DEVELOPMENT OF TESTING METHODS FOR

OFF-ROAD TYRE BEHAVIOUR

Alistair Jackson

B122335

May 21st 2015

Supervisor: Dr. Paul Cunningham

i

i. Executive Summary

Tyre modelling and testing is an expensive, time consuming process that has changed very

little since World War II. The significant improvements in computing power and the

complex software packages developed in recent years have the potential to radically alter

the way in which tyre testing is undertaken in the future.

A scale tyre test rig has been commissioned with support from Jaguar Land Rover (JLR) and

Psi to help observe and further understand the different tyre effects in different soil types.

Theoretical equations will be investigated which are able to predict the effects of tyres in soil

(sinkage, shear force exerted etc.) for comparison with the results measured by the rig, with

a view to developing the equations required for modelling tyres in the future. This would

reduce the requirement for full-scale tyre testing and reduce development cost and time.

After a thorough literature review of terramechanics theory and test rig design, it was

discovered that Lyasko’s equation was likely to be the most accurate equation for the bulk of

the study, with the Bekker equation being simpler, more validated, but less accurate. The

Janosi-Hanamoto equation was found to be best suited to establishing the shear forces

within the experiments. The required physical parameters of the test rig design were

established, allowing for components and sensors to be investigated, chosen and bought in.

The test rig was then designed around these components to allow for the required soil

characteristics to be obtained with minimal compromise of design.

During the design phase, attention was given to manufacturing methods. Knowing there

would be strict time constraints, that the rig would have to be fabricated in-house and that

there was a budget limit meant that consideration to materials and the manufacturing

processes attributed to them was of high importance in ensuring the rig could be made. Mild

steel and welding were the two primary choices.

The latter stages of the project focussed on the sensor arm, the most important part of the

rig, to improve the likelihood of having it designed, optimised and also fabricated, to ensure

it would be as accurate as possible for its intended purpose. The ancillaries of the rig, such as

the frame and soil bucket, were then designed, along with the wheel and tyre, which was

optimised for 3D printing, ensuring the full test rig was ready to be fabricated when time

permitted.

The sensor arm was fabricated, calibrated and tested on a sandy, cohesionless soil with both

the 3D printed wheel/tyre and bevameter plate, using an Instron machine to both apply

vertical load and aid the bought in sensors. Laboratory testing of dry sand, wet sand and

wet clay was carried out to ensure accuracy and to allow the project to expand in the future.

Testing was undertaken and results compiled to gauge the success of the rig, prove its

accuracy and obtain results which were able to allow the rig to be compared with the

equations found in the early stages of the project. Results proved the rig was accurate,

provided similar results between the wheel and bevameter plate and showed forces that

would be expected from the theory. Comparison with Bekker’s equation showed an

overestimation of sinkage but confirmed a common relationship between pressure/sinkage.

Also, the equation does not take the soil’s shear limit into account. Results from Lyasko’s

and Janosi-Hanamoto’s equations were not possible at this time due to time constraints.

ii

Table of Contents i. Executive Summary ...................................................................................................................... i

ii. List of Tables ....................................................................................................................................... iii

iii. List of Figures..................................................................................................................................... iv

iv. Foreword ........................................................................................................................................ vii

v. Nomenclature & Key .................................................................................................................... viii

v.i Key for CAD Images ............................................................................................................... viii

v.ii Nomenclature.......................................................................................................................... viii

1. Introduction .................................................................................................................................. 1

1.1 Aims & Objectives ................................................................................................................ 1

1.1.2 Objectives ............................................................................................................................. 1

2. Literature Review ......................................................................................................................... 2

2.1 Tyre/Soil Interaction Research ................................................................................................ 2

2.1.1 Pressure/Sinkage Relationships ....................................................................................... 2

2.1.2 Shear stress Investigation ....................................................................................................... 6

2.2 Existing Test Rig Designs .......................................................................................................... 7

2.3 Component Research ............................................................................................................... 10

2.3.1 Sensors ................................................................................................................................ 10

2.4 Drive system ............................................................................................................................. 13

2.4.1 Translation System ............................................................................................................ 13

2.4.2 Motors ................................................................................................................................. 15

2.5 Motor Control ............................................................................................................................. 18

3. Decisions for Best Progression .......................................................................................................... 19

4. Main Body ................................................................................................................................... 20

4.1 Pressure/Sinkage Estimation ................................................................................................. 20

4.2 Rig Design ................................................................................................................................. 21

4.3 Wheel and Tyre Design ........................................................................................................... 27

4.4 Finalised Rig Design ................................................................................................................ 32

4.4.1 Unbalanced Wheel Calculation [33] ............................................................................... 34

4.5 Usage with Instron Machine .................................................................................................. 40

4.6 Soil Bucket ................................................................................................................................. 40

4.7 Error Reduction ........................................................................................................................ 42

5. Testing ............................................................................................................................................... 44

5.1 Soil Testing ................................................................................................................................ 44

5.1.1 Soil Preparation ..................................................................................................................... 45

iii

5.2 Laboratory Test Procedure, Results and Discussion ........................................................... 46

6. Rig Testing, Calibration and Discussion ..................................................................................... 50

6.1 Load Cell setup and Calibration ............................................................................................ 51

6.2 Testing, Results and Discussion ............................................................................................. 52

6.3 Load vs. Sinkage ....................................................................................................................... 55

6.4 Experimental Difficulties ........................................................................................................ 57

7. Future Improvements/Development ............................................................................................... 58

8. Conclusions .................................................................................................................................... 60

9. Bill of Materials ................................................................................................................................. 61

10. References ..................................................................................................................................... 62

11. Appendices ............................................................................................................................. 65

11.1 Soil Testing Results .................................................................................................................... 65

11.2 Load Cell Datasheets ............................................................................................................. 69

11.3 Laser Sensor Datasheets ........................................................................................................ 71

11.4 Draw Wire String Potentiometer Data Sheets .......................................................................... 73

11.5 Grouser Plate CAD and Fabricated Versions ..................................................................... 75

11.6 Cone Penetrometer Length and Tip Size .................................................................................. 76

11.7 Completed Test Rig Views ......................................................................................................... 77

11.8 Manufactured Sensor Arm ........................................................................................................ 80

11.9 Soil Parameters Found By Wong ............................................................................................... 81

11.10 Meeting Logs ........................................................................................................................... 82

ii. List of Tables

Table 1 - Material Properties for High Carbon Steel [29] ............................................................. 23

Table 2 - Wheel and Tyre Statistics .................................................................................................. 34

Table 3 - Linear Bearing Properties ................................................................................................. 37

Table 4 - Summary of Peak Soil Test Results ........................................................................................ 49

Table 5 - Parameters used for Bekker's Equation ................................................................................. 56

Table 6 - Dry Sand Shear Box Test @2.5KPa ................................................................................... 65

Table 7 - Dry Sand Shear Box Test @5KPa ...................................................................................... 65

Table 8 - Dry Sand Shear Box Test @10KPa .................................................................................... 66

Table 9 - 10% Moisture Content Sand Shear Box Test @5KPa ..................................................... 66

Table 10 - 17% Moisture Clay Shear Box Test @5KPa ................................................................... 67

Table 11 - 17% Moisture Content Clay Shear Box Test @10KPa .................................................. 67

Table 12 - 17% Moisture Content Clay Shear Box Test @20KPa .................................................. 68

iv

iii. List of Figures

Figure 1 - Validation of Bekker's Equation (solid line), the LSA Equation (dashed line) and

Real World Results (points) With Varying Plate Sizes [5] .............................................................. 3

Figure 2 - Sinkage Expected with Varying Plate Width ................................................................. 4

Figure 3 - Variation of Cone Index with Moisture Content [9] ..................................................... 5

Figure 4 - Soil Surcharge [13] .............................................................................................................. 7

Figure 5 - Shear Force Generation from a Tyre [48] .............................................................................. 7

Figure 6 - Virginia Tech's Terramechanics Rig Filled with Silty Sand and Fitted with Off-

road Tyre ............................................................................................................................................... 8

Figure 7 - UPM Indoor Tyre Traction Test Rig [16] ........................................................................ 8

Figure 8 - UPM Indoor Tyre Traction Test Rig Soil Bucket [16] .................................................... 8

Figure 9 - NASA's Scale Tyre Test Rig .............................................................................................. 9

Figure 10 - S-type Load Cell ................................................................................................................... 11

Figure 11 - Quarter-bridge Strain Gauge Circuit [16] ............................................................................ 11

Figure 12 - Full Bridge Strain Gauge Circuit [20] .......................................................................... 12

Figure 13 - Workings of a String Potentiometer [41] ............................................................................ 12

Figure 14 - Laser Triangulation Displacement Sensor [21] .......................................................... 13

Figure 15 - Indexed Drive System Analysis ........................................................................................... 14

Figure 16 –Drive System Analysis (Non indexed Chain)........................................................................ 14

Figure 17 - Rack and Pinion Translation System [22] ................................................................... 15

Figure 18 - Lathe Style Dovetail Slide [23] ...................................................................................... 16

Figure 19 - Roller Coaster Carriage Securing Method [24] .......................................................... 16

Figure 20 - Cross Section of Linear Guide Rail, Showing Acceptable Forces and Design [25]17

Figure 21 - SKF Linear Guide Rail [26]............................................................................................ 17

Figure 22 - Duty Cycle Using PWM Technique vs Analogue [27] .............................................. 18

Figure 23 - Hardpan Depth 0.6m .......................................................................................................... 20

Figure 24 - Hardpan Depth 6m ............................................................................................................. 20

Figure 25 - Expected Lyasko Results (dotted lines) Showing Non-linear Result ..................... 20

Figure 26 - MATLAB Generated Pressure/Sinkage from Bekker's Equation ......................................... 21

Figure 27 - Experimental Pressure/Sinkage Results from [6] ............................................................... 21

Figure 28 - Current Design with Cross-talk ................................................................................... 22

Figure 29 - Design for Cross-talk Elimination [28] ........................................................................ 22

Figure 30 - First Design with Cross-Talk Eliminating Bearings and Shafts ............................... 23

Figure 31 - Potential Deformation under Load ..................................................................................... 24

Figure 32 - Original Bearing Location ............................................................................................. 25

Figure 33 - Updated Bearing Location and Moved Load Cell ..................................................... 25

Figure 34 - Added Buttressing to Support Load Cell ................................................................... 26

Figure 35 - Mounting Pads Added to Aid Manufacture and Alignment................................... 26

Figure 36 - Original Wheel and Tyre Design ......................................................................................... 27

Figure 37 - Lightweight Wheel with Realistic Tyre Profile .................................................................... 28

Figure 38 - Lightweight Wheel with Tread Block Only Tyre .................................................................. 28

Figure 39 -Finalised Wheel and Tyre Combination ............................................................................... 29

Figure 40 – Tread Block in ABS, Max Vertical Deflection 0.005mm@1000N (Youngs modulus

200000kPa) ........................................................................................................................................... 30

Figure 41 –Tread Block in ABS, Max Horizontal Displacement 0.01mm@1000N ................................ 30

v

Figure 42 – Tread Block in Polyurethane soft, Max Vertical Deflection 0.293mm @1000N (Youngs

modulus 40000kPa ................................................................................................................................ 30

Figure 43 –Tread Block in Polyurethane Soft, Maximum Horizontal Deflection 0.7mm@1000N........ 30

Figure 44 - FEM on Lightweight Wheel. 1kN Vertical Force Applied. Maximum Stress

2.7MPa ................................................................................................................................................. 31

Figure 45 - Finalised Sensor Arm for Test Rig Usage ................................................................... 31

Figure 46 - 3D Printed Wheel ................................................................................................................ 32

Figure 47 - Pads Allow Soil Bucket to Brace against Rig Frame .................................................. 32

Figure 48 - Rig Design with No Series Spring ........................................................................................ 33

Figure 49 -Rig Design with Series Spring ............................................................................................... 33

Figure 50 - Implementation of Series Spring within Test Rig ...................................................... 34

Figure 51 - Actuator with Rubber Bushing .................................................................................... 35

Figure 52 - Bevameter Plate Fitted in Place of Tyre ...................................................................... 36

Figure 53 - Showing Vertical Support and Laser Mount ....................................................................... 37

Figure 54 - Sensor Arm at 0 Degrees .................................................................................................... 38

Figure 55 - Sensor Arm at 30 Degrees .................................................................................................. 38

Figure 56 - Effect of Ground Pressure at a Given Depth ....................................................................... 38

Figure 57 - Finalised Design ............................................................................................................. 39

Figure 58 - Finalised Design -Rear View ........................................................................................ 39

Figure 59 - Finalised Design - Side View ........................................................................................ 39

Figure 60 - Instron Machine [47] .......................................................................................................... 40

Figure 61 - Sensor Arm Showing Plate to Fit Instron Machine ................................................... 40

Figure 62 - Constraints Imposed By Instron Machine .................................................................. 41

Figure 63 - Projected soil contact area ................................................................................................. 45

Figure 64 - Gardening Fork for Tilling ................................................................................................... 46

Figure 65 - Dynamic Cone Penetrometer in Sand ......................................................................... 47

Figure 66 - Shear Vane, H=50mm, D=20mm [46] ................................................................................. 47

Figure 67 - Shear Vane with 50mm Vane Head .................................................................................... 47

Figure 68 - Shear Vane Test Being Undertaken With Shear Vane Located in Sand .............................. 48

Figure 69 - Shear Box Test Apparatus ............................................................................................. 48

Figure 70 - Box after Test Showing Shear Displacement ...................................................................... 49

Figure 71 - 100 x 100mm Shear Box Loaded With Sand Shear ............................................................. 49

Figure 72 - Rig Setup for Testing ..................................................................................................... 50

Figure 73 - Sensor Arm with Bevameter Plate Attached ...................................................................... 50

Figure 74 - Sensor Arm with Wheel Attached ...................................................................................... 50

Figure 75 - Load Cell Hand Testing ........................................................................................................ 51

Figure 76 - Load Cell Calibration Converting mV to N and Observing Linearity ................................... 51

Figure 77 - Test 1- Bevameter Plate Lowered to Grouser Height (Fore/aft cell) .................................. 52

Figure 78 - Test 1 Bevameter Plate Lowered to Grouser Height (Lateral cell) ..................................... 52

Figure 79 - Test 2 - Load Increased to 200N (Fore/aft cell) .................................................................. 52

Figure 80 - Test 2 - Load Increased to 200N (Lateral Cell) .................................................................... 52

Figure 81 - Test 3 - 400N Vertical Load (Fore/aft cell) .......................................................................... 53

Figure 82 -Test 3 - 400N Vertical Load (Lateral Cell) ............................................................................. 53

Figure 83 - Test 4 - Wheel with 200N Vertical Load (Fore/aft Cell) ...................................................... 53

Figure 84 - Test 4 - Wheel with 200N Vertical Load (Lateral Cell) ........................................................ 53

Figure 85 - Test 5 - Wheel with 580N vertical Load (Fore/aft Cell) ...................................................... 54

Figure 86 - Depression Left by Wheel @580N ...................................................................................... 54

vi

Figure 87 - Depression Left by Bevameter Plate @400N ..................................................................... 54

Figure 88 – Test 6 - Load vs. Sinkage Plate 250N Load ......................................................................... 55

Figure 89 –Test 7 -Load vs. Sinkage Plate 20mm Sinkage..................................................................... 55

Figure 90 –Test 8 - Load vs. Sinkage Wheel 15mm Sinkage ................................................................. 55

Figure 91 – Test 9 - Load vs. Sinkage Plate 800N Load ......................................................................... 56

Figure 92 –Test 10 - Load vs. Sinkage Wheel 800N Load ...................................................................... 56

Figure 93 - Prediction of Load vs. Sinkage Using Bekker's Equation..................................................... 56

Figure 94 - Test Wheel Showing Furrow in Wet Sand and Filling of Tyre Void ..................................... 57

Figure 95 - After Tyre Driven Through Dry Sand Showing Furrow........................................................ 59

Figure 96 - Test Wheel in Dry Sand Showing Bulldozing Effect ............................................................ 59

vii

iv. Foreword

I would like to take the time to thank Dr. Paul Cunningham, my project supervisor, for his

patience throughout the design and fabrication of this project. His willingness to help was a

privilege and allowed me to progress at a much faster rate than would have been otherwise

possible. I fully exploited his “open door” policy and I believe because of these factors the

project has been completed to a much higher standard.

Also, I would like to thank Nigel Lines, the man in charge of fabricating the components of

the test rig. His work was of an impeccable standard, his attitude to the abundance of work I

continued to give him was flawless and it was a pleasure to be able to rely on a man of his

calibre. The work he produced was millimetre accurate and goes a long way to explaining

the quality of the results achieved.

I would also like to thank PhD students Chysostomos Bekakos and Agis Skarlas who helped

me throughout my project. Chysostomos provided me with a great deal of information

regarding terramechanics and the problems I would have to overcome. He also aided me in

solving any difficulties I came across, carrying out experiments and obtaining data for my

project which was highly appreciated.

Agis was thoroughly helpful when it came to the testing phase of my project, dedicating his

spare time, offering solutions and helping to run the Instron experiments I undertook. It

would have been much more difficult to progress as far as I did without his help.

Finally, I would like to thank Lewis Darwin from the Civil and Building Engineering

department. He helped me carry out all of the laboratory experiments and donated his time

to help me set up, understand and carry out the experiments. He allowed me to use all of the

experimental equipment I desired and also provided the Automotive Engineering

department with wet clay to allow the project to be continued at a later date. Without his

generosity, laboratory results would not have been able to be obtained so I am grateful for

his help.

viii

v. Nomenclature & Key

v.i Key for CAD Images

Colour Component

Bearings

Bearing Shaft Clamp

Load Cell

Laser Sensor

v.ii Nomenclature Term Description

A Area (m2)

B Plate Width (m)

C Soil Cohesion

d Diameter (m)

E Youngs Modulus

h Plate Length (m)

I Area of Moment of Inertia (m4)

Jx Shear Displacement

K Gauge Factor

Kc Bekker's cohesive modulus of soil sinkage and deformation of a load-sinkage curve

K’c Reece’s empirical cohesive modulus of soil sinkage

Kϕ Bekker's friction modulus of soil sinkage and deformation of a load-sinkage curve

K’ϕ Reece’s empirical internal friction modulus

Kx Estimated shear modulus

L Length (m)

n Exponent of load-sinkage curve

r Radius (m)

P Load (N)

R Resistance (Ω)

S Desired Sinkage (m)

τx Shear Stress

τmax Maximum Shear Stress

V0 Output Voltage (V)

V1 Input Voltage (V)

Z Plate sinkage (m)

ε Strain

ρ Resistivity (Ωm)

γs Soil Density

1

1. Introduction

Tyre testing is an area of great importance in modern day automotive engineering as the

tyres are the only means of power transmission from the engine to the ground. Also, tyres

are becoming one of the areas of most research in the automotive sector due to the rise in

popularity of far quieter electric motor propelled vehicles, which require a more efficient

vehicular design to attain extra range from their battery power supplies. As tyres are

responsible for the bulk of automotive noise [1] and are the only source of rolling resistance,

a great deal of pressure exists to reduce both noise and rolling resistance whilst keeping or

improving the original performance of the tyre. This is an area of particular importance in

the off-road segment where aggressive mud terrain tyres are common on 4x4 vehicles. These

offer excellent traction in off-road environments, but consistently record the highest noise

and highest fuel consumption on-road. Work to reduce these parameters would be

beneficial to the automotive industry.

This project will design a scale tyre test rig which could help reduce the time and cost

required to enable observable advancements in noise and fuel consumption by enabling the

understanding of fundamental soil/tyre interaction.

Working in conjunction with a PhD student will have the additional advantage of allowing

the test rig to be applicable for future use in finite element work, leading to advancements in

computerisation of tyre design and modelling.

1.1 Aims & Objectives

The purpose of this project is to design a scale test rig to observe and measure off-road tyre

behaviour when under different loads, speeds and steering angles. The scope of the project

is to design all components in full and have the main parts fabricated, calibrated and

possibly tested. There is also a requirement to source all sensors and necessary materials to

enable the completed design to be fabricated when time permits. This project also requires

the procuring and development of a theoretical set of equations that will enable further

understanding of soil/tyre interaction and allow the test rig’s accuracy to be observed and

improved by comparison with the equations.

1.1.2 Objectives

Identify suitable terramechanics equations suitable for use with a test rig

Fabricate test rig sensor arm

Conduct testing of sensor arm and compare results with terramechanics equations

Design full test rig, including the wheel/tyre, frame, linear translation system etc.

ready for commission

2

2. Literature Review

2.1 Tyre/Soil Interaction Research

To be able to accurately compare theory with practice, it was important to investigate and

understand the current problems involved in estimating tyre/soil interaction performance

and understanding why it is difficult to attain accurate results. It is also necessary to

determine which methods are currently being used to model tyre/soil interaction. In depth

research of the available literature resulted in a thorough understanding of the variables and

initial ideas about what would need to be measured and tested in the resulting rig.

2.1.1 Pressure/Sinkage Relationships

The pressure/sinkage relationship is the most important area in vehicular terramechanics,

helping to determine how much a vehicle will sink into a particular soil and therefore,

whether the vehicle will be able to propel itself. Over the last 70 years, much research has

been completed by many people.

Personal investigations showed that since the end of the Second World War, research has

been undertaken in relating the principles of civil engineering based soil mechanics to

vehicular situations. [2]

This research was chiefly carried out by Micklethwaite and his findings were published in

‘Soil Mechanics in Relation To Fighting Vehicles’ in 1944.

Despite this, the most widely cited source of soil terramechanics was in fact from Bernstein

and Goriatchkin, who created the fundamental pressure/sinkage relation [3]:

𝑝 = 𝑘. 𝑧𝑛

Where p= pressure and k and n are constants for a given soil and plate size.

Whilst this was accurate and useful in theory, it was severely limited as the result varied

with plate size and also required the constants k and n to be determined for each set of plate

dimensions and soil characteristics used which was difficult due to the values of k and n

varying drastically, meaning they had to be separately and empirically found. This also

meant results would be difficult to compare unless the experiment carried out by others was

precisely the same, using the same equipment and dimensions, which is almost impossible

due to the sensitivity of the constants.

Reading papers by Bekker, the leading authority on this subject throughout the early 20th

century, showed how the Bernstein-Goriatchkin equation could be evolved, creating the

benchmark in modern pressure/sinkage relationship equations [4]:

𝑝 = (𝑘𝑐𝐵+ 𝑘𝜑) . 𝑧

𝑛

The advantage of this equation over the original Bernstein-Goriatchkin equation is shown in

how the value of k in the original equation is replaced with the now empirical values kc and

3

kφ, helping to reduce some of the uncertainties and variations found with the usage of the

Bernstein-Goriatchkin equation.

Another advantage of the Bekker equation has been that it was verified with many different

soils, making it one of the most universally applicable equations available, something

particularly desirable in this field of study. Figure 1 shows the degree of accuracy of

Bekker’s equation against real world testing for sandy soils.

Figure 1 - Validation of Bekker's Equation (solid line), the LSA Equation (dashed line) and Real World Results (points) With Varying Plate Sizes [5]

Unfortunately, although Bekker’s equation was deemed to be relatively accurate, it did have

a number of restrictive shortcomings. The most problematic of these shortfalls in connection

with the verification of a scaled model, such as the one to be designed, is that the equation

has been understood to lose accuracy with tyre sizes less than 50cm [6]. Clearly care would

need to be taken when using this equation in a scaled environment.

Another problem with the Bekker equation stemmed from the fact that the result still

depended on the test plate geometry. This is problematic as it means the equation cannot be

used to predict the performance of a given soil, it can only be used to compare soils already

measured. Also, Bekker’s equation uses the parameters kc, kφ, and n all of which have

varying values, depending upon the type of soil tested [7]. This is problematic as not only

does each soil type have individual values, so too does the moisture content for each soil

type. This mean a database of many hundreds of soils and their respective moisture contents

would need to be compiled for discrete usage of this equation. [8]

4

Figure 2 - Sinkage Expected with Varying Plate Width

Figure 2, modelling of Bekker's equation, confirms how the plate width has a significant,

non-linear bearing on the anticipated sinkage. This is to be expected as the equation does not

take any soil characteristics into account, it merely requires the constants kc, kφ and n to be

found and these to be substituted and used.

Reece attempted to resolve the problem of not being able to predict soil parameters by using

the empirical parameters k’c, k’φ and n that were said to be invariant for a given set of soil

conditions. This would reduce the complexity of carrying out the study.

𝑝 = (𝐶0𝑘′𝑐 + 𝐵𝛾𝑠𝑘′𝜑)(𝑧

𝐵)𝑛

Researchers, however, found that these new values were in fact still ‘non-invariant’ meaning

they also had a dependency on plate dimensions. Coupled with the fact the tests would need

to be carried out for a variety of moisture contents, it can be seen that Reece’s equation was

little better than Bekker’s. [4]

The dependencies that these equations all had would make accurate comparisons with real

world tests difficult. To this end, further research was undertaken into the works of other

people. Lyasko was the result of such research and his equation was intended for use in this

study.

Lyasko developed an equation that was based on the principle of Bekker’s equation, but was

vitally different in that it took plate dimensions into account and included fundamental soil

characteristics, such as Youngs modulus and soil cohesion, instead of individual soil

constants (kc, kϕ etc.). This made the equation far more versatile and allowed comparable

results to be obtained over a broad range of test conditions and test rigs. Also, the soil

parameters that are used within the equation, crucially, are invariant which allows them to

be determined before testing, used for prediction (unlike Bekker) and also used with varying

test rigs. They are also easily attainable through common, simple tests.

Pla

te W

idth

(m

m)

Sinkage (mm)

5

Lyasko’s fundamental equation is noted:

𝑝 =1

𝐷1𝐵𝑖

+𝐷2𝐸 ∗ 𝑧

∗ 𝜔 ∗ 𝐵 ∗ ℶ

Where 𝐷1 =2

𝜋∗ arctan(

𝜋∗(𝐻−𝑧)

2∗𝐵) and 𝐷2 = arctan(

𝐻−𝑧

𝐴0∗𝐵), ω is a coefficient that depends on

factors such as hardpan depth and the size of the contact plate.

Other variables within the equation are defined in the nomenclature.

Crucially, it can be seen that Lyasko's equation requires the Youngs modulus, E, of the soil

to be used. In Bekker's equation this was not used, it was substituted by physical

measurements, which, whilst accurate for the exact soil used, were agreed to be time

consuming and difficult to attain. Using Youngs modulus is very useful as it introduces the

cone index calculation. Cone index is a soil specific parameter established by usage of a

penetrometer which takes moisture content into account along with bulk density, internal

friction and other soil characteristics. It is a variable that is influential in establishing

soil/tyre interaction as the moisture levels in a soil, for example, significantly influence the

soil’s fundamental characteristics, altering the tyre's expected sinkage. Figure 3 shows

how moisture content influences cone index. Using cone index makes Lyasko's equation far

quicker to solve and more universally applicable than the previously mentioned equations.

Figure 3 - Variation of Cone Index with Moisture Content [9]

Lyasko’s equation shows that all variables are standalone and do not require post

experimental soil constants to be evaluated, increasing the applicability of the equation and

improving it over others’ previously mentioned.

Using this equation as a baseline would help to understand the general trend of

pressure/sinkage relationships, creating the most accurate mathematical results possible. It

is therefore the most suitable equation for this study.

6

2.1.2 Shear stress Investigation

The Lyasko equation was suited to estimating the pressure/sinkage relationship but was not

able to predict the shear stress of the soil.

Maximum shear stress associated with soil can be known as the soil’s bearing capacity. This

is the maximum force able to be applied to a soil without it shearing and therefore failing.

Background research on bearing capacity was found by looking at works from Terzaghi, an

Austrian civil engineer regarded as the father of geomechanics [10]. As a tyre under load is

forced across a surface, it exerts a shear force upon the surface as shown in Figure 4. This is

of interest as it is necessary to confirm whether the soil will shear under a certain load,

leading to permanent soil damage and also a decrease in the friction coefficient between the

tyre/soil contact patch, felt as loss of grip by the driver, due to voids within the soil

collapsing and the crushing of soil peds; natural soil aggregates. Each soil type has a

different bearing capacity and thus will behave differently with tyre/soil interaction. It is

useful to be able to predict whether the soil’s bearing capacity will be breached as this will

affect the tyre’s performance. This will be an area for further research when the rig is used

for testing, as ensuring repeatable soil characteristics over numerous runs with soft soils

may prove difficult due to soil compaction influencing soil properties. Research into the

multi-pass effect studied in depth by Modest I Lyasko in [11]will be used to help to

eliminate such problems and better understand the phenomenon.

There are essentially two methods for estimating the soil sheer, one for brittle soils set by

Bekker and one for plastic soils set by Janosi and Hanamoto. Janosi and Hanamoto's work in

[12] put forth the equation:

𝜏𝑥(𝜃) = 𝜏𝑚𝑎𝑥(1 − 𝑒−𝑗𝑥𝑘𝑥 )

Where τx is the shear stress, τmax is the limiting shear stress, jx is the shear displacement of the

terrain and kx is the empirically estimated shear displacement modulus.

The limiting shear stress τmax can be related to the normal stress through the Mohr–Coulomb equation:

𝜏𝑚𝑎𝑥 = 𝑐 + 𝜎𝑛(𝜃)𝑡𝑎𝑛∅

Bekker’s equation combined the Mohr-Coulomb failure criterion but used slightly different

varying values for shear stress and shear displacement

𝜏𝑚𝑎𝑥 = (𝐶0 + 𝑝 ∗ tan(∅)) ∗ (1 − 𝑒−𝑗𝑘 )

C0 is the soil cohesion and Ǿ in this case is soil shear resistance, which is the internal friction

angle without the normal effective stress component.

The similarity between the two equations is evident, however, the Janosi-Hanamoto

equation has been found to be more accurate with types of soil traversed by tyres and so will

be the chosen equation for this report.

7

Figure 4 shows the two primary forces (Fys and Fybd) acting on a tyre as explained by Sandu

and Senatore [14] Fybd is known as the bulldozing force and is responsible for the soil

surcharge seen. This is due to the wheel compacting the terrain in the lateral direction and is

also a result of the tyre forcing soil from its lugs. This action wastes vehicle energy and is

particularly common in loose, sandy soils. Fys is simply the shear force due to the lateral slip

of the tyre imposed by a steering action. These forces are areas of interest to observe in the

physical test and are expected to be apparent when sand is tested.

2.2 Existing Test Rig Designs

In order to progress quickly, it was deemed useful to investigate existing tyre test rig

designs. This allows current practices to be observed and related to the department’s own

test rig to understand similarities and differences.

Shown in [15] is Virginia Tech’s “indoor tyre test rig” which features a single, full sized

wheel and tyre mounted on a 6-axis measurement hub used to record the loads exerted on

the wheel. The rig is primarily used to measure normal loads, slip forces and sinkage but it

can also measure parameters such as tyre pressure, wheel speed and wheel angle. It is useful

to study this test rig as even though it is full size, it is used for the same measurements as the

proposed scale rig.

This type of test rig would be difficult to transpose into the scale rig’s application due to its

size. Being a full sized rig, the large size allows the usage of the hub sensor for recording

results. This is simply not feasible in a scale rig environment as the small wheel size means

there would not be room for a hub mounted measurement device.

Virginia Tech’s rig also uses two pneumatic bags similar to those used on HGV lorry

suspension units to exert the vertical load. These have two problems when considered for

scale test rig use. Firstly, they are only accurate to 3% of the desired force value [15], a

tolerance that is not appropriate for a reference device using far lower forces such as the

scale rig. The second problem is the size of the units. Each bag, of which there are two to

ensure pure vertical loading, is over 300mm wide and 400mm tall. This simply would not fit

in the scale test rig. Whilst smaller examples exist and also whilst the air bag system has

positives in that the compressible nature of the bags would allow for noise damping and

Figure 5 - Shear Force Generation from a Tyre [48] Figure 4 - Soil Surcharge [13]

8

shock absorption associated with rough, pebbled soil mentioned in section 3.3, the

inaccuracy of the system rules it out.

Figure 6 - Virginia Tech's Terramechanics Rig Filled with Silty Sand and Fitted with Off-road Tyre

One of the advantages of Virginia Tech’s test rig is the ability to angle the wheel unit by up

to 25 degrees toe in and 6 degrees camber. These features allow for more realistic results that

can be more easily compared as the rig can be set to resemble different vehicle set-ups or to

simulate the vehicle turning or being heavily loaded. This adds practicality to the rig and

increases its useful range.

Further research highlighted in [16] is the frequent usage of a long test bed, in this instance

the test bed is 6.4m long, 0.6m wide and 0.8m deep. The sizing of this test bed allows for

three complete rotation of the test tyre which will help provide more accurate results as

comparisons between each instance or rotation within each test will be able to be carried out,

enabling test-to-test comparisons along with inter-test comparisons to be made. The long

test bed also helps to eliminate irregularities sourcing from the initial starting of the test rig

and also when it slows to come to a stop [16].

The distinct advantage of this form of test rig is its simplicity. It has no vertical force

actuation besides the weight of the rig. Whilst this adds simplicity, it does remove the ability

Figure 8 - UPM Indoor Tyre Traction Test Rig Soil Bucket [16]

Figure 7 - UPM Indoor Tyre Traction Test Rig [16]

9

to add variations, reducing the use of the rig. Another advantage is the number of sensors

on the rig, increasing the ability to interpret the data. The rig features load sensors that

operate in the horizontal and vertical planes as well as a carriage speed and a tyre rotation

encoder, further helping to decipher the rig’s test information.

One of the very few small scale wheel and tyre test rigs is used by NASA in partnership

with MIT and the JPL and is used to verify their research into Physics-Based Design,

Planning and Control of Robotic Systems in Space. The rig is very similar in nature to the

proposed design in this report. It is a slow speed device being used over sands and clays.

The rig has distinct advantages over UPM’s and Virginia Tech’s rigs, such as the low space

demands, the ability to quickly change the wheel’s direction and speed, and also the usage

of actuators to vary the normal pressure, increasing the accuracy.

It is interesting that the test rig utilises a smooth wheel in order to decrease variations in

results and simplify the operating conditions.

The main weakness of the design is its belt drive system. This may be suitable for low

normal loads but will likely produce inaccurate reading under high loads due to the elastic

nature of the belt. The wheel is also connected to a runner system that is over 500mm from

the ground. Again, under high normal loads, this is likely to deflect, reducing the accuracy

of the rig and requiring additional material.

Figure 9 - NASA's Scale Tyre Test Rig

These rigs all have interesting features that offer benefits to tyre testing, however, they all

have their shortcomings. By using ideas from these rigs and the Automotive Engineering

department’s own test rig, it is thought that a better suited rig will be able to be designed.

10

2.3 Component Research

Before attempting to design a test rig and choose the components required for its use, it was

deemed important to have a basic understanding of the forces required by the test rig as this

would influence the component choices, size, weight, cost and design of the rig. For this

reason, a rough maximum exerted force needed to be calculated.

It was deemed preferable to relate the test model and full sized vehicle by ground pressure

exerted by the tyres as this takes area into account, ensuring the contact patch of tyre will be

equivalent to that of a full sized tyre; therefore a square law relation was required. A tyre

diameter of 150mm was used as an initial guide:

𝐹𝑢𝑙𝑙𝑠𝑐𝑎𝑙𝑒𝑡𝑜𝑚𝑜𝑑𝑒𝑙𝑡𝑦𝑟𝑒𝑟𝑎𝑡𝑖𝑜(𝑚𝑚) =800

150= 5.33

𝐹𝑢𝑙𝑙𝑆𝑐𝑎𝑙𝑒𝑇𝑦𝑟𝑒𝐹𝑜𝑟𝑐𝑒(𝑁) =𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑚𝑎𝑠𝑠(𝑘𝑔) ∗ 𝑔𝑟𝑎𝑣𝑖𝑡𝑦(

𝑚𝑠2)

𝑛𝑢𝑚𝑏𝑒𝑟𝑜𝑓𝑤ℎ𝑒𝑒𝑙𝑠=2000 ∗ 9.81

4= 4905

This force is made equivalent to the model's force by using the tyre ratios previously found:

4905

5.332= 172.66𝑁

172.66N is therefore the calculated force required to be exerted by the test rig. It would be

sensible to design the rig to accept forces of at least 300N as this allows the rig to be adapted

to simulate heavier vehicles or larger wheels/tyres if required in the future.

By having an idea of the forces required by the test rig, a design could now be properly

investigated.

2.3.1 Sensors

To obtain accurate results with maximal repeatability, specific sensors were required. There

were two main areas of measurement. The first was a distance measurement to measure

sinkage and displacement of the rig. The second was a force sensor, to measure the loading

on the wheel/plate in all three planes.

2.3.1.1 Force sensor

The force sensor chosen was a load cell. A load cell was chosen as opposed to using strain

gauges, like those used in the department’s full sized rig, due to cross-talk existing in the full

sized rig. Cross-talk is where, due to the loading on the wheel not being perfectly aligned in

the x or y plane, along with internal stresses in the frame connected to the strain gauge,

components of unwanted force are picked up on the gauge. In other words, the strain

sensors do not isolate the forces into their respective x, y and z planes, making the results

less accurate.

11

By using a load cell for each of the axes, along with a suitable axis isolation arrangement,

discrete forces would be able to be measured, increasing the accuracy of the final result.

A load cell works in the same way as a strain gauge. As a load is applied, the geometry of

the gauge changes, meaning the metal temporarily changes shape, becoming longer and

thinner or shorter and wider. These changes have an electrical effect, changing the measured

resistance of the gauge. This is known as the piezoelectric effect and obeys the following rule

[17]:

𝑅 =𝜌𝐿

𝐴

Where R is measured resistance, ρ is the resistivity of the metal and A is the metal’s cross

sectional area.

By using an S-type load cell, as shown in Figure 10, a larger length of metal can be contained

within a gauge of a given volume, making smaller resistance changes more easily observed,

heightening the accuracy of the device. Measurement accuracy is important as the changes

are likely to be very small, in the region of 0.5Ω between fully loaded and unloaded.

Allowing this change to be effectively observed requires the usage of electrical circuitry. The

simplest form of circuit is a quarter bridge arrangement known as a Wheatstone bridge as

shown in Figure 11.

When the strain gauge is deformed by the applied load, its resistance changes in line with:

[18]

∆𝑅

𝑅= 𝐾𝜀

Where ε is gauge strain and K is the gauge factor, a constant factor given to each type of a

gauge. A metal gauge has a gauge factor of ≈2.

In the quarter-bridge setup, the resistances from the strain gauge and R2 are known (R3 and

R4 are unknown). When unloaded, the ratio of resistances from the strain gauge and R2

should equal those from R3 and R4, giving an output of 0. When a strain is applied to the

gauge, the resistance ratio changes and an output is produced [18]:

𝑉0𝑉𝑖

=1

4

∆𝑅1

𝑅1=1

4𝐾𝜀

Figure 10 - S-type Load Cell Figure 11 - Quarter-bridge Strain Gauge Circuit [16]

12

The 615 series load cell by PCM (11.2 Load Cell Datasheets) was chosen for the test rig as it

is designed for test rig applications where both static and dynamic measurement are

required [19]. The cell is a full-bridge design, increasing the accuracy of the result by using

three more strain gauges instead of the resistors R2, R3 and R4.

Figure 12 - Full Bridge Strain Gauge Circuit [20]

The equation now changes to: [18]

𝑉0𝑉𝑖

=1

4𝐾[𝜀1 − 𝜀2 − 𝜀3 − 𝜀4]

2.3.1.2 Distance Sensor

To measure the vertical displacement of the wheel accurately, a device with a very high

resolution was required. The standard sensor for measuring displacement in test rigs such as

this would be a string-potentiometer. These

devices work by having string attached to

the moving object and also to a drum within

the potentiometer which is attached to a

stationary part of the item to be measured.

When the device moves, the string is pulled

out, rotating the potentiometer and

changing its resistance by a known amount

per degree of rotation. This resistance

change can then be turned into a

displacement reading. For wheel sinkage,

required in the test rig, a string

potentiometer will not have the required

resolution as they are accurate to around 2-3mm, however, it will have good enough

resolution for the horizontal rig displacement reading, where millimetre level accuracy is

perfectly suitable. For this reason, an Applied Measurements WS17KT draw wire position

sensor is being chosen to measure the rig’s horizontal displacement along the track. By

having both horizontal and vertical displacement readings being taken at the same time, a

greater understanding of terramechanics can be attained due to measurements such as linear

profiles being available, where horizontal displacement against vertical displacement can be

plotted with the associated forces identified at their respective points.

Figure 13 - Workings of a String Potentiometer [41]

13

To gain the extra resolution for the plate and wheel sinkage reading, a Micro-Epsilon Opto

NCDT laser sensor has been chosen. These work by using triangulation of a laser light

signal. The light is projected onto the surface to be measured. This light is reflected and

imaged by an optical receiving system which contains a position-sensitive element. When

the light spot’s position changes, so too does the reflected spot on the receiving unit and the

change is evaluated, reporting a change in distance.

Figure 14 - Laser Triangulation Displacement Sensor [21]

For accurate reading, the sinkage laser sensor has to be located on an immovable part of the

test rig, separating it from the displacement of the wheel and tyre, enabling repeatable and

accurate recordings. There also needs to be a sensor plate to shine the laser against which is

to be situated at the same height as the wheel/plate axle and mounted to the same piece.

This will remove the effect of play coming from slack in the bearings, load cells and also the

rig itself. With this mounting strategy, every effort will be made to improve the accuracy of

the attained results and reduce sources of error.

2.4 Drive system

2.4.1 Translation System

The tyre test rig needs to be highly controllable with it being possible to apply very small

incremental changes at any given moment. Highly accurate, controlled motion allows for

greater reliability in the results attained and helps to remove effects from momentum,

jerking when changing speed or when the vertical load force changes, which may otherwise

occur.

To keep these unwanted effects to a minimum, the whole drive system of the rig has been

specially designed. The area that required most investigation was the linear displacement

system itself used to move the sensor arm and tyre as this could be the source of many

potential errors.

14

Initially, a simple pulley system was discussed. This would involve a motor at either end of

the rig that would pull the measurement apparatus along a track. This idea was quickly

discarded when it was understood that the cord used to winch the apparatus would likely

stretch, reducing the linearity of the results. Furthermore, under heavily loaded conditions,

the wheel and tyre may stick in the soil and thus not move, the extra displacement of the

pulley absorbed by the elastic nature of the pulley wire, and jolt largely as it is pulled free.

This would render the results inaccurate.

Another option was to use a chain drive system. The benefit of this design was the reduced

potential for non-linear results as the chain would not stretch. The chain drive also allowed

for indexing, meaning that both sides of the rig could be driven at the same speed, ensuring

that all displacement of the rig was in one plane only and would not be skewed by an off-

centre drive unit.

The problem with the chain drive system was two-fold. Firstly, designing and

manufacturing a connector that would allow for negligible play between the measuring

apparatus and the chain would be time consuming, reducing the likelihood of completing

the project. Secondly, chain drive systems have very little in the way of vertical constraints.

This would lead to inaccurate results as the measuring apparatus would be able to move up

and down when the load is increased. When accuracy greater than 1mm is required, this is

clearly not a viable option.

A third option for the drive system was a rack and pinion system. The immediate merit from

this system is that it can be purchased and bought in, substantially reducing the

manufacturing time of the rig. Another benefit is how the pinion gear locks into the rack,

removing the chance of the apparatus jolting when highly loaded.

The rack and pinion system can also be used as a pair, in parallel. This has the same benefit

as the chain drive system in that motion can be restricted to a single plane, increasing the

accuracy of the recordings.

A rack and pinion system was decided upon as the best method for translation of the

measuring apparatus.

Chain

driven side

Indexed chain

driven side

Direction of

travel

Chain driven

side Non chain

driven side

Direction of

travel

Figure 16 –Drive System Analysis (Non indexed Chain) Figure 15 - Indexed Drive System Analysis

15

Figure 17 - Rack and Pinion Translation System [22]

2.4.2 Motors

In order to move the measuring apparatus, motors needed to be specified. It was important

that the motors were:

Precisely controllable

Slow speed

High torque

The reason for requiring precise control is that with greater accuracy comes better results.

The rig needs to be set to move at a precise speed that does not vary with the applied load

for the most accurate results to be obtained.

It is important that the rig move slowly so that all results are directly related to the forces

applied vertically and the drag force from the linear displacement. If the speed was high,

effects from momentum would exist. It would also be harder to understand the results as the

maximum polling rate of the sensors (usually 10Hz) would be stressed and important

moments of the soil and tyre interaction, such as when friction force is overcome, would be

much harder to observe as the time frame would be so short.

Finally, high specific torque is important as space is limited, meaning small motors will have

to be chosen for packaging reasons. Also, with vertical forces potentially exceeding 300N

acting on the wheel/tyre, sinkage could be high, causing a great deal of friction that would

need to be overcome to allow the assembly to continue to operate even under full load.

Two 12V DC motors with a 504:1 reduction rate were chosen as these would provide over

5Nm of torque each. This would be enough to move the assembly even when fully loaded in

soil providing a coefficient of friction up to unity (Using a 40mm spur gear on the rack and

pinion system) as shown:

𝐹𝑜𝑟𝑐𝑒 =𝑇𝑜𝑟𝑞𝑢𝑒

𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

250𝑁 =5𝑁𝑚

0.02𝑚

2.4.3 Runner System

As the rig is movable, there needs to exist a runner system to allow the sensor arm to freely

move from one side to the other whilst under load. There are three major difficulties with

this proposition. The first difficulty is restricting the system to one plane. This is vital as all

16

measurements will be taken in one plane and it is imperative the rig does not rotate when

under vertical load or when being moved horizontally.

The second problem is limiting the force required to move the device. Many approaches are

appropriate for constraining the motion to one plane, but they are an inherent source of

friction, requiring larger motors to move and potentially distorting results when the rig is

loaded.

The third problem is the case of errors induced by the constraint system. Conditions such as

beam bending, bearing slack and degrees of freedom all need to be taken into account to

ensure that the runner system is as accurate as possible.

One potential option was a lathe style dovetail runner. These are very accurately machined,

making constraining the system to one plane very easy. They also remove any chance of

bending moments existing and can be very strong. To work effectively though, there is a

large contact area between the two parts of the dovetail. This has a negative effect on friction

and would require far more powerful motors to move the rig, especially when loaded.

Figure 18 - Lathe Style Dovetail Slide [23]

Another option was to use a double roller technique. The idea is similar to that of roller

coasters, where the cars are secured to the track by a pair of rollers above and below the

track. The advantage of this is that the rig would be kept constrained in all necessary planes

and would be easy to move both when the rig is unloaded and also when fully loaded as the

system uses wheels both above and below the track. The system would also have a low

friction coefficient, increasing measurement accuracy and requiring less powerful motors.

Figure 19 - Roller Coaster Carriage Securing Method [24]

The complexity of fabrication of the roller system and its requirement for high accuracy to

remove play meant that the design was modified to use a linear bearing instead of a

clamping wheel assembly. The major downfall of this solution was still in existence,

however. Linear bearings require a shaft to run along. As the track would be 1.5 metres long,

Area of high friction

17

the track would also have to be 1.5 metres long, but could only be supported at either end.

With a 500N vertical load there was the potential for a large bending moment to exist,

reducing the accuracy of the recorded results as the bending of the track would effectively

lift the rig up, suggesting sinkage is not as great as it would actually be. Simple calculations

were undertaken to assess the extent of expected deflection.

2.4.3.1 Beam deflection

I = 𝜋

4𝑟4 for circle

𝐷𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛(𝑚𝑚) =𝑃𝐿3

192𝐸𝐼

𝐷𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛(𝑚) =0.3 ∗ 1.53

192 ∗ 21 ∗ 107 ∗ (0.78 ∗ 0.0064)= 24.8𝑚𝑚

As the deflection was deemed too much to be acceptable, a further method was investigated.

The result was a linear guide rail which consists of a supporting bar fitted with a carriage.

The solution effectively combines the positive points of both the lathe style system and the

linear bearing solution.

SKF offer a system which allows for compact packaging and also positive and negative

vertical forces far greater than required for the scale tyre test rig made possible by using a

notched rail with a ball bearing carrier.

Figure 20 - Cross Section of Linear Guide Rail, Showing Acceptable Forces and Design [25]

The devices are also made to the required length and are expandable to suit further

modification of the design. The rail features in-built mounting holes, meaning it can be

secured at multiple points along its length, removing any bending moment.

Figure 21 - SKF Linear Guide Rail [26]

18

2.5 Motor Control

To control the speed of the rig, a motor controller was required. The usual technique for

controlling the speed of a motor is by varying the voltage. Reducing the voltage reduces the

current and so the motor slows down. Unfortunately, with this technique, torque is also

reduced. Power is equivalent to voltage multiplied by current and so by reducing these

values, torque decreases. Due to the rig requiring a large torque to be moved when under

load, a reduction in torque is not desired.

To combat the loss of torque, a specialist controller will be used, relying on pulse-width

modulation (PWM) to reduce the motor speed. PWM works by feeding the motors their

maximum voltage for a shorter period of time, depending on how slow the motor needs to

rotate. Due to power being related to voltage multiplied by current, as mentioned before,

using a PWM approach will allow maximum torque to be transmitted to the motors even

when they are not operating at maximum speed.

Figure 22 - Duty Cycle Using PWM Technique vs Analogue [27]

Evident from Figure 22 is how the PWM technique varies from the traditional analogue

approach. By using PWM, precise control of the motors will be possible with no loss in

torque.

Dotted lines are from analogue

signal. Equivalent PWM signal

represented by square form.

75%

50%

25%

19

3. Decisions for Best Progression

Consultations with members of staff, PhD students and workshop technicians, along with

having carried out further research regarding the novel aspects of the project led to some

changes from the original scope of the project, i.e. change from designing, fabricating,

testing the whole rig and comparing results against theory.

It was with a unanimous decision that the project was directed towards development of the

rig’s sensor arm. This is the part of the rig that houses the horizontal load cells, bevameter

test plate, wheel/tyre unit and laser sensor. The reason for this heading was due to the

ability to use machinery within Loughborough University to test the sensor arm, enabling

the arm to be fabricated, calibration to be achieved and the potential for basic results to be

attained. This was deemed to be of greater benefit to the university than merely designing

but not fabricating all parts of the test rig.

Further increasing productivity, it has been decided that at this stage, only two contrasting

types of soil would be tested; dry sand and wet clay. These types of soil are:

easily obtained

cheap

homogeneous and yet have very different properties from each other

easily modified with moisture content

Another main decision was the choice to use Bekker’s equation as opposed to the potentially

more accurate Lyasko’s equation at this stage of the project. This choice was due to Bekker’s

equation being well validated and having comparatively few variables, enabling testing to

commence more swiftly and comparable results quickly attained as explained later. Also,

Bekker’s equation will be even more appropriate as the chosen soils are cohesionless and

frictionless respectively, meaning kc in Bekker’s equation can be ignored when using sand

and kϕ can be ignored when using clay, further simplifying the equation and aiding with the

analysis of results. Lyasko’s equation is to be reinstated in the future when this project is

further developed.

20

4. Main Body

4.1 Pressure/Sinkage Estimation

In order to gauge the effectiveness of the test rig, a MATLAB code was developed to

estimate the expected test plate/tyre sinkage for a given load applied to it, replicating the

test rig’s action. The code was originally based around Lyasko’s equation due to its potential

to produce the most accurate results. Without having accurate input arguments, such as soil

cone index, Ageikin’s constant or moisture content, the results were of dubious quality as

shown in Figure 23 and Figure 24, where a hardpan depth of over 3 metres was required to

provide a sensible result (Figure 24). Even this ‘sensible’ result differs from results attained

by others as shown in Figure 25, where the expected outcome is not linear. This is due firstly

to a lack of primary data for input arguments and secondly due to having to use separate

theoretical equations to estimate input soil values as first hand data acquisition was not

possible at this time, reducing the accuracy of Lyasko’s equation dramatically.

Figure 25 - Expected Lyasko Results (dotted lines) Showing Non-linear Result

Figure 23 - Hardpan Depth 0.6m Figure 24 - Hardpan Depth 6m

21

As Bekker’s equation has been chosen for validating the test rig, a MATLAB code was

written to generate expected results.

The results generated from the code supplied (USB drive) created accurate results when

compared with research experimental results (Figure 26 and Figure 27). This lends

confidence to the usage of the equation for validation of the designed test rig.

4.2 Rig Design

Consulting the full scale departmental rig (Figure 28) it was apparent there was room for

improvement. The rig used a single arm that held the wheel assembly and this arm had two

strain sensors attached to it, one for the x-direction and one for the y-direction. Through

experimentation with the full sized rig, it had been proven that cross-talk exists, meaning

forces are erroneously recorded on both sensors even when the device is supposedly only

moving through one plane.

Studying [28] revealed a potential method for avoiding cross-talk by using a bearing system

that allowed only one degree of freedom for each load cell, thereby eliminating cross-talk

(Figure 29).

Figure 27 - Experimental Pressure/Sinkage Results from [6] Figure 26 - MATLAB Generated Pressure/Sinkage from Bekker's Equation

22

Figure 28 - Current Design with Cross-talk

Figure 29 - Design for Cross-talk Elimination [28]

As the bearing design removes cross-talk, an attempt was made to replicate such a method

for the scale test rig. The main problem encountered is that the scale test rig is far smaller

than the full scale test rig, leaving less room for bearings (magenta) and shafts. The original

design is shown in Figure 30.

Strain gauges

both located on

one arm

Bearing system only

allowing one degree of

movement,

eliminating cross talk.

23

In a further effort to increase accuracy and reduce the clutter around the central sensor arm,

the vertical force sensor (green, left) has been located far to the left hand side. There are two

main benefits to this approach. The first is that accuracy of vertical load readings is

increased due to the actuator acting directly on the load cell. In [28] the vertical load cell is

located by the wheel hub. This reduces the sensitivity of the cell to applied force from the

actuator due to slight bending moments existing as the rig is loaded. Secondly, due to the

bearings having a tolerance, a marginal amount of actuator elongation will occur before the

force is recorded by the load sensor. This is acceptable in a full sized rig where accuracy to

the nearest Newton is acceptable but not acceptable in the scaled rig where ultimate

accuracy is of most importance. Having the load cell located near the hub would increase its

sensitivity to changes in force stemming from the wheel as it rotates, useful in observing

instabilities in the wheel at high speeds, for example. In the scale rig scenario, where

rotational speed is far slower, it is much more important to accurately measure applied load

as this is what many of the results are based around, further explaining its location near the

actuator.

Calculations were carried out on the original bearing support design with a large 500N force

to assess whether it was likely to provide accurate results when used in the test rig and most

importantly, whether the beams would bend dramatically or fail when under load.

Table 1 - Material Properties for High Carbon Steel [29]

Youngs Modulus 200GPa

Ultimate Tensile Strength 515MPa

Yield Strength 205MPa

Movement limited

to single plane by

usage of bearings

and shafts.

Figure 30 - First Design with Cross-Talk Eliminating Bearings and Shafts

24

For solid round bar:

𝑀𝑜𝑚𝑒𝑛𝑡𝑜𝑓𝐼𝑛𝑒𝑟𝑡𝑖𝑎, 𝐼 = 𝜋 ∗𝑑4

64= 𝜋 ∗

12 ∗ 10−34

64= 1.02 ∗ 10−9

d=diameter

𝐷𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 =𝐿𝑒𝑛𝑔𝑡ℎ3 ∗ 𝐹𝑜𝑟𝑐𝑒

3 ∗ 𝐸 ∗ 𝐼=

100 ∗ 10−33∗ 500

3 ∗ 200 ∗ 109 ∗ 1.02 ∗ 10−9= 8.16 ∗ 10−4𝑚 = 0.86𝑚𝑚

E = Youngs Modulus

𝐵𝑒𝑛𝑑𝑖𝑛𝑔𝑆𝑡𝑟𝑒𝑠𝑠 =𝐹𝑜𝑟𝑐𝑒(𝑘𝑁) ∗ 𝐿𝑒𝑛𝑔𝑡ℎ

𝐼0.5 ∗ 𝐻𝑒𝑖𝑔ℎ𝑡

=0.5 ∗ 100 ∗ 10−3

1.02 ∗ 10−9

0.5 ∗ 12 ∗ 10−3

= 294117.65𝑃𝑎 = 0.294𝑀𝑃𝑎

The maximum allowable bending stress is said to be 60% of the yield limit [30], which in the

case of this steel is 123 MPa.

It was decided that the results for deflection were adequate but would benefit from

improvement due to the nature of the test rig, whilst the bending stress was absolutely fine.

Although this design is a marked step forward in design from the full size rig and a good

start, it was not free of problems. The main concern with the design was the strength of the

connections on the lower set of shafts illustrated in Figure 32. The design uses bearing blocks

that attach to box section beams. This is a simple and lightweight design but would likely

give potential incorrect readings, especially when under load. As the bearing blocks are

connected to the box section with two vertically opposed bolts, there is the potential for

them to move slightly when the rig is under load. This is a source of error and should be

removed.

Figure 31 demonstrates the exaggerated effect of loading, where tolerances in the bearing

blocks’ bolt holes and bolts allow for movement and misalignment.

To counter this problem, an Aluminium billet block was designed. This would allow the

linear bearings to be press fitted, reducing the movement solely to the tolerance of the

Figure 31 - Potential Deformation under Load

Shaft Bearing Block

25

bearing, rather than the bearing and its housing. The design is also easier to fabricate and

crucially, easier to manufacture to a tighter tolerance.

In Figure 32 and Figure 33 it is also possible to see how the lower load cell (green) has been

moved to be mounted horizontally and above the billet block. This serves to reduce the

length of the linear bearing rail by over a third, removing as much potential deflection as

possible and thus increasing measurement accuracy.

By changing to this design, the maximum bearing beam deflection under a 500N load is now

only 0.176mm. This was deemed far more acceptable.

Original design with

bearings mounted on box

section and vertically

mounted load cell.

Adapted design with bearing

mounted within solid billet

aluminium block and horizontal

load cell.

Figure 33 - Updated Bearing Location and Moved Load Cell

Figure 32 - Original Bearing Location

26

A small amount of buttressing was finally added to support the horizontal load cell (Figure

34) due to it being made from relatively soft aluminium. The added buttressing will help to

eliminate any incorrect readings from the supports deflecting.

To aid manufacture, simplify the design and allow for imperfections in the manufacturing

process stemming from metal deformation due to welding to be accounted for, 8mm pads

have been added to parts of the design connecting position sensitive components such as

bearings and load cells. The pads allow for tapping, meaning components can be attached to

the rig without the risk of deforming the relatively thin box section used in construction. By

having an 8mm pad, there is also sufficient room for skimming if the components do not

correctly line up, increasing speed and ease of manufacture whilst allowing the components

to be perfectly aligned.

Figure 35 - Mounting Pads Added to Aid Manufacture and Alignment

Added buttresses

to reduce

likelihood of

incorrect readings

8mm

mounting

pad

Figure 34 - Added Buttressing to Support Load Cell

27

4.3 Wheel and Tyre Design

One of the novel features of the scale tyre test rig is its ability to function both as a

bevameter and as a tyre test rig. For the latter function, a specialist wheel and tyre

combination will be used, enabling results to be more easily attained and compared.

Due to the complexities of soil behaviour and the many variables associated with attaining

accurate measurements, the wheel and tyre

combination must be designed such that it is not

overly complex and yet attains repeatable results.

In the fledgling stages of the project, a basic wheel

and tyre was created as shown in Figure 36. This

design had two major flaws to it. In terms of design, it

is unlike any off-road tyre in that its section width to

wheel diameter is far too small. This would make

comparison with a real world wheel and tyre difficult

to achieve as the contact patch would not be

representative.

The second flaw related to how it would be

manufactured. The design was completely solid,

meaning when 3D printed, a large amount of material

would be required, requiring more time to create and

also wasting expensive material. The wheel also had

no bead for the tyre which could prove to be problematic as when the wheel is rotated at an

angle the tyre could slip off.

The design was substantially changed (Figure 37), firstly to more closely represent a real off-

road tyre by being based around a common side wall height to section width ratio (0.65)

and secondly to use a wheel width that has more in common with a real wheel and tyre

combination (wheel width: wheel diameter =0.7). The tyre was also designed to feature a

30% void ratio, that is, the percentage of no tread to tread in the tyre volume. 30% was

discovered to be optimal for this form of study and was investigated at length by

Chrsostomos Bekakos in [31]. The tread pattern of the tyre was chosen to be a simple full

width ingot style block. This style has been chosen to allow easy analysis. The tread pattern

is:

Uniform – Allowing repeatable results independent of the tyre’s starting position

Simple – Allowing easier interpretation of results due to less variables

Angled – Reducing the chance of soil being picked up and transported and aiding

soil ejection

Notch like – Producing considerable shear forces on the soil allowing the shear

component of a tyre to be more easily understood

Figure 36 - Original Wheel and Tyre Design

28

The design of the wheel has also been targeted

around weight reduction to aid manufacturing time

and to waste least materials. The lightweight wheel

is shown in Figure 37.

To enable simpler modelling of the system and to

remove excess variables, it was decided that the

tyre component would be made from solid rubber,

removing pneumatics and effectively making the

tyre a solid block. With this in mind, the wheel and

tyre combination could be further altered to save

much material by increasing the size of the wheel

and reducing the sidewall thickness so that the tyre

is effectively just tread blocks moulded to the wheel

as shown in Figure 38.

The design for minimum weight included large

spoke gaps, arced spokes and many weight

reducing holes. This has proven to be

exceptionally effective at reducing the weight

from 1.2061kg to 0.54kg whilst still retaining

adequate strength. This is over 50% of weight

saving, something particularly important as 1kg

of printable material costs £400 and there being

no requirement for extra material to be used. The

other benefit of reducing the material is the

reduced manufacturing time that comes with it.

As 3D printing is still in its infancy, to produce

an item of this size may take over 24 hours. The

material saving has reduced manufacturing time

to under 10 hours.

For the validation process of the project, the Instron machine (explained in 4.5) will be used

to exert a vertical load, taking place of the vertical force applying actuator and aiding the

calibration of the rig’s sensors. As the Instron is not a purpose built test rig, it does not have

the space that would be available in the final rig. For this reason, a smaller wheel is required

such that at least one revolution is possible within the constraints of the Instron machine.

The wheel and tyre size was changed from a 150mm diameter to a 110mm diameter which

reduced the rolling radius from 0.47m to 0.345m, allowing a test bed to be more easily

designed. Due to the reduced size, requiring less material, the design could be made

Figure 37 - Lightweight Wheel with Realistic Tyre Profile

Figure 38 - Lightweight Wheel with Tread Block Only Tyre

29

stronger, reducing potential deflection under load

and increasing the accuracy of the results. The final

design weighs even less at 0.33kg and is shown in

Figure 39.

Space has been left to allow for bearings to be

inserted in each side of the wheel. This will greatly

reduce friction from motion, contributing to more

accurate readings. The chosen bearings have

rubber seals to help resist soil ingress, increasing

the longevity of the wheel and reducing friction

increase over time.

To prove the applicability of the final design for

testing, an FEM study was carried out on the rubber tread blocks and also the plastic wheel

to ensure that any deflection under maximum load was satisfactory and that stress did not

exceed the material’s maximum capacity, suggesting it would break. The tread blocks were

tested as ABS and also as an overly soft Polyurethane to serve as a ‘worst case scenario’ due

to the uncertainty of the printed rubber-like material’s properties.

The finite element analysis shows how with even a very soft rubber-like material for the

tread blocks, deflection at an extreme 1000N is expected to be less than one millimetre. The

final tread compound will be a 5%rubber mix with 95% plastic. This gives the tyre a more

realistic friction coefficient whilst retaining the required high strength in compression and

shear, aiding recorded sinkage accuracy. The expected maximum deflection is around

0.01mm.

Figure 39 -Finalised Wheel and Tyre Combination

30

An FEM study on the lightweight wheel also suggested that this lightweight design would

survive the rigors of compression testing. With a 1kN vertical load, maximum stress within

the wheel was a mere 2.7MPa. The plastic material is expected to have a yield close to

30MPa and so there is a high degree of certainty that the design will be adequate. The wheel

used for testing is the one shown in Figure 39 and is thus even stronger than that which had

the FEM study carried out upon it in Figure 44.

Figure 42 – Tread Block in Polyurethane soft, Max Vertical Deflection 0.293mm @1000N (Youngs modulus 40000kPa

Figure 41 –Tread Block in ABS, Max Horizontal Displacement 0.01mm@1000N

Figure 43 –Tread Block in Polyurethane Soft, Maximum Horizontal Deflection 0.7mm@1000N

Figure 40 – Tread Block in ABS, Max Vertical Deflection 0.005mm@1000N (Youngs modulus 200000kPa)

31

Figure 44 - FEM on Lightweight Wheel. 1kN Vertical Force Applied. Maximum Stress 2.7MPa

Figure 45 - Finalised Sensor Arm for Test Rig Usage

The wheel and tyre were printed on an Objet PolyJet 3D printer which has the ability to

print both rubber and plastic simultaneously. The device uses a liquid polymer that is

injected onto the print bed and then cured by ultraviolet light. The polymer is injected to a

200 micron degree of accuracy in layers of 16 microns, enabling intricate designs to be

successfully created. The concave areas of a design are created by printing a removable filler

material which takes up the void space, allowing the polymer to be printed on top of the

filler.

The rubber is part of the Tango Black family which is a printable material providing a

consistency similar to natural rubber. The advantage of the Objet machine over others is the

ability to print different proportions of each material as necessary. The rubber material can

be added in small increments to the plastic material, allowing the material properties to be

tailored to the desired application.

The completed, printed wheel is shown in Figure 46. Note the use of bearings and how the

simple tread blocks are not only fused to the wheel but impregnated within it as the rubber

32

layer is printed before the perimeter of the wheel is reached, increasing the shear strength of

the tread and increasing its usable life.

4.4 Finalised Rig Design

Taking all of the aforementioned factors into account, an optimised design has been

achieved. The designed rig has the ability to:

Measure pressure vs sinkage for a variety of soils

Accurately measure forces in x, y and z planes

Provide vertical forces of over 1kN

Allow for three full rotations of a 150mm diameter wheel and tyre

Enable measurements to be taken with wheel steer angles between 0° and 35°

The final rig will be made primarily of 40mm box section steel with a 3mm wall thickness.

This is a readily available size with excellent strength (280MPa [32]) and a low cost per metre

when compared with stainless steel or Aluminium. Another reason for choosing mild steel

was its ease of fabrication. The metal can be cut to size with readily available tools and,

crucially, it can be welded. By welding the rig, maximum strength can be attained in a very

quick time. The resulting bond is also extremely rigid, meaning the rig will not flex when

under load as it would with bolts, increasing the potential accuracy of the device.

Due to the strength offered by the welds, the rig has been designed to brace against itself

when the soil bucket is in place, removing the requirement to fasten it to the floor and

therefore increasing its portability and usability.

Figure 46 - 3D Printed Wheel

Bracing pads for soil

bucket to be placed

on.

Figure 47 - Pads Allow Soil Bucket to Brace against Rig Frame

33

One of the novel features of the test rig is its usage of a rubber bushing mounted in series

with the vertical actuator as shown in Figure 48 and Figure 51. The advantage of this will be

apparent in the results attained from the full rig. The actuator, originating from the full scale

test rig, supplied by the Automotive Engineering department and able to exert forces well

over 10kN, can work in one of two ways:

1. Force specified

2. Extension (sinkage) specified

The test rig will use the force specified method so that the sinkage from Bekker’s or Lyasko’s

equation can be observed and compared. The downfall of the actuator is that it is hydraulic,

meaning once the force has been applied, it is effectively rigid. The rigidity means that the

potential for noise to be recorded by the sensors stemming from the propulsion motors and

the tread blocks of the tyres is greatly increased. In normal tyre testing, there exists the

possibility that there will be pebbles and other small, hard, unwanted foreign objects in the

soil, especially when the rig is used for a wide variety of soils. These pebbles, when run over

by the test wheel would provide a much higher recorded vertical force than expected as the

pebble will have to be forced downwards into the soil due to the actuator not being able to

move up. In order to prevent this, a spring system was originally designed to be placed in

series with the actuator (shown in yellow, Figure 50) which would enable the force to be

soaked up much like the suspension system in a car, making the result much more accurate.

This is a technique used in the full scale test rig shown in Figure 28 with the effect shown in

Figure 48 and Figure 49.

Figure 49 -Rig Design with Series Spring Figure 48 - Rig Design with No Series Spring

34

Figure 50 - Implementation of Series Spring within Test Rig

In the full scale rig, the wheel also has the potential to spin up to full vehicular road speeds,

which means with even a slightly unbalanced wheel, a noticeable force can be generated

which, due to the sensitivity of the load cells, would make the recorded values inaccurate. A

calculation of an expected force is shown in 4.4.1:

4.4.1 Unbalanced Wheel Calculation [33]

Table 2 - Wheel and Tyre Statistics

Wheel Weight 25kg

Unbalanced mass 20g 0.45m from centre of wheel

Rotational speed 1000rpm

Damping ratio of tyre 0.15

Spring stiffness of tyre Assumed 1000Nm-1

𝐴𝑛𝑔𝑢𝑙𝑎𝑟𝑆𝑝𝑒𝑒𝑑, 𝛺 = 𝑅𝑃𝑀 ∗ 2𝜋

60=1000 ∗ 2𝜋

60= 104.7𝑟𝑎𝑑𝑠−1

𝑁𝑎𝑡𝑢𝑟𝑎𝑙𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝜔 = √𝑘

𝑚= √

1000

25= 7.07𝑟𝑎𝑑𝑠−1

𝑟 =𝛺

𝜔=104.7

7.07= 14.8

35

𝑀𝑎𝑥𝑖𝑚𝑢𝑚𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒, 𝑋0 =𝑚𝑢𝑟

2 𝑒𝑚

√(1 − 𝑟2)2 + (2 ∗ 𝜁 ∗ 𝑟)2)=

0.02 ∗ 14.82 ∗0.4520

√(1 − 14.82)2 + (2 ∗ 0.15 ∗ 14.8)2

= 0.00045𝑚

𝑀𝑎𝑥𝑖𝑚𝑢𝑚𝐹𝑜𝑟𝑐𝑒, 𝑃0 =𝑚𝑢𝑒𝛺2(

1 + (2 ∗ 𝜁𝑟)2

(1 − 𝑟2)2 + (2 ∗ 𝜁 ∗ 𝑟)2)0.5

= 98.66√1 + (2 ∗ 0.15 ∗ 14.8)2

(1 − 14.82)2 + (2 ∗ 0.15 ∗ 14.8)2= 2.06𝑁

This 2.06N force is enough to give poor quality readings from the load cells as they are

accurate to less than 0.1N. It is for this reason that the spring system is vital in the full sized

rig.

In the scale rig, speeds will be in the region of 0.1m/s meaning the rotational force generated

by the wheel will be negligible, also, homogeneous soils with no pebbles are to be used,

removing the need for such a complex system. Noise from spinning motors and moving

shafts will, however, still be present and there is a possibility for this to be picked up by the

sensitive sensors. For this reason, it has been decided that a rubber bushing will be placed in

series with the actuator instead of the spring. Rubber possesses both damping and spring

like qualities in this situation and will work to reduce noise whilst resisting large deflections

which would contribute to incorrect vertical displacement readings. Systems like this have

been shown to be very effective in the automobile industry where constrained items such as

engines and exhaust systems need to be mechanically damped whilst not moving. Rubber

bushes are used almost exclusively in these situations with negligible error rates.

Figure 51 - Actuator with Rubber Bushing

The test rig has been designed for versatility and for cost effectiveness. To this end, the rig is

able to function both as a bevameter and also a tyre test rig. The distinct advantage of this is

that the soil can be tested for its parameters, against the bevameter plate and then tested

Rubber Bushing

36

with the wheel/tyre in quick succession. It also means that only one test rig is required,

saving space, cost and time.

Visible in Figure 52, in orange, is the designed pressure plate for bevameter use. The

pressure plate uses the same mounting as the tyre and is the same height as the tyre,

meaning switching between the components is simple and requires no change in the rig’s

setup, whilst taking just 30 seconds. The plate is also secured by a 10mm bolt, the same as

the wheel/tyre, further aiding ease of changeover. It has been designed to represent the

same surface area of the tyre when sunk 15mm in to the soil, aiding its applicability for

usage with theoretical equations. Also, it features equi-spaced grousers, used to help with

the acquisition of shear stress results. Finally, it is a compact unit that is cheap and easy to

manufacture whilst being easily exchanged, making it very practical to use.

Figure 52 - Bevameter Plate Fitted in Place of Tyre

Increasing the rig’s versatility further, the finalised design has the ability to turn the wheel

and tyre in increments of 15 degrees. This will be of particular benefit to understanding the

more advanced characteristics of tyre and soil interaction when the vehicle is undertaking a

turn manoeuvre. The turning mechanism allows the entire sensor arm and tyre to be rotated

and locked into place, maintaining measurement accuracy. The mechanism works by

turning and locking the vertical shaft that the sensor arm is attached to as shown in Figure

54 and Figure 55.

Ensuring accuracy is maintained throughout operation, all moving parts run on bearings,

the measurement apparatus itself runs on 4 linear carriages as mentioned previously in 2.4.3.

The vertical actuation is enabled in much the same way as the sensor arm, by having a

combination of clamps and linear bearings. Care had to be taken at this stage to ensure

motion was not limited by the clamps as vertical movement may well be over 50mm. This is

shown in Figure 53 where 75mm of travel is available (between magenta bearing and blue

bearing clamp). The vertical shaft connecting the sensor arm is also fitted with a bearing at

each contact point to allow rotation to occur easily and precisely. After investigating many

different types of bearing [34] it was decided that linear bearings were most suited. The

specification of these bearings is shown in Table 3. Note that in the orientation to be used,

the load on the bearing will be very little.

37

Table 3 - Linear Bearing Properties

Feature Value

Dimensions (WxLxH) 28x40x17mm

Dynamic Load 695N

Static Load 510N

Weight 0.08kg

The location of measuring apparatus has been carefully designed, with the vertical laser

sensor (brown) mounted on the static upright of the rig. This is connected by 5mm steel

plate, ensuring negligible deflection, reducing the likelihood of resonance and increasing the

accuracy of the recorded results. The horizontal plate used as a target for the laser is

mounted at axle height, in line with the tyre/test plate. This increases the accuracy of results

as it will give a true reading of the vertical displacement, taking the tolerances of the various

components into account. The plate also maintains accuracy when the sensor arm is rotated,

adding practicality to the design.

A second laser sensor has been given its own bearing carriage and is mounted horizontally

on the track as shown in Figure 54 and Figure 55 (brown). This gives the notable advantage

of recording precise horizontal motion, beyond the accuracy of the string potentiometer.

This feature will be useful in the examining of the shear limit of the soil. It is expected that

there will be a change in speed of the rig as the shear limit of the soil is reached and this will

be observed by the horizontal laser sensor.

Figure 53 - Showing Vertical Support and Laser Mount

38

The soil bucket has been designed to be 500mm deep. This is fitting with that found by

Soehne in Figure 56 [35] where the depth is related to pressure, not mass, meaning a soil

depth the same as a full sized vehicle would be required.The soil bucket is also 500mm wide,

allowing the wheel to be steered whilst retaining two wheel diamteters from the side of the

bucket to remove soil bucket interference. The length of the bucket is 1500mm, allowing for

three complete rotations with space left at the end to reduce unwanted soil bucket

interference.

The final rig design is shown in Figure 57 to Figure 59 with further views shown in 11.7.

Detailed CAD and dimensioned engineering drawings enabling fabrication of all

components are also provided on the USB drive.

Figure 54 - Sensor Arm at 0 Degrees Figure 55 - Sensor Arm at 30 Degrees

Figure 56 - Effect of Ground Pressure at a Given Depth

39

Figure 57 - Finalised Design

Figure 59 - Finalised Design - Side View

Figure 58 - Finalised Design -Rear View

40

4.5 Usage with Instron Machine

To test the sensor arm and the sensors within it in the interim whilst the full rig is being

commissioned, the decision to use an Instron machine was made (Figure 60). An Instron

machine is a highly accurate test device that features a vertical actuator and a load cell able

to measure vertical forces. The departmental Instron machine also features a rolling runner

system which had the ability to be modified to accept a soil bucket to allow testing.

In order to successfully use the Instron machine, the

designed testing apparatus had to be adapted to allow

secure fitment. It was possible to redesign the apparatus

such that it could be used for both the Instron machine and

also the full test rig, when fabricated.

The main sensor arm was redesigned such that it accepted

the fitting on the Instron machine (Figure 61). This would

allow easy setup with minimal risk of incorrect readings

due to play within the system.

The test rig itself was then redesigned to accept the same

fitting as that from the Instron machine, increasing the

adaptability of the unit and enabling integration when the

rest of the rig is fabricated without further adaptation.

Figure 61 - Sensor Arm Showing Plate to Fit Instron Machine

4.6 Soil Bucket

As preliminary testing required usage of the Instron machine, a temporary soil bucket was

required such that accurate results could be attained from a less than ideal piece of testing

apparatus.

Instron fitting

bracket

Figure 60 - Instron Machine [47]

41

Due to the soil bucket for this application being a temporary solution, a low cost, easily

fabricated design was sought. The design had a number of minimum requirements:

Be large enough for at least one full wheel rotation

Allow for horizontal translation

Enable results to be attained up to 500N for versatility

Resist deflection up to the maximum load

Fit within the constraints of the Instron machine

To enable these criteria to be met, it was decided that the soil bucket would be made from

10mm Ply wood and feature a steel box section cross braced base to resist deflection when

loaded. The bucket itself would be 0.575m long as this would allow for one full rotation of

the wheel whilst retaining a distance of one wheel radius from each end of the bucket. The

extra distance will help to eliminate inaccuracies due to bulldozing effects and other soil

compaction phenomena should they arise.

The soil bucket will be 340mm wide as this is the maximum width available for usage in the

Instron machine. The width will be sufficient to reduce further the effects of soil compaction.

It has been decided that the bucket will be 250mm in height as this is the maximum height

available within the Instron machine after the sensor arm has been attached. This height will

allow for forces of 500N to be tested without the bottom of the bucket having an effect on the

results.

The bucket has been designed such that the built in runner system can be used. This reduces

the fabrication time, increases the accuracy and allows for more freedom in design.

Clearly, care has been taken to ensure the most accurate results possible can be attained.

Figure 62 - Constraints Imposed By Instron Machine

Soil bucket Constraints

imposed by

Instron

machine.

Instron

Runner

Overhang to

allow usage of

full soil bucket

length within

constraints.

42

4.7 Error Reduction

The experiment has a number of sources that could contribute to an error. Due to the

relative uncertainties associated with the experiment and the fact that the rig is designed as a

reference piece, it is imperative to remove all known sources of error to provide the most

accurate results.

The most notable source of error would come from the measurement of the forces

themselves. It is crucial to exert the precise force specified as the results may not be linear

and therefore accuracy would be compromised. The load cells have been purchased with a

factory calibration which should ensure complete accuracy. Before being placed in the test

apparatus, this calibration was checked with known masses to ensure linearity.

The rig also employs a string potentiometer and laser sensor on the same axis such that

measurement accuracy can be increased if desired, reducing the error that may be obtained

from relying on a lower accuracy sensor. This will be of particular benefit when advanced

research into the soil’s shear limit is undertaken. The rig will allow the exact point of shear

to be observed, along with how the tyre performs when at this limit.

As has been mentioned previously, by using a rack and pinion translation system in the test

rig (2..4.1), translational errors will be kept to their absolute minimum, ensuring no slippage

and also precise control, both aiding with the aforementioned shear limit observation.

Coupling this with the ability to swap out the rack and pinion system for a system with finer

teeth for greater displacement accuracy if required without needing any major re-fabrication

and also the usage of a linear carriage system used to move the sensor arm (2.4.3.1), all

possible unwanted motion in the X, Y and Z directions will be removed.

Potential errors also source from play in bearings and general slack in the machined parts.

This has been avoided as much as possible by using high quality components from the likes

of SKF and Bosch with interference fits, clamping components that are able to be clamped to

remove all motion from them and also ensuring beams are as short as possible and made

from high carbon steel to ensure minimum deflection. This, along with optimising the

design with items such as the billet aluminium blocks, buttressing and strategic sensor

locations such as placing the vertical load cell directly after the actuator, promotes minimum

error from these sources.

Error from the wheel and tyre compressing when under load, suggesting larger than actual

sinkage, has also been strived to be removed by using hard materials with low

compressibility. The wheel, for example, has also been designed to have a thick radial

circumference so that even though spokes exist, the potential deformation between them is

negligible. The tyre has also been designed for minimum error recording by being made

from a rubber material that is essentially textured plastic, removing nearly all its

compressibility (Figure 41-Figure 43). Bearings have also been used in the wheel to ensure

minimal inaccuracies due to friction and to further reduce compression from force

concentrations on the axle.

With the soil bucket and the measuring of tyre sinkage, errors could arise from feedback

from the sides and the floor of the soil bucket, along with soil bucket deflection. Whilst in

scale testing such as this, effects from the soil bucket are almost impossible to remove

43

entirely, work has been done to reduce them to a minimum. The bucket itself, for example,

has been made 575mm long, enabling a full rotation of the wheel whilst also leaving a gap of

one wheel diameter between the edge of the wheel and the end of the soil bucket. This will

drastically reduce the effect of the soil being compressed against the end of the bucket and

interfering with the results. This is particularly useful in this experiment where sand is being

tested meaning bulldozing effects are highly likely to be present. The bucket has also been

made 250mm deep which will allow forces up to 500N to be tested without feedback from

soil compressed against the bottom of the bucket being present.

These same techniques have been employed in the full size rig, where the soil bucket is

500mm deep to enable effects of the bucket floor to be removed when forces up to 1kN are

exerted. The commissioned bucket is also 500mm wide, allowing the wheel and tyre to be

rotated to any angle whilst retaining a distance of two wheel diameters from the bucket side.

This should remove any input from the bucket walls. By being 1.5m long, the rig allows for

three full wheel rotations and still retains a wheel diameter from either end of the bucket.

This will provide a large test area, ensuring accuracy.

All components, such as the actuator and the load cells, have been specified to work far

beyond the required range for the test rig. This was a deliberate choice as it allows all

components to work in their optimum zone. The laser sensor, for example, loses accuracy

when used outside of its operating window and therefore a laser with an operating range of

140mm has been chosen over the sensor with a 70mm range, even though the maximum

deflection should not exceed 65mm. The added performance of the specified components

allows for the rig to be upgraded without the need to replace expensive components. It also

reduces the likelihood of breaking a component by repeatedly pushing it to its limit.

As soil is being used, it is important to ensure that the sample is homogeneous and also the

same consistency for each test. To help remove any errors, the same soil sample will be used

for all tests and its parameters will be measured before and after the testing phase to ensure

it remains consistent throughout. Due to the soil’s performance under varying conditions

being relatively unknown, it is important to remove as much uncertainty as possible. For

this reason, the soil must be carefully prepared before every test run and the procedure for

this is described in section Preparation of this paper.

The design for minimum error was extensive and spans both macro and micro scales, from

material choice down to object location and it is hoped the design will provide highly

accurate results.

44

5. Testing

For ease of comparison, results attained from the physical testing will be compared with

Bekker’s equation:

𝑃 = (𝑘𝑐𝐵+ 𝑘𝜑)𝑍

𝑛

Although it has been discussed in the literature review that this is a less accurate equation

than the Lyasko equation, it has also been discussed that it is well validated and far simpler.

It is the simplicity that is of most importance as, due to time constraints, measuring of

complex soil parameters such as those required for Lyasko’s equation would not be possible

or would jeopardise the ability to complete the testing within time. Due to Bekker’s equation

being well validated, results from the test rig could be compared with reasonable certainty

against other experiments using Bekker’s equation, enabling the results to be compared and

errors more quickly understood. Using Bekker’s equation, therefore, serves as a stepping

stone to confirm the concept and prove the applicability of the test rig and its components.

5.1 Soil Testing

Theoretical modelling of soil behaviour requires knowledge of some basic soil parameters.

These parameters are those that are required by the chosen equations.

Due to Bekker’s equation being used, soil cohesion is a required value. Cohesion is the non-

friction contribution to a soil’s shear strength. It is soil specific and altered by attributes such

as moisture content and the amount of compression exerted on the soil.

Mentioned previously is how dry sand is being initially used as the test soil. This is because

sand is cohesionless when dry, removing a parameter and making results easier to decipher.

Friction angle is another parameter that is of interest in soil testing. It is the component of

the soil’s shear strength formed by the friction interaction within the soil. Soils such as peat

and very wet clays can have a friction angle close to zero. For this reason, clay will also be

tested as it will allow for results from both extremes of soil properties to be observed.

Finally, shear strength will be required. This is the soil’s ability to accept a shearing force

without failing which would therefore significantly change its parameters. Having a high

shear force is obviously a benefit for tyre traction and is common in cohesive materials such

as stiff clays. It is not common in sandy materials due to their lack of granulation.

All of these parameters can be measured by using the test rig as a bevameter. A grouser

plate has been designed for this operation as previously mentioned (section 4.4). The plate is

sized such that it represents the surface area of the wheel and tyre when sinkage to 15mm

has occurred, an estimated value that is expected to be frequently met. This would allow

accurate comparisons between the plate and tyre to be attained and is required for accurate

results from Bekker’s equation.

A 110x48.5mm wheel and tyre has been chosen, as discussed, meaning the projected soil

surface area resulting from 15mm of wheel sinkage would be approximately equivalent to

45

the rectangle shown in Figure 63, see the appendix (11.5) for a detailed look at the

manufactured soil testing plate:

The sizing for 15mm sinkage was estimated using:

ℎ = 2√𝑑 ∗ 𝑠 − 𝑠2

Where h is the plate length (m), d is the wheel diameter (m) and s is the desired sinkage (m)

Due to Bekker’s equation being used, it is important that the bevameter plate used is of

comparable size to the wheel and tyre’s contact area to ensure results are comparable and as

accurate as possible [5].

5.1.1 Soil Preparation

To conduct accurate, repeatable tests, the soil had to be prepared before each run to ensure

that the soil exhibited the expected characteristics and also the same characteristics for each

test run.

As scale testing is a relatively novel concept, techniques have been borrowed from full scale

testing and adapted as much as possible to fit.

There are 5 major steps in preparing the soil sample as illustrated in “Experimental testing of

an off-road instrumented tire on soft soil” [15]:

1. Loosen bulk of soil with shovel

2. Loosen top soil with tiller

3. Break minor clumps with rake

4. Level sample with flat blade

5. Compact soil

It is important to undertake this procedure as it enables repeatable test runs to be carried

out.

Loosening the soil with the shovel was achieved by forcing the gardening shovel down to

the bottom of the soil bucket and then lifting the shovel at an angle. This served to relieve

the soil of any stress built up be previous runs. According to [15] shovelling should be

undertaken every 16cm to provide adequate coverage.

48.5m

m

73mm Figure 63 - Projected soil contact area

46

In full scale testing, tilling of the soil is required to break up

clumps in the topsoil due to the large area that needs to be

covered. For the scale test rig, use of a gardening fork will be

sufficient to provide the same outcome. It is important to use

the fork after using the shovel as it is not possible to reach the

base of the soil bucket with the fork, meaning the soil

sample would not be fully reset.

Stages three and four are primarily for soil surface preparation. Performing these steps helps

to eliminate small voids created from the fork and any mounds created which would

influence the results. Levelling the soil was achieved with a flat blade the width of the soil

bucket. The blade was passed over the length of the bucket at a set height from the rim to

ensure consistency.

Finally, to create a compacted soil, a flat plate the width of the soil bucket and half its length

(for simplicity of design) was forced into the soil, compacting it. A roller will not be used in

the scale rig as used in [15] as it would be too cumbersome and is not necessary with the far

lower loads applied by the testing apparatus than for full scale testing.

To aid simplicity, it was decided that ideally dry sandy soil and wet clay would be used.

This would reduce the number of parameters that have an effect on the result, allowing

easier comparison with the theory. Drying the soil would eventually require the use of an

industrial oven, however, kiln dried sand was specifically bought in to remove the necessity

to initially dry the sample.

Sandy soils are suitable for base testing as they are cohesionless. This means that all of the

soil’s shear strength comes from friction [36] allowing the shear strength values to be more

easily understood and interpreted.

Sandy soils are also readily available and can have their properties changed easily and

precisely by changing the moisture content. Moisture content is one of the strongest factors

influencing the soil resistance to applied penetration and shear forces [5]. This is a benefit as

it allows tests for multiple soils to be more easily undertaken.

Clays are also suitable for base testing as they have very low internal friction, again

simplifying the equations used. They too can have their properties augmented with the

addition or subtraction of water and will be useful as they exist at the opposite end of the

spectrum to sand.

Due to a lack of time and access to the Instron machine, it was not possible to undertake rig

testing of the clay, however, wet and dry sand was eventually tested.

5.2 Laboratory Test Procedure, Results and Discussion

Laboratory condition testing was undertaken for dry sand, wet sand and wet clay to give a

baseline set of measurements for the soils. It was decided to test wet sand after the results

for dry sand were poor, as explained later. Both basic field type experiments and laboratory

only tests were carried out to allow firstly, a known accurate value to be attained from the

laboratory specific equipment and secondly to allow the field tests and test rig bevameter to

be independently compared with the accurate laboratory test. This will prove whether field

Figure 64 - Gardening Fork for Tilling

47

testing is suitable for attaining baseline soil parameters in the future, when full test rig

testing is undertaken.

The results will also give an understanding of the types of soil with which testing has been

carried out, allowing comparisons with other studies.

In journal papers such as [5], a dynamic cone penetrometer as described in ASAE standard

S313.2 (ASAE 1985) and SAE Standard J939 (SAE 1967) is used to give a simple, quick

estimation of soil strength. The method for using a dynamic cone penetrometer is simple.

The soil is prepared and then the weight built into the penetrometer is lifted to its maximum

height. The weight is then dropped, exerting a known force on the penetrometer, and the

sinkage of the tip of specified size recorded. The dropping of the weight is repeated until the

tip of the penetrometer has sunk 100mm into the soil. There should be at least 5 readings

taken to ensure accuracy.

This type of test was attempted for the dry soil. Unfortunately, due to using such fine, dry

sand, the dynamic cone penetrometer test failed. The 12kg mass of the penetrometer was

sufficient to sink the tip over 100mm into the soil with no blows required (Figure 65).

Secondly, a soil shear vane test was to be undertaken on the test soil whilst it was in situ. A

soil shear test should give results more representative of vehicular tractive performance. [37]

The result would be a rough representation of the soil’s shear strength which could be used

to gauge the soil’s friction angle and cohesion. The gradient of the line produced by

repeating the test a number of times would equal the friction angle and the y-intercept

Figure 67 - Shear Vane with 50mm Vane Head Figure 66 - Shear Vane, H=50mm, D=20mm [46]

Figure 65 - Dynamic Cone Penetrometer in Sand

Movable known

mass to initiate

blows

48

would equal the cohesion. The benchmark established by the shear vane test could then be

used as a target for experimentation using the test rig.

Shear vane tests are undertaken by pressing the instrument into the soil and then rotating it.

The rotation places a torque on the soil which is recorded by the instrument. The device is

rotated until the vanes within the soil begin to move, at which point the soil has sheared and

the result is read off.

Unfortunately, due again to using dried, fine sand with maximum particle size 0.5mm, this

soil did not provide any readable shear stress value when the shear vane was used. As a side

note, in an attempt to get a rough value, coarse, granular sand with 5mm pebbles was also

tested using the shear vane and provided similar negligible results, suggesting that dry

sand, as a whole, is not suitable for shear vane testing.

To gain accurate results, the laboratory experiment for measuring soil properties was

undertaken in the form of a shear box test. The test works by placing a sample of soil in a

box made up of two 1 inch plates on top of each other (Figure 70 and Figure 71 ). A lid is

placed on top of the sample to allow a predetermined load to act on the lid and compress the

soil sample by a known amount which is representative of the soil at a predetermined depth.

A force is then applied to the top section of the box and a displacement of 1.2mm/minute is

achieved. The displacement of the box along with the force exerted on it can then be

measured, allowing the shear force to be calculated. These results are summarised in Table 4

and shown in full in Table 6 - Table 9 in the Appendix.

Figure 68 - Shear Vane Test Being Undertaken With Shear Vane Located in Sand

Figure 69 - Shear Box Test Apparatus

49

The same approach was repeated with clay with greater success and the results for this can

be seen summarised in Table 4 and complete in Table 10 - Table 12. It is also worth noting

that the shear vane test provided a result of 32085.6KPa when sunk 45mm into the soil. This

is representative of the 2.5KPa shear box test (representative of <300mm soil depth) and thus

it is to be concluded that the result would be accurate enough to not require the shear box

test and would therefore also be suitable for in-situ experimental use.

Table 4 - Summary of Peak Soil Test Results

Soil and Normal Pressure (KPa)

Max Shear Force (KN/m^2) Max Friction Angle (°)

Dry Sand, 2.5 6.51 39.18

Dry Sand, 5 8.09 34.59

Dry Sand, 10 11.76 30.37

10% Moisture Sand, 5 7.36 36.38

17% Moisture Clay, 5 44.37 41.76

17% Moisture Clay, 10 41.98 22.78

17% Moisture Clay, 20 49.90 14.02

Results show how the clay has a lower friction angle than sand and also how the friction

angle decreases with an increase in vertical load due to the shear force not being able to

increase at the same rate as the additional applied normal pressure. The results are in line

with those shown in [38] but they are towards the higher end. The reason for the high

friction angle readings is because of the low normal loads applied. These loads represent the

very top layer of the soil which is not, by nature, as compressed as the lower layers. It is to

be concluded that the highest test normal pressure provides the most accurate friction angle.

The purpose of attaining laboratory results, as mentioned, was to enable the test rig to be

verified. By using the test rig as a bevameter, it was hoped that similar shear stress values

could be attained with the same soils. To achieve this, the bevameter plate was sunk into the

soil using a predetermined force. The soil bucket was then moved horizontally and the loads

recorded. The force, in theory, increases until the shear limit is reached, at which point it

plateaus and then reduces. The maximum value is the shear strength of the soil and would

be recorded. This procedure is repeated for a variety of loading forces such that it can be

observed how shear stress varies with soil compression. By plotting the various results on

the same graph, the friction angle can be read off as the difference between the gradient of

the line and the horizontal axis.

Figure 70 - Box after Test Showing Shear Displacement Figure 71 - 100 x 100mm Shear Box Loaded With Sand Shear

50

6. Rig Testing, Calibration and Discussion

Figure 72 - Rig Setup for Testing

Figure 74 - Sensor Arm with Wheel Attached Figure 73 - Sensor Arm with Bevameter Plate Attached

Instron Machine

Load Cell

Sensor Arm

Test Wheel

and Tyre

Soil Bucket

Runner

51

6.1 Load Cell setup and Calibration

To ensure consistent, reliable results, an adequate testing procedure was required. Due to

the Instron machine being used instead of the purpose built test rig, the emphasis of the

testing was aimed more towards calibration and validation of the testing instrumentation

such as the load cells and the laser sensor. The work would allow the measurement device to

be transferred to the main test rig once manufactured. Any results analysis would be

deemed a bonus due which, due to time constraints could not be carried out in great depth.

Before any testing could commence,

it was important to make sure the

load cells were recording data

correctly and that the data recorded

could be interpreted correctly.

Firstly, a simple verification test was

undertaken by squeezing the load

cell at common intervals with a

roughly consistent force. This would

serve to prove that the recording

was working correctly and that the

load cells were also working. This

can be seen in Figure 75.

Secondly, the load cells needed to

be calibrated such that the millivolt

(mV) output from the load cells

could be interpreted as a force.

This was established by placing

known masses on the load cell and

recording the mV output. By doing

this, the results could be plotted,

allowing the linearity of the cell to

be checked, as well as the

conversion between units. From

this, it was established that each

0.01mV increment was equivalent

to 500g and therefore a force of

4.905N, also, conveniently, the

load cells are completely linear.

-2.50E-01

-2.00E-01

-1.50E-01

-1.00E-01

-5.00E-02

0.00E+00

0 2000 4000 6000

Ou

tpu

t (

mV

)

Time (ms)

Figure 75 - Load Cell Hand Testing

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 500 1000 1500 2000

Mill

ivo

lts

(mV

)

Mass (g)

Figure 76 - Load Cell Calibration Converting mV to N and Observing Linearity

52

6.2 Testing, Results and Discussion

In the test rig environment, the first test performed was to see how the bevameter plate

fared with a constant vertical load and a constant horizontal force. This is the most basic

setup for the rig and would help determine whether the two lateral load cells were working

and providing realistic values. It is apparent from Figure 77 and Figure 78 that the test was a

success. It is worth noting how the force from the fore/aft load cell continues to increase the

longer the soil is pulled, likely due to the plate being dug into the sand. Also, it is deemed a

success to see the lateral cell reporting a far lower force which hovers around the zero value

throughout the test, suggesting the plate was facing the direction of travel and the load was

almost exclusively in the correct axis.

The second test was carried out with a 200N load on the plate. It was hoped this would

show a far greater force on the fore/aft load cell, but a similar load on the lateral load cell.

As is shown in Figure 79 and Figure 80, the load cells are reporting what can be assumed to

be accurate results. The fore/aft sensor clearly shows the increase in load as the soil bucket

is pulled and the soil interaction forces increase from near 0 up to 20N. Finally, the force

reduction is apparent when the horizontal load is removed as the load returns to near 0 in a

short space of time. The result is pleasing as the load is twice that of Test 1’s result, at 20N as

opposed to 10N, proving the theory that increased normal load would increase the required

tractive force. The lateral load cell also shows encouraging results. Whilst the fore/aft cell’s

load has increased substantially, the lateral force load cell’s force has remained constant at

between -1.5N and 2N as in test 1.

-2.00

-1.00

0.00

1.00

2.00

3.00

35000 37000 39000 41000 43000 45000Forc

e (N

)

Time (ms)

0.00

5.00

10.00

15.00

20.00

25.00

12000 14000 16000 18000

Forc

e (N

)

Time (ms)

Figure 77 - Test 1- Bevameter Plate Lowered to Grouser Height (Fore/aft cell)

-1.00

-0.50

0.00

0.50

1.00

1.50

0 10000 20000 30000 40000 50000

Forc

e (N

)Time (ms)

Figure 78 - Test 1 Bevameter Plate Lowered to Grouser Height (Lateral cell)

Figure 79 - Test 2 - Load Increased to 200N (Fore/aft cell) Figure 80 - Test 2 - Load Increased to 200N (Lateral Cell)

0

2

4

6

8

10

12

0 10000 20000 30000 40000 50000

Forc

e (N

)

Time (ms)

53

A final proof with the bevameter was attained by applying 400N of normal load to help

certify a trend, and as is shown in Figure 81 and Figure 82, the result continues to show the

desirable trend, this time with the fore/aft cell measuring a peak of 50N whilst the lateral

cell still remains near 0N.

These results prove that the sensor arm’s load cells are working properly and that the results

are likely to be at least of the correct magnitude. This is proved by the forward/aft load cell

increasing steadily with time as the plate digs further into the soil. It is also proved by the

lateral load cells being an order of magnitude lower in force and remaining around 0N

which was hoped for as the plate should be facing in the direction of travel, thereby exerting

no force laterally.

The tests were then repeated but with the wheel taking the place of the plate. This was likely

to produce slightly less accurate and consistent results due to the wheel’s ability to roll, its

eclipse like contact patch shape and the fact that the contact patch increases with increased

sinkage, de-linearising the results.

Visible in Figure 83 and Figure 84 is how the fore/aft load is initially far more constant as

the wheel is rolling across the surface instead of digging in to the soil like the bevameter

plate. The large rise in force at the end of the run has been attributed to the wheel not being

powered. In an ordinary vehicle, the wheel would pull itself over the soil, however, as the

wheel is effectively being pushed, soil bunches up in front of the wheel and is bulldozed

around and under the wheel, creating a great deal of additional force as predicted in 2.1,

already confirming Sandu and Senatore in [14]. It is pleasing to see the peak value

registered is very similar to that of the plate at 20N, suggesting comparable results would

likely be attained when analysed with theoretical equations.

0

10

20

30

40

50

60

0 1000 2000 3000

Forc

e (N

)

Time (ms)

Figure 81 - Test 3 - 400N Vertical Load (Fore/aft cell) Figure 82 -Test 3 - 400N Vertical Load (Lateral Cell)

0.00

5.00

10.00

15.00

20.00

25.00

0 5000 10000 15000 20000

Forc

e (N

)

Time (ms)

Figure 84 - Test 4 - Wheel with 200N Vertical Load (Lateral Cell) Figure 83 - Test 4 - Wheel with 200N Vertical Load (Fore/aft Cell)

-9.00

-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

0 5000 10000 15000 20000

Forc

e (N

)

Time (ms)

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

60000 62000 64000 66000 68000 70000

Forc

e (N

)

Time (ms)

54

It is believed the wheel, due to its larger size and rolling nature, is far more sensitive to

directional positioning accuracy. The lateral load cell suggests the wheel was turned during

the test run, explaining the fully negative result on the lateral load cell. It is still pleasing to

see how the values still only vary by 2-3N and are an order of magnitude less than the

fore/aft cell’s.

Through continued experimentation, it was found that attaining repeatable results with the

wheel in the dry sand was difficult. When adding more vertical force in order to increase the

potential to observe soil shear, it was concluded that forces beyond 200N were not possible

to be reached. As the load from the Instron machine increased, the soil simply moved out of

the way of the wheel, increasing sinkage, but not the force. It was thought that this would

potentially damage the wheel and/or sensor arm, along with creating such high levels of

sinkage that the wheel would be buried and thus immovable. With this in mind, it was

decided that the sand should be wetted, allowing a much firmer surface to exist, increasing

the potential to observe more realistic and predictable results.

The moisture content was increased to around 12% by adding 2 litres of water to the dry

sand.

Repeating the tests allowed a much higher force to be exerted and eventually, in an attempt

to see a large difference from the dry sand’s results, a 580N vertical force was applied to the

wheel which showed very pleasing results, looking very similar to those from the bevameter

plate and also to traditional terramechanics soil behaviour, with the fore/aft force recorded

much higher at 140N, as shown in Figure 85.

Evident in Figure 86 and Figure 87 is the

similarity between the depressions left by both

the wheel and the bevameter plate. This will

be of benefit when using Bekker’s equation

and suggests results should be both

comparable and reliable.

The wheel’s depression shows a larger soil

surcharge, visible as cracked soil. This has

been attributed to the higher force exerted on

the soil and the larger surface area of the

wheel due to its curvature.

0

20

40

60

80

100

120

140

160

0 2000 4000 6000 8000 10000 12000

Forc

e (N

)

Time (ms)

Figure 85 - Test 5 - Wheel with 580N vertical Load (Fore/aft Cell)

Figure 87 - Depression Left by Bevameter Plate @400N Figure 86 - Depression Left by Wheel @580N

55

6.3 Load vs. Sinkage

One of the advanced goals of the test rig was to be able to compare the real world results

with that of Bekker’s equation and eventually Lyasko’s equation. For this reason, a load vs.

sinkage test was carried out. This would allow the trends between pressure and sinkage to

be observed with the hope of firstly being able to observe terramechanics properties, such as

the bearing capacity of the soil being reached, and secondly to be able to observe the

measured results against Bekker’s prediction.

Firstly, a test with the bevameter plate was undertaken to observe the load/sinkage plot

with 250N applied. This would give a good indication of what is to be expected from a

pressure close to that of a vehicle (2.3). It was apparent from Figure 88 that a small amount of

sinkage resulted, with the rate of sinkage increase as extra force is applied decreasing after

0.05kN. At this load, the sinkage was almost linear, suggesting the bearing capacity had not

been approached. Due to the wheel/tyre sinkage equivalent of 15mm not being reached, the

test was repeated but this time, instead of specifying a load, a sinkage of 20mm was

specified. Figure 89 shows how the load now increased to 0.65kN to double the sinkage.

The test was repeated with the wheel and the Instron was set to record a 15mm sinkage. In

theory, the load at 15mm should be recorded as the same in both the bevameter plate and

the wheel (Figure 89 and Figure 90) due to the bevameter plate being the same cross sectional

area as the wheel at this depth. The recorded results are pleasing in that the variation is only

by around 50N. The variation has been put down to surface area the wheel and bevameter

plate being slightly different as the wheel is curved, therefore affecting its surface area. The

accuracy of the Instron load cell is also being held responsible for there being as large a

difference as there is. The cell is designed for loads up to 25kN and so variations of 50N are

0

0.2

0.4

0.6

0.8

0 2 4 6 8 10 12 14 16 18 20 22Lo

ad (

kN)

Sinkage (mm)

Figure 88 – Test 6 - Load vs. Sinkage Plate 250N Load Figure 89 –Test 7 -Load vs. Sinkage Plate 20mm Sinkage

0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12

Forc

e (k

N)

Sinkage (mm)

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

Forc

e (k

N)

Sinkage (mm)

Figure 90 –Test 8 - Load vs. Sinkage Wheel 15mm Sinkage

56

not easily detected, meaning the loads may in fact be the same, but electrical interference

and cell inaccuracy may have shown the incorrect reading.

In a test to prove the bearing capacity of the soil

and thoroughly test the strength of the fabricated

sensor arm by using forces nearing 1kN, a

specified sinkage of 20mm was set. The results in

Figure 91 were recorded. This was an excellent set

of results as it is immediately evident that the

bearing capacity of the soil has been reached and

observed at 16mm sinkage as sinkage increases

and yet the maximum load remains constant.

The goal was now to prove this same result using

the wheel as this would be of benefit to better

understand wheel and tyre performance in soils.

Figure 92 shows that even when a force greater than

that used by the bevameter plate was used, the

bearing capacity of the soil was not reached. It is

predicted that this was due to the shape of the

wheel. The curved wheel puts a lower stress on the

soil at all points except the part with greatest

sinkage. It also displaced the soil rather than

shearing it like the bevameter plate. To achieve a

similar pressure to that of the bevameter plate, a

sinkage of around 40mm would be required, which

would place far greater loads on the test rig and sensor

arm, something that was not required at this early stage

of testing.

Figure 93 shows the expected degree of sinkage from

a variety of loads from 0-0.8kN. Bekker’s equation was

used with the values shown in Table 5 as found to be

accurate for 15% moisture content sand by Wong in [39]

and section 11.9.

Comparing this result with that from Figure 91 and Figure 92 shows that Bekker’s equation

predicts a similar rate of increase of sinkage, especially when compared with Figure 91,

however, far greater levels of sinkage. The extra sinkage is attributed partially to the

uncertainty of the actual soil moisture content. The moisture content has a huge, non-linear

effect on the kc, kϕ and n values, which in turn have a drastic effect on expected sinkage. A

secondary cause for the disparity is as previously mentioned, Bekker’s equation is simply

not well suited to small plate dimensions. This also explains the poor resemblance to Figure

Parameter Value

kc 5.27

kϕ 1515.04

n 0.7

00.10.20.30.40.50.60.70.80.9

0 5 10 15 20 25 30 35

Load

(kN

)

Sinkage (mm)

Figure 92 –Test 10 - Load vs. Sinkage Wheel 800N Load

Figure 91 – Test 9 - Load vs. Sinkage Plate 800N Load

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 2 4 6 8 10 12 14 16 18 20 22

Load

(kN

)

Sinkage (mm)

Figure 93 - Prediction of Load vs. Sinkage Using Bekker's Equation

Table 5 - Parameters used for Bekker's Equation

57

92. Bekker’s equation uses flat plate dimensions, not wheel diameter, meaning the wheel’s

shape is not taken into account.

It is with regret that the shear force cannot be checked against the Janosi-Hanamoto criterion as

suggested in 2.1.2. This was impossible with the current setup as the shear limit could not be

observed in the horizontal direction due to not have a motor controlled soil bucket or sensor arm

able to exert a constant horizontal force. To observe the shear failure, the wheel/tyre needs to move

across the test surface with a predetermined velocity and this could not be achieved with the

confines of the Instron machine. The results from Figure 80 to Figure 85 show promise though, and

as the full test rig is constructed, it will be possible to attain the required results.

6.4 Experimental Difficulties

The undertaken experiments, although very useful, cannot be assumed to be entirely

accurate for a number of reasons.

The biggest challenge faced when undertaking the experiments was applying a desired

vertical load. It was common for either the load value to not increase or for it to increase and

then immediately reduce as the addition of load was stopped.

As has been discussed previously. The difficulty in adding additional load has been

attributed to the non-cohesive properties of dry sand, meaning it simply moves out of the

way. This was not the entire cause, however. The other severe limitation to the

experimentation came from using the Instron machine. Whilst it created a perfect platform

to start testing, the load cell available was suitable for forces up to 25kN. As the experiment

required forces up to 800N, varying by at maximum 50N increments, it has been discovered

that the load cell did not have the required accuracy at this level, making fine adjustments

and also applying low loads almost impossible, hampering the accuracy of the results.

It has been shown in the results that the theory is more closely followed when a greater force

is applied and with this setup, it cannot be concluded as to whether

this is due to terramechanics, or due to the load applied being more

accurate.

Another difficulty came from the very fine grain sand and the usage

of a small bevameter plate and wheel. These factors encouraged

sinkage and made obtaining conclusive results harder.

As discussed, moisture was added to aid the acquisition of results,

however, as the moisture was applied in-situ, it could not be

guaranteed that the water was equally mixed throughout the soil

sample, meaning the tested sand is likely to be in the range of 10-20%

moisture content, but a more accurate estimation cannot be made.

As shown in Figure 94, a further difficulty stemmed from the test tyre

picking up the test soil. This was not problematic with the recording

of data for the experiment as only one wheel revolution was

possible, removing the effect from the full voids. It should be noted,

however, that a more aggressive tyre void pattern may be required if high moisture content

sand is to be tested in the future with more than one wheel rotation.

Figure 94 - Test Wheel Showing Furrow in Wet Sand and Filling of Tyre Void

58

7. Future Improvements/Development

Though the project was deemed a success, it was not without flaws. When the project is

developed or if it was to be restarted, there would be number of changes made.

To progress well with the project, it would be most beneficial to continue to fabricate the rest

of the test rig based on the designs provided (USB drive). This would be highly

advantageous as it allows a more sensitive vertical load cell to be used which would give

more accurate readings over the loads required for testing at this scale. The usage of the

designed rig would further benefit the user as the laser sensor could be used, allowing

greater vertical and horizontal movement accuracy to be observed. At the current stage, the

horizontal movement could only be measured before and after the displacement had

occurred, meaning no soil conditions during the testing stages could be recorded, reducing

the amount of available soil interaction data which resulted in no shear force comparison

being possible. The designed rig also has the ability for three wheel rotations to be

measured, allowing novel tests such as steadily increasing load or displacement to be carried

out which would both replicate real wheel and tyre behaviour better whilst allowing greater

understanding of the repeatability and variations present within tyre/soil interaction.

In order to be able to use a wider variety of soils for testing, especially those more granular

such as gravel, it would be of benefit to develop the spring system mentioned in 4.4

Finalised Rig Design. As was discussed, it was not necessary at this stage due to the slow

rotational speed and the usage of homogeneous soils, however, for more complete and

potentially more accurate results, allowing a wider variety of soils to be tested, the spring

system may be of benefit.

To achieve better results from testing, a wider spread of forces should be covered. This

would allow trends between different loads to be observed, lending validation to the

experiment and allowing errors to be ignored and removed. The results could then be used

to obtain and compare results such as shear force and friction angle from the experiment

with that attained from the laboratory test. This was not possible at this stage due to a lack

of time.

It would be of exceptional value to test a wider variety of soils with specific moisture

contents. This would allow direct comparison with Wong’s soil parameters, proving

equation accuracy. Again, due to time constraints, only dry and wet sands were able to be

tested, reducing the variety of results attained. Testing more soils would greatly increase the

ability to understand the variation in tyre performance with respect to soil parameters. Also,

the recorded results could be checked against those found by Wong and Bekker, proving the

accuracy or scope for improvement of the test rig.

59

If the project was to be restarted, a more granular sand for

testing purposes would have been used. The fine grain sand

chosen was expected to be of most benefit due to having the

least possible cohesion and therefore acting most like the

theory. In reality, the lack of cohesion made attaining soil

parameters very difficult. It also lead to a great deal of sinkage

from the grouser plate and test tyre, making initial parameters

and test results hard to decipher and unpredictable. Visible in

Figure 95 is how the furrow left in the dry sand is ambiguous

and could be described as merely a relocation of the

uncompressed top layer of soil, avoiding the more realistic

compressed lower layers, which leads to poor quality results.

The wheel design would also be changed if the process was to be repeated. Due to the large

sinkage caused by the soft sand, soil made its way between the spokes of the wheel and was

not immediately ejected even though the wheel design featured a central camber to aid soil

expulsion. It would be beneficial to either have a larger tyre sidewall, more closely

representing a real tyre, or blocking off the hollows between the spokes of the wheel.

To allow for better comparison between the bevameter plate and test wheel/tyre, it would

be of benefit to have a number of bevameter plates of different surface areas to be fabricated.

The results from the different plate sizes could be compared to the results from the

wheel/tyre, meaning that results from different levels of sinkage could be compared

between the wheel/tyre and the supposedly more accurate bevameter plate. It has been

described in 6.3 Load vs. Sinkage how the forces from the wheel were slightly different to

that expected and by using a different size bevameter plate, the results would likely be more

similar, allowing easier analysis, especially with the usage of Bekker’s equation.

To aid usability, it would be beneficial to the project if the wheel

and sensor arm was remote controlled. This would allow more

realistic tyre/soil interaction to be observed as real world

situations such as wheel spin would be possible with a powered

wheel. It is shown in Figure 96 how sand has piled up in front of

the wheel. This soil is either forced under or around the tyre,

greatly increasing the force required for propulsion, making the

result less like the real world. A powered wheel would remove

much of this build up. Having a controllable senor arm would

also allow the direction of the wheel to be altered during testing,

enabling steering to be replicated which would increase the

number of scenarios able to be tested and help further the

understanding of vehicular tyre/soil interaction.

Figure 95 - After Tyre Driven Through Dry Sand Showing Furrow

Figure 96 - Test Wheel in Dry Sand Showing Bulldozing Effect

60

8. Conclusions

The project can be regarded as a success. The main objective of the project, that of designing

and fabricating the sensor arm, has been completed and, furthermore, it has been validated

against dry and wet sand, and is ready to be tested against the 17% moisture content clay (as

laboratory test results have already been obtained). These results indicate the main part of

the rig is validated for future use.

The sensor arm is accurately calibrated, provides consistent, accurate results and is strong

enough to be used with forces far higher than is likely to be required as proved by the

results. The design itself is a success and the goal of removing cross-talk in the sensors has

been successfully achieved whilst the strict packaging requirements of the sensor arm have

also been successfully met.

The results show a good trend between the bevameter plate and the wheel, leading to the

conclusion that with a small amount of adaptation, attained results will be directly

comparable.

The objective of testing the sensor arm against the theoretical equations has been carried out

fully against Bekker’s equation, however, due to the time required to attain the additional

specific soil parameters, it was not possible to confirm the test rig against Lyasko’s equation.

Also, as the full rig was unable to be fabricated, the shear force analysis using the Janosi-

Hanamoto equation was not possible.

With regard to terramechanics phenomena, it can be concluded from experimentation with

the test rig that Bekker’s equation is not accurate at predicting soil sinkage in soft dry or wet

sand, however, the input parameters of Bekker’s equation can be manipulated to give

accurate results, suggesting soil specific input parameters are vitally important to attaining

accurate results from Bekker’s equation. Bekker’s equation has also been proved to lose

accuracy as the soil reaches its bearing capacity as this limit is not taken into account within

the equation, meaning the exerted force will always rise with sinkage.

Predictions by Sandu and Senatore have been confirmed through experimentation with the

wheel/tyre. It has also been proved that the phenomena of reaching a soil limit where

sinkage can increase independent of force applied is correct.

It has been concluded that a force greater than the 178N predicted by the square law in 2.3

Component Research will be required to obtain adequate results with the designed wheel

and chosen soils. The decision to design the rig for forces of ≈1kN has therefore been

validated.

The full test rig has been designed, which completes the final objective, meaning the project

is in a fine position to be developed with there being very little re-design required. There is

no reason to believe that the full test rig design will provide anything but accurate, usable

results, meaning full testing and experimentation can begin in earnest within a very short

period of time.

61

9. Bill of Materials

Use Component Location Cost (£)

Frame/rig body 40x40mm box section mild steel with 3mm wall

thickness

University sourced ≈100.00

Vertical displacement

Hydraulic actuator (400mm throw)

Department full size test rig

N/A

Horizontal displacement

2x 5Nm 12V DC motors. 516:1

reduction ratio

RS online 46.98 ea.

Horizontal displacement guide

2x Rack and pinion system with 52mm

spur gear

SmartBayUKLtd 54.25 ea.

Guide system 2x SKF linear guide rail with 4x low profile standard length carriers

Brammer Leicester Rail: 150.00 ea. Carriage: 45.00 ea.

Bearings: Rig 4x SKF Linear Ball Bearing Unit LUHR

12-2LS

RS online 42.00 ea.

Bearings: Wheel/tyre

2x 6000-2RS HMEC eBay 1.98

Bearings: Sensor Arm

2x SKF Linear Ball Bearing LBCR 12 A-

2LS

RS online 42.00

Bearing clamp 4x SKF Linear Ball Bearing Block LSHS12

RS online 27.00

Bearing rail SKF 12mm stainless steel rail

RS online 36.00 per 600mm

String Potentiometer WS17KT draw wire

position sensor Applied

Measurements Ltd 460.00

Laser Sensor Micro-Epsilon Opto NCDT

Micro-Epsilon 737.00

Load cell 3x PCM BD-ST-615 PCM 142.00 ea

Data Acquisition Digitizer

3x PCM DACUSB PCM 287.00 ea.

Wheel/tyre 3D printed plastic/rubber

University 3D printer

≈200.00

Soil Samples 3x Kiln Dried Sand Wickes 5.00ea.

62

10. References

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power

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Terramechanics

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2009.

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” Journal of Terramechanics, vol. 48.

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soft soil,” Journal of Terramechanics, vol. 56, pp. 119-137, 2014.

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Terramechanics, vol. 44, no. 4, pp. 293-301, 2007.

[17] R. P.-A. a. J. G. Webster, Sensors and Signal Conditioning, Wiley, 1991.

[18] G. M. a. A. C. J Adlington, Resistance Strain Gauge Load Cells, Watford, 2001.

[19] “615 & 616 Bi-Directional S-Type Load Cells,” 2015. [Online]. Available: http://pcm-uk.com

/loadcell-bd-st-615.html.

[20] “Strain cells,” [Online]. Available: www.InstrumentationToday.com.

[21] Micro-Epsilon, “Laser Triangulation Displacement Sensors,” 2014.

[22] [Online]. Available: http://professeur.besnard.pagesperso-orange.fr/6/synthese/afot

/transmission.htm.

[23] “Linear slides,” [Online]. Available: www.Rab3D.com.

[24] “Roller coasters,” [Online]. Available: commons.wikimedia.com.

[25] “Gasgoo,” 02 03 2015. [Online]. Available: http://www.gasgoo.com/showroom/cnbearings007

/auto-products/1543440.html.

[26] “NSK linear,” [Online]. Available: http://www.nskamericas.com/cps/rde/xchg/na_en/hs.xsl

/linear-guides.html. [Accessed 26 02 15].

[27] “imagesco,” [Online]. Available: http://www.imagesco.com/articles/nitinol/07.html.

[Accessed 02 03 2015].

[28] L. Hylands, “Development of a Measuring Wheel-carrier for the Departmental Tyre Test-rig,”

2013.

[29] Azom, “Material Properties,” [Online]. Available: http://www.azom.com/article.aspx?ArticleID=

965. [Accessed 2015 04 13].

64

[30] AutoDesk, “Allowabe Stress,” AutoDesk, [Online]. Available:

http://download.autodesk.com/us/algor/userguides/mergedProjects/results/

Results_environment/REsults/Nomenclature.htm. [Accessed 27 04 2015].

[31] C. Bekkos, 2013.

[32] J. C. a. A. H. C. C.T.F. Ross, “Strength of Materials and Structures,” Butterworth-Heinemann,

1999.

[33] P. University, “Vibration: Rotating Unbalance,” in Mech 226, Plymouth, Plymouth University.

[34] “Bearing types,” [Online]. Available: www.SKF.com.

[35] Soehne, “Soil and Tillage Research,” Journal of Terramechanics, 1958.

[36] “Cohesion,” [Online]. Available: http://www.geotechdata.info/parameter/cohesion.html.

[37] S. A. Shoop, “Terrain Characterization for Trafficability,” 1993.

[38] GeotechData.info, “Soil Friction Angle,” [Online]. Available:

http://www.geotechdata.info/parameter/angle-of-friction.html. [Accessed 05 05 2015].

[39] J. Y. Wong, “Mean Values oF PArameters Characterising the pressure-sinkage relationshipof

various mineral terrains,” in Terramechanics and Offroad Vehicle Engineering, p. 86.

[40] C. E. Laboratories, “Unconfined Compression Test,” in Lab Experiments.

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acquisition-2/. [Accessed 14 04 2015].

[42] D. D. O'Boy, “Lecture notes,” 2013.

[43] B. MG, “Theory Of Land Locomotion,” Journal Of Terramechanics, 1956.

[44] D. W. J. M. S.K. Upadhyaya, “An instrumented device to obtain traction related parameters,”

Journal of Terramechanics, no. 30, 1993.

[45] J. a. Hanamoto, “J. Hanamoto, “Analytical determination of drawbar pull as a,” Proceedings of

the 1st international conference on terrain-vehicle, 1961.,” Journal of Terramechanics, 1961.

[46] “Vane Shear Test,” 15 08 2011. [Online]. Available:

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[47] “Project 2, Part 1: Uniaxial Loading,” [Online]. Available:

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Sensitive Environments,” [Online].

65

11. Appendices

11.1 Soil Testing Results Table 6 - Dry Sand Shear Box Test @2.5KPa

Shear Displacement

(mm)

Vertical Displacement

(mm)

Divisions Force

Force(kN) Area (m^2)

Shear Force (KN/m^2)

Friction Angle

0.00 10.40 1647.00 0.0000 0.0100 0.00 0.00

0.50 10.39 1583.00 0.0454 0.0100 4.57 29.74

1.00 10.45 1567.00 0.0568 0.0099 5.74 35.67

1.50 10.54 1560.00 0.0618 0.0099 6.27 38.11

2.00 10.64 1559.00 0.0625 0.0098 6.38 38.57

2.50 10.74 1558.00 0.0632 0.0098 6.48 39.03

3.00 10.83 1558.00 0.0632 0.0097 6.51 39.18

3.50 10.91 1558.50 0.0628 0.0097 6.51 39.16

4.00 10.95 1559.00 0.0625 0.0096 6.51 39.15

4.50 10.99 1564.00 0.0589 0.0096 6.17 37.66

5.00 11.00 1565.00 0.0582 0.0095 6.13 37.47

Table 7 - Dry Sand Shear Box Test @5KPa

Shear Displacement

(mm)

Vertical Displacement

(mm)

Divisions Force

Force(kN) Area (m^2)

Shear Force (KN/m^2)

Friction Angle

0.00 17.19 1649.00 0.0000 0.0100 0.00 0.00

0.50 17.18 1554.00 0.0675 0.0100 6.78 29.48

1.00 17.26 1542.00 0.0760 0.0099 7.67 32.61

1.50 17.35 1540.00 0.0774 0.0099 7.86 33.23

2.00 17.45 1542.00 0.0760 0.0098 7.75 32.88

2.50 17.53 1541.00 0.0767 0.0098 7.86 33.26

3.00 17.59 1536.00 0.0802 0.0097 8.27 34.59

3.50 17.64 1539.00 0.0781 0.0097 8.09 34.01

4.00 17.66 1542.00 0.0760 0.0096 7.91 33.42

4.50 17.67 1545.00 0.0738 0.0096 7.73 32.81

5.00 17.69 1547.00 0.0724 0.0095 7.62 32.44

66

Table 8 - Dry Sand Shear Box Test @10KPa

Shear Displacement

(mm)

Vertical Displacement

(mm)

Divisions Force

Force(kN) Area (m^2)

Shear Force (KN/m^2)

Friction Angle

0.00 21.26 1650.00 0.0000 0.0100 0.00 0.00

0.50 21.25 1555.00 0.0675 0.0100 6.78 18.73

1.00 21.28 1525.00 0.0888 0.0099 8.96 24.16

1.50 21.33 1505.00 0.1030 0.0099 10.45 27.61

2.00 21.40 1497.00 0.1086 0.0098 11.08 29.01

2.50 21.47 1494.00 0.1108 0.0098 11.36 29.61

3.00 21.54 1490.00 0.1136 0.0097 11.71 30.37

3.50 21.60 1494.00 0.1108 0.0097 11.48 29.87

4.00 21.66 1491.00 0.1129 0.0096 11.76 30.47

4.50 21.70 1501.00 0.1058 0.0096 11.08 29.00

5.00 21.73 1504.00 0.1037 0.0095 10.91 28.63

Table 9 - 10% Moisture Content Sand Shear Box Test @5KPa

Shear Displacement

(mm)

Vertical Displacement

(mm)

Divisions Force

Force(kN) Area (m^2)

Shear Force (KN/m^2)

Friction Angle

0.00 8.20 1648.00 0.0000 0.0100 0.00 0.00

0.50 8.20 1567.00 0.0575 0.0100 5.78 30.04

1.00 8.10 1568.00 0.0568 0.0099 5.74 29.86

1.50 8.20 1571.00 0.0547 0.0099 5.55 29.05

2.00 8.40 1571.00 0.0547 0.0098 5.58 29.17

2.50 8.50 1565.00 0.0589 0.0098 6.04 31.16

3.00 8.60 1562.00 0.0611 0.0097 6.29 32.21

3.50 8.60 1561.00 0.0618 0.0097 6.40 32.64

4.00 8.70 1558.00 0.0639 0.0096 6.66 33.67

4.50 8.70 1554.00 0.0667 0.0096 6.99 34.97

5.00 8.90 1553.00 0.0675 0.0095 7.10 35.39

5.50 9.00 1550.00 0.0696 0.0095 7.36 36.38

6.00 9.00 1551.00 0.0689 0.0094 7.33 36.25

6.50 9.00 1554.00 0.0667 0.0094 7.14 35.54

67

Table 10 - 17% Moisture Clay Shear Box Test @5KPa

Shear Displacement (mm)

Vertical Displacement (mm)

Divisions Force

Force(kN) Area (m^2)

Shear Force (KN/m^2)

Friction Angle

0.00 15.11 1722.00 0.0000 0.0100 0.00 0.00

0.50 15.14 1641.00 0.0575 0.0100 5.78 6.60

1.00 15.17 1646.00 0.0540 0.0099 5.45 6.22

1.50 15.19 1589.00 0.0944 0.0099 9.59 10.86

2.00 15.21 1506.00 0.1534 0.0098 15.65 17.39

2.50 15.24 1390.00 0.2357 0.0098 24.18 25.82

3.00 15.34 1352.00 0.2627 0.0097 27.08 28.46

3.50 15.48 1328.00 0.2797 0.0097 28.99 30.12

4.00 15.67 1202.00 0.3692 0.0096 38.46 37.59

4.50 15.85 1193.00 0.3756 0.0096 39.33 38.21

5.00 16.13 1185.00 0.3813 0.0095 40.13 38.77

5.50 16.40 1165.00 0.3955 0.0095 41.85 39.95

6.00 16.67 1157.00 0.4012 0.0094 42.68 40.50

6.50 16.98 1146.00 0.4090 0.0094 43.74 41.20

7.00 17.24 1144.00 0.4104 0.0093 44.13 41.45

7.50 17.50 1144.00 0.4104 0.0093 44.37 41.60

Table 11 - 17% Moisture Content Clay Shear Box Test @10KPa

Shear Displacement

(mm)

Vertical Displacement

(mm)

Divisions Force

Force(kN) Area (m^2)

Shear Force (KN/m^2)

Friction Angle

0.00 23.47 1649.00 0.0000 0.0100 0.00 0.00

0.50 23.47 1470.00 0.1271 0.0100 12.77 7.28

1.00 23.50 1328.00 0.2279 0.0099 23.02 12.97

1.50 23.55 1290.00 0.2549 0.0099 25.88 14.52

2.00 23.58 1265.00 0.2726 0.0098 27.82 15.55

2.50 23.64 1246.00 0.2861 0.0098 29.35 16.36

3.00 23.70 1227.00 0.2996 0.0097 30.89 17.17

3.50 23.77 1206.00 0.3145 0.0097 32.59 18.06

4.00 23.82 1187.00 0.3280 0.0096 34.17 18.87

4.50 23.90 1172.00 0.3387 0.0096 35.46 19.54

5.00 24.00 1161.00 0.3465 0.0095 36.47 20.05

5.50 24.11 1150.00 0.3543 0.0095 37.49 20.56

6.00 24.25 1144.00 0.3586 0.0094 38.14 20.89

6.50 24.39 1135.00 0.3649 0.0094 39.03 21.33

7.00 24.54 1126.00 0.3713 0.0093 39.93 21.78

7.50 24.70 1119.00 0.3763 0.0093 40.68 22.15

8.00 24.86 1112.00 0.3813 0.0092 41.44 22.52

8.50 25.06 1108.00 0.3841 0.0092 41.98 22.78

68

Table 12 - 17% Moisture Content Clay Shear Box Test @20KPa

Shear Displacement

(mm)

Vertical Displacement

(mm)

Divisions Force

Force(kN) Area (m^2)

Shear Force (KN/m^2)

Friction Angle

0.00 20.00 1580.00 0.0000 0.0100 0.00 0.00

0.50 19.99 1483.00 0.0689 0.0100 6.92 1.98

1.00 19.98 1358.00 0.1576 0.0099 15.92 4.55

1.50 19.99 1177.00 0.2861 0.0099 29.05 8.27

2.00 20.04 1067.00 0.3642 0.0098 37.17 10.53

2.50 20.10 1041.00 0.3827 0.0098 39.25 11.11

3.00 20.15 1011.00 0.4040 0.0097 41.65 11.77

3.50 20.21 1088.00 0.3493 0.0097 36.20 10.26

4.00 20.27 1067.00 0.3642 0.0096 37.94 10.75

4.50 20.33 1051.00 0.3756 0.0096 39.33 11.13

5.00 20.40 1036.00 0.3862 0.0095 40.66 11.50

5.50 20.48 1021.00 0.3969 0.0095 42.00 11.87

6.00 20.56 1088.00 0.3493 0.0094 37.16 10.53

6.50 20.66 995.00 0.4154 0.0094 44.42 12.53

7.00 20.74 981.00 0.4253 0.0093 45.73 12.89

7.50 20.84 969.00 0.4338 0.0093 46.90 13.20

8.00 20.95 962.00 0.4388 0.0092 47.69 13.42

8.50 21.07 956.00 0.4430 0.0092 48.42 13.62

9.00 21.19 953.00 0.4452 0.0091 48.92 13.75

9.50 21.29 951.00 0.4466 0.0091 49.35 13.87

10.00 21.40 951.00 0.4466 0.0090 49.62 13.94

10.50 21.50 951.00 0.4466 0.0090 49.90 14.02

69

11.2 Load Cell Datasheets

70

71

11.3 Laser Sensor Datasheets

72

73

11.4 Draw Wire String Potentiometer Data Sheets

74

75

11.5 Grouser Plate CAD and Fabricated Versions

76

11.6 Cone Penetrometer Length and Tip Size

1800mm

77

11.7 Completed Test Rig Views

78

79

80

11.8 Manufactured Sensor Arm

81

11.9 Soil Parameters Found By Wong

82

11.10 Meeting Logs

83

84

85