AM16 IMPROVEMENT IN THE DESIGN OF WINCHES
submitted by Lim Buan Teck, Danny
Department of Mechanical Engineering
In partial fulfillment of the requirements for the Degree of
Bachelor of Engineering National University of Singapore
Session 2004/2005
SUMMARY
This is a collaborative project with the Plimsoll Cooperation Pte Ltd. In this project, the
objective of this project is to analysis and improves the current design of an anchor
handling and towing winch. A winch is made up of many components: drum, shaft, brake
assembly, hydraulic system and etc but the main focus of study is on the drum. The drum
of the winch is like a thin wall shell structure with rope wound on it in layers. As the
layers of rope wounding increases, the hoop stress generated in the shell increases and it
is important to study the relationship between multi layering and stress generated. The
cost of manufacturing a drum rises very sharply with the increasing thickness. Therefore,
determination of critical thickness of the drum is crucially important to balance
manufacturing cost and safety of operation.
Two Standards, Standards Association of Australia and Det Norske Veritas Standard,
have been developed for winch and crane designing criteria. The Standards provide the
requirement for determining the critical thickness and was followed in reference to
calculate the thickness under specified loadings. The results from the calculation require
a larger thickness of drum than those currently being designed. Furthermore, the result
from each Standard deviates by a large amount. There seems to be a discrepancy in the
requirement given by the Standard. No analysis was provided on how the empirical
formulae were derived.
i
Two experiments have been conducted on the prototype to simulate the actual loading on
the drum under loading. The aim of the first experiment is to verify the validity of the
requirement and the experimented results show that it was too conservative and the
application is too generalized. The aim of the second experiment is to observe the hoop
stress behavior in relation to loading condition. The first experiment is done by loading
the prototype in the beginning and wounding to lift the load is carried out. The loading of
the second experiment is done after a specific wounding is pre-set and the hoop stress
generated was found to be lower than the first experiment and requirement.
The results from the experiment prove that the requirement given in the Standards was
too conservative and the generated hoop stress depends largely on the loading conditions.
A reason for such phenomenon is called the rope relaxation. As the wounding continue to
load on another layer of rope on the wounded layer of rope, the inner wounded rope will
experience lesser pulling force from the load. The inner layer of rope acts to be part of or
additional thickness to the cylinder, and therefore, the hoop stress generated is much
lower. Further improvements can be made to refine the results and to study the effect of
rope relaxation so as to achieve the objective in this thesis.
ii
ACKNOWLEDGEMENTS
The author wishes to express sincere appreciation of the assistance given by:
• The supervisor of this research, A/P Chew Chye Heng, for his kind guidance,
support and sharing of his knowledge
• Plimsoll Cooperation Pte Ltd, for the collaboration of the research and the visit
and data provided.
• Mr Leow Beng Kwang, and fellow research students for their advice and support
• All the technicians in the Dynamics/Vibration Lab for their assistance.
iii
TABLE OF CONTENTS
TOPIC Page
SUMMARY i
ACKNOWLEDGEMENT iii
TABLE OF CONTENTS iv
LIST OF FIGURES vi
LIST OF TABLES viii
LIST OF SYMBOLS ix
CHAPTER ONE: INTRODUCTION 1
1.1 OBJECTIVE 1
1.2 BACKGROUND 1
1.3 SCOPE 4
CHAPTER TWO: LITERATURE RESEARCH 5
2.1 DEFINATION OF A WINCH 5
2.2 RESEARCH DONE 6
CHAPTER 3: MATHEMATICAL FORMULATION 8
3.1 DERIVATION OF FORMULAE 8
3.2 DNV STANDARD 12
3.2.1 HOOP STRESS 12
3.2.2 MINIMUM REQUIRED THICKNESS 13
3.3 SAA STANDARD 15
3.3.1 MINIMUM REQUIRED THICKNESS 15
iv
3.3.2 HOOP STRESS 16
3.4 ANALYSIS OF DATA 17
CHAPTER 4: EXPERIMENTAL RESEARCH 18
4.1 EXPERIMENTAL SET UP 18
4.2 MATERIAL 19
4.3 STRAIN GAUGE 19
4.4 STRAIN METER 21
4.5 EXPERIMENTAL PROCEDURES 21
CHAPTER 5 OBSERVATION AND ANALYSIS 23
5.1 EXPERIMENT ONE 24
5.2 EXPERIMENT TWO 28
CHAPTER 6 CONCLUSION 30
CHAPTER 7 RECOMMENDATIONS 32
REFERENCES 34
APPENDICES
1. APPENDIX A 35
2. APPENDIX B 42
3. APPENDIX C 46
v
LIST OF FIGURES
Figure Page
1 A winch for marine application 1
2 Trend on Steel Prices over the past 2 years 2
3 A unprocessed drum 3
4a Cylindrical shell 8
4b Long thin cylindrical shell with closed ends under 8
internal pressure.
4c Circumferential and longitudinal stresses in a thin 8
cylinder with closed ends under internal pressure.
5 Derivation of circumferential stress 9
6a Schematic Diagram of loading on rope and cylinder 10
6b Free body diagram of cylinder due to coiled wire rope 10
under pulling force, S
6c Free body diagram of wire rope due to pulling force, S 10
7 Schematic drawing of setup of prototype 18
8 Schematic drawing of strain gauges positions 20
8a A fixed strain gauge 20
9a Strain indicator unit 21
9b Switch and balance unit 21
10a Position of strain gauges and loading condition 24
10b Actual setup 24
10c Actual coiling condition during experiment 24
vi
11 Strain Reading vs Layer of Rope Loading For 7kg 25
12a Position of strain gauges and loading condition 28
12b Actual setup 28
13 Proposed setup for detail experiment data collection 32
vii
LIST OF TABLES
Table Page
1 Data for hoop stress and drum thickness from DNV Standard 14
2 Data for hoop stress and drum thickness from SAA Standard 16
3 Strain Readings for Experiment One 25
4 Tabulated Result from Experiment One 27
5 Strain Readings for Experiment Two 28
6 Tabulated Results from Experiment Two 29
viii
List of Symbols
Symbol Page
D.C. Direct Current 5
SAA Standards Association of Australia 6
DNV Det Norske Veritas 6
σh,σ1 Circumferential (Hoop) stress 8
σ2 Longitudinal stress 8
P Pressure 8
r Radius of Shell 8
t Thickness of shell 8
1ε Circumferential strain 9
E Young’s Modulus 9
ν Poisson Ratio 9
2ε Longitudinal strain 9
p Pitch of rope coil 10
S Pulling force (Rope Tension) 10
C Rope layer factor (DNV) 11
tav Thickness of drum (DNV) 11
TDC Empirical Thickness (SAA) 11
KRL Rope layer factor (SAA) 11
PRS Maximum rope load 11
FC Permissible compressive/hoop stress 11
WRC Wire-rope core 11
ix
WSC Wire-strand core 11
N Newton 12
m Meter 12
mm Millimeter 12
PMMA Polymethylmethacrylate 19
SG Strain gauge 20
x
CHAPTER 1
INTRODUCTION
1.1 OBJECTIVE The objective of this project is to analyze and improve the current design of an anchor
handling and towing winch. Improvements of the design of winch shown in Fig. 1
include redesigning the winch to cut down on the materials use for production.
Fig 1 A winch for marine application (source: [1])
1.2 BACKGROUND
The price of steel material has increased by about 80% over the last 2 years resulting
from supply shortage around the world. China has been consuming greatly on steel
material to build up its infrastructure and rapidly expanding its economy as many foreign
Multi-National Companies (MNCs) have set up their manufacturing plants there.
According to MEPS statistic of world steel price, the price for a ton of cold rolled coil
steel in Dec 2002 has soared from USD$400 to Nov 2004 USD$735 in only 2 years time
as shown in Fig. 2.
1
World Carbon Steel Product Prices
0
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Dec(02
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Jun(0
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Date
$US/
tonn
e) Hot Rolled CoilCold Rolled CoilHot Rolled Plate
Fig 2 Trend on Steel Prices over the past 2 years (source [2])
Due to economic downturn around the world, instead of passing the increase in steel
price to the consumers, stiff competition is forcing steel users to absorb the higher costs.
This in turn has caused companies manufacturing steel products to cut cost in all its
expenses in order to remain profitable; but cutting cost is definitely not the long term
solution for companies to stay competitive. Material-efficient design is one of the
solutions to cushion the increased price of steel. A material-efficient design has many
benefits:
1. The cost of purchasing unprocessed steel material will be minimized.
2. The manufacturing methods can be simplified.
3. Transportation costs from steel supplier to manufacturing plant and finally to the
consumer can be minimized.
2
The aim of a material-efficient design is to eliminate excess material without
compromising the safety and strength criteria. A good example of a material-efficient
design from nature would be the eggshell, the thickness of the egg may be thin but it can
support a compressive stress loading of 7 MPa between its two ends. Thus by applying a
material-efficient design, eliminating the excess materials from the design would ensure
lower steel consumption and thus minimization of total purchasing cost of unprocessed
steel material.
The main component of the winch under loading is the drum. The production of the drum
is to bent and coil a flat steel plate under immense pressure. When the flat steel is rolled
into a round barrel as the two ends meets, the joint is welded and the drum is produced
after several finishing processes. The pressure required to coil the steel plate depends on
the thickness of the plate, the thicker the plate, the higher the pressure required to coil.
Thus the cost of manufacture a winch rises very sharply with the thickness of the drum
shell. A material-efficient design will provide a minimum required thickness of the drum
to simplify the manufacturing process and to reduce the manufacturing cost.
Fig 3 A unprocessed drum
3
Reducing the materials needed for manufacturing the winch will in turn reduce the
overall weight of the winch. The manufacturing plant requires unprocessed steel
materials to be first shipped to Singapore. These unprocessed steels will be processed to
build the winch and thus sold by shipping it to consumers in any part of the world. The
transportation of the materials to the winch can be costly and transportation cost of
logistic company depends on the weight of the cargo. A reduction in material used will
lead to a significant reduction in overall weight, the transportation costs of steel supplier
to the manufacturing plant and to the consumer can also be minimized significantly.
Considering the benefits of a material-efficient design can provide to decrease production
and transportation cost, and save steel consumption. It is of paramount importance to
analysis the stress loading of a winch and improves the current design of an anchor
handling and towing winch to be material-efficient.
1.3 SCOPE
This is a collaborative project with the Plimsoll Cooperation Pte Ltd. The main focus area
of study is to analysis the stress loading on drum and the effects of multi layer rope
coiling on drum.
The main sections of the reports are as follows: Chapter 2 deals with literature review
done, Chapter 3 deals with detail explanations of formulae derived and results of the
calculations. Chapter 4 deals with the experimenting on a prototype modal, Chapter 5
deals with the observation of results and analysis, Chapter 6 deals with the conclusion
and Chapter 7 deals with the recommendations.
4
CHAPTER 2
LITERATURE RESEARCH
2.1 DEFINITION OF A WINCH
Winches are lifting, hauling or holding devices in which a tensioned rope is wound round
a rotating drum. They are extensively used for transporting people or goods, and they can
be found especially in mines and in marine applications. Winches are the fundamental
elements, for example, in crane and mooring systems, for activating cable cars, lifts and
as a matter of fact, whenever a dynamic pull is required from a flexible rope. Throughout
history winches have been used and probably the earliest illustration of a directly coupled
winch is the mechanism used at a well-head for lifting water containers.
Fundamentally the term “winch” describes the whole machine which consists of a drum
or pulley carrying rope and driven by some form of power unit. The choice of drum/rope
configuration, drive transmission and power unit depends upon the designed application.
There is also a brake system to lock the drum from rotating for holding load and safety
reasons. The drum can be manually driven or by electric, hydraulic or steam power
depending on the application, and the driving device is coupled to the drum directly or
indirectly according to the availability of torque and the torque requirements. An indirect
coupling would be to use a clutch or gear and the intermediate of both components. Most
systems are gear coupled when the power source is not capable of producing adequate
torque, but when it can be used, the direct coupling system is mechanically better. It
eliminates gearing, reduces the number of bearings and simplifies the overall design.
5
Hydraulic and D.C. drive system are popular choice nevertheless because they can be
speed and torque controlled over a wide range of conditions.
Most winch carry braking system, either dynamic or static. In D.C. electric and
hydraulically powered machines, regenerative braking can be use to control the system
dynamically. However, there is fitted usually a static holding brake which may or may
not be capable of arresting the system from speed. This is generally of a simple
mechanical type, caliper or band, acting on a brake rim on the drum itself and can be
water-cooled if some dynamic action is required.
The main parts of the winding drum are the barrel and flanges. In the past drums were
designed mainly to withstand the loads they were subjected to. But nowadays, with
increasingly high loads and commercial competition safety becomes not the only
criterion. Proper analysis and careful manufacturing become vital. Economy, size, weight
and strength are all factors which must be weighted carefully against safety.
2.2 RESEARCH DONE
The overall dimension of the drum is normally governed by the rope diameter and length:
these in turn, depend on the load and shaft depth. It follows that for a very deep mine if
multi layering was not to be used, a long drum of large diameter would be needed in
order to accommodate all the rope. This is not possible for both economical reasons and
the availability of space. In these cases the rope is wound on a smaller drum in more than
one layer and hence the name of multi layered drum.
6
There have been research done on stress analysis on multi layering on winch drum, but
many of them are not published. The only published works that could be found are the
Standards Association of Australia (SAA) on Crane Code and the Det Norske Veritas
(DNV). The SAA Standard is derived from the papers ‘Ein Verfahren zur Berechunung
ein – und mehrlagig bewickelter Seiltrommeln’ by Dilp.-Ing. Peter Dietz, published in
the Journal of Verein Deutscher Ingenieure (VDI-Verlag GmbH, Dusseldorf) Series 13,
No12 July 1972, and ‘Untersuchungen űber die Beanspruchung der Seiltrommeln von
Kranen und Winden’ by Dr.-Ing. Helmut Ernst, published in Mitt.Forsch. Anst. GHH-
Konzern, September 1938. According to SAA Standard, it states the minimum
requirement on thickness of the drum based on the layers of wire coiled from the papers
done. And according to the DNV Standard, it has a different requirement based on
industrial practice. Both of the requirements do not provide the background and data on
the research done and the papers derived are written in German language and thus, there
is no alternative to verify the reliability of the requirements. Nevertheless, the
calculations are done on of both the Standards and can be found in the next chapter. The
detailed formulae derivation, calculated requirement and the analysis will be shown and
discussed in Chapter 3.
7
CHAPTER 3
MATHEMATICAL FORMULATION
3.1 DERIVATION OF FORMULAE
Hoop stress or circumferential stress is produced when a cylindrical shell is under an
external/internal pressure. Suppose a long circular shell is subjected to an internal
pressure p, which may be due to enclosed gas or fluid within it. The internal pressure
acting on the circumferential surface along the cylinder gives rise to the hoop stress in its
wall. If the ends of the cylinder are closed, the pressure acting on the ends is transmitted
to the walls of the walls of the cylinder, thus producing a longitudinal stress in the walls.
Fig. 4b Long thin cylindrical shell with closed ends under internal pressure.
P
Fig 4c Circumferential and longitudinal stresses in a thin cylinder with closed ends under internal pressure.
Fig. 4a Cylindrical shell
Suppose r is the mean radius of the cylinder, and that its thickness t is small, compared
with r. consider a unit length of the cylinder remote from the closed ends, as in Fig 4a;
Suppose the unit length is cut with a diametric plane, as in Fig 4b, the tensile stresses
acting on the cut sections are σ1, acting circumferentially, and σ2, acting longitudinally.
8
However, since the focus of the thesis is only on the hoop stress generated, therefore the
derivation of σ1 will only be studied. There is an internal pressure P on the inside of the
half shell. Consider equilibrium of the half-shell in a plane perpendicular to the axis of
the cylinder, as in Fig 4c; the total force due to the internal pressure P in the direction OA
is
( )12 ×× rP with a unit length of the cylinder. This force is opposed by the stresses σ1; for equilibrium
( ) ( 1212 1 ××=×× trP )σ Then
t
Pr1 =σ (3.1)
This stress σ1 is also known as the hoop (or circumferential) stress.
t
rP
O
A
σ1 σ1
Fig 5 Derivation of circumferential stress
The circumferential and longitudinal stresses are accompanied by direct strains. If the
material of the cylinder is elastic, the corresponding strains are given by
( ) ⎟⎠⎞
⎜⎝⎛ −=−= ννσσε
211Pr1
211 EtE (3.2)
( ) ⎟⎠⎞
⎜⎝⎛ −=−= ννσσε
211Pr1
122 EtE (3.3)
9
The equation for hoop stress as shown in equation is only applicable to only a constant
pressure acting on the surface. In the case of a wire rope coiling around the drum, the
pressure applied is cause by the tension pulling force in the wire rope. Therefore, for
direct calculation of hoop stress, the term pressure should be converted into the rope
pulling tension. The relationship can be determined by examining Fig 6a.
Fig 6a Schematic Diagram of loading on rope and cylinder
t
P
O
A
σ1σ1
Fig 6b Free body diagram of cylinder due to coiled wire rope under pulling force, S
P
O
A
S S Fig 6c Free body diagram of wire rope due to pulling force, S
S S σ1 σ1
Wire rope Cylinder
p
When the wire coil onto the cylinder is tensioned by a pulling force, a hoop stress is
generated onto the cylinder. By separating the two components into two free body
diagrams, Fig 6b showing the hoop stress in the cylinder and Fig 6c showing the pulling
force acting on the rope, the hoop stress acting on cylinder can be seen to be opposed by
the pulling forces S on rope; for equilibrium
( ) Spt 221 =××σ , where p is the pitch of rope coil
tp
S×
=1σ (3.4)
10
The conversion to create relationship between the rope tension and hoop stress is
achieved but it is only applicable to loading of 1 layer of rope. It is of no economical
sense to build a long drum of large diameter to hold 1 layer of rope; Multi-layering of
rope will help to reduce the length and diameter of drum but the stresses involved will be
more complex. Researches have been done to determine the effect of multi-layering and
two Standards have been followed in this thesis. The first Standard to be studied is the
DNV, and the formulae and rope layer factor derived is:
tp
SCh ××=σ , S is rope tension, p is pitch of rope grooving, tav is thickness of
drum and C is rope layer factor.
From the DNV Standard, the rope layer factor, C is given as
C = 1 for 1 layer.
= 1.75 for more than three layers.
The formulae and rope layer factor derived by the SAA Standard is given by
c
RSRLDC Fp
PKT
×=
1000 , KRL is the rope layer factor and rigidity constant of drum
shell, PRS is the maximum rope load (kN), p is the pitch of
rope coils (mm) and FC is the permissible
compressive/hoop stress (MPa).
11
From the SAA Standard, the rope layer factor, KRL is given as
KRL = 1.0 for single layer
= 1.3 for two layers of rope with wire-rope core(WRC) or wire-strand
core (WSC)
= 1.4 for two layers of rope with fibre core (FC)
= 1.5 for three layers of rope with WRC or WSC
= 1.6 for three layers of rope with FC
= 1.6 for more than three layers of rope with WRC or WSC
= 1.8 for more than three layers of rope with FC
With these formulas provided by the two Standards, the working hoop stress can be
calculated and the minimum thickness required can be determined by applying the rope
load.
3.2 DNV STANDARD
3.2.1 HOOP STRESS
According to DNV Standard, the hoop stress must not exceed 85% of the yield stress of
the material. Therefore, the thickness of the drum must be sufficient thick to ensure that
the drum will not buckle under the wire rope tension. The wire rope tension to be
calculated is taken to be 110% of the design rope load for safety reason. The maximum
rope load capacity of the winch studied is 200Tonnes.
Assumptions
1. The wire rope tension is 110% of the design rope load.
2. The pitch of the wire rope is 0.1m
3. The drum is calculated without stiffeners.
12
Ultimate Pulling Force, S = 1.1 x 200 x 103 x 9.81 = 2158.2kN
Using the designed thickness of 70mm, hoop stress
avh tp
SC×
=σ
C07.01.0102.2158 3
××
=
2/3.308 mMN=
, for C = 1 2/3.308 mmN=
2/6.539 mMN=
, for C = 1.75 2/6.539 mmN=
Allowable hoop stress = 0.85 x 350 = 297.5N/mm2
Percentage difference = %63.3%1005.297
5.2973.308=×
− , for C = 1.
Percentage difference = %4.81%1005.297
5.2976.539=×
− , for C = 1.75.
3.2.2 MINIMUM REQUIRED THICKNESS
From the above section, the calculated hoop stress is more than the allowable hoop stress.
Therefore, the designed thickness is insufficient to withstand the rope load. By
rearranging the formula into
hav p
SCtσ×
= (3.5)
the minimum required thickness can be calculated for different C, rope layer factors.
13
Using the allowable hoop stress to calculate the required thickness,
hav p
SCtσ×
= (3.6)
C6
3
105.2971.0102.2158××
×=
, for C=1 m0725.0=
, for C=1.75 m1270.0=
Percentage difference = %57.3%10070
705.72=×
− , for C = 1.
Percentage difference = %4.81%10070
70127=×
− , for C = 1.75
Hoop stress from
designed thickness (N/mm2)
Allowable hoop stress
(N/mm2)
Percentage difference
(%)
Thickness from
allowable hoop stress
(m)
Original thickness
(m)
Percentage difference
(%)
C = 1 308.3 3.63% 0.0725 3.57% C = 1.75 539.6 297.5 81.4% 0.208 0.07 81.4% Table 1- Data for hoop stress and drum thickness from DNV Standard
14
3.3 SAA STANDARD
3.3.1 MINIMUM REQUIRED THICKNESS
According to SAA Standard, the hoop stress must not exceed 60% of the yield stress of
the material. Therefore, the thickness of the drum must be sufficient thick to ensure that
the drum will not buckle under the wire rope tension. The wire rope tension to be
calculated is taken to be 110% of the design rope load for safety reason. The maximum
rope load capacity of the winch studied is 200Tonnes.
Assumptions
1. The wire rope tension is 110% of the design rope load.
2. The pitch of the wire rope is 0.1m
3. The drum is calculated without stiffeners.
Ultimate Pulling Force, S = 1.1 x 200 x 103 x 9.81 = 2158.2kN
Allowable compressive/hoop stress = 0.85 x 350 = 210N/mm2
Using the allowable hoop stress, the minimum required thickness is
c
RSRLDC Fp
PKT
×=
1000
210100
2.21581000×
××= RLK
mm8.102= , KRL is 1
mm4.164= , KRL is 1.6
mm0.185= , KRL is 1.8
15
Percentage difference = %9.46%10070
708.102=×
− , for KRL = 1.
Percentage difference = %9.134%10070
704.164=×
− , for KRL = 1.6
Percentage difference = %3.164%10070
700.185=×
− , for KRL = 1.8
3.3.2 HOOP STRESS
From the above section, the calculated minimum thickness is more than the designed
thickness. Therefore, the designed thickness is insufficient to withstand the rope load. By
rearranging the formula into
DC
RSRLc Tp
PKF
×=
1000 (3.7)
the working hoop stress can be calculated for different KRL, rope layer factors.
Using the designed wall thickness to calculate the working hoop stress,
DC
RSRLc Tp
PKF
×=
1000
701002.21581000
×××
= RLK
, K2N/mm3.308= RL is 1
, K2N/mm3.493= RL is 1.6
, K2N/mm0.555= RL is 1.8
16
Percentage difference = %8.46%100210
2103.308=×
− , for KRL = 1
Percentage difference = %9.134%100210
2103.493=×
− , for KRL = 1.6
Percentage difference = %3.164%100210
2100.555=×
− , for KRL = 1.8
Hoop stress from
designed thickness (N/mm2)
Allowable hoop stress
(N/mm2)
Percentage difference
(%)
Thickness from
allowable hoop stress
(m)
Original thickness
(m)
Percentage difference
(%)
KRL = 1 308.3 46.8% 0.103 46.9% KRL = 1.6 493.3 134.9% 0.164 134.9% KRL = 1.8 555.0
210 164.3% 0.185
0.07 164.3%
Table 2- Data for hoop stress and drum thickness from SAA Standard
3.4 ANALYSIS OF DATA
From the two tables tabulated the results shows that the designed thickness is insufficient
to withstand the working hoop stress generated by the allowable rope load. However, the
drum had never failed in the past 10 years of operations. The assumption would be that,
the empirical calculation made was too conservative or the drum has not been loaded to
its maximum capacity. In addition, although the formula in the two Standards is similar,
the results calculated are different from each other. The SAA Standard is found to be
more conservative than the DNV Standard by comparing the percentage difference in
wall thickness and the generated hoop stress. Furthermore, the derivation for the given
rope factors is not given in both the Standard and the rope factors maybe given to be
larger than required. Therefore, the next chapter will deal with setting up with a prototype
modal to conduct experiment to determine the rational behind the given rope factor given
in the DNV Standard.
17
CHAPTER 4
EXPERIMENTAL RESEARCH
4.1 EXPERIMENTAL SET UP
In order to determine the rational behind the rope factors given by the Standards, a
simplified prototype is designed to simulate in laboratory and examine the stresses
generated. The objectives of the experiment are:
a) To determine the effect of multi-layering.
b) To determine the effect of different loading conditions
Wire rope was securely attached onto the cylinder on one end and hook with a hanger on
the other end. Variable loads can be applied to the hanger to examine the effect of multi
layering by rotating the cylinder to pull the load vertically up and the accumulated wire
rope is coiled one layer on top of the other. Strain gauges are placed at specific locations
on the inner surface of the cylinder and readings are read with a static strain measuring
indicator. Figure 7 shows the principle and setup of the load system done schematically.
Hollow cylinder
Load
Wire rope
Support Support
Hanger
18
Fig 7 Schematic drawing of setup
4.2 MATERIAL
The actual material used for the designed winch is a high strength steel that has a large
Young’s modulus value. The large value in Young’s modulus is advantageous for
industrial applications like high strength to resist deformation. However, in this
experiment, we are interested on the relationship on the strain generated due to multi
layering. Therefore, a material that is of lower Young’s Modulus has to be chosen to
build the prototype. There are two types of material manufactured for hollow cylinder
that are readily available in the market: Metal and Plastic. Comparison on the advantages
and disadvantages are done on both the material and Polymethylmethacrylate (PMMA)
plastic material was selected to build the prototype based on the factors stated below:
a) PMMA material has lower Young modulus as compared to the original material.
Thus, lower stress is needed to generate a measurable strain.
b) PMMA cylinder is ready make in the market and is easier to machine.
c) The cost of material and fabrication is much lower compared to metal.
The Young’s Modulus, E of the material provided by the manufacturer is given as
3.3GPa and Poisson Ratio, ν to be 0.4
4.3 STRAIN GAUGE
4 linear strain gauges designed for PMMA are selected and placed at 90º apart at mid
span of the cylinder supported at both ends. The objective of placing the strain gauges is
to determine the critical strain among the four positions and the effect of the multi layer
on each position. The strain gauges are fixed in the inner layer of the cylinder in order to
take the direct strain value under wire rope loading shown in Fig 8.
19
All the strain gauges were carefully fixed. The procedure followed was:-
a) Marking of strain gauge position on inner surface of cylinder.
b) Surface cleaning with low grade sand paper.
c) Cleaning with acetone.
d) Cleaning with water
e) Position strain gauge on cylinder using cellulose tape.
f) Applying small drop of cyanoacrylate adhesive at intermediate surface.
g) Hold for one minute till cure.
h) Apply connecting terminal to strain gauge.
i) Solder gauge tails to terminal.
j) Solder wire cables to terminal
k) Check for continuity and resistance.
The strain gauges were made by Tokyo Sokki Kenkyujo Co. Ltd and wired in a three
cable configuration for connection to the strain measuring indicator. The specifications of
the stain gauge are resistance 120 ohms, 5mm long and stated accuracy on gauge factor
±0.3 ohms. All gauges were used from the same batch having a gauge factor of 2.11.
L ½L
SG 2
SG 3
SG 4
SG 1
SG: Strain Gauge Fig 8a A fixed strain gauge
Fig 8 Schematic drawing of strain gauges positions
20
4.4 STRAIN METER
VISHAY Measurement Group static strain indicator unit and switch and balance unit was
used to measure and record the strain generated. The switch and balance unit has ten
channels for connection to 10 sets of strain gauges. A balancing potential meter is
connected to each channel for zeroing the measuring value before taking measurement.
The switch and balance unit has three pre-set configurations of bridge circuits internally:
Quarter Bridge, Half Bridge and Full Bridge. Quarter bridge configuration is selected for
measuring due to space constraint and physical conditions of measurement does not vary
a lot. The switch and balance is connected to the strain indicator to convert the change in
resistance into digital output for recording.
Fig 9a Strain indicator unit Fig 9b Switch and balance unit
4.5 EXPERIMENTAL PROCEDURES
There are two set of experiment data to be collected. The first experiment is to determine
the strain generated from accumulating rope layering from a static load applied at the
start of the experiment. The second experiment is to determine the strain generated from
a pre-set number of rope layering before a load is applied. The aim of doing the two
experiments is to determine if there is any difference in the stress generated from two
different loading conditions.
21
Both the experiment follows the same procedures
• Connect the strain gauges to the strain meter using, the quarter bridge
configuration.
• Zero the gauge reading on the strain meter before conducting the experiment
• Load the cylinder with weight accordingly and at each layering, record the strain
readings.
o For first experiment, the weight is added at the beginning with and the
cylinder is rotated to accumulate the number of coiled layer.
o For second experiment, the number of wire layering was determined
before the load weight is added.
• Unload the weight and repeat the experiment procedures with incrementing
weights.
The recorded results are tabulated and attached as Appendix A and B. The analysis on
results of experiments is done on Chapter 5.
22
CHAPTER 5
OBSERVATION AND ANALYSIS
This chapter deals with the observation and analysis of the data collected from the
experiments describe in Chapter 4. There are two sets of data collected based on the two
experiments and the detail results for each experiment can be found in Appendix section:
Appendix for experiment one and Appendix for experiment two. The focus of this
chapter is done on the most “representative” strain readings recorded for each experiment
and observation is done on the graph plotted for the “representative” readings. The
remaining graphs plotted for each loading in the first experiment can be found in
Appendix A.
23
5.1 EXPERIMENT ONE
According to the results found in Appendix A, the data collected for the strain readings
from an applied load of 7kg is followed. The labeling of the strain gauges is shown in Fig
10a, the actual setup is shown in Fig 10b and the actual coiling is shown is Fig 10c.
SG 2
SG 3
SG 4
SG 1
Load
Rope
Rotation
Fig 10a Position of strain gauges Fig 10b Actual setup and loading condition
Fig 10c Actual coiling condition during experiment
24
The data for the strain readings are tabulated in Table 3 and the graph is plotted as Fig 11.
Weight = 7 kg Strain, ε1 (x10-6) Layer SG 1 SG 2 SG 3 SG 4
0 -236 -126 -53 -77 1 -370 -244 -117 -165 2 -488 -350 -173 -235 3 -550 -425 -201 -297 4 -580 -456 -219 -323
Table 3 – Strain Readings for Experiment One
Strain Reading vs Layer of Rope Loading (Applied Load = 7Kg)
-700
-600
-500
-400
-300
-200
-100
0
100
0 1 2 3 4
Layer
Stra
in
541 2 3 4 1 2 3
SG 4
SG 2SG 3
SG 1
Fig 11 – Strain Reading vs Layer of Rope Loading For 7kg
From the graphs, the largest strain value was found to be from SG 1. The value of the
strain readings increase inversely proportional to increasing number of rope layering
which agree the Standards studied. However, the strain values of each strain gauge were
found to differ from each other. This shows that the derivation of formulae used by the
25
Standards assuming that the stress is uniformly distributed on the loaded circumferential
area is inaccurate. Further analysis is done to compare the experimental stress and the
empirical stress as followed in the DNV Standard.
From equation 3.1
tPr
1 =σ
and equation 3.2
( ) ⎟⎠⎞
⎜⎝⎛ −=−= ννσσε
211Pr1
211 EtE
as discussed in Chapter 3, the relationship for the hoop stress and corresponding strain
can be shown as
⎟⎠⎞
⎜⎝⎛ −
××
= ν
σ
ε211
1
1 Et
rr
t
⎟⎠⎞
⎜⎝⎛ −= ν
σε
2111
1 E
⎟⎠⎞
⎜⎝⎛ −
×=
ν
εσ
211
11
E (5.1)
The empirical hoop stress from DNV is calculated by
tpSCh ×
×=σ , C = 1 for 1 layer.
= 1.75 for more than three layers
The ratio of experimental stress and empirical stress can be found as
1σ
σ h= (5.2)
26
The sample calculation and the complete data for all the result in experiment one can be
found in Appendix A.
Weight = 7 kg Strain, ε1(x10-6)
Layer SG 1 Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From
DNV, σh(N/mm2)
Ratio
1 370 1.662 3.434 2.066 2 488 2.013 3.434 1.706 3 550 2.269 3.434 1.513 4 580 2.347 6.009 2.560
Table 4 – Tabulated Result from Experiment One
Table 4 shows the hoop stress generated in experiment and the empirical hoop stress from
DNV Standard generated by multi layering and there is a large discrepancy between
them. The experimental value differs by about 2 times in the first layer loading and
decreases until a rope factor of 1.75 is multiple to the stress calculated for 3 or more
layers in the Standard. From the result, the rope factor can be considered to be too
conservative and the method of applying it is too general as the strain values at 4
locations are different. The empirical formulae is derived based on a uniform pressure
acting on circumferential area which is not directly relevant. The rope factor can be
applied at a lower value and at each layer so avoid over designing.
27
5.2 EXPERIMENT TWO
According to the results found in Appendix B, the different layering is set before a load is
applied and then the data collected for the strain readings. The labeling of the strain
gauges is shown in Fig 12a and the actual setup is shown in Fig 12b.
SG 2
SG 3
SG 4
SG 1
Load Rope
Rotation
Fig 12a Position of strain gauges Fig 12b Actual setup and loading condition
The data for the strain reading of SG 1 is considered and are tabulated in Table 5.
SG 1, ε1 (x10-6) Weight Layer 7kg 6 5 4 3
1 -142 -137 -125 -115 -102 2 -154 -150 -145 -136 -128 3 -200 -177 -165 -150 -142 4 -230 -200 -192 -175 -156
Table 5 – Strain Readings for Experiment Two
28
The strain for the applied load of 7kg is focus for observation and analysis as it is the best
“representative” strain readings. The detailed data record and calculations for all the
loadings can be found in Appendix B. The data for the strain reading for weight load of
7kg is tabulated and compared with the value collected in previous sections in Table 6.
Weight = 7 kg
Experiment Two
Layer Strain, ε1 (x10-6)
Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From DNV, σh(N/mm2)
Ratio
1 142 0.586 3.434 5.86 2 154 0.635 3.434 5.40 3 200 0.825 3.434 4.16 4 230 0.949 6.009 6.33
Table 6 – Tabulated Results from Experiment Two
Table 6 shows the hoop stress generated in experiment two and compared with the
empirical hoop stress from DNV Standard generated by multi layering and there is a large
discrepancy between the comparisons. The experiment two values differ by more than 5.5
times in the first layer loading and decreases to around 4 times before a rope factor of
1.75 is multiple to the stress calculated for 3 or more layers in the Standard. From the
result, the rope factor can be considered to be too conservative and the method of
applying it is too general. In addition, the hoop stress generated also depend on the
conditions the load is applied. For example if the load is applied with the cylinder coiled
with pre-existing rope layering, the generated hoop stress is 5 times smaller than the
empirical hoop stress. A reason for such phenomenon would be the relaxation effect of
the inner rope. The rope tension from load is transmitted to the outer layers of the coiling
and not affecting the inner layer and therefore the inner layers of rope act to increase the
thickness of drum.
29
CHAPTER 6
CONCLUSION
From the observation and analysis done in Chapter 5, there are two inferences that can be
deduced from the experiments conducted and the empirical calculation followed in
Standard. They are:
1) The rope factor derived by the Standard is too conservative and the method of
application is too general.
2) The hoop stress generated in the cylinder depends on the condition of the loading.
The thickness derived from the Standard in Chapter three is too thick to manufacture and
the cost of manufacturing will be too uneconomical to build. Beside that the calculated
thickness, two Standards have been followed and there seems to have a discrepancy in
the minimum thickness required and factors for rope layering. Therefore, an experiment
of two forms is conducted to verify the rational behind the rope factor given and effect of
different load loading conditions.
In the first experiment, the experimental hoop stresses were found to be lower than
empirical values provided by the DNV Standard. The formulae is derived from a general
formulae of calculating hoop stress generated by a constant pressure acting on all the
surface of the cylinder. However, the hoop stress generated by the rope in our experiment
is over a concentrated area under the rope. Therefore, the large difference in values show
that the formulae derived is too generalized. The rope factor given for more than 3 rope
layering is also too conservative and the application of it is too standardized. The rope
30
factor given is too large by comparing and it should be given according to each layer for
specific requirement to prevent over designing.
In the second experiment, the experimental hoop stress is found to be lower as compared
to the values in the first experiment and the empirical values from calculation. A reason
for such observation would be that the inner layer of rope is not affected by the pulling
force as compared to the outer layer of rope due to the loading condition. The rope is
coiled before the load is added and therefore, the pulling force is distributed and
concentrated on the outer layer. The inner layer of rope acts to be part or additional
thickness to the cylinder, and therefore, the hoop stress generated is much lower. This
phenomenon is referred as rope relaxation under multi layering loading.
From the two experiments, although the objective of the thesis is not completely
achieved, however the results and analysis have provided some groundwork for future
analysis. While the results have provided evidence for further development to be
research, improvement can be made to refine the findings. Further accumulation of rope
layering can be done to find the critical layering where the hoop stress becomes constant
with increasing layering. Heavier load can be experimented to observe the effect of hoop
stress due to multi layering and also rope relaxation at loads equivalent to its yield
strength. An additional experiment can be carried out to find out the effect of hoop stress
of a fully wounded drum in length and layering. Details of the experiment will be
discussed in the Chapter 7 Recommendation.
31
CHAPTER 7
RECOMMENDATIONS
Some recommendations that can improve the outcome are:
1. Increase loading and number of layering so as to attain a more conclusive results. The
trends derived from the 5 loadings and 4 layering in the two experiments may not be
large enough to establish accurate conclusion. However, the height of supports has to
be increased as the length of rope will be much longer than experimented. Better
facilities and automating the experiment have to be found and done to perform the
experiment.
2. Perform experiment with rope wounding the whole length of cylinder before building
on next layering of rope. The real case scenario of rope wounding on the winch is
done on the length of winch and the experiments done is only done on accumulating
layering on a single coil. The hoop stress generated maybe different due to effect of
rope relaxation on the pervious wounded ropes and when a subsequence wounding of
next layer of rope is wound as discussed. A simplified diagram of setup shown in Fig
12 is provided for reference.
32
Pulley
Load
Coiling Drum
Uncoiling Drum
Rope
Fig 13 Proposed setup for detail experiment data collection
3. Performing the experiment with similar or equivalent material to build the prototype.
The results perform in this thesis is based on a PMMA material built for prototype
setup. Although the fabrication and cost of PMMA is advantageous to test in lab
condition, but the loading conditions and parameters are different. The hardness value
and strength is different even thought the theory behind the experiment is similar for
different materials. The feasibility of such implementation again depends on the
funding and facilities.
4. Perform analysis on other components of winch to achieve optimum design to reduce
excess material and weight. Although the drum undergoes the direct stress created by
the wire rope, other components such as the shaft, the hull and the flange can be
improved on design by determining the critical stress acting on component and
resizing the required dimensions. Redesigning of components if possible is also an
alternative to improve the design of the winch. Example would be to remove the shaft
hidden in the winch by simply welding the two protruding shaft onto the flanges. The
redesign effort is to avert the shaft from undergoing torsion and excess material can
be removed. Analysis on component done can be found in Appendix C.
33
REFERENCES
1. http://www.plimsollcorp.com
2. http://www.meps.co.uk/World%20Carbon%20Price.htm
3. Case J., Chilver L. & Ross C.T.F. (1999) Strength of Materials and Structures
London : Arnold
4. Collins J.A. (2003) Mechanical Design of Machine Elements
New York : John Wiley
5. Orthwein W.C. (2004) Clutches and Brakes: Design and Selection
New York : Marcel Dekker
6. Shigley J.E. & Mischke C.R. (2001) Mechanical Engineering Design
Boston: McGraw Hill
7. Young W.C. & Budynas R.C. (2002) Roark’s Formulas for Stress and Strain
New York : McGraw Hill
8. Standards Association of Australia: AS 1418-1977 : [parts 1, 3 and 7]
North Sydney, N.S.W.
34
APPENDIX A
Data and Results from Experiment One
35
Weight = 7 kg
Strain, ε1 (x10-6) Layer SG 1 SG 2 SG 3 SG 4 Initial Loading -236 -126 -53 -77
1 -370 -244 -117 -165 2 -488 -350 -173 -235 3 -550 -425 -201 -297 4 -580 -456 -219 -323
Table 1 – Strain Readings from Experiment One
Strain Reading vs Layer of Rope Loading (Applied Load = 7Kg)
-700
-600
-500
-400
-300
-200
-100
0
100
0 1 2 3 4
Layer
Stra
in
542 311 2 3 4
SG 1SG 2SG 3SG 4
Graph 1 – Strain Reading vs Layer of Rope Loading For 7kg
Weight = 7 kg Strain, ε1(x10-6)
Layer SG 1 Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From
DNV, σt(N/mm2)
Ratio
1 370 1.662 3.434 2.25 2 488 2.013 3.434 1.71 3 550 2.269 3.434 1.51 4 580 2.347 6.009 2.51
Table 2 – Tabulated Result for Load = 7kg
36
Sample Calculations
Experimental Stress at Layer 1, ( )
269
11 /662.1
4.0211
10403103.3
211
mmNE=
⎟⎠⎞
⎜⎝⎛ −
×××=
⎟⎠⎞
⎜⎝⎛ −
×=
−
ν
εσ
Experimental Stress at Layer 4, ( )
269
11 /347.2
4.0211
10569103.3
211
mmNE=
⎟⎠⎞
⎜⎝⎛ −
×××=
⎟⎠⎞
⎜⎝⎛ −
×=
−
ν
εσ
Theoretical Stress from DNV, tp
SCt ××=σ
5481.97
××
×= C
434.3×= C 1
75,/434.3 2 == CmmN
.1,/009.6 2 == CmmN The ratio of experimental stress and empirical stress in layer 1
25.2662.1434.3
1
===σσ t
The ratio of experimental stress and empirical stress in layer 4
51.2347.2009.6
1
===σσ t
37
Weight = 6 kg Strain, ε1 (x10-6) Layer SG 1 SG 2 SG 3 SG 4
Initial Loading -205 -138 -40 -85 1 -320 -211 -96 -133 2 -440 -284 -136 -197 3 -468 -327 -165 -227 4 -493 -358 -177 -247
Table 3 – Strain Readings from Experiment
Strain Reading vs Layer of Rope Loading (Applied Load = 6Kg)
-600
-500
-400
-300
-200
-100
0
100
0 1 2 3 4 542 31
Layer
Stra
in
1 2 3 4
SG 4
SG 2SG 3
SG 1
Graph 2 – Strain Reading vs Layer of Rope Loading For 6kg
Weight = 6 kg Strain, ε1(x10-6)
Layer SG 1 Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From
DNV, σt(N/mm2)
Ratio
1 320 1.469 2.943 2.23 2 440 1.815 2.943 1.62 3 468 1.931 2.943 1.52 4 493 2.034 5.150 2.53
Table 4 – Tabulated Result for Load = 6kg
38
Weight = 5 kg Strain, ε1 (x10-6) Layer SG 1 SG 2 SG 3 SG 4
Initial Loading -150 -100 -32 -50 1 -270 -200 -68 -117 2 -320 -254 -101 -156 3 -369 -300 -128 -210 4 -381 -314 -145 -231
Table 5 – Strain Readings from Experiment
Strain Reading vs Layer of Rope Loading (Applied Load = 5Kg)
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
50
0 1 2 3 4 542 31
Layer
Stra
in
1 2 3 4
SG 4
SG 2SG 3
SG 1
Graph 3 – Strain Reading vs Layer of Rope Loading For 5kg
Weight = 5 kg Strain, ε1(x10-6)
Layer SG 1 Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From
DNV, σt(N/mm2)
Ratio
1 270 1.114 2.453 2.20 2 320 1.320 2.453 1.86 3 369 1.522 2.453 1.61 4 381 1.572 4.292 2.73
Table 6 – Tabulated Result for Load = 5kg
39
Weight = 4 kg Strain, ε1 (x10-6) Layer SG 1 SG 2 SG 3 SG 4
Initial Loading -124 -90 -26 -49 1 -211 -140 -58 -77 2 -290 -203 -82 -115 3 -320 -238 -107 -151 4 -341 -255 -117 -163
Table 7 – Strain Readings from Experiment
Strain Reading vs Layer of Rope Loading (Applied Load = 4Kg)
-400
-350
-300
-250
-200
-150
-100
-50
0
50
0 1 21 32 43 544 1 2 3
SG 4
SG 2SG 3
SG 1
Layer
Stra
in
Graph 4 – Strain Reading vs Layer of Rope Loading For 4kg
Weight = 4 kg Strain, ε1(x10-6)
Layer SG 1 Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From
DNV, σt(N/mm2)
Ratio
1 211 0.870 1.962 2.25 2 290 1.196 1.962 1.64 3 320 1.320 1.962 1.49 4 341 1.407 3.434 2.44
Table 8 – Tabulated Result for Load = 4kg 40
Weight = 3 kg Strain, ε1 (x10-6) Layer SG 1 SG 2 SG 3 SG 4
Initial Loading -72 -61 -20 -31 1 -155 -115 -52 -71 2 -184 -151 -74 -100 3 -215 -180 -91 -128 4 -227 -196 -105 -145
Table 9 – Strain Readings from Experiment
Strain Reading vs Layer of Rope Loading (Applied Load = 3Kg)
-250
-200
-150
-100
-50
0
50
0 1 2 3 4 542 31
Layer
Stra
in
1 2 3 4
SG 4
SG 2SG 3
SG 1
Graph 5 – Strain Reading vs Layer of Rope Loading For 3kg
Weight = 3 kg Strain, ε1(x10-6)
Layer SG 1 Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From
DNV, σt(N/mm2)
Ratio
1 155 0.639 1.472 2.30 2 184 0.759 1.472 1.94 3 215 0.887 1.472 1.66 4 227 0.936 2.575 2.75
Table 10 – Tabulated Result for Load = 3kg
41
APPENDIX B
Data and Results from Experiment Two
42
SG 1, ε1 (x10-6)
Weight Layer 7kg 6 5 4 3 1 -142 -137 -125 -115 -102 2 -154 -150 -145 -136 -128 3 -200 -177 -165 -150 -142 4 -230 -200 -192 -175 -156
Table 1 – Strain Readings from Experiment
Weight = 7 kg
Experiment Two
Layer Strain, ε1 (x10-6)
Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From DNV, σt(N/mm2)
Ratio
1 142 0.586 3.434 5.86 2 154 0.635 3.434 5.40 3 200 0.825 3.434 4.16 4 230 0.949 6.009 6.33
Table 2 – Tabulated Result for Load = 7kg Sample Calculations
Experimental Stress at Layer 1, ( )
269
11 /586.0
4.0211
10142103.3
211
mmNE=
⎟⎠⎞
⎜⎝⎛ −
×××=
⎟⎠⎞
⎜⎝⎛ −
×=
−
ν
εσ
Experimental Stress at Layer 4, ( )
269
11 /949.0
4.0211
10230103.3
211
mmNE
=⎟⎠⎞
⎜⎝⎛ −
×××=
⎟⎠⎞
⎜⎝⎛ −
×=
−
ν
εσ
Theoretical Stress from DNV, tp
SCt ××=σ
5481.97
××
×= C
434.3×= C 1,/434.3 2 == CmmN 75.1,/009.6 2 == CmmN
43
Percentage difference in two experimental stresses
%65100662.1
586.0662.11001 =×−
=×−
=t
t
σσσ
The ratio of experimental stress and empirical stress in layer 1
86.5586.0434.3
1
===σσ t
The ratio of experimental stress and empirical stress in layer 1
33.6949.0009.6
1
===σσ t
Weight = 6 kg
Experiment Two
Layer Strain, ε1 (x10-6)
Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From DNV, σt
(N/mm2) Ratio
1 137 0.565 2.943 5.21 2 150 0.619 2.943 4.76 3 177 0.730 2.943
Table 3 – Tabulated Result for Load = 6kg
4.03 4 200 0.825 5.150 6.24
Weight = 5kg
Experiment Two
Layer Strain, ε1 (x10-6)
Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From DNV, σt
(N/mm2) Ratio
1 125 0.517 2.453 4.76 2 145 0.598 2.453 4.10 3 165 0.681 2.453 3.60 4 192 0.792 4.292 5.42
Table 4 – Tabulated Result for Load = 5kg 44
Weight = 4kg
Experiment Two
Layer Strain, ε1 (x10-6)
Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From DNV, σt
(N/mm2) Ratio
1 115 0.474 1.962 4.14 2 136 0.561 1.962 3.50 3 150 0.619 1.962 3.17 4 175 0.722 3.434 4.76
Table 5 – Tabulated Result for Load = 4kg
Weight = 3kg
Experiment Two
Layer Strain, ε1 (x10-6)
Compressive
Experimental Stress, σ1 (N/mm2)
Empirical Stress From DNV, σt
(N/mm2) Ratio
1 102 0.421 1.472 3.50 2 128 0.528 1.472 2.79 3 142 0.586 1.472 2.51 4 156 0.644 2.575 4.00
Table 6 – Tabulated Result for Load = 3kg
45
APPENDIX C
Analysis of Winch Components
46
The aim of the calculations is to determine whether the new axle welded to the drum will be able to withstand the pulling and braking forces. First the magnitude and position of all the forces are determine and analyzed in different situation. The axle will be thoroughly examined at the support side, weld side, etc. The drum will be examined again with the new design to check whether the original sizing is safe under all operating conditions. In the calculation, the axle and the drum is considered as a rigid body as they are welded together.
Acting Forces
Rope Tension
F1
F1
F2
F2
R2
R1
R2
R1
Upper Drum
Lower Drum
From the diagrams above, the axle of the lower drum will be undergoing more stress then the upper drum. Therefore, the lower drum is examined to calculate the required diameter of axle. Assumptions
1. The highest torque will be from the wire rope. 2. The brake will counteract to the torque of the wire rope at 110% of the designed
braking force. 3. The pulling force will be 120% of the designed braking force to ensure the
material will not fail before the brake starts to slip. Calculations Designed Brake Force = 2943kN (300Tonne) Ultimate Brake Force, FB = 1.1 x 2943 = 3237.3kN Ultimate Pulling Force, FP = 1.2 x 2943 = 3531.6kN 47
Friction Coefficient, μ = 0.3 Wrap Angle, α = 325˚ = 5.67rad Braking Torque, TB = 3237.3 x 0.5 = 1618.7kN
From equations μαeFF
=2
1 and ( )rFFTB 21 −= , we can calculate the resultant forces on the
brake band. μαe
FF
=2
1
(1) 67.53.021
×=⇒ eFF
( )rFFTB 21 −= ( ) 9.07.1618 21 FF −=⇒ (2)
Sub (1) in (2), ( ) 9.07.1618 2
67.53.02 FeF −= ×
( ) 267.53.0 9.09.07.1618 Fe −= ×
( )9.09.07.1618
67.53.02 −= ×e
F
(3) kNF 5.4012 =⇒Sub (3) in (1),
67.53.01 5.401 ×= eF
F1 kNF 0.22001 =⇒
Ra
Rb
F2
(iii) (ii) (i)
Ra Rb Lower Drum
F2X Rope Tension
48
Considering the horizontal force of F2,
2
255cosFF X=°
°= 55cos22 FF X °×= 55cos5.4012 XF
F2X
F2
55°
F2Y
kNF X 3.2302 = The vertical force component of F2 is
X
Y
FF
2
255tan =°
°= 55tan22 XY FF °×= 55tan3.2302YF kNF Y 9.3282 =
(iii) (ii) (i)
3531.6kN
Ra Rb
230.3kN The horizontal force component is calculated before the vertical force component. The resultant force will then be calculated with the data found. Case (i) - The wire rope is acting on the leftmost end of the drum. Assumption
1. The drum is slipping due to a pulling force greater than braking torque. 2. Only one layer of wire rope around the drum is considered. 3. The axle is welded to the flange of the drum and free to rotate. Therefore, there is
no moment at the bearing support sides.
,0=∑ aRM
49
( ) ( ) ( )691.2443.23.230508.06.3531 bR=+ kNRb 8.875=
,0=∑ YF 3.2306.3531 +=+ ba RR 8.8759.3761 −=aR
kNRa 1.2886= Case (ii) - The wire rope is acting on the center of the drum. Assumption
1. The drum is slipping due to a pulling force greater than braking torque. 2. Only one layer of wire rope around the drum is considered. 3. The axle is welded to the flange of the drum and free to rotate. Therefore, there is
no moment at the bearing support sides.
,0=∑ aRM ( ) ( ) ( )691.2443.23.2303455.16.3531 bR=+
kNRb 9.1974= ,0=∑ YF
3.2306.3531 +=+ ba RR 9.19749.3761 −=aR kNRa 0.1787= Case (iii) - The wire rope is acting on the rightmost end of the drum. Assumption
1. The drum is slipping due to a pulling force greater than braking torque. 2. Only one layer of wire rope around the drum is considered. 3. The axle is welded to the flange of the drum and free to rotate. Therefore, there is
no moment at the bearing support sides.
,0=∑ aRM ( ) ( ) ( )691.2443.23.230183.26.3531 bR=+
kNRb 0.3074= ,0=∑ YF
3.2306.3531 +=+ ba RR 0.30743.3761 −=aR kNRa 9.687= 50
The vertical force component calculated.
Rb
2200.0kN Ra
F2Y Assumption
1. The vertical force component of F2 and F1 are in the same plane. 2. The axle is welded to the flange of the drum and free to rotate. Therefore, there is
no moment at the bearing support sides.
,0=∑ aRM ( )( ) ( )691.2443.29.3280.2200 bR=−
kNRb 7.1698= ,0=∑ YF
9.3280.2200 −=+ ba RR 7.16981.1871 −=aR kNRa 4.172= The resultant force and angle is calculated for each case Case (i) - The wire rope is acting on the leftmost end of the drum.
RR RY Resultant force at Ra,
22aYaXaR RRR +=
22 4.1721.2886 +=aRR kNRaR 2.2891=
51
Angle of resultant force,
1.2886
4.172tan 1−=β
°= 4.3β Resultant force at Rb,
22bYbXbR RRR +=
22 7.16988.875 +=bRR kNRbR 2.1911=
Angle of resultant force,
8.8757.1698tan 1−=β
°= 7.62β Case (ii) - The wire rope is acting on the center of the drum. Resultant force at Ra,
22aYaXaR RRR += RY
22 4.1720.1787 +=aRR kNRaR 3.1795=
Angle of resultant force,
0.17874.172tan 1−=β
°= 5.5β Resultant force at Rb,
22bYbXbR RRR +=
22 7.16989.1974 +=bRR kNRbR 0.2605=
Angle of resultant force,
9.19747.1698tan 1−=β
°= 7.40β
52
Case (iii) - The wire rope is acting on the rightmost end of the drum. Resultant force at Ra,
RX
RR RY 22aYaXaR RRR +=
22 4.1729.687 +=aRR kNRaR 2.709=
Angle of resultant force,
9.6874.172tan 1−=β
°= 1.14β Resultant force at Rb,
22bYbXbR RRR +=
22 7.16980.3074 +=bRR kNRbR 1.3512=
Angle of resultant force,
0.30747.1698tan 1−=β
°= 9.28β Table 1 – Calculated forces and resultant forces
Horizontal Forces Vertical Forces Resultant Forces Case Ra Rb Ra Rb Ra Angle Rb Angle (i) 2886.1 875.8 2891.2 3.4 1911.2 62.7 (ii) 1787.0 1974.9 1795.3 5.5 2605.0 40.7 (iii) 687.9 3074.0
172.4 1698.7 709.2 14.1 3512.1 28.9
From the data tabulated, the largest force acting on the bearing support will be at Rb in case 3.
53
Acting Moments
(iii) (ii) (i)
3531.6kN
Ra Rb 230.3kN Using the forces from the above calculations, the moments on the drum and axle can be calculated to analysis whether the original is sufficiently large for all operating conditions. Similar to the above calculations, the winch will be calculated to the largest force applied. The lower drum is undergoing higher stress and therefore, will be considered with three position of wire rope tension calculated to find the highest acting moment. Assumptions
1. The highest torque will be from the wire rope. 2. The brake will counteract to the torque of the wire rope at 110% of the designed
braking force. 3. The pulling force will be 120% of the designed braking force to ensure the
material will not fail before the brake starts to slip. 4. The bearing supports are design to be free from moments.
The horizontal moment component is calculated before the vertical force component. The resultant moment will then be calculated with the data found. The horizontal forces are resolved and will be directly taken from table for use. Calculations Case (i) - The wire rope is acting on the leftmost end of the drum. Assumption
1. The drum is slipping due to a pulling force greater than braking torque. 2. Only one layer of wire rope around the drum is considered. 3. The axle is welded to the flange of the drum and free to rotate. Therefore, there is
no moment at the bearing support sides.
54
MH
(i)
Ra Fs Moment at (i),
MH = 2886.1 x 0.508 = 1466.1kNm
Moment at brake,
(i)
MH Ra
MH = 2886.1 x 2.443 - 3531.6 x 1.935 = 217.1kNm
Case (ii) - The wire rope is acting on the center of the drum. Assumption
4. The drum is slipping due to a pulling force greater than braking torque. 5. Only one layer of wire rope around the drum is considered. 6. The axle is welded to the flange of the drum and free to rotate. Therefore, there is
no moment at the bearing support sides. Moment at (ii),
Fs
(ii)
MH
Ra
MH = 1787.0 x 1.3455
55
= 2404.4kNm
(ii)
MH
Ra Moment at brake,
MH = 1787.0 x 2.443 - 3531.6 x 1.0975 = 489.7kNm
Case (iii) - The wire rope is acting on the rightmost end of the drum. Assumption
7. The drum is slipping due to a pulling force greater than braking torque. 8. Only one layer of wire rope around the drum is considered. 9. The axle is welded to the flange of the drum and free to rotate. Therefore, there is
no moment at the bearing support sides.
MH (iii)
Ra Fs Moment at (iii),
MH = 687.9 x 2.183 = 1501.7kNm
56
MH
(iii)
Ra Moment at brake,
MH = 687.9 x 2.443 - 3531.6 x 0.26 = 762.3kNm
The vertical moment component calculated at case (i), (ii) and (iii) and at brake.
2200.0kN Ra Rb
F2Y Assumption
3. The vertical force component of F2 and F1 are in the same plane. 4. The axle is welded to the flange of the drum and free to rotate. Therefore, there is
no moment at the bearing support sides. Moment at (i),
Fs
(i)
MV Ra
MV = 172.4 x 0.508
57
= 87.6kNm
(ii)
MV Ra
Fs Moment at (ii),
MV = 172.4 x 1.3455 = 232.0kNm
(iii)
MV Ra
Fs Moment at (iii),
MV = 172.4 x 2.183 = 376.3kNm
Moment at brake,
MV = 172.4 x 2.443
Fs
MV
Ra
= 421.2kNm
Case (i) - The wire rope is acting on the leftmost end of the drum.
Resultant moment, 22VHR MMM +=
22 6.871.1466 +=
58
kNm7.1648=Resultant moment at brake,
22VHR MMM +=
22 1.4211.217 += kNm8.473= Case (ii) - The wire rope is acting on the center of the drum.
Resultant moment, 22VHR MMM +=
22 0.2324.2404 += kNm6.2415= Resultant moment at brake,
22VHR MMM +=
22 1.4217.489 += kNm9.645= Case (iii) - The wire rope is acting on the rightmost end of the drum.
Resultant moment, 22VHR MMM +=
22 3.3767.1501 += kNm1.1548= Resultant moment at brake,
22VHR MMM +=
22 1.4213.762 += kNm9.870= Table 2 - Calculated moments and resultant moments
Vertical moment MVHorizontal moment MH Resultant moment MR
Case Moment at brake Case Moment at
brake Case Moment at brake
(i) 1466.1 217.1 87.6 1468.7 473.8 (ii) 2404.4 489.7 232.0 2415.6
645.9 (ii) 1501.7 762.3 376.3
421.1 1548.1 870.9
59
Analysis of components
Stress on axle at support side Bearing stress of axle at support,
103260
109.3633 3
××
=bearingσ
2/1.131 mmNbearing =σ Shear stress of axle at support,
4260
101.35122
3
××
=π
τ bearing
2/2.66 mmNbearing =τ Maximum shear stress for circular area,
2.6634×=bearingτ
2/3.88 mmNbearing =τ Using the bearing stress and shear stress, the principle stress and shear can be determined by Mohr circle. From the Mohr circle, the principle stress is 176N/mm2 and shear stress is 110N/mm2. Allowable bearing stress = 0.9 x 350 = 315N/mm2
Percentage difference = %1.44%100315
315176−=×
−
Allowable shear stress = 0.4 x 350 = 140N/mm2
Percentage difference = %4.21%100140
140110−=×
−
Table 3 – Calculated bearing stress and shear of axle at support side
Principle stress
Allowable bearing stress
Percentage difference
Principle shear stress
Allowable shear stress
Percentage difference
178 315 -44.1% 112 140 -21.4% From the comparison, the diameter of the axle at the bearing support can be reduced.
60
Weld joint at axle and flange From the drawing, the reaction force will be equally distributed by the two flange on the axle and while the bending stress will act on the weld on the outer flange.
Stress on weld Assumption
1. The reaction force will act between the two flange and spread evenly them. 2. The bending stress will be acting on the outer flange weld.
MR
RbR
,0=∑M ( )133.0bRR RM =
133.01.3512 ×= kNm1.467=
Allowable stress on welded joint = 93 N/mm2 Bending stress on weld,
IMr
=σ
( )
6429.0
145.0101.4674
3
π××
=
2/1.195 mMN= 2/1.195 mmN=
Percentage difference = %8.109%10093
931.195=×
−
61
Shear stress on weld,
IMr
=τ
2
3
145.0707.0145.0101.467
×××××
=πh
038.0,/2.263 2 == hmMN 2/1.263 mmN=
Percentage difference = %9.182%10093
931.263=×
−
Table 4 – Bending and shear stresses on weld joint Principle bending
stress
Allowable stress
Percentage difference
Principle shear stress
Allowable stress
Percentage difference
195.1 93 109.8% 263.1 93 182.9%
Bearing and shear stress on axle For the shear stress on axle, the analysis will be studied in two cases. One of it will be with moment present at outer flange and shear force equally distributed. Another will only have reaction forces with no moment. The two cases will be analyzed and discussed. Case 1 - Moment present at outer flange and shear force equally distributed Assumption
1. The reaction force will act between the two flange and spread evenly them. 2. The bending stress will be acting on the outer flange weld.
MR
FS
RbR
,0=∑ YF bRS RF =
62
kNFS 1.3512= Bearing stress on axle,
29.0038.02×
=
SF
σ
01102.0
101.1756 3×=
2/4.159 mMN= 2/4.159 mmN=
Shear stress on axle,
429.0
22×
=π
τSF
0661.0
101.1756 3×=
2/6.26 mMN= 2/6.26 mmN= Maximum shear stress for circular area,
6.2634×=τ
2/5.35 mmN= From the Mohr circle, the principle stress is 164N/mm2 and shear stress is 82N/mm2. Allowable bearing stress = 0.9 x 350 = 315N/mm2
Percentage difference = %9.47%100315
315164−=×
−
Allowable shear stress = 0.4 x 350 = 140N/mm2
Percentage difference = %4.41%100140
14082−=×
−
Table 5 – Bearing and shear stresses on axle at flanges
Principle stress
Allowable bearing stress
Percentage difference
Principle shear stress
Allowable shear stress
Percentage difference
178 315 -47.9% 112 140 -41.4%
63
Case 2 – Reaction forces only Assumption
1. The reaction force will act accordingly at the two different flanges. 2. No bending stress will be acting on the outer flange weld.
F2
,01=∑ FM
( )2F ( 162.0257.0 )bR=
( )257.0
162.01.35122 =F
kN9.2213=,0=∑ YF
bRFF += 21
1.35129.2213 += 1.35129.2213 += kN0.5726= Bearing stress on axle at outer flange,
29.0038.01
×=
Fσ
01102.0
105726 3×=
= 2/6.519 mMN 2/6.519 mmN=
Bearing stress on axle at inner flange,
29.0038.02
×=
Fσ
01102.0
109.2213 3×=
2/9.200 mMN=
Rb
F1
64
2/9.200 mmN=Shear stress on axle on outer flange,
429.0 2
1
×=π
τF
0661.0
100.5726 3×=
2/6.86 mMN= 2/6.86 mmN= Maximum shear stress for circular area,
6.8634×=τ
2/5.115 mmN= Shear stress on axle on inner flange,
429.0 2
2
×=π
τF
0661.0
109.2213 3×=
2/5.33 mMN= 2/5.33 mmN= Maximum shear stress for circular area,
5.3334×=τ
2/7.44 mmN= From the Mohr circle, the principle stress at outer flange is 545N/mm2 and shear stress is 285N/mm2. Allowable bearing stress = 0.9 x 350 = 315N/mm2
Percentage difference = %0.73%100315
315545=×
−
Allowable shear stress = 0.4 x 350 = 140N/mm2
Percentage difference = %6.103%100140
140285=×
−
65
From the Mohr circle, the principle stress at inner flange is 210N/mm2 and shear stress is 100N/mm2. Allowable bearing stress = 0.9 x 350 = 315N/mm2
Percentage difference = %3.33%100315
315210−=×
−
Allowable shear stress = 0.4 x 350 = 140N/mm2
Percentage difference = %6.28%100140
14082−=×
−
Table 6 – Bearing and shear stresses on axle at outer flange
Principle stress
Allowable bearing stress
Percentage difference
Principle shear stress
Allowable shear stress
Percentage difference
545 315 73.0% 285 140 103.6% Table 7 – Bearing and shear stresses on axle at inner flange
Principle stress
Allowable bearing stress
Percentage difference
Principle shear stress
Allowable shear stress
Percentage difference
210 315 -33.3% 82 140 -28.6%
66