of the shaft shall be evaluated using the following range of values34:

TABLE III.B.1-4

Using the equation for .30 < D ≤ 2.0 for the pinion shaft and 2.0 < D < 10.0 for the gear

shaft:

Pinion Eqn III.B.1-10

Cs = (D/0.3) -.11 = (1.75/.3)-.11

32


ed., p. 174 33


ed., p. 175 34


ed., p. 175

Cs = .8237

Gear Eqn III.B.1-11

Cs = .859 - .02125D = .859 - .02125 × 3.00

CS = .7953

Substituting the obtained values to Eqn III.B.1-9

Pinion

Sn’ = 38E3 (1.00)(1.00)(.81)(.8237)

Snp’ = 25353.49 psi

Gear

Sn’ = 38E3 (1.00)(1.00)(.81)(.7953)

Sng’ = 24479.33 psi

READJUSTED SHAFT DIAMETERS

The final shaft diameters left to be determined are those at the section of the bearing.

Considering that neither torque nor bending moment occurs at the bearings from both

the pinion and the gear shaft, the equation for the shaft diameter at these sections is

applied:

D = (2.94KtVN/Sn’).5 Eqn III.B.1-12

Where

N = Shaft factor of safety = 3 (shock load, certain data)

Kt = Stress concentration factor = 1.5 (round fillet)

Pinion

D = (2.94 × 1.5 × 2116.26 × 3/25353.49).5

D = 1.0501 in

Gear

D = (2.94 × 1.5 × 2116.26 × 3/24479.33).5

D = 1.0695 in

TABULAR SUMMARY

The acquired values for the shaft diameters, including the preferred basic sizes, are

summarized in a table:

TABLE III.B.1-5

Pinion

D1 D2 D3

Nominal Size 1.05 in 1.75 in 1.05 in

Preferred basic size 1.20 in 1.80 in 1.20 in

Gear

D1 D2 D3

Nominal Size 1.0695 in 3.00 in 1.0695 in

Preferred basic size 1.20 in 3.00 in 1.20 in

2. GEAR HUB

Mott and Faires recommend empirical methods for calculating the hub diameter and

hub length, respectively.

Dh = 1.5Ds Eqn III.B.2-135

Lh = 1.25 ~ 2Ds Eqn III.B.2-236

HUB DIAMETER

Substituting values of Ds for both the gear and the pinion to Eqn III.B.2-1

Pinion

Dhp = 1.50 × 1.80

Dhp = 2.70 in

Gear

Dhg = 1.50 × 3.00

Dhg = 4.50 in

HUB LENGTH

Substituting values of Ds for both the gear and the pinion to Eqn III.B.2-2

Pinion

Dhp = 1.7 5 × 1.80

Dhp = 2.25 in

Gear

Dhg = 1.25 × 3.00

Dhg = 3.75 in

35


ed., p. 440 36

Design of Machine Elements, 4th

ed., p. 388

3. BEARING SELECTION

Bearings are selected next for the design. Note that bearing selection may affect pre-

determined shaft dimensions according to size compatibility.

BEARING DYNAMIC LOAD CB

The bearing dynamic load is given by the formula:

CB = V(Nc/1E6)1/k Eqn III.B.3-137

Where

CB = Rated bearing load

V = Shear force

Nc = Number of life cycle (See III.A.3, STRESS CYCLE FACTOR)

k = life-load ratio

Substituting the values accordingly for both the pinion and the gear, with k = 3.3 for

ball bearings, bearing dynamic load is evaluated as:

Pinion

CBp = 2116.26 (8.1E8/1E6)1/3.3

CBp = 16103.79 lbs

Gear

CBg = 2116.26 (1.6E8/1E6)1/3.3

CBg = 9851.09 lbs

SELECTION FROM BEARING CATALOGUE

For its local availability, this design will use bearings manufactured by Svenska

Kullagerfabriken (SKF). Select products from the catalogue are included in Appendix E.

37


ed., p. 611

The bearings are selected according to their dynamic load capacity and bore diameter

such that stress concentration will be minimized, i.e. the bore should be only slightly

smaller than the diameters at the gear pair section.

The figure38 should serve as a guide in selecting bearings with respect to their bore

diameter:

Fig III.B.3-1

Note that to achieve stress concentration factor Kt = 1.5, the step ratio of the shaft

diameters must not exceed 1.25. Therefore, for the pinion shaft, the minimum bore

diameter:

D1p = D2p/1.25 = 1.80/1.25 Eqn III.B.3-2

D1p = 1.44 in

while for the gear, minimum bore diameter

D1g = D2g/1.25 = 3.00/1.25 Eqn III.B.3-3

D1g = 2.40 in

38


ed., p. A-27

For the pinion shaft, the SKF NUP 2208 ECP roller bearing will be used.

Fig III.B.3-2

For the gear shaft, the SKF NU 1014 ML roller bearing will be used

Fig III.B.3-3

ADJUSTED DIAMETERS

The shaft diameters for both the pinion and the gear shafts are adjusted to

accommodate the selected bearings. The new dimensions are tabulated as follows:

TABLE III.B.3-1

D1 D1s D2 D3

PINION 1.5475 in 1.8504 in 1.80 in 1.5475 in

GEAR 2.7559 in 3.0709 in 3.00 in 2.7559 in

4. TOLERANCES AND FITS

Tolerances shall be applied to the gear pair sections of the shafts while fits shall be

applied to the bearing sections. Given the design load and speed, a tolerance of RC5 and

a force fit of FN2 will be used. For convenience, only the shaft dimensions will be

adjusted while the dimensions of the holes are maintained.

Using the ANSI/ASME Clearance Fits and Force Fits charts39, the clearances/fits for the

diameter:

Pinion

TABLE III.B.4-1a

D1 D1s D2 D3

Dimension 1.5475 in 1.8504 in 1.80 in 1.5475 in

Hole + 0 No Adjustment + 0 + 0

Shaft +.0024 in No Adjustment -.0030 in +.0024 in

Gear

TABLE III.B.4-1b

D1 D1s D2 D3

Dimension 2.7559 in 3.0709 in 3.00 in 2.7559 in

Hole + 0 No Adjustment + 0 + 0

Shaft +.0029 in No Adjustment -.0037 in +.0029 in

39

See Appendix F

5. KEYS AND COUPLINGS

ORIGINAL SPECIFICATION FOR THE KEYS

The problem specifies that the material for the keys is AISI C1118 CD. Summarizing its

properties:

TABLE III.B.5-1






For this design, the axial area for the shaft and coupling keys are empirically selected

from the TABLE III.B.5-240 whilst the key length is given by the formula:

Lk = (4TN)/(DsWSy) Eqn III.B.5-141

Where

W = face width

Value of T, W, and D are different for both the pinion and the gear. Hence, they shall be

solved separately. In all cases, factor of safety N = 3.00

PINION KEY

Upon inspection at TABLE III.B.5-2, nominal face width and height for a square key

configuration for the pinion shaft Ds = 1.80 in is obtained:

Wp = Hp = ½ in

Substituting the variables from Eqn III.B.5-1:

40


ed., p. 495 41


ed., p. 500

TABLE III.B.5-2

Lkp = (4 × 6300 × 3)/( 1.80 × .5 × 75000)

Lkp = 1.12 in

GEAR KEY

Upon inspection at TABLE III.B.5-2, nominal face width and height for a square key

configuration for the pinion shaft Ds = 3.00 in is obtained:

Wg = Hg = .75 in


Lkg = (4 × 31809.26 × 3)/( 3.00 × .75 × 75000)

Lkg = 2.26 in

PINION COUPLER KEY

For this design, the diameter of the shaft that elongates to the coupling is given the

same diameter as the diameter of the section of the shaft that is adjacent to the bearing.

In this regard, axial dimension of the pinion coupler key for Ds = 1.5475 in is given as:

Wpc = Hpc = .3125 in


Lkpc = (4 × 6300 × 3)/( 1.5475 × .3125 × 75000)

Lkpc = 2.084 in

GEAR COUPLER KEY

Axial dimension of the pinion coupler key for Ds = 2.7559 in is given as:

Wgc = Hgc = .75 in


Lkgc = (4 × 31809.26 × 3)/( 2.7559 × .75 × 75000)

Lkgc = 2.46 in

COUPLING SELECTION

Manufactured couplings are selected accordingly for this design. See Appendix G for a

select catalogue range from Svenska Kullagerfabriken.

The parameters for the flexible coupling selection are the minimum allowed shaft

diameter, torque capacity, and angular speed capacity. Assigning a value of 4.00 in as

the distance of the elongated portion of the shafts from their respective bearings to

their couplings also limits possible and practical choices. For this design, disc flexible

couplings are employed.

For the pinion, the SKF KD2-153 satisfies all parameters for the pinion coupling.

Fig III.B.5-1

For the gear, the SKF KD2-303 satisfies all parameters for the gear coupling.

Fig III.B.5-2

READJUSTED KEY DIMENSIONS

The key lengths are further adjusted in order to be compatible with their respective

hubs.

TABLE III.B.5-2

PINION KEY GEAR KEY PINION

COUPLER KEY

GEAR

COUPLER KEY

ORIGINAL 1.12 in 2.26 in 2.084 in 2.46 in

ADJUSTED 2.00 in 3.50 in 2.00 in 3.25 in

C. RIM AND ARMS

1. PRELIMINARY DIMENSIONS

For this design, only the gear will use rim and arms in order to reduce mass and cost.

Rim thickness and the number of arms are determined empirically. This design will also

incorporate the ring bead to the rim for easier manufacturing and to keep the material

homogenous.

RIM THICKNESS

A suggested empirical value for the rim thickness is given by the formula:

tR = .56Pc = .56π/Pd Eqn III.C.1-142

Since this design incorporates the bead to the rim, and the bead having the same

formula for the rim thickness, Eqn III.C.1-1 is modified to:

tR = 2(.56π/Pd) = 2(.56π/6) Eqn III.C.1-2

tR = .5864 in

Note that this value of tR is within the prescribed range for the rim thickness factor

determined earlier. The radial distance will be subtracted from the dedendum line.

NUMBER OF ARMS

The number of arms is also empirically suggested43:

TABLE III.C.1-1

Gear diameter(mm) Arms

300-500 4-5

500-1500 6

42

Design of Machine Elements, Faires, 4th

ed., p. 390 43

Design of Machine Elements, Bhandari, 4th

ed., p. 670

1500-2400 8

>2400 10-12

The gear diameter, Dg = 16 in = 403 mm, suggests a recommended number of arms NA

= 4 ~ 5. For this design, NA = 4.

The figure illustrates the preliminary dimensions of the gear pitch diameter, hob, rim,

and shaft bore.

Fig III.C.1-1

2. ARM GEOMETRY

Appropriate arm dimensions are calculated such that the arms, acting as cantilever

beams, will be able to withstand the applied tangential forces. To proceed with the

design, the shape of the cross section must be determined. Faires lists common cross

section shapes for gear arms44. For this design, elliptical arms are selected for their

smaller tendency for stress concentration.

Using the stress formula for beams:

σ = M/S = Sy/N = M/S Eqn III.C.1-3

Where

M = Moment

S = Section modulus

N = Factor of safety = 4

∴ S = 4M/(270 ksi)

Solving for the value of the moment evenly distributed to the four arms:

M = WtL/NA = 3977.27 × 4.955 /5 Eqn III.C.1-4

M = 3941.48 lbs-in

The section modulus of an elliptical cross section in which the major diameter is twice

the minor diameter is given by the formula:

S = πh3/64 Eqn III.C.1-545

Substituting the values to Eqn III.C.1-3

πh3/64 = 4M/(270 ksi)

∴h = ((64 × 4 × 3941.48)/(270E3 × π))1/3

44


ed., p. 389 45


ed., p. 389

h = 1.06 in

TABULAR SUMMARY

TABLE III.C.2-1

RIM THICKNESS .5864 in

RIM BEAD INCORPORATED IN RIM

HUB BEAD NONE

NUMBER OF ARMS 5

ARM LEGNTH 4.955 in

ARM GEOMETRY ELLIPTICAL (h = 1.06 in)

To illustrate the assembly, consider the figure:

Fig III.C.1-2

D. HOUSING

1. INITIAL ILLUSTRATION

To proceed with the gearbox design, an initial illustration, determined by other

dimensions previously designated, e.g., bearings, is provided in order to have a general

idea of the gearbox configuration. Also note that a .5 in clearance from the gear pair is

provided.

Fig III.D.1-1

Further modifications will be made according to recommended dimensions and

material selection.

2. GEARBOX DIMENSIONS

Actual gearbox dimensions are solved as follows:

GEARBOX THICKNESS

Professors Gopinath and Mayuram of the Indian Institute of Technology, Madras,

provide a rule of thumb in determining gear house thickness. 46

TABLE III.D.1-1

Wall thickness ‘s’ in mm of the gearboxes Material

Non-case hardened gears

Case hardened gears

CI castings 0.007L + 6 mm 0.010 L + 6 mm

Steel castings 0.005L + 4 mm 0.007L + 4 mm

Welded construction 0.004L + 4 mm 0.005L + 4 mm

For this design, cast iron castings will be used. Using the empirical formula for CI

castings and case hardened gear, gearbox thickness s is determined:

s = 0.010 L + 6 mm Eqn III.D.1-1

Where

L = largest dimension of the housing

L = 20.167 in = 532.18 mm

s = 0.010 (532.18) + 6 mm

s = 11.122 mm = .44 in

s ≅ . 45 in

46

Indian Institute of Technology, Machine Design 2, Module 2, Lecture 17

2. OTHER DIMENSIONS

Other necessary dimensions for the gearbox are as follows47:

TOP COVER THICKNESS

sc = .8s = .8 × .45 in Eqn III.D.1-2

sc = .36 in

COVER FLANGE THICKNESS

scf = 2s = 2 × .44 Eqn III.D.1-3

scf = .9 in

COVER FLANGE BOLT DIAMETER Eqn III.D.1-4

Dcb = 1.5s = 1.5 × .44

Dcb = .675 in

Dcb = .75 in (standard)

COVER FLANGE WIDTH Eqn III.D.1-5

Wcf = 2.5Dcb = 2.5 × .75

Wcf = 1.875 in

COVER FLANGE BOLT SPACING

wcs = 6Dcb = 6 × .75

wcs = 4.5 in

FOUNDATION FLANGE BOLT DIAMETER Eqn III.D.1-6

Dfb = (1.38E-5Tg)1/3 = (1.38E-5 × 31809.26)1/3

Dfb = .7598 in

Dfb = .8750 in (standard)

47

Indian Institute of Technology, Machine Design 2, Module 2, Lecture 17

FOUNDATION FLANGE THICKNESS Eqn III.D.1-7

sff = 1.5Dfb = 1.5 × .8750

sff = 1.3125 in

FOUNDATION FLANGE WIDTH Eqn III.D.1-8

Wff = 2.5Dfb = 2.5 × .875

Wfc = 2.1875

BEARING HOUSING DIAMETER

Bearing housing diameter on the gearbox is given by:

Dbh = 1.2Dob Eqn III.D.1-10

Pinion

Dpbh = 1.2 × 3.1496

Dpbh = 3.80 in

Gear

Dgbh = 1.2 × 4.3307

Dgbh = 5.20 in

TABULAR SUMMARY

Summarizing the computed values of gearbox dimensions:

TABLE III.D.1-2

WALL THICKNESS .45 in

TOP COVER THICKNESS .36 in

COVER FLANGE THICKNESS .90 in

COVER FLANGE BOLT DIAMETER .75 in

COVER FLANGE WIDTH 1.875 in

COVER FLANGE BOLT SPACING 4.5 in

FOUNDATION FLANGE BOLT DIAMETER .875 in

FOUNDATION FLANGE THICKNESS 1.3125 in

FOUNDATION FLANGE WIDTH 2.1875 in

PINION BEARING HOUSING DIAMETER 3.80 in

GEAR BEARING HOUSING DIAMETER 5.20 in

To illustrate a general idea for the gearbox dimensions, consider the figure below. Note

that the illustration excludes the top cover and the holes.

Fig III.D.1-2

IV. RECOMMENDATIONS

1. Improve alignment upon assembly to avoid stress due to misalignment

2. Operate according to prescribed temperature determined for the temperature factor.

Properly insulate if extreme temperatures are unavoidable.

3. Apply lubricant appropriate with the operating temperature

4. Ensure case hardening is properly conducted.

5. Improve surface finish of shaft.

6. Refer to Fig III.B.3-1 for the appropriate fillet radii.

7. Also apply fillet radii on gear arm joints to avoid stress concentration.

8. Drill horizontal sluice on gearbox cover for ease of lubricant application.

9. Regular, commercially available retaining ring may be used for the unit.

10. Conduct cleaning according to the working environment of the unit.

V. APPENDIX

A. DERIVATION OF THE CONTACT RATIO FORMULA

CR = AB/Pb

AB = AB + PB

Pb = π/(Pdcosϕ)

CR = (AB + PB)/ (πcosϕ/Pd) = (AOgsinθ3 + BOpsinθ2)/(sinα πcosϕ/Pd)

AOg = Rg + 1/Pd

BOp = Rp + 1/Pd

CR = ((Rg + 1/Pd)sin(180 - (α + β3)) + (rp +1/Pd)sin(180 - (α + β2)))/(sinα πcosϕ/Pd)

CR = ((Rg + 1/Pd)sin(180 - α - sin-1(Rgsinα/(Rg + 1/Pd))) + (rp +1/Pd) sin(180- α - sin-1

(Rpsinα/(Rp + 1/Pd)))/(sinα πcosϕ/Pd)

Note that:

α = 90° + ϕ

c = Rg + Rp

Substituting these values yields a function for the contact ratio in terms of either the

pinion or the gear radius.

B. RESTRICTIONS FOR THE EMPIRICAL METHOD FOR Cmf

From ANSI/AGMA 2001-D04, clause 15.3:

“The face load distribution factor accounts for the non--uniform distribution of load

across the gearing face width. The magnitude of the face load distribution factor is

defined as the peak load intensity divided by the average load intensity across the face

width.

This factor can be determined empirically or analytically. This standard provides an

empirical method only, but includes a theoretical discussion for analytical analysis in

annex D. Either method can be used, but when using the analytical approach, the

calculated load capacity of the gears should be compared with past experience since it

may be necessary to re--evaluate other rating factors to arrive at a rating consistent with

past experience. Also see AGMA 927--A01.

The empirical method requires a minimum amount of information. This method is

recommended for relatively stiff gear designs which meet the following requirements:

-- Net face width to pinion pitch diameter ratio, F/d, ≤ 2.0. (For double helical gears the

gap is not included in the face width).

-- The gear elements are mounted between bearings (see following paragraph for

overhung gears).

-- Face width up to 40 inches.

-- Contact across full face width of narrowest member when loaded.

CAUTION: If F/d > 2.4 -- 0.002Kwhere K = the contact load factor (see equation 6), the

value of Km determined by the empirical method may not be sufficiently conservative.

In this case, it may be necessary to modify the lead or profile of the gears to arrive at a

satisfactory result. The empirical method shall not be used when analyzing the effect of a

momentary overload. See 16.3.

When gear elements are overhung, consideration must be given to shaft deflections and

bearing clearances. Shafts and bearings must be stiff enough to support the bending

moments caused by the gear forces to the extent that resultant deflections do not

adversely affect the gear contact. Bearing clearances affect the gear contact in the same

way as offset straddle mounted pinions. However, gear elements with their overhang to

the same support side can compound the effect. This effect is addressed by the pinion

proportion modifying factor, Cpm. When deflections or bearing clearances exceed

reasonable limits, as determined by test or experience, an analytical method must be

used to establish the face load distribution factor.

When the gap in a double helical gear set is other than the gap required for tooth

manufacture, for example in a nested design, each helix should be treated as a single

helical set.

Designs which have high crowns to centralize tooth contact under deflected conditions

may not use this method.

This method will give results similar to those obtained in previous AGMA standards.

Designs falling outside the above F/d ranges require special consideration.”

C. METALLURGICAL FACTORS FOR CARBURIZED CASE HARDENING

D. HARDNESS CONVERSION TABLE48

Hardness Conversion Chart

Rockwell Rockwell Superficial Brinell Vickers Shore

A B C D E F 15-N 30-N 45-N 30-T 3000 kg 500 kg 136 Approx Tensile

Strength (psi)

60kg Brale

100kg 1/16"

Ball 150kg Brale

100kg Brale

100kg 1/8" Ball

60kg 1/16"

Ball 15kg Brale

30kg Brale

45kg Brale

30 kg 1/16"

Ball

10mm Ball

Steel 10mm

Ball Steel Diamond Pyramid

Sciero-scope

86.5 --- 70 78.5 --- --- 94.0 86.0 77.6 --- --- --- 1076 101 ---

86.0 --- 69 77.7 --- --- 93.5 85.0 76.5 --- --- --- 1044 99 ---

85.6 --- 68 76.9 --- --- 93.2 84.4 75.4 --- --- --- 940 97 ---

85.0 --- 67 76.1 --- --- 92.9 83.6 74.2 --- --- --- 900 95 ---

84.5 --- 66 75.4 --- --- 92.5 82.8 73.2 --- --- --- 865 92 ---

83.9 --- 65 74.5 --- --- 92.2 81.9 72.0 --- 739 --- 832 91 ---

83.4 --- 64 73.8 --- --- 91.8 81.1 71.0 --- 722 --- 800 88 ---

82.8 --- 63 73.0 --- --- 91.4 80.1 69.9 --- 705 --- 772 87 ---

82.3 --- 62 72.2 --- --- 91.1 79.3 68.8 --- 688 --- 746 85 ---

81.8 --- 61 71.5 --- --- 90.7 78.4 67.7 --- 670 --- 720 83 ---

81.2 --- 60 70.7 --- --- 90.2 77.5 66.6 --- 654 --- 697 81 320,000

80.7 --- 59 69.9 --- --- 89.8 76.6 65.5 --- 634 --- 674 80 310,000

80.1 --- 58 69.2 --- --- 89.3 75.7 64.3 --- 615 --- 653 78 300,000

79.6 --- 57 68.5 --- --- 88.9 74.8 63.2 --- 595 --- 633 76 290,000

79.0 --- 56 67.7 --- --- 88.3 73.9 62.0 --- 577 --- 613 75 282,000

78.5 120 55 66.9 --- --- 87.9 73.0 60.9 --- 560 --- 595 74 274,000

78.0 120 54 66.1 --- --- 87.4 72.0 59.8 --- 543 --- 577 72 266,000

77.4 119 53 65.4 --- --- 86.9 71.2 58.6 --- 525 --- 560 71 257,000

76.8 119 52 64.6 --- --- 86.4 70.2 57.4 --- 500 --- 544 69 245,000

76.3 118 51 63.8 --- --- 85.9 69.4 56.1 --- 487 --- 528 68 239,000

75.9 117 50 63.1 --- --- 85.5 68.5 55.0 --- 475 --- 513 67 233,000

75.2 117 49 62.1 --- --- 85.0 67.6 53.8 --- 464 --- 498 66 227,000

74.7 116 48 61.4 --- --- 84.5 66.7 52.5 --- 451 --- 484 64 221,000

74.1 116 47 60.8 --- --- 83.9 65.8 51.4 --- 442 --- 471 63 217,000

48

Carbide Depot, https://www.carbidedepot.com/formulas-hardness.htm

https://www.carbidedepot.com/formulas-hardness.htm

https://www.carbidedepot.com/resources.htm

73.6 115 46 60.0 --- --- 83.5 64.8 50.3 --- 432 --- 458 62 212,000

73.1 115 45 59.2 --- --- 83.0 64.0 49.0 --- 421 --- 446 60 206,000

72.5 114 44 58.5 --- --- 82.5 63.1 47.8 --- 409 --- 434 58 200,000

72.0 113 43 57.7 --- --- 82.0 62.2 46.7 --- 400 --- 423 57 196,000

71.5 113 42 56.9 --- --- 81.5 61.3 45.5 --- 390 --- 412 56 191,000

70.9 112 41 56.2 --- --- 80.9 60.4 44.3 --- 381 --- 402 55 187,000

70.4 112 40 55.4 --- --- 80.4 59.5 43.1 --- 371 --- 392 54 182,000

69.9 111 39 54.6 --- --- 79.9 58.6 41.9 --- 362 --- 382 52 177,000

69.4 110 38 53.8 --- --- 79.4 57.7 40.8 --- 353 --- 372 51 173,000

68.9 110 37 53.1 --- --- 78.8 56.8 39.6 --- 344 --- 363 50 169,000

68.4 109 36 52.3 --- --- 78.3 55.9 38.4 --- 336 --- 354 49 165,000

67.9 109 35 51.5 --- --- 77.7 55.0 37.2 --- 327 --- 345 48 160,000

67.4 108 34 50.8 --- --- 77.2 54.2 36.1 --- 319 --- 336 47 156,000

66.8 108 33 50.0 --- --- 76.6 53.3 34.9 --- 311 --- 327 46 152,000

66.3 107 32 49.2 --- --- 76.1 52.1 33.7 --- 301 --- 318 44 147,000

65.8 106 31 48.4 --- --- 75.6 51.3 32.5 --- 294 --- 310 43 144,000

65.3 105 30 47.7 --- --- 75.0 50.4 31.3 --- 286 --- 302 42 140,000

64.7 104 29 47.0 --- --- 74.5 49.5 30.1 --- 279 --- 294 41 137,000

64.3 104 28 46.1 --- --- 73.9 48.6 28.9 --- 271 --- 286 41 133,000

63.8 103 27 45.2 --- --- 73.3 47.7 27.8 --- 264 --- 279 40 129,000

63.3 103 26 44.6 --- --- 72.8 46.8 26.7 --- 258 --- 272 39 126,000

62.8 102 25 43.8 --- --- 72.2 45.9 25.5 --- 253 --- 266 38 124,000

62.4 101 24 43.1 --- --- 71.6 45.0 24.3 --- 247 --- 260 37 121,000

62.0 100 23 42.1 --- --- 71.0 44.0 23.1 82.0 240 201 254 36 118,000

61.5 99 22 41.6 --- --- 70.5 43.2 22.0 81.5 234 195 248 35 115,000

61.0 98 21 40.9 --- --- 69.9 42.3 20.7 81.0 228 189 243 35 112,000

60.5 97 20 40.1 --- --- 69.4 41.5 19.6 80.5 222 184 238 34 109,000

59.0 96 18 --- --- --- --- --- --- 80.0 216 179 230 33 106,000

58.0 95 16 --- --- --- --- --- --- 79.0 210 175 222 32 103,000

57.5 94 15 --- --- --- --- --- --- 78.5 205 171 213 31 100,000

57.0 93 13 --- --- --- --- --- --- 78.0 200 167 208 30 98,000

56.5 92 12 --- --- --- --- --- --- 77.5 195 163 204 29 96,000

56.0 91 10 --- --- --- --- --- --- 77.0 190 160 196 28 93,000

55.5 90 9 --- --- --- --- --- --- 76.0 185 157 192 27 91,000

55.0 89 8 --- --- --- --- --- --- 75.5 180 154 188 26 88,000

54.0 88 7 --- --- --- --- --- --- 75.0 176 151 184 26 86,000

53.5 87 6 --- --- --- --- --- --- 74.5 172 148 180 26 84,000

53.0 86 5 --- --- --- --- --- --- 74.0 169 145 176 25 83,000

52.5 85 4 --- --- --- --- --- --- 73.5 165 142 173 25 81,000

52.0 84 3 --- --- --- --- --- --- 73.0 162 140 170 25 79,000

51.0 83 2 --- --- --- --- --- --- 72.0 159 137 166 24 78,000

50.5 82 1 --- --- --- --- --- --- 71.5 156 135 163 24 76,000

50.0 81 0 --- --- --- --- --- --- 71.0 153 133 160 24 75,000

49.5 80 --- --- --- --- --- --- --- 70.0 150 130 --- --- 73,000

49.0 79 --- --- --- --- --- --- --- 69.5 147 128 --- --- ---

48.5 78 --- --- --- --- --- --- --- 69.0 144 126 --- --- ---

48.0 77 --- --- --- --- --- --- --- 68.0 141 124 --- --- ---

47.0 76 --- --- --- --- --- --- --- 67.5 139 122 --- --- ---

46.5 75 --- --- --- 99.5 --- --- --- 67.0 137 120 --- --- ---

46.0 74 --- --- --- 99.0 --- --- --- 66.0 135 118 --- --- ---

45.5 73 --- --- --- 98.5 --- --- --- 65.5 132 116 --- --- ---

45.0 72 --- --- --- 98.0 --- --- --- 65.0 130 114 --- --- ---

44.5 71 --- --- 100.0 97.5 --- --- --- 64.2 127 112 --- --- ---

44.0 70 --- --- 99.5 97.0 --- --- --- 63.5 125 110 --- --- ---

43.5 69 --- --- 99.0 96.0 --- --- --- 62.8 123 109 --- --- ---

43.0 68 --- --- 98.0 95.5 --- --- --- 62.0 121 107 --- --- ---

42.5 67 --- --- 97.5 95.0 --- --- --- 61.4 119 106 --- --- ---

42.0 66 --- --- 97.0 94.5 --- --- --- 60.5 117 104 --- --- ---

41.8 65 --- --- 96.0 94.0 --- --- --- 60.1 116 102 --- --- ---

41.5 64 --- --- 95.5 93.5 --- --- --- 59.5 114 101 --- --- ---

41.0 63 --- --- 95.0 93.0 --- --- --- 58.7 112 99 --- --- ---

40.5 62 --- --- 94.5 92.0 --- --- --- 58.0 110 98 --- --- ---

40.0 61 --- --- 93.5 91.5 --- --- --- 57.3 108 96 --- --- ---

39.5 60 --- --- 93.0 91.0 --- --- --- 56.5 107 95 --- --- ---

39.0 59 --- --- 92.5 90.5 --- --- --- 55.9 106 94 --- --- ---

38.5 58 --- --- 92.0 90.0 --- --- --- 55.0 104 92 --- --- ---

38.0 57 --- --- 91.0 89.5 --- --- --- 54.6 102 91 --- --- ---

37.8 56 --- --- 90.5 89.0 --- --- --- 54.0 101 90 --- --- ---

37.5 55 --- --- 90.0 88.0 --- --- --- 53.2 99 89 --- --- ---

37.0 54 --- --- 89.5 87.5 --- --- --- 52.5 --- 87 --- --- ---

36.5 53 --- --- 89.0 87.0 --- --- --- 51.8 --- 86 --- --- ---

36.0 52 --- --- 88.0 86.5 --- --- --- 51.0 --- 85 --- --- ---

35.5 51 --- --- 87.5 86.0 --- --- --- 50.4 --- 84 --- --- ---

35.0 50 --- --- 87.0 85.5 --- --- --- 49.5 --- 83 --- --- ---

34.8 49 --- --- 86.5 85.0 --- --- --- 49.1 --- 82 --- --- ---

34.5 48 --- --- 85.5 84.5 --- --- --- 48.5 --- 81 --- --- ---

34.0 47 --- --- 85.0 84.0 --- --- --- 47.7 --- 80 --- --- ---

33.5 46 --- --- 84.5 83.0 --- --- --- 47.0 --- 79 --- --- ---

33.0 45 --- --- 84.0 82.5 --- --- --- 46.2 --- 79 --- --- ---

32.5 44 --- --- 83.5 82.0 --- --- --- 45.5 --- 78 --- --- ---

32.0 43 --- --- 82.5 81.5 --- --- --- 44.8 --- 77 --- --- ---

31.5 42 --- --- 82.0 81.0 --- --- --- 44.0 --- 76 --- --- ---

31.0 41 --- --- 81.5 80.5 --- --- --- 43.4 --- 75 --- --- ---

30.8 40 --- --- 81.0 79.5 --- --- --- 43.0 --- 74 --- --- ---

30.5 39 --- --- 80.0 79.0 --- --- --- 42.1 --- 74 --- --- ---

30.0 38 --- --- 79.5 78.5 --- --- --- 41.5 --- 73 --- --- ---

29.5 37 --- --- 79.0 78.0 --- --- --- 40.7 --- 72 --- --- ---

29.0 36 --- --- 78.5 77.5 --- --- --- 40.0 --- 71 --- --- ---

28.5 35 --- --- 78.0 77.0 --- --- --- 39.3 --- 71 --- --- ---

28.0 34 --- --- 77.0 76.5 --- --- --- 38.5 --- 70 --- --- ---

27.8 33 --- --- 76.5 75.5 --- --- --- 37.9 --- 69 --- --- ---

27.5 32 --- --- 76.0 75.0 --- --- --- 37.5 --- 68 --- --- ---

27.0 31 --- --- 75.5 74.5 --- --- --- 36.6 --- 68 --- --- ---

26.5 30 --- --- 75.0 74.0 --- --- --- 36.0 --- 67 --- --- ---

26.0 29 --- --- 74.0 73.5 --- --- --- 35.2 --- 66 --- --- ---

25.5 28 --- --- 73.5 73.0 --- --- --- 34.5 --- 66 --- --- ---

25.0 27 --- --- 73.0 72.5 --- --- --- 33.8 --- 65 --- --- ---

24.5 26 --- --- 72.5 72.0 --- --- --- 33.1 --- 65 --- --- ---

24.2 25 --- --- 72.0 71.0 --- --- --- 32.4 --- 64 --- --- ---

24.0 24 --- --- 71.0 70.5 --- --- --- 32.0 --- 64 --- --- ---

23.5 23 --- --- 70.5 70.0 --- --- --- 31.1 --- 63 --- --- ---

23.0 22 --- --- 70.0 69.5 --- --- --- 30.4 --- 63 --- --- ---

22.5 21 --- --- 69.5 69.0 --- --- --- 29.7 --- 62 --- --- ---

22.0 20 --- --- 68.5 68.5 --- --- --- 29.0 --- 62 --- --- ---

21.5 19 --- --- 68.0 68.0 --- --- --- 28.1 --- 61 --- --- ---

21.2 18 --- --- 67.5 67.0 --- --- --- 27.4 --- 61 --- --- ---

21.0 17 --- --- 67.0 66.5 --- --- --- 26.7 --- 60 --- --- ---

20.5 16 --- --- 66.5 66.0 --- --- --- 26.0 --- 60 --- --- ---

20.0 15 --- --- 65.5 65.5 --- --- --- 25.3 --- 59 --- --- ---

--- 14 --- --- 65.0 65.0 --- --- --- 24.6 --- 59 --- --- ---

--- 13 --- --- 64.5 64.5 --- --- --- 23.9 --- 58 --- --- ---

--- 12 --- --- 64.0 64.0 --- --- --- 23.5 --- 58 --- --- ---

--- 11 --- --- 63.5 63.5 --- --- --- 22.6 --- 57 --- --- ---

--- 10 --- --- 62.5 63.0 --- --- --- 21.9 --- 57 --- --- ---

--- 9 --- --- 62.0 62.0 --- --- --- 21.2 --- 56 --- --- ---

--- 8 --- --- 61.5 61.5 --- --- --- 20.5 --- 56 --- --- ---

--- 7 --- --- 61.0 61.0 --- --- --- 19.8 --- 56 --- --- ---

--- 6 --- --- 60.5 60.5 --- --- --- 19.1 --- 55 --- --- ---

--- 5 --- --- 60.0 60.0 --- --- --- 18.4 --- 55 --- --- ---

--- 4 --- --- 59.0 59.5 --- --- --- 18.0 --- 55 --- --- ---

--- 3 --- --- 58.5 59.0 --- --- --- 17.1 --- 54 --- --- ---

--- 2 --- --- 58.0 58.0 --- --- --- 16.4 --- 54 --- --- ---

--- 1 --- --- 57.5 57.5 --- --- --- 15.7 --- 53 --- --- ---

--- 0 --- --- 57.0 57.0 --- --- --- 15.0 --- 53 --- --- ---

E. SELECTED BEARING CATALOG

Pinion

Gear

F. FITS AND TOLERANCE CHARTS

CLEARANCE FITS

FORCE FITS

F. SELECTED COUPLING CATALOG

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