Improvement of Design of Winches

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

http://www.plimsollcorp.com/images/Products/Winches/Winch-ahtw.jpg

World Carbon Steel Product Prices

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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.


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)


(%)

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


708.102=×

− , for KRL = 1.


704.164=×

− , for KRL = 1.6


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


2103.308=×

− , for KRL = 1


2103.493=×

− , for KRL = 1.6


2100.555=×

− , for KRL = 1.8

Hoop stress from

designed thickness (N/mm2)

Allowable hoop stress

(N/mm2)


(%)

Thickness from

allowable hoop stress

(m)

Original thickness

(m)


(%)

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


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


-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





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


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


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


-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






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


38


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



-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






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


39


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



-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






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


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



-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






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


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


Weight = 7 kg

Experiment Two


Compressive


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


269

11 /586.0

4.0211

10142103.3

211

mmNE=

⎟⎠⎞

⎜⎝⎛ −

×××=

⎟⎠⎞

⎜⎝⎛ −

×=

−

ν

εσ


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


86.5586.0434.3

1

===σσ t


33.6949.0009.6

1

===σσ t

Weight = 6 kg

Experiment Two


Compressive


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


4.03 4 200 0.825 5.150 6.24

Weight = 5kg

Experiment Two


Compressive



(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


Compressive



(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


Weight = 3kg

Experiment Two


Compressive



(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


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



,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



,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


,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=


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=


0.17874.172tan 1−=β


22bYbXbR RRR +=

22 7.16989.1974 +=bRR kNRbR 0.2605=


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=


9.6874.172tan 1−=β


22bYbXbR RRR +=

22 7.16980.3074 +=bRR kNRbR 1.3512=


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



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


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



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.


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.


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


315176−=×

−

Allowable shear stress = 0.4 x 350 = 140N/mm2


140110−=×

−

Table 3 – Calculated bearing stress and shear of axle at support side

Principle stress

Allowable bearing stress


Principle shear stress

Allowable shear stress


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=


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=


931.263=×

−

Table 4 – Bending and shear stresses on weld joint Principle bending

stress

Allowable stress



Allowable stress


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


315164−=×

−



14082−=×

−

Table 5 – Bearing and shear stresses on axle at flanges

Principle stress






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×=


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×=


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


315545=×

−



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


315210−=×

−



14082−=×

−

Table 6 – Bearing and shear stresses on axle at outer flange

Principle stress






545 315 73.0% 285 140 103.6% Table 7 – Bearing and shear stresses on axle at inner flange

Principle stress






210 315 -33.3% 82 140 -28.6%

66

Documents

Improvement of Design of Winches