Designing and Analysis of Farm Tyre size: 12.4/11-28 Using CAD Software,

Uni Graphics (NX) and Analysis Software, ANSYS

Final Year Project Report

Group: 33 Batch: 2010-2011

Name Seat No.

Syed Huzaifa Ahmed ME-10148

Farhan Jawed ME-10153

Ubaid Arif ME-10163

Mohammad Osama Quddus ME-10206

Internal Advisor: Miss Erum Khan

Assistant Professor

Department of Mechanical Engineering

NED University of Engineering & Technology

External Advisor: Mr. Sohail Azim

Manager Product Industrialization

General Tyre and Rubber Company

Reference# 33 /2014

CERTIFICATE

It is to certify that the following students have completed their project “Designing and

analysis of Farm tyre size: 12.4/11-28 using CAD Software, Uni Graphics (NX) and analysis

software, ANSYS” satisfactorily.

Group: 33 Batch: 2010-2011

Name Seat No.

Syed Huzaifa Ahmed ME-10148

Farhan Jawed ME-10153

Ubaid Arif ME-10163

Mohammad Osama Quddus ME-10206

Internal Advisor Miss Erum Khan

Assistant Professor

Department of Mechanical Engineering

NED University of Engineering &

Technology.

External Advisor

Mr. Sohail Azim

Manager Product Industrialization

General Tyre and Rubber Company

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DEDICATION

We dedicate this project to our parents who have been our first teachers and who guided us in

every thick and thin of our lives.

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ACKNOWLEDGMENT

For many years, obtaining a bachelor’s degree in engineering has been our highest professional

goal. Taking the steps to achieve this goal has proved challenging yet rewarding. During the

process, many have influenced and contributed to our development both as students as well as

persons.

First of all, we would like to thank The Almighty ALLAH who gave us the potential to

successfully complete this project.

Dr. Mubashir Ali Siddiqui, the chairperson of our department and Dr. Shakaib, our project

coordinator, in spite of their busy schedules have provided us with necessary information

regarding this project and have helped us whenever needed.

Miss Erum Khan, our final year class and internal project advisor, has provided unwavering

support and leadership throughout our academic career. Her professional accomplishments are

inspiring and her strong encouragement has helped us remain focused and motivated

throughout our academic career at NED University. We are deeply indebted to Miss Erum

Khan for her time and thoughtful consideration.

We also thank Mr. Sohail Azim, the manager product industrialization of ‘General Tyre and

Rubber Company’ and our external project advisor, for providing the documents related to tyre

mechanics and CAD models. We would like to express our deep appreciation to him for his

continuous technical help during the course of this project.

On a personal note, we would like to give thanks to our parents for their endless guidance and

care. They have taught us hard work, dedication and commitment. The personal opportunities

that they have provided would take more than a lifetime to repay. We also thank our brothers,

sisters and friends for their encouragement during this endeavor.

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ABSTRACT

Designing and development are a major part of a country’s economics these days. This project

focuses on the designing and developing aspect of a product widely used in Pakistan. This

project was offered by the ‘General Tyre and Rubber Company’.

The focus of this project was to bring Pakistani designing capabilities in general and GTR’s

designing capabilities in particular, one step closer to competing counterparts. Currently, most

designing in Pakistan is being done on one of the oldest software like AUTOCAD. The

company intends to change that by bringing its engineers up to speed with the top designing

software like NX.

Furthermore, it was decided that instead of making prototypes and doing field-testing, it might

be a better idea to perform analysis and tests on a computer software like ANSYS. Sure,

however advanced, the artificial intelligence cannot produce the results performed in the field

but it has a major advantage. We can do it all while in the comfort of our own office and saving

a lot of company assets simultaneously.

This report documents 5 chapters in total. The first 3 chapters include all the basics of tyres

including basic design parameters. Whereas, the last 2 chapters show the work on NX and

ANSYS.

For the first part of the project, company provided a 2D tyre design, developed on AUTOCAD.

This was used to produce the exact same design on NX in 3D, which would resemble the final

product. This is discussed in chapter 4.

Secondly, the tyre designed in NX was imported in ANSYS to perform analysis. This was a

little bit tricky as ANSYS is a completely different software and quiet a lot of modifications

were required before the analysis could begin. The results of the analysis is shown in chapter

5.

Needless to say, but this project was a good learning experience both academically and

professionally and we firmly believe that this will be mutually beneficial for us and the

‘General Tyre and Rubber Company’.

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TABLE OF CONTENTS

Nomenclature ........................................................................................................................... 14

1 Introduction to Tyre .......................................................................................................... 15

1.1 Manufacturing ........................................................................................................... 16

1.2 Components ............................................................................................................... 16

1.2.1 Tread .................................................................................................................. 17

1.2.2 Bead ................................................................................................................... 18

1.2.3 Sidewall.............................................................................................................. 18

1.2.4 Shoulder ............................................................................................................. 19

1.2.5 Ply ...................................................................................................................... 19

1.3 Types of Tyres ........................................................................................................... 19

1.3.1 According to Season: ......................................................................................... 19

1.3.2 According to Pattern: ......................................................................................... 21

1.3.3 According to Vehicle: ........................................................................................ 24

1.4 Specifications ............................................................................................................ 27

1.4.1 Tyre Pressure Monitoring System ..................................................................... 27

1.4.2 Inflation Pressure ............................................................................................... 28

1.4.3 Load Rating ........................................................................................................ 30

1.4.4 Speed Rating ...................................................................................................... 30

1.4.5 Service Rating .................................................................................................... 30

1.4.6 Treadwear Rating ............................................................................................... 30

1.4.7 Rotation .............................................................................................................. 31

1.4.8 Wheel Alignment ............................................................................................... 31

1.4.9 Retread ............................................................................................................... 31

1.5 Performance Characteristics ...................................................................................... 32

1.5.1 Balance ............................................................................................................... 32

1.5.2 Camber Thrust ................................................................................................... 33

1.5.3 Centrifugal Growth ............................................................................................ 33

1.5.4 Circle of Forces .................................................................................................. 33

1.5.5 Contact Patch ..................................................................................................... 33

1.5.6 Cornering Force ................................................................................................. 33

1.5.7 Dry Traction ....................................................................................................... 33

1.5.8 Force Variation .................................................................................................. 33

1.5.9 Load Sensitivity ................................................................................................. 34

1.5.10 Pneumatic Trail .................................................................................................. 34

1.5.11 Relaxation Length .............................................................................................. 34

1.5.12 Rolling Resistance ............................................................................................. 34

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1.5.13 Self-Aligning Torque ......................................................................................... 35

1.5.14 Slip Angle .......................................................................................................... 35

1.5.15 Stopping Distance .............................................................................................. 35

1.5.16 Work Load ......................................................................................................... 35

1.5.17 Tread Wear......................................................................................................... 35

1.5.18 Wet Traction ...................................................................................................... 36

1.6 Regularity Bodies ...................................................................................................... 36

1.6.1 DOT ................................................................................................................... 36

1.6.2 NHTSA .............................................................................................................. 36

1.6.3 UTQG ................................................................................................................ 36

1.6.4 T&RA ................................................................................................................ 36

1.6.5 ETRTO ............................................................................................................... 37

1.6.6 JATMA .............................................................................................................. 37

1.6.7 TREAD Act ....................................................................................................... 37

2 The Agricultural Tractor Tyre .......................................................................................... 38

2.1 Introduction ............................................................................................................... 38

2.1.1 General ............................................................................................................... 38

2.1.2 Justification ........................................................................................................ 38

2.1.3 Development ...................................................................................................... 39

2.1.4 Classification of Types ...................................................................................... 39

2.2 Functional Requirements and Limitations ................................................................ 40

2.2.1 Functional Requirements ................................................................................... 40

2.2.2 Performance Limitations .................................................................................... 40

2.3 Systems and Power Outlets ....................................................................................... 41

2.3.1 Engine ................................................................................................................ 41

2.3.2 Power Transmission Systems and Outlets ......................................................... 42

2.3.3 Wheels................................................................................................................ 46

3 Tractor Mechanics ............................................................................................................ 47

3.1 Ideal Analysis ............................................................................................................ 47

3.1.1 Speed Analysis ................................................................................................... 47

3.1.2 Force/Torque Analysis ....................................................................................... 50

3.1.3 Power Analysis .................................................................................................. 51

3.2 Analysis With Loses.................................................................................................. 52

3.2.1 Speed Analysis ................................................................................................... 53

3.2.2 Force/Torque Analysis ....................................................................................... 54

3.2.3 Power Analysis .................................................................................................. 54

3.2.4 Other Measures of Performance ........................................................................ 55

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4 Designing of Agricultural Tyre on NX ............................................................................. 61

4.1 Computer Aided Design ............................................................................................ 61

4.2 Designing Objectives ................................................................................................ 62

4.3 Current Status at General Tyre and Rubber Company .............................................. 62

4.3.1 Current Design Application: AUTOCAD ......................................................... 62

4.4 Considered Future Design Application: NX ............................................................. 63

4.5 AUTOCAD Design ................................................................................................... 64

4.6 NX Design ................................................................................................................. 66

4.6.1 New Design ........................................................................................................ 66

4.6.2 Cross-Section ..................................................................................................... 69

4.6.3 Top View ........................................................................................................... 72

4.7 3D Model................................................................................................................... 74

4.8 Problems Associated With Designing ....................................................................... 79

4.8.1 Import or Re-design ........................................................................................... 79

4.8.2 Tolerances in Sketching ..................................................................................... 80

4.8.3 Solid or Shell...................................................................................................... 81

4.8.4 Axial and Radial Curvature in Lugs .................................................................. 82

5 Stress Analysis of Agricultural Tyre Using Finite Element Analysis .............................. 84

5.1 Introduction ............................................................................................................... 84

5.2 Materials and methods .............................................................................................. 85

5.2.1 Model of the Cord-Rubber Ply Composite ........................................................ 85

5.2.2 Element Types ................................................................................................... 85

5.2.3 Model of the Rubber Material............................................................................ 98

5.2.4 Model of the Tyre–Road Contact ...................................................................... 98

5.2.5 Assessment of the Accuracy of the FE Model ................................................... 99

5.2.6 Physical Material Properties Description........................................................... 99

5.2.7 Boundary Condition ......................................................................................... 101

5.3 Tyres Inflation Pressure .......................................................................................... 102

5.3.1 Deflection Imposed on Tyre Due to Load & Pressure ..................................... 102

5.4 Analysis Results ...................................................................................................... 104

5.4.1 Contact Analysis of Curved Ply and Ground ................................................... 104

5.4.2 Meshing on the Tyre Geometry ....................................................................... 106

5.4.3 Axisymmetric Modelling of the Rib and its Stress Concentrations ................. 107

5.4.4 4 Layered Axisymmetric Modelling of the Cross-Section .............................. 108

5.4.5 Analysis of the Lugs ........................................................................................ 109

5.5 Conclusion ............................................................................................................... 111

5.5.1 ANSYS Results’ Comparison with Actual Prototype Testing ........................ 111

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5.5.2 Future Work and Optimization ........................................................................ 112

Advantages for the ‘General Tyre and Rubber Company’ .................................................... 112

Works Cited ........................................................................................................................... 113

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TABLE OF FIGURES

Figure 1-1: Structure of styrene-butadiene copolymer ............................................................ 16

Figure 1-2: Cross-section of a car tyre showing various tyre components .............................. 16

Figure 1-3: Tread components ................................................................................................. 17

Figure 1-4: A typical summer tyre ........................................................................................... 19

Figure 1-5: A typical studded snow tyre (left) and a studless snow tyre (right) ...................... 20

Figure 1-6: A typical all season tyre ........................................................................................ 20

Figure 1-7: Graph showing the performance of all tyres ......................................................... 21

Figure 1-8: Various types of passenger tyres ........................................................................... 24

Figure 1-9: A trailer tyre .......................................................................................................... 24

Figure 1-10: A nose gear of an aircraft .................................................................................... 25

Figure 1-11: A heavy duty truck tyre ....................................................................................... 25

Figure 1-12: A motorcycle tyres .............................................................................................. 26

Figure 1-13: A bicycle tyre ...................................................................................................... 26

Figure 1-14: An agricultural tyre ............................................................................................. 26

Figure 1-15: An OTR tyre........................................................................................................ 27

Figure 1-16: A racing tyre ........................................................................................................ 27

Figure 2-1: Typical power trains (a) for a conventional tractor and (b) for walking tractor /

power tiller ............................................................................................................................... 41

Figure 2-2: A walking tractor .................................................................................................. 44

Figure 3-1: Speed analysis of tractor under ideal conditions ................................................... 49

Figure 3-2: Force/Torque analysis of tractor under ideal conditions ....................................... 49

Figure 3-3: Speed analysis of tractor with losses..................................................................... 54

Figure 3-4: Force/Torque analysis of tractor with losses ......................................................... 54

Figure 4-1: User interface of AUTOCAD ............................................................................... 63

Figure 4-2: User interface of NX ............................................................................................. 64

Figure 4-3: Tyre cross-section on AUTOCAD ........................................................................ 65

Figure 4-4: Top view of Lugs .................................................................................................. 65

Figure 4-5: Initializing the NX software .................................................................................. 66

Figure 4-6: Cross-section of the tyre ....................................................................................... 70

Figure 4-7: 2D view of 2 complete Lugs ................................................................................. 72

Figure 4-8: Sketching the lugs ................................................................................................. 73

Figure 4-9: Final sketch of a pair of lugs ................................................................................. 74

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Figure 4-10: One sided revolved portion of the cross-section in wireframe view (left) and solid

view (right)............................................................................................................................... 75

Figure 4-11: Fully revolved portion of the cross-section in wireframe view .......................... 76

Figure 4-12: Fully revolved portion of the cross-section in solid view ................................... 76

Figure 4-13: Sketch of lugs on the tyre geometry .................................................................... 77

Figure 4-14: Extruding the lugs ............................................................................................... 77

Figure 4-15: A series of lugs on tyre geometry ....................................................................... 78

Figure 4-16: Blending of lugs on tyre's top surface ................................................................. 78

Figure 4-17: Tyre's different views and lugs dimensioning on a sheet of paper ..................... 79

Figure 4-18: A view of NX when a part file is imported ......................................................... 80

Figure 4-19: Solid 3D model with arbitrary thickness ............................................................. 81

Figure 5-1: Selection of curved ply as SOLID46 layered element .......................................... 85

Figure 5-2: Selection of lugs as SHELL281 8 node element ................................................... 85

Figure 5-3: SOLID46 geometry ............................................................................................... 86

Figure 5-4: SOLID46 stress output .......................................................................................... 86

Figure 5-5: A window showing the selection of 4 layers of SOLID46 ................................... 88

Figure 5-6: SHELL281 geometry ............................................................................................ 90

Figure 5-7: A window showing our D.O.F selection ............................................................... 90

Figure 5-8: SHELL208 geometry ............................................................................................ 91

Figure 5-9: TARGE170 geometry ........................................................................................... 93

Figure 5-10: TARGE170 segments ......................................................................................... 94

Figure 5-11: CONTA173 geometry ......................................................................................... 96

Figure 5-12: Tyre deformation under the action of an external applied force ....................... 103

Figure 5-13: The model of the curved ply ............................................................................. 104

Figure 5-14: Stress concentration on curved ply ................................................................... 105

Figure 5-15: Fixed rim and meshing ...................................................................................... 105

Figure 5-16: The nodal model of the tyre (front view) .......................................................... 106

Figure 5-17: The nodal model of tyre (side view) ................................................................. 106

Figure 5-18: The rib-only model............................................................................................ 107

Figure 5-19: Stress concentration at rib corners .................................................................... 107

Figure 5-20: Cross-section for axisymmetric modelling ....................................................... 108

Figure 5-21: Result of the axisymmetric modelling of the cross-section .............................. 108

Figure 5-22: The close view of the rim section ..................................................................... 109

Figure 5-23: The lugs ............................................................................................................. 109

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Figure 5-24: Free meshing of the lugs ................................................................................... 110

Figure 5-25: Stress concentration on lugs .............................................................................. 110

Figure 5-26: Comparison of actual prototype testing with ANSYS result ............................ 111

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TABLE OF TABLES

Table 1: Properties of rubber ................................................................................................... 99

Table 2: Fabrication properties of nylon ................................................................................ 100

Table 3: Tyre dimensions (left and right) .............................................................................. 101

Table 4: Various material properties used in deflection analysis .......................................... 103

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TABLE OF GRAPHS

Graph 3.1: Travel speed vs transmission ratio at fixed Ne and wheel dia. =28 inch ............... 48

Graph 3.2: Travel speed vs engine speed at fixed transmission ratio and wheel dia. =28 inch

.................................................................................................................................................. 49

Graph 3.3: Drawbar pull vs engine torque at fixed transmission ratio and wheel dia. = 28 inch

.................................................................................................................................................. 50

Graph 3.4: Drawbar pull vs transmission ratio at fixed engine torque and wheel dia. = 28 inch

.................................................................................................................................................. 51

Graph 3.5: Travel speed vs drawbar pull at different transmission ratio ................................. 52

Graph 3.6: Travel speed vs transmission ratio at fixed slip, engine speed =1800 rpm and wheel

dia. =28 inch ............................................................................................................................ 53

Graph 3.7: Tractive efficiency vs wheel slip at different soil conditions ................................ 56

Graph 3.8: Fuel consumption vs engine power ....................................................................... 58

Graph 3.9: Specific fuel consumption vs engine power .......................................................... 58

Graph 5.1: Load rating (kg) vs speed (km/hr) ....................................................................... 102

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NOMENCLATURE

Vo: Ideal travel speed i: Wheel slip

V: Linear speed of wheels 𝜂𝑡: Tractive efficiency

Ne: Engine speed 𝜂𝑟: Tractive efficiency

Nw: Drive wheel speed 𝜂𝑒: Engine efficiency

q: Overall transmission ratio 𝜂𝑜: Overall efficiency

Te: Engine torque 𝜉, Tractive coefficient

Tw: Drive wheel torque f:: Tyre deformation

S: Soil reaction F: Vertical load on the wheels

P: Drawbar pull R: Free radius of the wheel

R: Rolling resistance force r: Radius of the tyre running in cross-section

Qe: Engine power Rs: Static tyre radius

Qd: Drawbar power L: Length of contact chord

Va: Actual travel speed pi: Pressure inside tyre

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CHAPTER 1

1 INTRODUCTION TO TYRE

Tyres are among the most essential components of ground vehicles. They perform many

important functions during vehicle operation. For example, they support vehicle weight enough

according to its own rated load capacity. They also transmit sufficient driving, braking, and

cornering efforts between the rim and road surfaces. They have the ability to resist the

longitudinal, lateral, and vertical reaction forces from the road surface without severe

deformation or failure. Further, they also relieve shocks from road surface irregularities to a

certain degree due to their damping and energy dissipation nature. Eventually, tyres provide a

safe and comfortable environment for passengers and luggage. If tyres cannot perform all these

tasks properly, the driver may easily lose control of the vehicle and face serious safety problems.

In order to satisfy these performance requirements mentioned above, tyres need to be robust

enough to withstand the applied vertical wheel load, frictional shear forces, and wear generated

on the tyre-road contact area. At the same time, tyres need to be soft and flexible enough to

absorb shocks due to road surface irregularities.

Whenever a new type of tyre is designed and manufactured, tyre testing is required to

characterize the performances of the new tyre. Many tyre testing set-ups have been developed

to measure static and dynamic tyre responses in a laboratory or a test field. However, the

experimental tyre testing is usually costly and difficult to build. In addition, experiment

equipment, its set-up, data acquisition, and analysis need highly experienced skills and long

testing time. Sometimes, the experimental tyre testing is governed by weather and temperature

of the test field environment. In addition, some extreme cases such as high tyre loading and/or

high speed of tyre rotation cannot be conducted by using conventional testing equipment. It

can also take large amount of time and effort to repeat same or similar tyre tests. In order to

overcome these limitations of the experimental tyre testing, many researchers have tried to

build alternative tyre testing environments during the last few decades.

Fortunately, modern computer technology enables to open a new era of tyre testing. Through

tyre model simulations, most of the laboratory tyre tests can be duplicated. Even limited tyre

tests that cannot be performed in laboratory, such as high speed and/or loading operations, are

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possible with the tyre model simulations. Among tyre models, a rigid ring and a finite element

analysis (FEA) tyre models are widely used.

1.1 MANUFACTURING

Pneumatic tyres are manufactured in about 450 tyre factories around the world. Over one

billion tyres are manufactured annually, making the tyre industry a major consumer of natural

rubber. It is estimated that by 2015, 1.72 billion tyres are expected to be sold globally. Tyre

production starts with bulk raw materials such as rubber, carbon black, and chemicals and

produces numerous specialized components that are assembled and cured. Many kinds of

rubber are used, the most common being styrene-butadiene copolymer.

Figure 1-1: Structure of styrene-butadiene copolymer

{http://en.wikipedia.org/wiki/Tyre#mediaviewer/File:ESBR.png}

1.2 COMPONENTS

A tyre carcass is composed of several parts: the tread, bead, sidewall, shoulder, and ply.

Figure 1-2: Cross-section of a car tyre showing various tyre components

{http://pictures.dealer.com/m/markleymotors/0927/8e1327dd4046387200095b8adc73dbbf.jpg}

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1.2.1 Tread

Tread is made from a mixture of many different kinds of natural and synthetic rubbers. The

tyre tread provides the gripping action and traction that prevents our vehicle from slipping or

sliding, especially when the road is wet or icy.

The tread is that portion of the tyre that comes in contact with the road. The tread is a thick

rubber compound formulated to provide a high level of traction that does not wear away too

quickly. The tread pattern is characterized by the geometrical shape of the grooves, lugs, and

voids. Grooves run circumferentially around the tyre, and are needed to channel away water.

Lugs are that portion of the tread design that contacts the road surface. Voids are spaces

between lugs that allow the lugs to flex. Tread patterns feature non-symmetrical lug sizes

circumferentially in order to minimize noise.

Treads are often designed to meet specific product marketing positions. High performance tyres

have small void ratios to provide more rubber in contact with the road for higher traction, but

may be compounded with softer rubber that provides better traction, but wears quickly. Mud

and snow tyres are designed with higher void ratios to channel away rain and mud, while

providing better gripping performance. When installing two new tyres with a deep tread, they

should be placed in the rear to minimize the chance of over steer.

Tread is a lot more than the rubber blocks around the outside of our tyre. The proper choice of

tread design for a specific application can mean the difference between a comfortable, quiet

ride, and a poor excuse for a tyre that leaves us feeling exhausted whenever we get out of our

car.

Figure 1-3: Tread components

{http://www.sonirodban.com/images/auto-articles-images/tyre-tread.gif}

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A proper tread design improves traction, improves handling and increases durability. It also

has a direct effect on ride comfort, noise level and fuel efficiency. The diagram above gives a

rundown of what they look like, what they're called and why the tyre manufacturers spend

millions each year fiddling with all this stuff.

Sipes are the small, slit-like grooves in the tread blocks that allow the blocks to flex. This added

flexibility increases traction by creating an additional biting edge. Sipes are especially helpful

on ice, light snow and loose dirt.

Grooves create voids for better water channeling on wet road surfaces. Grooves are the most

efficient way of channeling water from in front of the tyres to behind it. By designing grooves

circumferentially, water has less distance to be channeled.

Blocks are the segments that make up the majority of a tyre's tread. Their primary function is

to provide traction.

Ribs are the straight-lined row of blocks that create a circumferential contact "band."

Dimples are the indentations in the tread, normally towards the outer edge of the tyre. They

improve cooling.

Shoulders provide continuous contact with the road while maneuvering. The shoulders wrap

slightly over the inner and outer sidewall of a tyre.

The Void Ratio is the amount of open space in the tread. A low void ratio means a tyre has

more rubber is in contact with the road. A high void ratio increases the ability to drain water.

Sports, dry-weather and high performance tyres have a low void ratio for grip and traction.

Wet-weather and snow tyres have high void ratios.

1.2.2 Bead

The bead is the part of the tyre that contacts the rim on the wheel. The bead is typically

reinforced with steel wire and compounded of high strength, low flexibility rubber. The bead

seats tightly against the two rims on the wheel to ensure that a tubeless tyre holds air without

leakage.

1.2.3 Sidewall

The sidewall is that part of the tyre that bridges between the tread and bead. The sidewall is

largely rubber but reinforced with fabric or steel cords that provide for tensile strength and

flexibility. The sidewall contains air pressure and transmits the torque applied by the drive axle

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to the tread to create traction but supports little of the weight of the vehicle, as is clear from the

total collapse of the tyre when punctured. Sidewalls are molded with manufacturer-specific

detail, government mandated warning labels, and other consumer information.

1.2.4 Shoulder

The shoulder is that part of the tyre at the edge of the tread as it makes transition to the sidewall.

1.2.5 Ply

Plies are layers of relatively inextensible cords embedded in the rubber to hold its shape by

preventing the rubber from stretching in response to the internal pressure. The orientations of

the plies play a large role in the performance of the tyre and is one of the main ways that tyres

are categorized.

1.3 TYPES OF TYRES

1.3.1 According to Season:

1.3.1.1 Summer Tyre

As a tyre for use in seasons without snow (spring, summer, and fall), the summer or general

tyre is optimized for reduced noise, smooth driving and safe handling at high speeds.

Figure 1-4: A typical summer tyre

{http://www.hankooktyre-eu.com/technology/types-of-tyres/according-to-season.html}

1.3.1.2 Snow Tyre

Snow tyres provide good steering and are designed to have high braking and tractive force in

snow. These characteristics are due to the treads with deep grooves which aggressively grab

onto soft snow. When driving with snow tyres, the snow that is stuck in the grooves of the tread

is compressed in an up and down direction and hardened to form a firm snow pillar. If snow

tyres are used in seasons without snow, wear occurs faster than for regular tyres so it is more

economical to change to regular tyres once winter is over.

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Studded Snow Tyre

While snow tyres perform better on icy roads than regular tyres, they cannot provide major

propulsion capability, braking capability and prevention of side slippage. To improve driving

performance on icy roads, steel studs were embedded onto snow tyres.

Studless Snow Tyre

While studded snow tyres perform well on icy, frozen roads, the studs tend to damage roads

and cause debris. Due to such problems, the studless tyre was born. The studless tyre is one

which shows maximized driving performance on slippery, frozen roads. Compared to existing

snow tyres, its snow capabilities are improved to near those of studded tyres.

Figure 1-5: A typical studded snow tyre (left) and a studless snow tyre (right)

{http://www.hankooktyre-eu.com/technology/types-of-tyres/according-to-season.html}

1.3.1.3 All Season Tyre

These tyres are developed to relieve the difficulty of changing from summer tyres to winter

ones in regions with short snow seasons, the all season has more tread kerfs than the summer

tyre. This means the all-weather tyres are unlikely to be as good as the best specialist tyre in

the respective seasons but can be expected to work better on wintry roads than a summer tyre,

and better on a summer road than a winter tyre. The main benefit is that one will avoid the

hassle and cost of swapping tyres twice a year.

Figure 1-6: A typical all season tyre

{http://www.hankooktyre-eu.com/technology/types-of-tyres/according-to-season.html}

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Figure 1-7: Graph showing the performance of all tyres

{http://www.tyrereviews.co.uk/Article/Summer-VS-Winter-tyres-Warm-weather-performance.htm}

1.3.2 According to Pattern:

With the exception of certain special tyres, various characteristics exist for tyre treads (the part

of the tyre that meets the road). These characteristics are becoming more complicated as

applications grow more diverse with the development of roads and vehicles.

1.3.2.1 Rib Type

Advantages

Low rolling resistance and heat generation

High resistance to side slippage, good steering and safety

Less vibration and good rideness

Disadvantages

Relatively lower braking, driving power

Grooves are sensitive to fatigue

Main applications

Paved roads, high speeds

Mainly used for passenger cars and buses as well as light trucks

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1.3.2.2 Lug Type

Advantages

Good driving, braking power

Good for unpaved roads

Disadvantages

Relatively higher rolling resistance (low fuel economy)

Relatively greater noise

Relatively lower resistance to side slippage

Main applications

Regular roads, unpaved roads

Used for trucks, buses, light trucks

Most construction vehicles and industrial vehicles use the lug type

1.3.2.3 Rib-Lug Type

Advantages

Good steering and safety due to use of both rib and lug patterns

Good for vehicles that use both paved and unpaved roads

Disadvantages

Greater wear on ends of lugs

Rips in rib grooves

Lower driving, braking power than lug type

Main applications

Paved, unpaved roads

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Used for trucks, buses

1.3.2.4 Block Type

Advantages

Good propulsion, braking

Good braking, steering, safety good in snow & mud

Disadvantages

Wears faster than rib or lug types

High rolling resistance

Main applications

Snow tyre

Used for sand service vehicles

1.3.2.5 Asymmetrical Type

Advantages

Uniform contact area

Good wear and braking

No need to rotate tyres

Disadvantages

Not in much use

Little compatibility with other sizes

Main applications

Passenger use tyre (high speed)

Some trucks

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1.3.3 According to Vehicle:

1.3.3.1 Passenger Vehicles

Passenger vehicle tyres are of bias and radial configuration and are further classified as summer,

winter/snow and all season tyres which are described briefly in previous sections.

Figure 1-8: Various types of passenger tyres

{http://i01.i.aliimg.com/img/pb/077/358/775/775358077_082.jpg}

1.3.3.2 Light Trailer

Often they are bias ply rather than radial tyres, and they often don't have as aggressive a tread

pattern as standard road tyres. They are not built for high traction in most cases, because in

most cases it is not vital that trailer tyres have as good a traction as that of the vehicle towing

the trailer.

Figure 1-9: A trailer tyre

{http://pimg.tradeindia.com/00182306/b/0/Tractor-Trailer-Tyre.jpg}

1.3.3.3 Aircraft

Aircraft tyres are designed to withstand extremely heavy loads for short durations. Aircraft tyre

tread patterns are designed to facilitate stability in high crosswind conditions, to channel water

away to prevent hydroplaning, and for braking effect.

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Aircraft tyres are usually inflated with nitrogen or helium to minimize expansion and contraction

from extreme changes in ambient temperature and pressure experienced during flight.

Figure 1-10: A nose gear of an aircraft

{http://www.desser.com/store/product_images/o/902/280_2504_6ply__94652_zoom.jpg}

1.3.3.4 Heavy Duty Trucks

Heavy duty tyres are also referred to as Truck/Bus tyres. Truck tyres are sub-categorized into

specialties according to vehicle position such as steering, drive axle, and trailer. Each type is

designed with the reinforcements, material compounds, and tread patterns that best optimize

the tyre performance.

Figure 1-11: A heavy duty truck tyre

{http://image.made-in-china.com/43f34j00EKJtjBZyyqkW/Superhawk-Tyre-Long-Mileage-Heavy-Duty-Truck-Tyre-Radial-

Truck-Bus-Tyre-315-80r22-5-.jpg}

1.3.3.5 Motorcycle

There are many different types of motorcycle tyres:

Sport Touring

These tyres are generally not used for high cornering loads, but for long straights, good for

riding across the country.

Sport Street

These tyres are for aggressive street riders that spend most of their time carving corners on

public roadways.

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Track or Slick

These tyres are for track days or races. They have more of a triangular form, which in turn

gives a larger contact patch while leaned over.

Figure 1-12: A motorcycle tyres

{http://www.northhantstyres.com/images/tyre-photo-zoom/indian-tyres/indian-motorcycle-tyre.jpg}

1.3.3.6 Bicycle

This classification includes all forms of bicycle tyres, including road racing tyres, mountain

bike tyres, snow tyres, and tubular tyres, used also with other human-powered vehicles. Bicycle

tyres consist of a cloth casing covered by rubber treads.

Figure 1-13: A bicycle tyre

{http://3.imimg.com/data3/YQ/XY/MY-9041727/ranger-bicycle-rubber-tyres-250x250.jpg}

1.3.3.7 Agricultural

The agricultural tyre classification includes tyres used on farm vehicles, typically tractors and

specialty vehicles like harvesters. Driven wheels have very deep, widely spaced lugs to allow

the tyre to grip soil easily.

Figure 1-14: An agricultural tyre

{http://www.firestone.eu/agri/en/tyres/tractor/r8000ss?id=186}

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1.3.3.8 Heavy Construction Vehicles

These vehicles employ off-the-road (OTR) tyres. The vehicles include wheel loaders, backhoes,

graders, trenchers, and the like; as well as large mining trucks. OTR tyres can be of either bias

or radial construction although the industry is trending toward increasing use of radial. Bias

OTR tyres are built with a large number of reinforcing plies to withstand severe service

conditions and high loads.

Figure 1-15: An OTR tyre

{http://img.weiku.com/IMG_1/2012/3/6/15/OTR-Tyre-24-00R35-2012361575521_s.jpg}

1.3.3.9 Racing

Racing tyres are highly specialized according to vehicle and race track conditions. Tyres are

specially engineered for specific race tracks according to surface conditions, cornering loads,

and track temperature. Racing tyres often are engineered to minimum weight targets.

Figure 1-16: A racing tyre

{http://image.facesource.net/39103/361547_racing-uhp-tyre-225.jpg}

1.4 SPECIFICATIONS

1.4.1 Tyre Pressure Monitoring System

Tyre pressure monitoring systems (TPMS) are electronic systems that monitor the tyre

pressures on individual wheels on a vehicle, and alert the driver when the pressure goes below

a warning limit. There are several types of designs to monitor tyre pressure. Some actually

measure the air pressure, and some make indirect measurements, such as gauging when the

relative size of the tyre changes due to lower air pressure.

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1.4.2 Inflation Pressure

Tyres are specified by the vehicle manufacturer with a recommended inflation pressure, which

permits safe operation within the specified load rating and vehicle loading. Most tyres are

stamped with a maximum pressure rating. For passenger vehicles and light trucks, the tyres

should be inflated to what the vehicle manufacturer recommends, which is usually located on

a decal just inside the driver's door or in the vehicle owners handbook. Tyres should not

generally be inflated to the pressure on the sidewall; this is the maximum pressure, rather than

the recommended pressure.

Many pressure gauges available at fuel stations have been de-calibrated by manhandling and

the effect of time, and it is for this reason that vehicle owners should keep a personal pressure

gauge with them to validate the correct tyre pressure.

Inflated tyres naturally lose pressure over time. Not all tyre-to-rim seals, valve-stem-to-rim

seals, and valve seals themselves are perfect. Furthermore, tyres are not completely

impermeable to air, and so lose pressure over time naturally due to diffusion of

molecules through the rubber. Some drivers and stores inflate tyres with nitrogen (typically at

95% purity), instead of atmospheric air, which is already 78% nitrogen, in an attempt to keep

the tyres at the proper inflation pressure longer. The effectiveness of the use of nitrogen vs. air

as a means to reduce the rate of pressure loss is baseless, and has been shown to be a bogus

marketing gimmick. One study noted a 1.3 psi (9.0 kPa; 0.090 bar) difference (from an initial

pressure of 30 psi (210 kPa; 2.1 bar)) for air-filled vs. nitrogen-filled tyres. However, the

statistical significance of the purported 1.3 psi (9.0 kPa; 0.090 bar) difference in the latter study

is questionable, since no t-test nor p values were reported. Furthermore, and more importantly,

the experimental design of the latter study was flawed, since the experiment was not repeated

for the air-filled tyres switched with the nitrogen-filled tyres. Such an experimental design

would have controlled for the possibility that the putative faster-leaking air-filled tyres was not

due to leaking issues associated with the quality of the various seals (tyre-to-rim, valve-stem-

to-rim, and the valve itself), rather than being due to differences in through-rubber diffusion

rates, as implied.

The tyre contact patch is readily reduced by both over-and-under inflation. Over-inflation may

increase the wear on the center contact patch, and under-inflation will cause a concave tread,

resulting in less center contact. Most modern tyres will wear evenly at very high tyre pressures,

but will degrade prematurely due to low (or even standard) pressures. An increased tyre

pressure has many benefits, including decreased rolling resistance. It has been found, that an

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increased tyre pressure almost exclusively results in shorter stopping distances, except in some

circumstances that may be attributed to the low sample size. If tyre pressure is too low, the tyre

contact patch is changed more than if it were over-inflated. This increases rolling resistance,

tyre flexing, and friction between the road and tyre. Under-inflation can lead to tyre overheating,

premature tread wear, and tread separation in severe cases.

1.4.2.1 High Pressure

High performance and dynamic drivers often increase the tyre pressure to near the maximum

pressure as printed on the sidewall. This is done to sacrifice comfort for performance and safety.

A tyre at higher pressure is more inclined to keep its shape during any encounter, and will thus

transmit the forces of the road to the suspension, rather than being damaged itself. This allows

for an increased reaction speed, and "feel" the driver perceives of the road. Modern tyre designs

allow for minimal tyre contact surface deformity during high pressures, and as a result the

traditional wear on the center of the tyre due to reasonably high pressures is only known to

very old or poorly designed tyres.

It may be, that very high tyre pressures have only two downsides: The sacrifice in comfort; and

the increased chance of obtaining a puncture when driving over sharp objects, such as on a

newly scraped gravel road. Many individuals have maintained their tyre pressures at the

maximum side wall printed value (inflated when cold) for the entire lifetime of the tyre, with

perfect wear until the end. This may be of negative economic value to the rubber and tyre

companies, as high tyre pressures decrease wear, and minimize side wall blow outs.

1.4.2.2 Low Pressure

It is dangerous to allow tyre pressure to drop below the specification recommended on the

vehicle placard. Low pressure increases the amount of tyre wall movement resulting from

cornering forces. Should a low-pressure tyre be forced to perform an evasive maneuver, the

tyre wall will be more pliable than it would have been at normal pressure and thus it will "roll"

under the wheel. This increases the entire roll movement of the car, and diminishes tyre contact

area on the negative side of the vector. Thus only half the tyre is in contact with the road, and

the tyre may deform to such an extent that the side wall on the positive vector side becomes in

contact with the road. The probability of failing in the emergency maneuver is thus increased.

When driving on sand or in deep snow, tyre pressure is sometimes lowered to reduce the chance

of bogging down.

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Furthermore, the tyre will absorb more of the irregular forces of normal driving. With this

constant bending of the side wall as it absorbs the contours of the road, it heats up the tyre wall

to possibly dangerous temperatures. Additionally, this flexing degrades the steel wire

reinforcement; this often leads to side wall blow-outs.

Low pressure tyres can be subject to pinching. If the vehicle drives into a pot-hole, the side

wall can temporarily collapse, thereby pinching the tyre between the steel wheel and road. This

can result in a tyre laceration and blow-out, as well as a damaged wheel.

Feathering occurs on the junction between the tyre tread and side wall, as a result of too low

tyre pressures. This is as a result of the inability of the tyre to perform appropriately during

cornering forces, leading to aberrant and shearing forces on the feathering area. This is due to

the tyre moving sideways underneath the wheel as the tyre pressures are insufficient to transmit

the forces to the wheel and suspension.

1.4.3 Load Rating

Tyres are specified by the manufacturer with a maximum load rating. Loads exceeding the

rating can result in unsafe conditions that can lead to steering instability and even rupture. For

a table of load ratings, see tyre code.

1.4.4 Speed Rating

The speed rating denotes the maximum speed at which a tyre is designed to be operated. For

passenger vehicles these ratings range from 160 to 300 km/h (100 to 200 mph). For a table of

speed ratings, see tyre code.

1.4.5 Service Rating

Tyres (especially in the U.S.) are often given service ratings, mainly used on bus and truck

tyres. Some ratings are for long haul, and some for stop-start multi-drop type work. Tyres

designed to run 500 miles (800 km) or more per day carrying heavy loads require special

specifications.

1.4.6 Treadwear Rating

The treadwear rating or treadwear grade is how long the tyre manufacturers expect the tyre to

last. A Course Monitoring Tyre (the standard tyre that a test tyre will be compared to) has a

rating of "100". If a manufacturer assigns a treadwear rating of 200 to a new tyre, they are

indicating that they expect the new tyre to have a useful lifespan that is 200% of the life of a

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Course Monitoring Tyre. The "test tyres" are all manufacturer-dependent. Brand A's rating of

500 is not necessarily going to give us the same mileage rating as Brand B's tyre of the same

rating. The testing is non-regulated and can vary greatly. Treadwear ratings are only useful for

comparing Brand A's entire lineup against itself. Tread wear, also known as tyre wear, is caused

by friction between the tyre and the road surface. Government legal standards prescribe the

minimum allowable tread depth for safe operation.

1.4.7 Rotation

Tyres may exhibit irregular wear patterns once installed on a vehicle and partially worn.

Furthermore, front-wheel drive vehicles tend to wear the front tyres at a greater rate compared to

the rear tyres. Tyre rotation is the procedure of moving tyres to different car positions, such as

front-to-rear, in order to even out the wear, thereby extending the life of the tyre. However care

must be taken with unidirectional tyres (tyres that are designed to rotate in one direction only,

for a vehicle that is going forward) so that the correct rotational direction - indicated on the

side wall with an arrow-like symbol - is maintained after the swap.

1.4.8 Wheel Alignment

When mounted on the vehicle, the wheel and tyre may not be perfectly aligned to the direction

of travel, and therefore may exhibit irregular wear. If the discrepancy in alignment is large,

then the irregular wear will become substantial if left uncorrected.

Wheel alignment is the procedure for checking and correcting this condition through

adjustment of camber, caster and toe angles. These settings also affect the handling

characteristics of the vehicle.

1.4.9 Retread

Tyres that are fully worn can be re-manufactured to replace the worn tread. This is known as

retreading or recapping, a process of buffing away the worn tread and applying a new

tread. Retreading is economical for truck tyres because the cost of replacing the tread is less

than the price of a new tyre. Retreading passenger tyres is less economical because the cost of

retreading is high compared to the price of new cheap tyres, but favorable compared to high-

end brands.

Worn tyres can be retreaded by two methods, the mold or hot cure method and the pre-cure or

cold one. The mold cure method involves the application of raw rubber on the previously buffed

and prepared casing, which is later cured in matrices. During the curing period, vulcanization

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takes place and the raw rubber bonds to the casing, taking the tread shape of the matrix. On the

other hand, the pre-cure method involves the application of a ready-made tread band on the

buffed and prepared casing, which later is cured in an autoclave so that vulcanization can occur.

During the retreading process, retread technicians must ensure the casing is in the best

condition possible to minimize the possibility of a casing failure. Casings with problems such

as capped tread, tread separation, unrepairable cuts, corroded belts or sidewall damage, or any

run-flat or skidded tyres, will be rejected.

In most situations, retread tyres can be driven under the same conditions and at the same speeds

as new tyres with no loss in safety or comfort. The percentage of retread failures should be

about the same as for new tyre failures, but many drivers, including truckers, are guilty of not

maintaining proper air pressure on a regular basis, and, if a tyre is abused (overloaded,

underinflated, or mismatched to the other tyre on a set of duals), then that tyre (new or

recapped) will fail.

Many commercial trucking companies put retreads only on trailers, using only new tyres on

their steering and drive wheels. This procedure increases the driver's chance of maintaining

control in case of problems with a retreaded tyre.

1.5 PERFORMANCE CHARACTERISTICS

The interaction of a tyre with the pavement is a very complex phenomenon. Many of the details

are modeled in Pacejka's Magic Formula. Some are explained below.

1.5.1 Balance

When a wheel and tyre rotate, they exert a centrifugal force on the axle that depends on the

location of their center of mass and the orientation of their moment of inertia. This is referred

to as balance, imbalance, or unbalance. Tyres are checked at the point of manufacture for

excessive static imbalance and dynamic imbalance using automatic tyre balance machines.

Tyres are checked again in the auto assembly plant or tyre retail shop after mounting the tyre

to the wheel. Assemblies that exhibit excessive imbalance are corrected by applying balance

weights to the wheels to counteract the tyre/wheel imbalance.

To facilitate proper balancing, most high performance tyre manufacturers place red and yellow

marks on the sidewalls to enable the best possible match-mounting of the tyre/wheel assembly.

There are two methods of match-mounting high performance tyre to wheel assemblies using

these red (uniformity) or yellow (weight) marks.

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1.5.2 Camber Thrust

Camber thrust and camber force are the force generated perpendicular to the direction of travel

of a rolling tyre due to its Camber angle and finite contact patch.

1.5.3 Centrifugal Growth

A tyre rotating at higher speeds tends to develop a larger diameter, due to centrifugal forces that

force the tread rubber away from the axis of rotation. This may cause speedometer error. As the

tyre diameter grows, the tyre width decreases. This centrifugal growth can cause rubbing of the

tyre against the vehicle at high speeds. Motorcycle tyres are often designed with reinforcements

aimed at minimizing centrifugal growth.

1.5.4 Circle of Forces

The circle of forces, traction circle, friction circle, or friction ellipse is a useful way to think

about the dynamic interaction between a vehicle's tyre and the road surface.

1.5.5 Contact Patch

The contact patch, or footprint, of the tyre, is the area of the tread that is in contact with the

road surface. This area transmits forces between the tyre and the road via friction. The length-

to-width ratio of the contact patch affects steering and cornering behavior.

1.5.6 Cornering Force

Cornering force or side force is the lateral (i.e. parallel to the road surface) force produced by

a vehicle tyre during cornering.

1.5.7 Dry Traction

Dry traction is measure of the tyre's ability to deliver traction, or grip, under dry conditions.

Dry traction is a function of the tackiness of the rubber compound.

1.5.8 Force Variation

The tyre tread and sidewall elements undergo deformation and recovery as they enter and exit

the footprint. Since the rubber is elastomeric, it is deformed during this cycle. As the rubber

deforms and recovers, it imparts cyclical forces into the vehicle. These variations are

collectively referred to as tyre uniformity. Tyre uniformity is characterized by radial force

variation (RFV), lateral force variation (LFV) and tangential force variation. Radial and lateral

force variation is measured on a force variation machine at the end of the manufacturing

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process. Tyres outside the specified limits for RFV and LFV are rejected. Geometric

parameters, including radial run-out, lateral run-out, and sidewall bulge, are measured using a

tyre uniformity machine at the tyre factory at the end of the manufacturing process as a quality

check. In the late 1990s, Hunter Engineering introduced the GSP9700 Road Force balancer,

which is equipped with a load roller similar to the force variation machine used at the factory

to grade tyre uniformity. This machine can find the best position for the tyre on a given wheel

so that the over-all assembly is as round as possible.

1.5.9 Load Sensitivity

Load sensitivity is the behavior of tyres under load. Conventional pneumatic tyres do not

behave as classical friction theory would suggest. Namely, the load sensitivity of most real

tyres in their typical operating range is such that the coefficient of friction decreases as the

vertical load increases.

1.5.10 Pneumatic Trail

Pneumatic trail of a tyre is the trail-like effect generated by compliant tyres rolling on a hard

surface and subject to side loads, as in a turn. More technically, it is the distance that the

resultant force of side-slip occurs behind the geometric center of the contact patch.

1.5.11 Relaxation Length

Relaxation length is the delay between when a slip angle is introduced and when the cornering

force reaches its steady-state value.

1.5.12 Rolling Resistance

Rolling resistance is the resistance to rolling caused by deformation of the tyre in contact with

the road surface. As the tyre rolls, tread enters the contact area and is deformed flat to conform

to the roadway. The energy required to make the deformation depends on the inflation pressure,

rotating speed, and numerous physical properties of the tyre structure, such as spring force and

stiffness. Tyre makers seek lower rolling resistance tyre constructions to improve fuel

economy in cars and especially trucks, where rolling resistance accounts for a high proportion

of fuel consumption. Pneumatic tyres also have a much lower rolling resistance than solid tyres.

Because the internal air pressure acts in all directions, a pneumatic tyre is able to "absorb"

bumps in the road as it rolls over them without experiencing a reaction force opposite to the

direction of travel, as is the case with a solid (or foam-filled) tyre. The difference between the

rolling resistance of a pneumatic and solid tyre is easily felt when propelling wheelchairs or

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baby buggies fitted with either type so long as the terrain has a significant roughness in relation

to the wheel diameter.

1.5.13 Self-Aligning Torque

Self-aligning torque, also known as the aligning torque, is the torque that a tyre creates as it

rolls along that tends to steer it, i.e. rotate it around its vertical axis.

1.5.14 Slip Angle

Slip angle or sideslip angle is the angle between a rolling wheel's actual direction of travel and

the direction towards which it is pointing (i.e., the angle of the vector sum of wheel translational

velocity and sideslip velocity).

1.5.15 Stopping Distance

Performance-oriented tyres have a tread pattern and rubber compounds designed to grip the

road surface, and so usually have a slightly shorter stopping distance. However, specific

braking tests are necessary for data beyond generalizations.

1.5.16 Work Load

The work load of a tyre is monitored so that it is not put under undue stress, which may lead to

its premature failure. Work load is measured in Ton Kilometer per Hour (TKPH). The

measurement's appellation and units are the same. The recent shortage and increasing cost of

tyres for heavy equipment has made TKPH an important parameter in tyre selection and

equipment maintenance for the mining industry. For this reason, manufacturers of tyres for

large earth-moving and mining vehicles assign TKPH ratings to their tyres based on their size,

construction, tread type, and rubber compound. The rating is based on the weight and speed

that the tyre can handle without overheating and causing it to deteriorate prematurely. The

equivalent measure used in the United States is Ton Mile per Hour (TMPH).

1.5.17 Tread Wear

There are several types of abnormal tread wear. Poor wheel alignment can cause excessive

wear of the innermost or outermost ribs. Gravel roads, rocky terrain, and other rough terrain

causes accelerated wear. Over-inflation above the sidewall maximum can cause excessive wear

to the center of the tread. Modern tyres have steel belts built in to prevent this. Under-inflation

causes excessive wear to the outer ribs. Unbalanced wheels can cause uneven tyre wear, as the

rotation may not be perfectly circular. Tyre manufacturers and car companies have mutually

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established standards for tread wear testing that include measurement parameters for tread loss

profile, lug count, and heel-toe wear. See also Work load above.

1.5.18 Wet Traction

Wet traction is the tyre's traction, or grip, under wet conditions. Wet traction is improved by

the tread design's ability to channel water out of the tyre footprint and reduce hydroplaning.

However, tyres with a circular cross-section, such as those found on racing bicycles, when

properly inflated have a sufficiently small footprint to not be susceptible to hydroplaning. For

such tyres, it is observed that fully slick tyres will give superior traction on both wet and dry

pavement.

1.6 REGULARITY BODIES

1.6.1 DOT

The United States Department of Transportation (DOT) is the U.S. governmental body

authorized by the U.S. Congress to establish and regulate transportation safety in the United

States of America.

1.6.2 NHTSA

The National Highway and Traffic Safety Administration (NHTSA) is a U.S. government body

within the Department of Transportation tasked with regulating automotive safety in the United

States.

1.6.3 UTQG

The Uniform Tyre Quality Grading System (UTQG), is a system for comparing the

performance of tyres, established by the United States National Highway Traffic Safety

Administration according to the Code of Federal Regulations 49 CFR 575.104. The UTQG

regulation requires labeling of tyres for tread wear, traction, and temperature.

1.6.4 T&RA

The Tyre and Rim Association (T&RA) is a voluntary U.S. standards organization to promote

the interchangeability of tyres and rim and allied parts. Of particular interest, they published

key tyre dimension standards, key rim contour dimension standards, key tyre valve dimension

standards, and load / inflation standards.

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1.6.5 ETRTO

The European Tyre and Rim Technical Organization (ETRTO) is the European standards

organization "to establish engineering dimensions, load/pressure characteristics and operating

guidelines" for tyres, rims and valves. It is analogous to T&RA.

1.6.6 JATMA

The Japanese Automobile Tyre Manufacturers Association (JATMA) is the Japanese standards

organization for tyres, rims and valves. It is analogous to T&RA and ETRTO.

1.6.7 TREAD Act

The Transportation Recall Enhancement, Accountability and Documentation Act (TREAD

Act) is a United States federal law that sets standards for testing and the reporting of

information related to products involved with transportation such as cars and tyres.

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CHAPTER 2

2 THE AGRICULTURAL TRACTOR TYRE

2.1 INTRODUCTION

2.1.1 General

The agricultural tractor is one of the class of mobile machines that involves the ‘traction’

process. The word 'traction' and name 'tractor' come from the word to 'draw' or 'pull' so a tractor

is basically a machine for pulling; other mobile machines such as locomotives are in the same

class. Vehicles like road trucks and even motor cars, which are essentially vehicles for carrying

loads, also involve the traction process.

The tractor is also in the class of machines that involves operation under what are known as

'off-road' conditions.

Others in this class include machines used in earth moving, mining and military work, also

four-wheel drive motor vehicles for cross - country operation.

2.1.2 Justification

The question is often asked as to what is so special about the tractor and its operation that would

justify its study as a machine in its own right. This may be answered by considering the

conditions under which the tractor is expected operate.

The agricultural soils, on which the tractor operates, are 'weak', i.e., they slip (shear)

when loaded horizontally and compact (compress) when loaded vertically. This

condition, which the tractor and its attached implement are frequently being used to

produce, is usually ideal from an agricultural point of view but is not conducive to

efficient operation from a tractive point of view.

The loading conditions on the tractor are variable from job to job and, for efficient

operation, ideally require the tractor to be set up to suit each condition.

The operating conditions for the tractor are highly variable both in time and place,

which requires continual monitoring and adjustment of both tractor and implement in

operation.

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The ground surfaces are rough and sloping, hence both tractor and implement control

is difficult; instability is an ever-present danger. This is important because the tractor

must be able to be operated by non-specialists.

A clearance above growing crops and the ability for the operator to see the ground.

2.1.3 Development

The tractor evolved in the second half of the 19th century and first half of the 20th into its

present, conventional, two wheel drive form and four wheel drive variation. This form owes

much to history but also the fact that it is an inherently logical arrangement.

Designers followed early tractor designs that were simply replacements for horses or

other draught animals.

The layout takes advantage of the transfer of weight to the main driving wheels at the

rear, as the drawbar pull on the tractor increases.

The layout is inherently stable in the horizontal plane because the implement commonly

being pulled behind the tractor tends to follow the latter and to pull it into straight line

operation.

Rear mounted implements offer a minimum of offset loading and moment in the

horizontal plane; this contrasts with, for example side mounted implements.

As a result there has been little or no major change in the basic lay-out of tractor / implement

systems over their period of development although there have been major improvements in

engines, transmissions, tyres, control systems and drivers' accommodation.

2.1.4 Classification of Types

Tractors may be classified according to their basic form, which in turn depends on the function

that each type is designed to achieve. They may be classified as follows.

Number of axles

o one – walking

o two - conventional, riding

Number of driven axles

o one - conventional and walking

o two - four wheel drive

Ground drive elements

o wheels and tyres, lugs, strakes

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o tracks - crawler, track laying

Use of wheels

o traction – conventional

o propulsion / cultivation - power tiller

2.2 FUNCTIONAL REQUIREMENTS AND LIMITATIONS

2.2.1 Functional Requirements

Although it is able to undertake a multitude of specific tasks, the functions of the tractor can

be reduced to the following:

The provision of up to full power in the form of a large drawbar pull (compared to the

weight of the tractor) at low speeds. The highly variable loading that occurs in

agricultural work requires consideration of tractor performance at part load, particularly

with respect to fuel consumption.

The provision of power for driving and control of a range of implements and machines

performing various tasks and attached in a variety of ways.

The provision of power as the basis for a transport system in both on- and off-road

conditions.

There are of course other ways by which tractors might be evaluated such as by their economy,

reliability, safety or ease of operation. These are important but are beyond the scope of this

book.

2.2.2 Performance Limitations

Since its main function is to pull (or push), the question arises as to how well and within what

limits the tractor succeeds in performing those functions. How we might measure and represent

that performance is also of interest.

This output is expressed, as in engineering mechanics, in terms of force (engine torque and

drawbar pull), speed (rotational and travel), power (engine and drawbar) and non-dimensional

numbers (wheelslip, tractive efficiency).

The input is performance is expressed in terms of fuel consumption (actual and per unit power

output).

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Figure 2-1: Typical power trains (a) for a conventional tractor and (b) for walking tractor / power tiller

2.3 SYSTEMS AND POWER OUTLETS

Tractors are built in many forms and sizes according to the particular functions that they are

required to perform.

However, in reviewing their performance it is sufficient to consider the major systems and

power outlets that are common to most tractors. The block diagram of the main components in

the power transmission system, including the power outlets and forms, is shown in Figure 2-1

(a) for a conventional tractor with PTO and hydraulic power outlets and in Figure 2-1 (b) for a

walking tractor / power tiller.

The following systems can be identified.

2.3.1 Engine

The engine, which is the immediate source of energy for the operation of the tractor, varies in

type and size according to the type and size of the tractor to which it is fitted. It is a mechanism

which, using air, extracts the energy from the fuel and transforms it into a mechanical

(rotational) form.

Its output (in terms of torque, speed and power) is determined by the physical size of the engine

(which determines the amount of air that can be drawn in), the fuel burnt in that air and its

speed of operation. Its performance, which is represented in terms of the fundamental

characteristic for the engine, i.e., the relationship between the torque and (rotational) speed,

largely determines and of course limits the performance of the tractor.

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Many other aspects of engine design and operation affect its performance. These include the

engine processes (the cycle of strokes on which it operates), the type of fuel and its method of

ignition (spark or compression ignition) and the mechanical details such as the design of the

components (pistons, crankshaft, valves) and the services such as the lubrication and cooling

systems. These details are covered in books on engine design and operation and will not be

considered further here.

Engines as used in agricultural tractors may be classified as follows:

Operational cycle

o two strokes per revolution

o four strokes per revolution

Fuel ignition

o spark - gasoline, petrol, natural gas

o compression - diesel

Air induction

o unlimited- diesel

o throttled - spark ignition

o pressurized - super-charged

Speed control

o governed - automatic

o ungoverned - manual

2.3.2 Power Transmission Systems and Outlets

The transmission systems on the tractor serve to transmit power from the engine to the power

outlets, viz:

Traction system (wheels / drawbar / three point linkage)

Power take off

Hydraulic (oil) supply

The transmission elements which comprise these systems, may be classified according to their

principle of operation:

Mechanical

o gears

o belts / chains

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Hydrostatic

o fluid pressure

Hydro-kinetic

o fluid momentum - fluid coupling

o torque converter

The three transmission systems that transmit power to the three main outlets are discussed

below.

2.3.2.1 Traction Transmission

2.3.2.1.1 Conventional tractors

The components generally referred to as the `transmission´ and / or the `gear box´ transmit the

rotation of the engine to the rear wheels as shown in Figure 1.1 and 1.2. In the conventional

tractor this is usually a mechanical system with shafts, gears etc. Because the engine rotates at

high speed (a few 1000's of rpm) and the tractor wheels must operate at low speed (a few 10´s

of rpm), the traction transmission has the function of reducing the speed of rotation of the

engine to that required for the rear wheels. Further, because not all operations require the tractor

to travel at the same speed, the transmission also has the function of enabling the speed

reduction from engine to wheels to be varied by the operator. Thus the travel speed may change

in from 6 to 12 steps, i.e., from about 1 km/hr in a `low´ gear with a 'large' reduction ratio to

about 20 km/hr in a 'high' gear with a 'small' reduction ratio. The variable ratio is achieved by

'changing gears' (that are in mesh) so that the drive (motion) passes through gears of different

sizes. This has the effect of altering the overall ratio of the transmission and causing the wheels

to run faster or slower.

The (traction) clutch, which is usually of the friction type, is placed between the engine and the

transmission. It enables the driver to temporarily disconnect the engine from the rest of the

transmission and to make a gradual connection when power transmission is required and the

tractor begins to move. Such transmission clutches usually consist of one or more friction

surfaces connected to the engine, which are pressed by springs on either side of a disc

connected to the remainder of the transmission. Removal of the pressure on the surfaces

(disengaging the clutch with the pedal) allows the engine to continue to turn without turning

the transmission and the wheels.

That part of the transmission known as the 'differential' has the function of dividing the drive

to the wheels and allowing them to turn at different speeds as the tractor turns a corner. Both

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wheels still drive because the input torques to them remain equal, but they turn at different

speeds, corresponding to the respective radii of the curves on which they are travelling. Many

tractors have a device to lock the differential. This forces both of the rear wheels to turn at the

same speed and so allows the tractor to be driven out of a situation where the differential, in

normal operation, allows one wheel to slip and the other to not rotate at all. With the lock

engaged the wheel speeds are now equal but the torques are different; hence it is not possible

(or difficult) to turn a corner.

A further common component in the transmission is the 'final drive' which consists of speed

reduction gears after the differential. These are placed in this position near the wheels to avoid

the low speed / high torque in the previous parts of the transmission.

2.3.2.1.2 Walking tractor

In the two-wheel or walking tractor, the transmission usually consists of a variable speed V

belt drive from the engine, which also acts as a clutch as it is tightened or loosened. A small

gear-box may then be fitted, which in turn drives the wheels through chains.

Figure 2-2: A walking tractor

{http://www.china-tractors.com/component/joomgallery/image.raw?view=image&type=img&id=67}

Such tractors are not usually fitted with a power take-off but while stationary may be used to

drive equipment such as a pump. The belt drive to the wheels is removed and is used to drive

the attached equipment directly.

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Power losses in the mechanical transmission systems of tractors are usually small, probably

less than 10%.

2.3.2.2 Power Take-off Transmission

An ('engine speed') power take-off (PTO) which is frequently fitted to conventional tractors

consists of a transmission from the engine to shaft which passes to the outside of the tractor,

usually at the rear, and may be engaged to drive attached machines. The power passes from the

engine through a friction clutch which is frequently operated with the same pedal as the

transmission clutch. This, and an engaging mechanism, allows the drive to the power take-off

to be stopped and started as required, independently from the drive to the wheels. Hence the

driven machine may continue to operate and process the crop even though the tractor and

machine are not moving forward. This is a very convenient arrangement and a great advantage

over older tractors with a single clutch and especially over ground driven machines.

PTO speed is determined by engine speed, (with a fixed ratio 3 or 4:1) irrespective of travel

speed (traction transmission ratio). Power losses in the PTO drive are very small, usually less

than 5%.

A "ground-speed" PTO may also be fitted. Here the drive to the PTO shaft is connected to the

drive to the wheels after the traction transmission and hence the PTO speed changes as the

traction transmission ratio is changed. The ground speed PTO rotates slowly (a few revolutions

per unit distance traveled) and may be used as a replacement for a ground drive on machines

such as seed drills where a fixed relationship between the movement of the tractor and the

function of the machine is important.

The two engaging mechanisms for the PTO drive are such that only one of these can be engaged

at one time.

2.3.2.3 Hydraulic (Oil) Supply

Here oil under pressure from a hydraulic pump, continuously driven by the engine, is available

to operate linear actuators (cylinders, rams) usually for the purpose of controlling (raising and

lowering) implements, or driving rotating actuators (motors). One such ram, in-built into the

tractor, is used to raise the three-point linkage.

Power losses in the hydraulic system may be moderate but are accepted because this outlet is

a flexible and very convenient way of controlling machines and operating auxiliaries on the

tractor and on attached machines.

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The details of the design and operation of the components in the three tractor transmission

systems are covered in books on mechanical analysis and machine design. They will not be

considered further in this book.

2.3.3 Wheels

The tractor wheels and associated tyres have the function of supporting the tractor and of

converting rotary motion of the engine to linear motion of the tractor as a whole.

The wheels must be chosen to:

Support the weight of the tractor (together with any transferred weight from attached

implements) while limiting the sinkage into the soil surface and the resultant rolling

resistance.

Engage with the soil (or surface) and transmit the traction, braking and steering forces

(reactions) while limiting relative movement and the resultant slip / skid / side slip.

Provide ground following ability together with some springing and shock absorption.

The important variables in relation to the tyres include:

Size (diameter and width) which determines their tractive capacity and rolling

resistance.

Strength, expressed in terms of ply rating, which in turn determines the pressure that

can be used and hence the weight that the tyre can carry; this in turn also determines

the tractive capacity and the rolling resistance.

Tread pattern which, together with the surface characteristics, determines the

engagement and / or contact with the surface.

The losses in power at the wheel / surface interface are often great, particularly on soft surfaces

(i.e., their efficiency is low), and hence the power available at the tractor drawbar may be much

less than the power of the engine. Hence the choice of the tyres and the weight on them is

crucial in determining the overall performance of the tractor.

Various types of wheels and / or tyres may be used on the tractor, depending mainly on the

surface on which it is working.

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CHAPTER 3

3 TRACTOR MECHANICS

The tractor is a machine and the application of the general principles of mechanics to it provides

a simple but fundamental understanding of its operation and ideal performance. The actual

performance will be less than this, and may be much less, mainly because of the losses which

occur at the wheel / ground contact surface.

In a similar way to other engineering disciplines, we can define the elements or components of

the tractor in terms of general mechanics without needing to know their detailed form. Thus

the engine (power source) can be represented in terms of its torque and speed without having

to specify its type (thermodynamic or electrical), its operating principle (internal or external

combustion), its operating cycle (two or four stroke) or its fuel source (diesel or petrol

(gasoline)). Similarly the transmission system can be expressed in terms of the transmission

ratio without specifying its form or operating principle (mechanical (gears, chains, belts),

hydrostatic (fluid pressure) etc.).

3.1 IDEAL ANALYSIS

Consider a tractor operating on a firm surface. Although the tractor is moving, the equations of

equilibrium can be applied to it because it is assumed that there is no acceleration.

Consider the engine running at a rotational speed Ne driving the drive wheels without losses

through a transmission with an overall ratio of q. As a consequence of the reduction in speed

by a factor of 1/q, there is a corresponding increase in torque by a factor of q. These values

correspond to the `velocity ratio´ and the `mechanical advantage´ from elementary physics.

3.1.1 Speed Analysis

For the tractor as shown in Figure 3-1:

Drive wheel diameter = D

Engine speed = Ne

Travel speed = Vo

Linear speed of wheels = V

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Overall transmission ratio = q

Drive wheel rotational speed = Nw

Where,

𝑞 = 𝐸𝑛𝑔𝑖𝑛𝑒 𝑆𝑝𝑒𝑒𝑑, 𝑁𝑒

𝐷𝑟𝑖𝑣𝑒 𝑊ℎ𝑒𝑒𝑙 𝑆𝑝𝑒𝑒𝑑, 𝑁𝑤

And,

𝑁𝑤 = 𝑁𝑒

𝑞

If we assume that there are no losses in motion due to slip between the wheel and the surface,

then:

𝑇𝑟𝑎𝑣𝑒𝑙 𝑠𝑝𝑒𝑒𝑑, 𝑉𝑜 = 𝐿𝑖𝑛𝑒𝑎𝑟 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑤ℎ𝑒𝑒𝑙𝑠, 𝑉

So,

𝑉𝑜 = 𝜋 𝐷 𝑁𝑒

𝑞

Graph 3.1: Travel speed vs transmission ratio at fixed Ne and wheel dia. =28 inch

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7

Trav

el s

pe

ed

, m/s

Overall transmission ratio

Vo at Ne=1800 rpm Vo at Ne=2400 rpm

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Graph 3.2: Travel speed vs engine speed at fixed transmission ratio and wheel dia. =28 inch

This analysis shows that the travel speed depends directly on the engine speed and inversely

on the gear ratio.

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Trav

el s

pe

ed

, m/s

Engine speed, rpm

Vo at q=3 Vo at q=5

Engine

Vo

Nw

Ne

Figure 3-2: Force/Torque analysis of tractor under ideal conditions

Figure 3-1: Speed analysis of tractor under ideal conditions

Engine

S

Tw

Te

P

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3.1.2 Force/Torque Analysis

For the tractor as shown in Figure 3-2:

Engine torque = Te

Drive wheel torque, Tw = q Te

Equilibrium requires that this torque is equal and opposite to the moment of the soil reaction,

S on the wheel:

𝑆𝐷

2= 𝑇𝑤 = 𝑞 𝑇𝑒

=> 𝑆 = 2 𝑞 𝑇𝑒

𝐷

If we assume that there are no other horizontal external forces, equilibrium also requires that:

Drawbar pull, P = Soil reaction, S

=> 𝑃 = 2 𝑞 𝑇𝑒

𝐷

Graph 3.3: Drawbar pull vs engine torque at fixed transmission ratio and wheel dia. = 28 inch

0

5

10

15

20

25

30

35

40

0 20 40 60 80 100 120 140 160 180 200

Dra

wb

ar p

ull,

KN

Engine torque, Nm

P at Gear 3 P at Gear 5 P at Gear 7

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Graph 3.4: Drawbar pull vs transmission ratio at fixed engine torque and wheel dia. = 28 inch

This analysis shows that the drawbar pull depends directly on the torque generated by the

engine and on the gear ratio. This assumes that the wheel / ground contact can generate the

reaction to P.

3.1.3 Power Analysis

Engine power = Qe

And,

𝑄𝑒 = 2𝜋 𝑇𝑒 𝑁𝑒

Drawbar power = Qd

And,

𝑄𝑑 = 𝑃 𝑉𝑜

=> 𝑄𝑑 = (2 𝑞 𝑇𝑒

𝐷 )(

𝜋 𝐷 𝑁𝑒

𝑞)

=> 𝑄𝑑 = 2𝜋 𝑇𝑒 𝑁𝑒

=> = 𝑄𝑒

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 1 2 3 4 5 6

Dra

wb

ar p

ull,

N

Transmission ratio

P at Te=900 Nm P at Te=1000 Nm

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=> = 𝐸𝑛𝑔𝑖𝑛𝑒 𝑝𝑜𝑤𝑒𝑟

Graph 3.5: Travel speed vs drawbar pull at different transmission ratio

Thus, if we neglect losses in forward motion due to wheelslip and in drawbar pull due to rolling

resistance, all of the power from the engine is available at the drawbar.

The above represents the ideal situation which might apply approximately to the tractor

working on hard surfaces with small drawbar pulls and small wheelslips.

However, in many agricultural situations, wheelslip is significant, hence the travel speed of the

tractor will be less, and may be much less, than the ideal value calculated above. Also, much

of the torque on the rear wheels goes to drive the tractor forward against the rolling resistance

of both the driving and the rolling wheels. Hence the drawbar pull will be less, and may be

much less, than the ideal value calculated above.

3.2 ANALYSIS WITH LOSES

Consider a tractor again operating on a firm surface as shown in Figure 3-3. Although the

tractor is again moving, the equations of equilibrium can be applied to it because it is assumed

that there is no acceleration.

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35 40

Trav

el s

pee

d, k

m/h

r

Drawbar pull, KN

Vo at Gear 3 Vo at Gear 5 Vo at Gear 7 Max power performance

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3.2.1 Speed Analysis

The tractor is now moving with a speed Va (less than the ideal travel speed, Vo above). We

can then define wheelslip as:

𝑊ℎ𝑒𝑒𝑙𝑠𝑙𝑖𝑝, 𝑖 = 𝑉𝑜 − 𝑉𝑎

𝑉𝑜

Where,

Vo = Theoretical travel speed

Va = Actual travel speed

From above equation,

𝑉𝑎 = 𝑉𝑜 (1 − 𝑖) = 𝜋 𝐷 𝑁𝑒

𝑞(1 − 𝑖)

Graph 3.6: Travel speed vs transmission ratio at fixed slip, engine speed =1800 rpm and wheel dia. =28 inch

This analysis shows that travel speed reduces if wheel slip is considered. Higher the wheel slip,

the lesser will be the actual travel velocity.

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7

Trav

el s

pe

ed

, m/s

Overall transmission ratio

Va at i=0 Va at i=0.05

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3.2.2 Force/Torque Analysis

A rolling resistance force (R) which is assumed to act horizontally on the wheel at the wheel /

ground contact patch, opposes motion of the tractor, Figure 3-4.

For equilibrium of the external horizontal forces acting on the tractor will be;

Soil reaction = Drawbar pull + Rolling resistance force

Or;

S = P + R

3.2.3 Power Analysis

Considering power transmission at the wheels.

Output power = Input power - Power loss

It means;

Drawbar power = Wheel power - Power loss

Or;

=> Power loss = Wheel power - Drawbar power

Engine

Va

Nw

Ne

Engine

S

Tw

Te

P

R

Figure 3-3: Speed analysis of tractor with losses

Figure 3-4: Force/Torque analysis of tractor with losses

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Hence;

=> Power loss = 2𝜋 𝑇𝑤 𝑁𝑤 − 𝑃 𝑉𝑎

=> 𝑃𝑜𝑤𝑒𝑟 𝑙𝑜𝑠𝑠 =2𝜋 𝐷 𝑆 𝑉𝑜

2 𝜋 𝐷− 𝑃 𝑉𝑎 = 𝑆 𝑉𝑜 − 𝑃 𝑉𝑎

=> 𝑃𝑜𝑤𝑒𝑟 𝑙𝑜𝑠𝑠 = 𝑆 𝑉𝑜 − (𝑆 − 𝑅)𝑉𝑎 = 𝑆(𝑉𝑜 − 𝑉𝑎) + 𝑅 𝑉𝑎

=> 𝑃𝑜𝑤𝑒𝑟 𝑙𝑜𝑠𝑠 = 𝑆 𝑉𝑜 𝑖 + 𝑅 𝑉𝑎 = 𝑆 𝑉𝑠 + 𝑅 𝑉𝑎

Here, Vs is the slip velocity, i.e. the velocity of the wheel relative to the surface at the surface

/ wheel contact.

3.2.4 Other Measures of Performance

3.2.4.1 Efficiency

3.2.4.1.1 Tractive efficiency

We define tractive efficiency,

𝜂𝑡 = 𝑂𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟

𝐼𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟=

𝐷𝑟𝑎𝑤𝑏𝑎𝑟 𝑝𝑜𝑤𝑒𝑟

𝑊ℎ𝑒𝑒𝑙 𝑝𝑜𝑤𝑒𝑟

=> 𝜂𝑡 = 𝑃 𝑉𝑎

𝑆 𝑉𝑜 =

(𝑆 − 𝑅)(1 − 𝑖)

𝑆

=> 𝜂𝑡 = (1 −𝑅

𝑆)(1 − 𝑖)

=> 𝜂𝑡 = (𝑃

𝑃 + 𝑅)(1 − 𝑖)

The tractive efficiency that appears here contains two terms:

𝑃

𝑃+𝑅 which represents a ‘force’ efficiency; thus when there is no rolling resistance (R = 0) this

factor in the tractive efficiency = 1.

(1 − 𝑖) which represents a ‘speed’ efficiency; again when there is no wheelslip (i = 0), this

factor in the tractive efficiency = 1.

Hence, it is necessary to determine the tractive efficiency by measuring drawbar and wheel

power directly by measuring:

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Drawbar pull, P, with a tension load (force) cell between the tractor and a load vehicle

or implement

Travel speed, Va, by timing over a known distance

Wheel torque, Tw, with a torque load cell in the transmission to the driving wheels

Wheel speed, Nw , by counting wheel revolutions over a known time period

Then tractive efficiency,

𝜂𝑡 = 𝑃 𝑉𝑎

2𝜋 𝑇𝑤 𝑁𝑤

Graph 3.7: Tractive efficiency vs wheel slip at different soil conditions

This shows that tractive efficiency depends basically on ground conditions. It depends upon a

factor which is different for every kind of soil/ground and is not discussed here. The softer the

ground such as sand or dunes the lesser will be the tractive efficiency. The tractive efficiency

will be higher on concrete and cemented roads.

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0 0.1 0.2 0.3 0.4 0.5 0.6

Trac

tive

eff

icie

ncy

Wheel slip

Firm soil Tilled soil Sandy soil

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3.2.4.1.2 Transmission efficiency

We can define transmission efficiency:

𝜂𝑟 = 𝑃𝑜𝑤𝑒𝑟 𝑡𝑜 𝑤ℎ𝑒𝑒𝑙𝑠

𝑃𝑜𝑤𝑒𝑟 𝑓𝑟𝑜𝑚 𝑒𝑛𝑔𝑖𝑛𝑒 =

2𝜋 𝑇𝑤 𝑁𝑤

2𝜋 𝑇𝑒 𝑁𝑒

The maximum transmission efficiency is dependent on the design and the quality of the

transmission elements. In a geared transmission there is little or no loss in velocity, Nw = Ne/q

Hence any losses are due to a loss in torque; thus Tw < q Te

For good quality gears the maximum efficiency is about 98% per pair of gears; hence with, say,

3 pairs of gears in the change transmission and another 2 pairs in the differential / final drive,

the maximum efficiency will be

(0.98)^5 = 90%. Little improvement in efficiency can be obtained by more accurate or elaborate

gearing; other types of transmission will be no more efficient.

3.2.4.1.3 Engine efficiency

We can define engine efficiency:

𝜂𝑒 = 𝑃𝑜𝑤𝑒𝑟 𝑓𝑟𝑜𝑚 𝑒𝑛𝑔𝑖𝑛𝑒

𝑃𝑜𝑤𝑒𝑟 𝑖𝑛 𝑓𝑢𝑒𝑙

=> 𝜂𝑒 = 2𝜋 𝑇𝑒 𝑁𝑒

1000𝐹𝐶 𝐶

Where;

FC = Fuel consumption rate (kg/min)

C = Calorific value of the fuel (kJ/kg)

The maximum value for engine efficiency is dependent on and strictly limited by the

thermodynamics of the engine processes. A maximum value of about 35% for a diesel engine

can be expected; other types of engine will, in general, be less efficient.

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Graph 3.8: Fuel consumption vs engine power

Graph 3.9: Specific fuel consumption vs engine power

These graphs show that as engine power increases, total fuel consumption also increases but

decreasing the specific fuel consumption.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25 30

Fue

l co

nsu

mp

tio

n,

kg/h

r

Engine power, kW

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30

Spe

cifi

c fu

el c

on

sum

pti

on

, g/

kWh

Engine power, kW

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3.2.4.1.4 Overall efficiency

We can also define the overall efficiency for the tractor:

𝜂𝑜 = 𝐷𝑟𝑎𝑤𝑏𝑎𝑟 𝑝𝑜𝑤𝑒𝑟

𝐹𝑢𝑒𝑙 𝑝𝑜𝑤𝑒𝑟

=> 𝜂𝑜 = 𝐸𝑛𝑔𝑖𝑛𝑒 𝑝𝑜𝑤𝑒𝑟

𝐹𝑢𝑒𝑙 𝑝𝑜𝑤𝑒𝑟 .

𝑊ℎ𝑒𝑒𝑙 𝑝𝑜𝑤𝑒𝑟

𝐸𝑛𝑔𝑖𝑛𝑒 𝑝𝑜𝑤𝑒𝑟 .

𝐷𝑟𝑎𝑤𝑏𝑎𝑟 𝑝𝑜𝑤𝑒𝑟

𝑊ℎ𝑒𝑒𝑙 𝑝𝑜𝑤𝑒𝑟

=> 𝜂𝑜 = 𝐸𝑛𝑔𝑖𝑛𝑒 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 . 𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 . 𝑇𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦

=> 𝜂𝑜 = 𝜂𝑒 . 𝜂𝑡 . 𝜂𝑟

Consider typical maximum values for these variables:

𝜂𝑜 = 0.3 x 0.90 x 0.75

=> 𝜂𝑜 = 20%

Because the maximum tractive efficiency is low and highly variable and the other efficiencies

are high (transmission) or strictly limited (engine), any significant increase in the overall

efficiency of tractor performance will be achieved by increasing the tractive efficiency.

Research into an understanding of the traction process and into more efficient traction devices

is directed to this end.

3.2.4.1.5 Tractive coefficient (pull - weight ratio)

As will be shown later, the performance of a tractor depends to a significant degree on its

weight and, in particular, on the weight on the driving wheels. It is therefore useful to define a

non-dimensional drawbar pull weight ratio termed:

𝑇𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡, 𝜉 = 𝐷𝑟𝑎𝑤𝑝𝑢𝑙𝑙

𝑊𝑒𝑖𝑔ℎ𝑡 𝑜𝑛 𝑑𝑟𝑖𝑣𝑖𝑛𝑔 𝑤ℎ𝑒𝑒𝑙𝑠

The tractive coefficient is a number which characterizes the interaction between the wheel and

the surface in an analogous way to which coefficient of (sliding) friction characterizes the

interaction between two bodies sliding on each other. Where a different wheel and surface may

be considered similar to those for which the tractive coefficient is known, then for the same

wheelslip:

Drawbar pull = Tractive coefficient x weight on wheel

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Where a tractor operates on a slope the tractive coefficient should logically be based on the

total force parallel to the ground, i.e., on the drawbar pull plus the component of the weight of

the tractor down the slope.

Where a four-wheel tractor is considered, and with other tractors also, the weight used may be

the total weight on all wheels. In quoting values of tractive coefficient, it is therefore necessary

to state which weight has been used.

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CHAPTER 4

4 DESIGNING OF AGRICULTURAL TYRE ON NX

4.1 COMPUTER AIDED DESIGN

In industrial product design, it is not an easy and everyday task to switch from one design

solution to another. Mechanical designs these days are almost exclusively done with 3D-CAD

applications (Computer Aided Design). These applications are costly and complicated. They

are often used in connection with PLM applications (Product Life-Cycle Management), which

are even more costly and complicated.

A large industrial company often uses one CAD/PLM solution for a decade or even decades.

When switching, the solution typically comes from the same solution provider, to allow for a

reasonable amount of effort; switching to a different providers CAD/PLM environment may -

in the worst-case - require a complete redesign of all products.

When a decision to switch is made, there are many viewpoints to consider:

Arguments for and against the switch

Capabilities of the considered CAD application(s)

What amount of re-design is needed

Compatibility with other used internal and external CAD systems and file formats

Software and hardware requirements and costs

Upgradability and expandability

Support availability and cost

Existing product knowledge; building the missing competences

Within engineering services: customer requirements

This thesis aims to look into a switch from AUTOCAD, originally developed in 1983, to more

modern Siemens NX. There will be a case project, in which a very large assembly of a complex

tyre will be designed and the necessary mechanical drawings will be created, using NX.

The case provides a relatively easy situation for the switch: Both the CAD software are widely

used but later is gaining popularity rapidly.

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Complicating the switch and bottlenecking the design though is the fact that for an intermediate

period of time both AUTOCAD and NX will need to be used simultaneously. They will need

to interoperate and be able to exchange product data and designs, although only in one

direction: from the older AUTOCAD to NX. In the case project, options will be tested for the

data exchange between AUTOCAD and NX.

In the case project, some of these older formats will be shown to see how they work for the

purpose of the case project and a new project based on older model would be developed.

The case project will be done as a service to ‘General Tyre and Rubber Company’ and its

customers. These services have been provided with AUTOCAD.

The original product customer and its products will not be identified in this thesis report.

4.2 DESIGNING OBJECTIVES

The objectives of the thesis are to:

Research whether it is possible to use Siemens NX instead of the AUTOCAD in the design

and 3D assembly models of one product in one specific customer product group and to

make the related drawings.

Outline the process of product design in an NX environment and compare difference.

Problems associated with product designing on NX.

4.3 CURRENT STATUS AT GENERAL TYRE AND RUBBER COMPANY

GTR provides a multitude of services to the customers, including participation in the design of

one of their main product groups. GTR also currently creates the main top-level product

drawings for each customer Tyre using AUTOCAD.

4.3.1 Current Design Application: AUTOCAD

In GTR, many design applications are used. For the product group which includes the product

of the case project, the currently used design application is AUTOCAD. AUTOCAD was

originally developed by AUTODESK in 1983.

AUTOCAD is a powerful 2D CAD application and it is used by many large industrial

companies, including the globally operating Ford and General Motors. Nevertheless, its user

interface is outdated and it is increasingly difficult for companies to find personnel trained to

use it. Also, its functionalities are outdated: for instance its parametric modeling capabilities

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are limited. As a result, it is strongly advised to abandon this software and move on to the new

software.

Figure 4-1: User interface of AUTOCAD

4.4 CONSIDERED FUTURE DESIGN APPLICATION: NX

The considered future design application is the design oriented module of Siemens NX, “NX

for Design”, from now on “NX” for short. NX, in contrast with AUTOCAD, has a modern user

interface, which functions as expected by users familiar with modern applications designed to

run in the Microsoft Windows operating environment.

NX is modular and includes modules for computer aided design (CAD, manufacturing (CAM)

and engineering analysis (CAE). ‘General Tyre and Rubber Company’ uses it to provide

services to several customers.

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Figure 4-2: User interface of NX

Also like in other CAD software, NX also features the use

of either simple or advance working environment which

can be turned on and off any time. This feature has been

given a name “Roles”. Any kind of user, be it a beginner

or advanced can select his/her role based on his/her

working experience of the software. Advance role puts

more buttons or menus to be used which is basically off

for beginner role.

4.5 AUTOCAD DESIGN

The original design of the tyre in question was generated by ‘General Tyre and Rubber

Company’ using AUTOCAD. This 2D CAD model was provided to us so that the exact same

model can be reproduced in 3D using NX.

It is displayed below:

Tyre Cross-Section shows various radii being used in the tyre.

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Figure 4-3: Tyre cross-section on AUTOCAD

Figure 4-4: Top view of Lugs

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Tyre top view shows information about the lugs, their curvature, smoothing radiuses involved

and how the finished product would leave a footprint when used in soil.

4.6 NX DESIGN

Now we will see how to initiate and completely replicate the given design using NX. Since NX

is a completely new and relatively advance software, a basic AUTOCAD user might find it

difficult to operate but for a new user, the learning curve is not as steep as it is for other CAD

software available in the market.

Figure 4-5: Initializing the NX software

4.6.1 New Design

First thing is to open NX. Then select new file option clearly visible in the top right corner.

This opens up a new window that shows different types of files that can be developed using

NX. For our designing and drafting need, we will select ‘Model’. The drop down menu lets us

choose the units in which to work. Other than that we can define out part file’s name and

location where to store it and then click ok to continue.

When we hit ok it will take us to the modeling interface that was shown earlier.

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Now the first option to do in NX is to define ‘Datum Planes’. These actually define where the

origin of our geometry is located. Also, these Datum planes are where we actually

design/draw/draft our 2D drawing. We can define as many planes as we like but initial 3 Datum

planes should be created for our own convenience. Usually people ignore datum planes and

define planes along the drafting purpose but this leads to problems in complex part geometries

and could lead to wastage of time.

To define

these datum

planes we can

select the

option in the

top menu bar.

When we

click on it, a new dialogue box appears where all the planes can be defined. There are various

options to define but we will stick to discussing the options that lead to the creation of the

designing of the tyre part geometry.

When we click that option a dialogue box appears where we can select planes in XC, YC and

ZC direction. Also the planes can be defined at an angle and at a distance from the origin etc.

This is shown below. All planes are defined that we will utilize later and a plane that is away

from the origin.

After defining the required

geometry planes, we will

move on to sketching. For that

we can select sketch option

present in the top left corner of

the screen.

This shows a new dialogue

box which lets us choose

which plane to draft on. Here the previously defined datum planes will come in handy. Then

there is sketch orientation where we can select which side of the design would be positive and

which would be negative. The robustness of this software lets us decide the negative and

positive side of a sketch per plane.

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When we click ok and

define a plane that we want

to start sketching with, the

window changes to

complete 2D view of that

plane and will show us the

new options that will help

us create the design.

Options like line, circle,

arc, erase, trim, etc. are very

common and work almost

identically in each and

every CAD software

available today.

As it is seen in the picture

below, a line has been

drawn first and then an arc.

Various ways are available

to use each option and each can be used according to our liking. The line option can be used

by defining the length and angle or actually drawing it in the working space. Similarly arcs or

circles can be drawn using a center and radius or by defining 3 points on the arc which results

in an arc or circle of required dimensions. Basic sketch options are used similarly and relatively

easily this way.

The last thing to notice

here is part navigator.

Here after datum

planes, a new entry can

be seen named as

Sketch (4). This is very

important to note as

this tells us which

sketch we are currently

working on. Currently,

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multiple sketches are not present in different axes so it looks simple but once a complex part

geometry is formed it is extremely difficult to track back and modify designs per our

requirement. Hence, it is a good practice to rename our sketches so they are recognizable at a

glance. Say, we develop the cross-section of the tyre on this sketch, so after finishing we will

rename it cross-section for reference later.

4.6.2 Cross-Section

Now that the basics are covered, we can move on to the actual reproduction of the design based

on the AUTOCAD drawing. Some might argue that the sketch can be imported directly and

used. But the reason for making it from the scratch and its associated problems would be

discussed in upcoming section.

Now for the cross-sectional view

of the tyre we will refer to the

figure of cross-section shown in

previous section. There we

observe a complete cross-section

made on AUTOCAD. The cross-

section approximately provided

90% of the information required

with other 10% information

redacted for confidentiality

purposes.

As described in previous section,

we will first select a plane, in this

case plane XZ and then start

sketching. It is simple as

described earlier, the 2 commonly

used commands while sketching were line and arc.

Now since we are working on an advanced CAD software, we do not need to replicate the

entire sketch. A skillful CAD designer can, in a glance, see what parts of the sketch he/she

needs to replicate to get the entire sketch which would result in a 3D part model exactly as the

finished product.

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We have, in this project, taken a similar approach. Using basic CAD commands we just

sketched a part of the cross-section. The original dimensions were used. The sketching although

had many problems which would be discussed later, the parts shown in the sketch on the next

page were drawn first.

Only the cross-section shown here is used in the sketching on NX.

Figure 4-6: Cross-section of the tyre

In the picture the blue lines indicate dimensions. The green curve is the sketched drawing.

Other than that, the datum plane XZ shows that we created earlier. This comes in handy when

starting the sketch. We start by measuring the tyre’s rim area, divide it by 2 and put a point at

that location. Next we select line command and start sketching accurately as was shown in the

cross-section of the original drawing. Now if we compare the two sketches, we would notice

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that only half of the cross-section is drawn not the complete cross-section that was shown in

previous section. Also the inner periphery is clearly outlined and outer curves are still missing.

This is because in NX we do not always need to sketch the entire thing. This is all that is needed

to get a tyre shaped element in 3D.

When we click finish, NX comes out of 2D drawing mode and

shows the sketch in the 3D environment.

Now to get a tyre shaped element we would use a few

commands like revolve or extrude to get an element that is

shaped like a tyre.

So the next step in sketching would be to define a curve that

defines some sort of tyre diameter along which this curve of

cross-section would be revolved.

Now the basic instinct is to start again at datum planes but

since the diameter defining curve would be simple and would only contain a single curve used

for the sole purpose of revolve command we will define a new plane for this. Refer back to

previous section where we defined datum planes. But here for our own convenience we will

select a plane where the

calculations of sketch are

kept to a minimum.

For skilled NX user it is

apparent that we define one

on the lower most point on

the curve. The plane would

be in ZY direction and

would be half the cross-

sectional length away from

the origin.

After defining the plane we

would note the radii of the

tyre and mark a point that is

on this new ZY plane. If the

origin of the new plane is at

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the point of contact of the two curves we will mark a point straight in negative Z direction that

is equal to the radius of the finished tyre. And then use this point to create a circle as shown.

When we click finish sketch the 3D environment sketch shows like this with circle showing

the rim radius of the tyre. This circle would be used later to create the 3D model.

4.6.3 Top View

For the top view of the tyre we will follow steps same as we will in next section, but this time

it would be on a different plane. Apart from that, if we observe the top view drawing, we notice

that the pattern is repeated. Now instead of designing the whole pattern again and again we can

select a repeating unit and draw just that. After that, the repeating unit can be patterned or

arrayed over part geometry for the required results.

Now according to our design, we will consider plane XY that is perpendicular to the plane we

previously used. We will go again to the datum planes but instead of start drawing there, we

can define a new plane that is parallel to XY plane but is at a distance from the datum plane.

We took the distance equal to the radii of the tyre so that when the drafting is complete we get

the top design (tread pattern) on top of the tyre.

Now from previous section we selected the following repeating unit.

Figure 4-7: 2D view of 2 complete Lugs

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Only the two complete lugs are the part of the repeating unit. The half lug showing in the

picture is not.

Figure 4-8: Sketching the lugs

We will again

start sketching

on our newly

created plane.

Below are some

pictures of the

development of

repeating unit.

Some people

might confuse

the repeating

unit and consider

only a single lug

as a repeating

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unit as shown above. This is not correct. As it can be seen that a single lug is passing through

the centre line. Meaning if cut along y-axis, the lug would not be complete. Hence a repeating

unit should be defined such that it can be repeated or patterened along any axis of symmetry.

This is the complete repeating unit and it looks like this when observed in sketch view. Also

visible are the datum and the plane that we drew on.

After we click finish sketch. We will get one nice and clean repeating unit of tyre tread pattern

as shown here.

Figure 4-9: Final sketch of a pair of lugs

Now when the 3D model is generated this lug design would be located right on top of it and it

will be very easy to extrude it as per our requirement.

4.7 3D MODEL

Now to generate the first 3D model of the tyre we will refer back to the design we created in

previous section. Now remember if we use the sketch we previously created and revolve it with

the guiding circle we will get something like this.

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Figure 4-10: One sided revolved portion of the cross-section in wireframe view (left) and solid view (right)

Its only one side of the tyre. Now we will use other commands to complete the basic tyre part

geometry.

This can also be seen in the top view of the

tyre as only half the tyre is present. Now to

complete it, we will use a mirror feature.

Notice that there is a plane sticking to the

axial symmetry of the tyre which is not a

datum plane or the plane that was used to

generate the guide curve. We will utilize

this plane as a plane of symmetry and

generate the other identical part of the tyre.

This will complete our basic tyre part

geometry.

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After the mirror command has been used we will get the result as shown below in various views

and forms.

Figure 4-11: Fully revolved portion of the cross-section in wireframe view

Figure 4-12: Fully revolved portion of the cross-section in solid view

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The remaining portion of the tyre can easily be generated by using extrude command. Refer

back to previous section where we sketched the lugs. Now this will come in handy. The lugs

are sketched almost on the radii of the tyre. We will use that to extrude and attach the lugs to

the basic periphery of the tyre to complete our 3D model.

Now when we view our sketch with basic tyre geometry, it will look as follows.

Figure 4-13: Sketch of lugs on the tyre geometry

After using the extrude command on our sketch. We will get the results like this.

Figure 4-14: Extruding the lugs

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Subsequently, we will use an array command to get the repeating unit on our part geometry.

Figure 4-15: A series of lugs on tyre geometry

After the array command we will use blending options to assign smooth radiuses to the lugs

and base tyre. These radiuses will help us reduce the stresses that play an important role in our

tyre life. These stresses would be the focus point of our next chapter.

A finished part drawing can now be shown usinf drawing sheet tool in the NX. Number of

views, cross-sections and other geometry details worth mentioning in this sheet can be selected

using appropraite commands.

Figure 4-16: Blending of lugs on tyre's top surface

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We will display a top view, a side view and a section view of the tyre and according to defined

axes; front, side and cross-section respectively. This can be compared to the top and cross-

sectional view shown in the section 3.5 that was originally developed using AUTOCAD.

 

Figure 4-17: Tyre's different views and lugs dimensioning on a sheet of paper    

4.8 PROBLEMS ASSOCIATED WITH DESIGNING  

In this section we will discuss various problems encountered during the designing phase of the

project and what was done to overcome those.    

4.8.1 Import or Re-design  

The first question that was raised after watching the AUTOCAD file was to check if the design

could be imported which would significantly reduce the work load. NX can import part files

created in any CAD software if it is saved in proper format. Upon converting the file to a

suitable format for NX; we imported the file and the results were as follows.                

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Figure 4-18: A view of NX when a part file is imported

It resulted in a shape like this. This was unusable as it divided the part in various bodies and

rendered it useless for further modifications.

This is when we decided to redesign the entire part.

4.8.2 Tolerances in Sketching

The first problem

which we faced while

sketching was the

tolerance. Since

AUTOCAD is an old

software, the issue of

tolerances hardly

arises in it. But when

we talk about latest

and robust software

like NX or Catia, such

problems do take

place. When we were

designing the part, we

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noticed that all the lines in the curve were not intersecting or were not tangent properly. This

was observed when zoomed in about 200%.

This created a problem as NX would not revolve the curve unless it was singular. To overcome

this we decided to use options like extend and offset to get intersection curves and then

trimming the additional lines to get one smooth curve.

4.8.3 Solid or Shell

The initial problem that came when we started the 3D modeling was whether the tyre model

should be a solid body or a shell. Or if a body is generated then what should be its thickness.

Figure 4-19: Solid 3D model with arbitrary thickness

In initial stages, we were not provided with tyre curing sketch. Hence, the information

regarding tyre wall thickness was missing. So we took an arbitrary thickness and started

working with it. With this thickness, more problems started generating. If the thickness was

offset with the cross-section, then the smaller curves representing the section where the rim

would fit, would get distorted completely.

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It can be clearly seen in

this picture that two small

features of the cross-

section did not remain in

their original form. One

curve was completely

removed in the offset

while the other was

extrapolated and increased

in size. Although barely

visible, these small

problems made it very

difficult to reproduce. To

overcome this problem,

we used the shell model

approach and designed a

shell only not a solid body or a hollow body with arbitrary thickness.

4.8.4 Axial and Radial Curvature in Lugs

One of the major problems came during

the generation of lugs. As there is 2-

dimensional curvature present across the

entire periphery of the tyre, the same

curvature is present in lugs too. Initially

after creating the base part geometry,

when we extruded the lugs to their

appropriate heights, they looked like as

shown in the figure. They were attached

from the center of the tyre but left the tyre

surface as soon as the curvature initiated.

If the lug sketch was projected on the tyre the sketch would become shorter and would not

cover the entire width of the tyre.

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This problem was overcome by creating an offset of the base tyre geometry equal to the

maximum height of the lugs. Then a line offset was generated for guidance. After this the lug

part intersecting out of the shell offset was trimmed. After trimming the entire sheet we got

lugs that were not sticking out and were according to the required specifications. . The lugs

achieved during this method can be viewed in ‘3D Model’ section.

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CHAPTER 5

5 STRESS ANALYSIS OF AGRICULTURAL TYRE USING

FINITE ELEMENT ANALYSIS

5.1 INTRODUCTION

It is known that proper exploitation of wheel tyres of tractors is difficult and it depends on

many influencing factors. Tyre inflation pressure has a significant importance on their stress

and strain distribution. Tyre strain influences the size of the contact surface with the rolling

track. Low pressure generates an exaggerated flexing of the tyre carcass, increasing the rolling

resistance of the wheel. Too large pressure causes the decrease of tyre adhesion, irregular and

faster wear, especially for the driving wheels. For various soil conditions depending on the tyre

pressure, different soil stress distributions can be obtained. The paper presents an analysis a

model of a 65 HP tractor driving wheel tyre, by means of the Finite Element Method. A model

of the tyre is developed, for which the parameters characterizing the elastic behavior of tyre

rubber were defined. The study was developed for various tyre air pressures (0.5, 0.8, 1.1, 1.4,

1.7, and 2 bars). The results and conclusions obtained from the study are useful in the

identification of optimal operating parameters for the tyres of the driving wheels of agricultural

tractors, and this FEM model can be adapted and used for other tractors and agricultural

machinery.

Tyres provide the following functions for a land vehicle: attenuate the shocks caused by uneven

rolling tracks, ensure proper adhesion to the rolling track, and ensure safety and resistance to

high speed movement, take the loads distributed on wheels, contribute to passengers or

operators comfort. The complex geometry and the multitude of factors influencing the

mechanical behavior make the modelling of stresses and strains distribution in the tyres of

agricultural land vehicles difficult. The interaction between the tyre and rolling track is a very

complex research topic and has been considered a critical problem in the design of agricultural

vehicles. Tyre inflation pressure is particularly important for the shape of the contact surface

between the tyre and soil, and thus on the soil stress distribution. For various soil conditions,

depending on tyre pressure, different distributions of soil stresses can be obtained.

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5.2 MATERIALS AND METHODS

This section describes the methodology and the element types used to perform modelling and

analysis on ANSYS APDL. The static contact analysis was carried out separately on:

5.2.1 Model of the Cord-Rubber Ply Composite

A pneumatic tractor tyre is a flexible structure in the shape of a toroid filled with compressed

air. The most important structural elements of the tyre are the carcass and belt. They are made

up of a number of layers of flexible cords having a high modulus of elasticity encased in a

matrix of low modulus rubber compounds and there are different anisotropic material

properties for each layer.

5.2.2 Element Types

The FE type selected for analyzing the belt and carcass layers was SOLID46, which has layer

thickness, material direction angles, and orthotropic material properties. The element possesses

three degrees of freedom at each node; translations along the nodal x, y and z directions. The

input for the SOLID46 element can be either in layer form or matrix form; layer form was

chosen so that the layer thickness was computed by scaling the specified constant thickness

inputs to ensure consistent thickness between the nodes. The other element types for different

components are also described here.

Figure 5-1: Selection of curved ply as SOLID46 layered element

Figure 5-2: Selection of lugs as SHELL281 8 node element

1. Curved Ply 2. Lugs

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5.2.2.1 SOLID46 (3D 8-Node Layered Structural Solid)

5.2.2.1.1 SOLID46 Element Description

SOLID46 is a layered version of the 8-node structural solid (SOLID45) designed to model

layered thick shells or solids. The element allows up to 250 different material layers. If more

than 250 layers are required, a user-input constitutive matrix option is available. The element

may also be stacked as an alternative approach. The element has three degrees of freedom at

each node: translations in the nodal x, y, and z directions.

Figure 5-3: SOLID46 geometry

xo = Element x-axis if ESYS is not supplied.

x = Element x-axis if ESYS is supplied.

Figure 5-4: SOLID46 stress output

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5.2.2.1.2 SOLID46 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure

5-3. The element is defined by eight nodes, layer thicknesses, layer material direction angles,

and orthotropic material properties. Shear moduli GXZ and GYZ must be within a factor of

10,000 of each other.

The element z-axis is defined to be normal to a flat reference plane, using real constant KREF

may have values of 0 (mid plane), 1 (bottom), or 2 (top). If the nodes imply a warped surface,

an averaged flat plane is used. The default element x-axis is the projection of side I-J, side M-

N, or their average (depending on KREF) onto the reference plane. The orientation within the

plane of the layers may be changed using ESYS in the same way it is used for shell elements

as described in Coordinate Systems. To reorient the elements (after automatic meshing) one

should use EORIENT. With EORIENT, we can make SOLID46 elements match an element

whose orientation is as desired, or set the orientation to be as parallel as possible to a defined

axis.

The input may be either in matrix form or layer form. For matrix form, the matrices must be

computed outside of ANSYS.

For layer (non-matrix) input, the total number of layers must be specified (NL). If KEYOPT(2)

= 0, the maximum number of layers is 250; if KEYOPT(2) = 1, the maximum is 125. The

properties of all layers should be entered (LSYM = 0). If the properties of the layers are

symmetrical about the mid thickness of the element (LSYM = 1), only half of properties of the

layers, up to and including the middle layer (if any), need to be entered. While all layers may

be printed, two layers may be specifically selected to be output (LP1 and LP2, with LP1 usually

less than LP2). Each layer of the layered solid element may have a variable thickness (TK).

The thickness is assumed to vary bilinearly over the area of the layer, with the thickness input

at the corner node locations. If a layer has a constant thickness, only TK(I) need be input. If

the thickness is not constant, all four corner thicknesses must be input using positive values.

Zero thickness layers may be used to model dropped plies. The layer thicknesses used are

computed by scaling the input real constant thicknesses to be consistent with the thicknesses

between the nodes.

Each layer of the layered solid element may have a variable thickness (TK). The thickness is

assumed to vary bilinearly over the area of the layer, with the thickness input at the corner node

locations. If a layer has a constant thickness, only TK(I) need be input. If the thickness is not

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constant, all four corner thicknesses must be input using positive values. Zero thickness layers

may be used to model dropped plies. The layer thicknesses used are computed by scaling the

input real constant thicknesses to be consistent with the thicknesses between the nodes.

The node locations may imply that the layers are tilted or warped. However, the local

coordinate system for each layer is effectively reoriented parallel to the reference plane, as

shown in Figure 5-4. In this local right-handed system, the x'-axis is rotated an angle

THETA(LN) (in degrees) from the element x-axis toward the element y-axis.

The material properties of each layer may be orthotropic in the plane of the element. The real

constant MAT is used to define the layer material number instead of the element material

number applied with MAT. MAT defaults to 1 if not input. The material X direction

corresponds to the local layer x' direction.

Element loads are described in Node and Element Loads. Pressures may be input as surface

loads on the element faces as shown by the circled numbers on Figure 5-4.

Figure 5-5: A window showing the selection of 4 layers of SOLID46

5.2.2.1.3 SOLID46 Input Summary

Nodes

I, J, K, L, M, N, O, P

Degrees of Freedom

UX, UY, UZ

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Real Constants

The real constants vary, depending on the KEYOPT(2) setting.

Material Properties

If KEYOPT(2) = 0 or 1, supply the following 13*NM properties where NM is the number of

materials (maximum is NL): EX, EY, EZ, ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or

THSX, THSY, THSZ), (PRXY, PRYZ, PRXZ, or NUXY, NUYZ, NUXZ), DENS, GXY, GYZ,

GXZ, for each of the NM materials.

If KEYOPT(2) = 3, supply none of the above.

5.2.2.2 SHELL281 (8-Node Structural Shell)

5.2.2.2.1 SHELL281 Element Description

SHELL281 is suitable for analyzing thin to moderately-thick shell structures. The element has

eight nodes with six degrees of freedom at each node: translations in the x, y, and z axes, and

rotations about the x, y, and z-axes. (When using the membrane option, the element has

translational degrees of freedom only.)

SHELL281 is well-suited for linear, large rotation, and/or large strain nonlinear applications.

Change in shell thickness is accounted for in nonlinear analyses. The element accounts for

follower (load stiffness) effects of distributed pressures.

SHELL281 may be used for layered applications for modeling composite shells or sandwich

construction. The accuracy in modeling composite shells is governed by the first-order shear-

deformation theory (usually referred to as Mindlin-Reissner shell theory).

The element formulation is based on logarithmic strain and true stress measures. The element

kinematics allow for finite membrane strains (stretching). However, the curvature changes

within a time increment are assumed to be small.

5.2.2.2.2 SHELL281 Input Data

The following figure shows the geometry, node locations, and the element coordinate system

for this element. The element is defined by shell section information and by eight nodes (I, J,

K, L, M, N, O and P).

Mid-side nodes may not be removed from this element. A triangular-shaped element may be

formed by defining the same node number for nodes K, L and O.

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Figure 5-6: SHELL281 geometry

xo = Element x-axis if element orientation ESYS is not provided.

x = Element x-axis if element orientation is provided.

5.2.2.2.3 SHELL281 Input Summary

Nodes

I, J, K, L, M, N, O, P

Degrees of Freedom

UX, UY, UZ, ROTX, ROTY, ROTZ if KEYOPT(1) = 0

UX, UY, UZ if KEYOPT(1) = 1

Figure 5-7: A window showing our D.O.F selection

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Material Properties

EX, EY, EZ, (PRXY, PRYZ, PRXZ, or NUXY, NUYZ, NUXZ), ALPX, ALPY, ALPZ (or

CTEX, CTEY, CTEZ or THSX, THSY, THSZ), DENS, GXY, GYZ, GXZ, ALPD

5.2.2.3 SHELL208 (2-Node Axisymmetric Shell)

5.2.2.3.1 SHELL208 Element Description

The SHELL208 element is suitable for modeling thin to moderately thick axisymmetric shell

structures, such as oil tanks, pipes, and cooling towers. It is a two-node element with three

degrees of freedom at each node: translations in the x, and y directions, and rotation about the

z-axis. A fourth translational degree of freedom in z direction can be included to model uniform

torsion (KEYOPT(2) = 1). When the membrane option is used, the rotational degree of freedom

is excluded. An extra internal node is available via KEYOPT(3) = 2. (SHELL209 incorporates

this extra node by default.)

SHELL208 allows us to account for large strain effects, transverse shear deformation, hyper

elasticity and layers in our models. The element is intended to model finite strain with pure

axisymmetric displacements; transverse shear strains are assumed to be small.

SHELL208 can be used for layered applications for modeling laminated composite shells or

sandwich construction.

Figure 5-8: SHELL208 geometry

5.2.2.3.2 SHELL208 Input Data

The figure shows the geometry, node locations, and element coordinate system for SHELL208.

The element is defined by two nodes. For material property labels, the local x-direction

corresponds to the meridional direction of the shell element. The local y-direction is the

circumferential. The local z-direction corresponds to the through-the-thickness direction.

Element formulation is based on logarithmic strain and true stress measures. Element

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kinematics allows for finite membrane strains (stretching). However, the curvature changes

within an increment are assumed to be small.

Element loads are described in Nodal Loading. Pressure may be input as surface loads on the

element faces as shown by the circled numbers on previous figure. Positive pressures act into

the element.

5.2.2.3.3 SHELL208 Input Summary

Nodes

I, J

Degrees of Freedom

UX, UY, ROTZ -- If KEYOPT(1) = 0 and KEYOPT(2) = 0

UX, UY -- If KEYOPT(1) = 1 and KEYOPT(2) = 0

UX, UY, UZ, ROTZ -- If KEYOPT(1) = 0 and KEYOPT(2) = 1

UX, UY, UZ -- If KEYOPT(1) = 1 and KEYOPT(2) = 1

Real Constants

None

Section Controls

E11, ADMSUA

Material Properties

EX, EY, EZ, PRXY, PRYZ, PRXZ (or NUXY, NUYZ, NUXZ),

ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ),

DENS, GXY, GYZ, GXZ,

ALPD, BETD

5.2.2.4 TARGE170 (3D Target Segment)

5.2.2.4.1 TARGE170 Element Description

TARGE170 is used to represent various 3D "target" surfaces for the associated contact

elements (CONTA173, CONTA174, CONTA175, CONTA176, and CONTA177). The contact

elements themselves overlay the solid, shell, or line elements describing the boundary of a

deformable body and are potentially in contact with the target surface, defined by TARGE170.

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This target surface is discretized by a set of target segment elements (TARGE170) and is paired

with its associated contact surface via a shared real constant set. We can impose any

translational or rotational displacement, temperature, voltage, and magnetic potential on the

target segment element. We can also impose forces and moments on target elements. To

represent 2-D target surfaces, use TARGE169, a 2-D target segment element.

For rigid target surfaces, these elements can easily model complex target shapes. For flexible

targets, these elements will overlay the solid, shell, or line elements describing the boundary

of the deformable target body.

Figure 5-9: TARGE170 geometry

5.2.2.4.2 TARGE170 Input Data

The target surface is modeled through a set of target segments, typically, several target

segments comprise one target surface.

The target surface can either be rigid or deformable. For modeling rigid-flexible contact, the

rigid surface must be represented by a target surface. For flexible-flexible contact, one of the

deformable surfaces must be over layed by a target surface.

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The target and associated contact surfaces are identified via a shared real constant set. This real

constant set includes all real constants for both the target and contact elements.

Each target surface can be associated with only one contact surface, and vice-versa. However,

several contact elements could make up the contact surface and thus come in contact with the

same target surface. Likewise, several target elements could make up the target surface and

thus come in contact with the same contact surface. For either the target or contact surfaces,

we can put many elements in a single target or contact surface, or we can localize the contact

and target surfaces by splitting the large surfaces into smaller target and contact surfaces, each

of which contain fewer elements.

If a contact surface may contact more than one target surface, we must define duplicate contact

surfaces that share the same geometry but relate to separate targets, that is, that have separate

real constant set numbers.

Figure 5-10: TARGE170 segments

The figure shows the available segment types for TARGE170. The general 3D surface

segments (3-node and 6-node triangles, and 4-node and 8-node quadrilaterals) and the primitive

segments (cylinder, cone, and sphere) can be paired with 3D surface-to-surface contact

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elements, CONTA173 and CONTA174, the 3D node-to-surface contact element, CONTA175,

and the 3D line-to-surface contact element, CONTA177. The line segments (2-node line and

3-node parabola) can only be paired with the 3D line-to-line contact element, CONTA176, to

model 3D beam-to-beam contact.

For any target surface definition, the node ordering of the target segment element is critical for

proper detection of contact. For the general 3D surface segments (triangle and quadrilateral

segment types), the nodes must be ordered so that the outward normal to the target surface is

defined by the right hand rule. Therefore, for the surface target segments, the outward normal

by the right hand rule is consistent to the external normal. For 3D line segments (straight line

and parabolic line), the nodes must be entered in a sequence that defines a continuous line. For

a rigid cylinder, cone, or sphere, contact must occur on the outside of the elements; internal

contacting of these segments is not allowed.

5.2.2.4.3 TARGE170 Input Summary

Nodes

I, J, K, L, M, N, O, P (J - P are not required for all segment types)

Degrees of Freedom

UX, UY, UZ, TEMP, VOLT, MAG (ROTX, ROTY, ROTZ for pilot nodes only)

Real Constants

R1, R2, [the others are defined through the associated CONTA173, CONTA174, CONTA175,

CONTA176, or CONTA177 elements]

Material Properties

None

5.2.2.5 CONTA173 (3D 4-Node Surface-to-Surface Contact)

5.2.2.5.1 CONTA173 Element Description

CONTA173 is used to represent contact and sliding between 3D "target" surfaces (TARGE170)

and a deformable surface, defined by this element. The element is applicable to 3D structural

and coupled field contact analyses. This element is located on the surfaces of 3D solid or shell

elements without mid-side nodes (SOLID65, SOLID70, SOLID96, SOLID185, SOLID285,

SOLSH190, SHELL28, SHELL41, SHELL131, SHELL157, SHELL181, and MATRIX50). It

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has the same geometric characteristics as the solid or shell element face with which it is

connected. Contact occurs when the element surface penetrates one of the target segment

elements (TARGE170) on a specified target surface. Coulomb friction, shear stress friction,

and user defined friction with the USERFRIC subroutine are allowed. This element also allows

separation of bonded contact to simulate interface delamination. Other surface-to-surface

contact elements (CONTA171, CONTA172, CONTA174) are also available.

Figure 5-11: CONTA173 geometry

R = Element x-axis for isotropic friction

xo = Element axis for orthotropic friction if ESYS is not supplied (parallel to global X-axis)

x = Element axis for orthotropic friction if ESYS is supplied

5.2.2.5.2 CONTA173 Input Data

The geometry and node locations are shown in the figure above. The element is defined by four

nodes (the underlying solid or shell element has no mid-side nodes). If the underlying solid or

shell elements do have mid-side nodes, use CONTA174. The node ordering is consistent with

the node ordering for the underlying solid or shell element. The positive normal is given by the

right-hand rule going around the nodes of the element and is identical to the external normal

direction of the underlying solid or shell element surface. For shell elements, the same nodal

ordering between shell and contact elements defines upper surface contact; otherwise, it

represents bottom surface contact. Remember the target surfaces must always be on its outward

normal direction.

The 3-D contact surface elements are associated with the 3-D target segment elements

(TARGE170) via a shared real constant set. ANSYS looks for contact only between surfaces

with the same real constant set. For either rigid-flexible or flexible-flexible contact, one of the

deformable surfaces must be represented by a contact surface.

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If more than one target surface will make contact with the same boundary of solid elements,

we must define several contact elements that share the same geometry but relate to separate

targets (targets which have different real constant numbers), or we must combine the two target

surfaces into one (targets that share the same real constant numbers).

5.2.2.5.3 CONTA173 Input Summary

Nodes

I, J, K, L

Degrees of Freedom

UX, UY, UZ (if KEYOPT(1) = 0)

UX, UY, UZ, TEMP (if KEYOPT(1) = 1)

TEMP (if KEYOPT(1) = 2)

UX, UY, UZ, TEMP, VOLT (if KEYOPT(1) = 3)

TEMP, VOLT (if KEYOPT(1) = 4)

UX, UY, UZ, VOLT (if KEYOPT(1) = 5)

VOLT (if KEYOPT(1) = 6)

MAG (if KEYOPT(1) = 7)

Real Constants

R1, R2, FKN, FTOLN, ICONT, PINB,

PMAX, PMIN, TAUMAX, CNOF, FKOP, FKT,

COHE, TCC, FHTG, SBCT, RDVF, FWGT,

ECC, FHEG, FACT, DC, SLTO, TNOP,

TOLS, MCC, PPCN, FPAT, COR, STRM

FDMN, FDMT, FDMD, FDMS, TBND

See Table 173.1: CONTA173 Real Constants for descriptions of the real constants.

Material Properties

MU, EMIS (MP command)

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FRIC (TB command)

CZM (TB command)

5.2.3 Model of the Rubber Material

Rubber is generally considered to be a non-linear, incompressible or nearly incompressible,

hyper-elastic material, which often experiences very large deformations upon loading. The

element selected for analyzing the rubber material was SHELL281, which was used in

conjunction with the two-term Mooney–Rivlin material model. The SHELL281 element was

defined by eight nodes with three degrees of freedom (D.O.F) at each node; translations along

the nodal x, y and z directions. The element is applicable for nearly incompressible rubber-like

materials with arbitrarily large displacements and strains. The hyper-elastic formulation is non-

linear and requires an iterative solution. The FE stiffness matrices and force vectors relating to

the element are formulated using the mixed u/p (displacement/pressure) formulation. This

allows for the element matrices to be formed by variational principles with pressure introduced

to enforce the incompressibility constraint. The input data include eight nodes, the isotropic

material properties, and the constants defining the Mooney–Rivlin strain energy function. This

element type is described above.

5.2.4 Model of the Tyre–Road Contact

Contact is a physical interaction between bodies at their boundary surfaces. In studying the

contact between two bodies, the surface of one body is conventionally taken as a contact surface

and the surface of the other body as a target surface. For rigid-flexible contact, the contact

surface is associated with the deformable body (tyre); and the target surface (rigid surface) to

form a contact pair. The target and contact elements selected for analyzing the contact pair

were TARGE170, and CONTA173, 4-node elements which are available in the ANSYS

element library. The target surface was separated by a set of target segments, which were

coupled with their associated contact elements and an iterative algorithm was employed to

determine the contact surface and elements corresponding to given loading condition. These

surface-to-surface elements are well suited for the tyre–road contact problem and support large

deformations with the various friction models. The friction in the contact patch was considered

to be low, assuming smooth and uniform contacting surfaces to facilitate the solution process.

The most popular method that allows constraints resulting from contact to be taken into account

in global FE method equations is the augmented Lagrangian method which is employed to

solve the non-linear contact problem. The use of this method in conjunction with the mixed FE

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method results provides a more effective computational modelling procedure for tyre contact

problems. These element types are described in previous section.

5.2.5 Assessment of the Accuracy of the FE Model

A mesh convergence study was conducted to determine the accuracy of the numerical results

and the mesh density used in this analysis. The analyses were run with a series of progressively

finer FE meshes. The predicted maximum and minimum values of contact pressure results were

compared for each mesh until the changes in the numerical results become sufficiently small

(less than 5%).

5.2.6 Physical Material Properties Description

A radial tractor tyre, specifically a General Tyre 12.4/11-28 agricultural tractor tyre, was

selected as a common and representative tyre. The tyre model was developed using essential

features of the tyre structure and cross-section geometry, such as the number of belts and

carcass layers, tread geometry, section height and width, thickness of layers, number of cords

and cord angles. The bead and end effects of the belts are neglected in order to derive a more

efficient model with reasonable demands on the computer run time. The following tables were

useful in our analysis.

Compound Testing 300 Modulus Tensile Strength Elongation At Break Shore Hardness

Code

Issue N

o.

Tim

e

Tem

p

To

leran

ce

Actio

n

Lim

its

Ta

rget

Low

er

Tolera

nce L

imit

Low

er Actio

n

Lim

it

Ta

rget

Low

er

Tolera

nce L

imit

Low

er Actio

n

Lim

it

Ta

rget

To

leran

ce

Actio

n

Lim

its

Ta

rget

Min C MPa MPa MPa MPa MPa MPa % % %

A 15 160 3-11 6-8 7 9.7 10.7 13.7 320 340 400 53-

63

55-

61 58

B 007 15 160 3-9 5-7 6 7 8 10 420 440 500 50-

60

52-

58 55

C 15 160 6-11 7-10 8.5 7 8 11 320 340 400 58-

68

60-

66 63

D 15 160 5-9 6-8 7 7 8 11 320 340 400 56-

66

58-

64 61

Table 1: Properties of rubber

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Where;

Compound Composition

A: Drum Squeezer Compound: NR: 20% SBR: 29%

B: Ply Compound NR: 15% SBR: 38%

C: Farm Cap Compound NR: 10% SBR: 38%

D: Farm Base Compound NR: 9.7% SBR: 36%

Here;

NR= Natural rubber

SBR= Styrene butadiene rubber

Orientation of the 4 layers of rubber compound = 38 degrees

Tests Performed Test GTR Specs.

Method Si Units

H-Adhesion (Un-Cal) F-1600 80.1 N Min

Elongation F-1108 9.0 @ 10lbs (44n)

Elongation @ Break F-1108 19% Min

Breaking Strength F-1108 144n

Shrinkage In Hot Air

150 Degree Celsius X

30 Min

6% Max

Dip Pick-Up F-2414 4.5

Moisture Content 1% Max

Single Core Stiffness F-1305 30 Gms Max

Turns Ply (Z) F-1201 472

Cable(S) F-1201 472

Fabric Gauge 0.559mm

Fabric Width 1.38cm

No. Cords 1500

E.P.I Wrap 28

P.P.I Weft 3

Weft Mat. Cotton 20s

Fabric Length 1600 Meters

Tabby Width And

Location

75 Both Ends

Table 2: Fabrication properties of nylon

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Following are the tables showing the basic dimensions of “Black Bull” that would be produced

and sold commercially and whose analysis is to be performed.

5.2.7 Boundary Condition

The tyre model was developed by assuming that the inflated tyre is connected or fixed to the

rigid rim through common nodes on the rigid rim. The tyre model was subjected to loading in

two sequential steps. The initial loading was caused by the tyre inflation pressure, which was

assumed to be uniform within the tyre. The inflated static tyre is then subjected to normal

loading through the application of a specified normal deflection of the tyre at the contact region.

Mold Cavity Dim.

C R Width=254MM C S Width = 303MM

0 D = 1275 Mm

N S Depth C/L = 40.5mm Ns Depth Sh = 53.94mm

Cured Tyre Data

Total Crown GA = 47.45MM

Thread GA At C/L = 42.5MM

Thread Base At C/L = Mm

Total Shoulder GA = 64 Mm

Thread Shoulder GA = 60MM

Total Sidewall GA = 8.53MM

Sidewall GA = 3.8MM

Bead Width = 23.40

Layout Data

Toe-Toe Develop Length(Nom) = 675.15MM

Toe-Toe Develop Length(Clamp) = Mm

Scale = 1.1

Tyre Size = 12.4/11-28

Design = Black Bull

Ply Rating 12/4+0

Mold Drawing No = Eq-1340

Station Thread

GA. (Mm)

Total GA.

(Mm) C/L 47.45

A 52.01

B 64.73

C 17.00

D 8.53

E 17.19

U/Thread 6.00

Table 3: Tyre dimensions (left and right)

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The analysis was designed with load rating (12.5kN), and recommended inflation pressure

(230kPa).

5.3 TYRES INFLATION PRESSURE

Tyres provide the following functions for a land vehicle: attenuate the shocks caused by uneven rolling

tracks, ensure proper adhesion to the rolling track, and ensure safety and resistance to high speed

movement, take the loads distributed on wheels, contribute to passengers or operators comfort. The

complex geometry and the multitude of factors influencing the mechanical behavior make the modelling

of stresses and strains distribution in the tyres of agricultural land vehicles difficult. The interaction

between the tyre and rolling track is a very complex research topic and has been considered a critical

problem in the design of agricultural vehicles.

Graph 5.1: Load rating (kg) vs speed (km/hr)

Tyre inflation pressure is particularly important for the shape of the contact surface between the tyre

and soil, and thus on the soil stress distribution. For various soil conditions (soil type, moisture, etc.),

depending on tyre pressure, different distributions of soil stresses can be obtained.

5.3.1 Deflection Imposed on Tyre Due to Load & Pressure

Under the action of an external load (weight per wheel),

According to Hedekel’s equation, tyre deformation is given by the following relationship:

990 1075 1160 1510

1040 1140 12251590

1095 1205 12851670

1160 1270 1365

1215 1330 1425

1855

1270 1390 14901935

1270 1390 1490 1935

1320 1450 1550 2015

50 40 30 10

Inflation 100 KPa Inflation 110 KPa Inflation 120 KPa Inflation 130 KPa

Inflation 140 KPa Inflation 150 KPa Inflation 160 KPa Inflation 170 KPa

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𝑓 =𝐹

2𝜋𝑝𝑖√𝑅𝑟

Where;

F = vertical load on the wheel, N

pi = air pressure inside tyre, MPa

R = free radius of the wheel, mm

r = radius of the tyre running path in cross-section, mm

Figure 5-12: Tyre deformation under the action of an external applied force

Also;

The static tyre radius is given by:

𝑅𝑠 = 𝑅 − 𝑓

And the length of the contact chord is:

𝐿 = 2√𝑅2 − 𝑅𝑠2

In our case, the following data were considered for the analysis:

Variables Symbol Magnitude

Vertical load on the wheel F 12500N

Air pressure inside the tyre pi 0.230 MPa

Free radius of the wheel R 1562 mm

Radius of the tyre running path in cross-section r 210 mm

Tyre deformation f 15 mm

Static tyre radius Rs 1547 mm

Length of contact chord L 432 mm

Table 4: Various material properties used in deflection analysis

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5.4 ANALYSIS RESULTS

In this section, the results of the analysis is shown. The result yields that high stress is generated

on rib corners as it was already predicted. Also, it should be noted that when tyre rotates on the

ground, the weakest part to generate stresses are the surfaces that come in contact with the

ground most and the blending portion of the lugs due to its geometry generate a large amount

of stress which also results in the wear of lugs. In case of lugs, the major portions of stress

concentration are the blend curves and contact surface.

5.4.1 Contact Analysis of Curved Ply and Ground

A rigid ground was constructed in FEA to simulate contact analysis

• Target Element (Ground)

• Contact Element (Curved Ply)

Figure 5-13: The model of the curved ply

The figure above shows the contact analysis of the tyre. A target element was made and tyre’s

deflection was checked against vertical loading and pressure. The data we used is calculated

above. Also, the target element we used was TARGE170 and the contact element was

CONTA173. The maximum stress obtained is 0.5655MPa.

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Figure 5-14: Stress concentration on curved ply

The maximum stress is produced at the edges of the curved ply and its value is 1750kPa or

1.75MPa.

Figure 5-15: Fixed rim and meshing

The rim is fixed at its circumference. A vertical load of 12500N which is the total load on the

tyre and an inside pressure of 230kPa is applied to it. The target ground was also fixed. The

meshing was done and the result yielded 15mm of displacement which is same as we have

calculated before. This means that, with an inside air pressure of 230kPa and a vertical load of

12.5kN, the tyre having the material properties given by GTR, will show a deflection of 15mm.

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5.4.2 Meshing on the Tyre Geometry

Below are the pictures which show the meshing we have done in our model that includes curved

ply and the rib. The center portion (in side view) is the rib while the rest can be considered as

the curved ply. The meshing on these two portions is indicated with different colour. Also, it

can be seen that the concentration of the mesh is greater at the edges due to the curvature change.

Figure 5-16: The nodal model of the tyre (front view)

Figure 5-17: The nodal model of tyre (side view)

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5.4.3 Axisymmetric Modelling of the Rib and its Stress Concentrations

The element type used in axisymmetric modelling was SHELL208. Rib cross-section was made

and its axisymmetric model was generated and can be seen by going to PlotCtrls>Style>Size

and Shape>[/ESHAPE=on].

Figure 5-18: The rib-only model

Figure 5-19: Stress concentration at rib corners

As expected, the stress concentration is maximum along the rib corners. The maximum stress

produced along the corners is 900.934kPa and negligible stress at the outer boundary of the rib.

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5.4.4 4 Layered Axisymmetric Modelling of the Cross-Section

Similarly, as the rib, we also did axisymmetric modelling of the cross section. The same

element type was used in this case, i.e. SHELL208. The cross section was imported from

AUTOCAD and 230kPa of pressure was applied from inside. 4 layers of rubber materials were

selected and 38 degrees of orientation was given to each layer. These data were provided by

‘General Tyre and Rubber Company’.

Figure 5-20: Cross-section for axisymmetric modelling

Figure 5-21: Result of the axisymmetric modelling of the cross-section

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Figure 5-22: The close view of the rim section

These above results will vary if we change the angle/orientation of the layers and if different

rubber compounds are used. An optimum result can be generated if the above procedure is

repeated several times with different properties and parameters.

5.4.5 Analysis of the Lugs

The lugs were imported from NX but it was not in the expected form. Several surfaces and

edges were removed and several surfaces were added to make the lugs look like the following

in ANSYS.

Figure 5-23: The lugs

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After the lugs had been imported and modified, material properties were added. SHELL281

was selected as its element type. The free meshing was done as the lugs were quite complicated.

The meshing done was of triangular type but square or rectangular type of meshing could also

be done.

Figure 5-24: Free meshing of the lugs

Now, with the lugs meshed, it was a time to do its analysis. The analysis yielded the following

result.

Figure 5-25: Stress concentration on lugs

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It was seen that higher stresses were produced along sharp edges and corners of the lugs. A

maximum stress of 2.176MPa was observed.

Now, it can be noticed from the result that why lugs fail from these locations.

5.5 CONCLUSION

A non-linear multi-laminated FE model such as has been developed in the present investigation

is a significant step forward in the material analysis and design for tractor tyres for “General

Tyre and Rubber Company”. This model or the whole report will be available for free for

research or for any kind of study related to modern agricultural tyres. Road damage would be

reduced if contact stresses are not concentrated at a tyre centerline. Based on adequately

measured geometric and material properties, the model is able to provide reliable stress fields

in the tyre–road stress under a wide range of normal loads and inflation pressures.

Moreover, the analysis yields that the max stress in curved ply is 1.75MPa and having factor

of safety (F.O.S) of 3.42. Max stress in lugs (Farm Base Compound) is 2.2 MPa and having

factor of safety (F.O.S) of yield strength/max stress (7/2.3) is 3.0. Recommended F.O.S is 4 for

the given agricultural tyre.

5.5.1 ANSYS Results’ Comparison with Actual Prototype Testing

The analysis of the lugs yielded the realistic result in comparison with the actual prototype

testing done in GTR.

Figure 5-26: Comparison of actual prototype testing with ANSYS result

(This picture (left) is the property of GTR and is copied with the company’s permission)

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The actual figure shows that the tyre fails at lugs edges and corners. We can see the actual

cracks produced which later make the lugs wear out completely, resulting in the complete

failure of the tyre or sometimes in fatal accidents. If we look at the ANSYS figure, the result

is quite similar. The orange and red colour show the high stresses that also tell us that the lug

will wear out from these locations. It means, without doing the actual testing, the software can

yield a very satisfactory result!

5.5.2 Future Work and Optimization

These results, obtained from our project, would be discussed with the company where they

would decide whether there should be modification needed or if they are satisfied with the

product. If there is a weak point in their product, the design parameters in the 3D model will

be optimized and based on the optimization, the analysis will be done again and again until the

better results are obtained.

The results obtained through ANSYS yields that the maximum value of stress is obtained along

cornered portions of the lugs. Stress concentration is the major reason of lugs’ failure.

Therefore, it can be recommended that stresses can be reduced if one of the following cases is

applied:

• Incorporation of greater radii to lug’s geometry which will reduce the concentration of

stress generated due to sharp edges.

• Using a slightly different rubber material with modulus of elasticity greater than that of

the current rubber material.

ADVANTAGES FOR THE ‘GENERAL TYRE AND RUBBER

COMPANY’

The success of this project provided the company with the following benefits:

The company:

• Can now shift its work to NX which is far more advanced and powerful than AutoCAD.

• Has got realistic results without testing prototypes which is extremely time consuming.

• Can now optimize its product by just changing different parameters at ANSYS.

• Has acquired a 3D model of its product “Black Bull” locally without any Chinese help.

• Has saved a lot of money which would be spent to acquire 3D drawings from Chinese

tyre companies.

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WORKS CITED

[1] “AG-Data Book”. Michelin.

[2] Sameul K. Clark. “Mechanics of Pneumatic Tyre”.

[3] F. Koutny. “Geometry and Mechanics of Pneumatic Tyres”.

[4] Omar S. Ali and Edward Mckyes. “Effect of lug position on soil thrust for lug

models research paper”. Department of Agricultural Engineering, McGill University.

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[17] Types of Tyres According to Pattern. Retrieved from http://www.hankooktyre-

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[18] Difference between Radial and Biased Tyres. Retrieved from

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[22] “Mechanics of Pneumatic Tyres”. Retrieved from

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[24] Study of SOLID46. Retrieved from

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made.html

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[29] R.H. Macmillan. “The Mechanics of Tractor – Implement Performance”.

[30] “Mechanics of Pneumatic Tyres”.

[31] “Mitas-Data Book”. Mitas