Thermomechanical fatigue life investigation of an ultra-large mining dump truck tire

225 Pages·2017·7.31 MB·English

by  Wedam Nyaaba

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Doctoral Dissertations Student Theses and Dissertations
Summer 2017
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Wedam Nyaaba
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Nyaaba, Wedam, "Thermomechanical fatigue life investigation of an ultra-large mining dump truck tire"
(2017). Doctoral Dissertations. 2596.
https://scholarsmine.mst.edu/doctoral_dissertations/2596
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THERMOMECHANICAL FATIGUE LIFE INVESTIGATION OF AN ULTRA-
LARGE MINING DUMP TRUCK TIRE

by

WEDAM NYAABA

A DISSERTATION

Presented to the Faculty of the Graduate School of the
MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY
In Partial Fulfillment of the Requirements for the Degree

DOCTOR OF PHILOSOPHY

in

MINING ENGINEERING

2017

Approved
Samuel Frimpong, Advisor
Grzegorz Galecki
Nassib Aouad
Xiaoming He
K. Chandrashekhera
ii

 2017
Wedam Nyaaba
All Rights Reserved
iii

ABSTRACT
The cost benefits associated with the use of heavy mining machinery in the surface
mining industry has led to a surge in the production of ultra-large radial tires with rim
diameters in excess of 35 in. These tires experience fatigue failures in operation. The use
of reinforcing fillers and processing aids in tire compounds results in the formation of
microstructural inhomogeneity in the compounds and may serve as sources of crack
initiation in the tire. Abrasive material cutting is another source of cracks in tires used in
mining applications. It suffices, then, to assume that every material plane in the tire consists
of a crack precursor of some known size likely to nucleate under the tire’s duty cycle loads.
This assumption eliminates the need for prior knowledge of the location and geometry of
crack features to be explicitly included in a tire finite element model, overcoming the key
limitations of previous approaches.
In this study, a rainflow counting algorithm is used to consistently count strain
reversals present in the complex multiaxial variable amplitude duty-cycle loads of the tire
to assess fatigue damage on its material planes. A critical plane analysis method is then
used to account for the non-proportional loading on the tire material planes in order to
identify the plane with the highest fatigue damage. The size of the investigated tire is
56/80R63, and it is typically fitted to ultra-class trucks with payload capacities in excess
of 325 tonne (360 short ton). Experimental data obtained from extracted specimens of the
tire were used to characterize the stress-strain and fatigue behavior of the tire finite element
model in ABAQUS. A sequentially coupled thermomechanical rolling analysis of the tire
provided stress, strains, and temperature data for the computation of the tire’s component
fatigue performance in the rubber fatigue solver ENDURICA CL. The belt endings (tire
shoulder), lower sidewall, and tread lug corners are susceptible to crack initiation and
subsequent failure due to high stresses.
This pioneering research effort contributes to the body of knowledge in tire
durability issues in relation to mining applications. In addition, it provides a basis for off-
road tire compounders and developers to design durable tires to minimize tire operating
costs in the mining industry.
iv

ACKNOWLEDGMENTS
I am highly indebted to my Lord and savior Jesus Christ, who by His abundant
grace and love I am where I am today. A special thanks goes to my research advisor, Dr.
Samuel Frimpong, whose unrelented support and guidance has brought about this success.
I am grateful to my research committee members, Dr. Xiaoming He, Dr. K.
Chandrashekhara, Dr. Grzegorz Galecki, and Dr. Nassib Aouad, for their inconceivable
patience and advice. I could not have made it without their invaluable expertise.
My deepest thanks go to my parents, Mr. Sakazele Nyaaba and Mrs. Mary Nyaaba,
for investing in my education. Although you both did not get any formal education, you
endeavored to give me one. Thank you! I also thank my siblings (Joseph, Alagnona,
Comfort, and Grace) for the love shared with me during my study away from home. I am
also grateful to all my friends, especially Ms. Maame Yaa Gyimah, Ms. Elsie Assan, Ms.
Emelia Yeboah, Ms. Jennifer Gbadam, Ms. Carol Hudler, and Ms. Mavis Tetteh for their
motivation and support. I am indepted to the Rolla First Assembly of God Church (and All
Nations Christian Fellowship) for creating a home away from home for me during my stay
in Rolla.
Special thanks to the Missouri University of Science and Technology (Missouri
S&T) Mining Engineering program staff: Mrs. Shirley Hall, Mrs. Tina Alobaidan, and Mrs.
Judy Russell for their precious help during my stay in the department. I appreciate the help
of the Missouri S&T IT Research Support Services for granting me access to use the
university’s high-performance cluster computing system. I also thank the Technical Editor,
Ms. Emily Seals, for her editorial services.
I am grateful to the Department of Mining and Nuclear Engineering at Missouri
S&T for the funding support from the Saudi Mining Polytechnic Program. I also appreciate
the testing services provided by Axel Products Inc. Finally, I am indebted to Dr. William
V. Mars and Jesse Suter of Endurica LLC for the software sponsorship, technical support
and direction they freely offered me throughout this study. Their contribution and critique
were very helpful in completing the research study.
v

TABLE OF CONTENTS
Page
ABSTRACT ....................................................................................................................... iii
ACKNOWLEDGMENTS ................................................................................................. iv
LIST OF ILLUSTRATIONS ............................................................................................. ix
LIST OF TABLES ........................................................................................................... xiii
NOMENCLATURE ........................................................................................................ xiv
SECTION
1. INTRODUCTION ...................................................................................................... 1
1.1. BACKGROUND OF RESEARCH PROBLEM ................................................ 1
1.2. STATEMENT OF THE RESEARCH PROBLEM ............................................ 3
1.3. OBJECTIVES AND SCOPE OF STUDY ......................................................... 6
1.4. RESEARCH METHODOLOGY........................................................................ 7
1.5. SCIENTIFIC AND INDUSTRIAL CONTRIBUTIONS ................................... 8
1.6. RESEARCH PHILOSOPHY .............................................................................. 9
1.6.1. How Tires Are Made. ............................................................................. 10
1.6.1.1 Mixing. ........................................................................................10
1.6.1.2 Calendering. ................................................................................10
1.6.1.3 Extrusion. ....................................................................................11
1.6.1.4 Vulcanization. .............................................................................11
1.6.2. The 56/80R63 Tire Construction and Service Demand. ........................ 12
1.6.3. Thermomechanical Fatigue Problem. ..................................................... 13
1.6.4. Analytical Philosophy and Solution Procedures. ................................... 14
1.7. STRUCTURE OF DISSERTATION ............................................................... 16
2. LITERATURE REVIEW ......................................................................................... 17
2.1. STRUCTURE OF A PNEUMATIC TIRE ....................................................... 17
2.1.1. Bias-ply Tires. ........................................................................................ 19
2.1.2. Radial Tires. ........................................................................................... 19
2.1.3. Tire Materials. ........................................................................................ 20
2.1.3.1 Reinforcing particles. ..................................................................20
2.1.3.2 Reinforcing cords. .......................................................................20
vi

2.1.3.3 Rubber. ........................................................................................22
2.1.4. Tire Forces and Moments. ...................................................................... 24
2.2. HEAT GENERATION IN TIRES .................................................................... 25
2.2.1. Measurement of Viscoelastic Properties. ............................................... 26
2.2.2. Heat Generation and Temperature Rise Prediction. ............................... 32
2.3. TIRE FATIGUE STUDIES .............................................................................. 38
2.3.1. Continuum Mechanics Approach. .......................................................... 39
2.3.2. Fracture Mechanics Approach. ............................................................... 43
2.4. TIRE WEAR ..................................................................................................... 50
2.5. RATIONALE FOR PHD RESEARCH ............................................................ 51
2.6. SUMMARY ...................................................................................................... 54
3. TIRE THERMOMECHANICS ................................................................................ 57
3.1. TIRE THERMOMECHANICAL PROBLEM ................................................. 57
3.2. THERMAL SUBPROBLEM............................................................................ 58
3.2.1. Weak Formulation of the Thermal Subproblem. .................................... 60
3.2.2. Finite Element Discretization of the Thermal Subproblem. ................... 61
3.2.3. Boundary Treatment of the Thermal Subproblem. ................................ 63
3.3. MECHANICAL SUBPROBLEM .................................................................... 65
3.3.1. Weak Formulation of the Mechanical Subproblem. .............................. 67
3.3.2. Finite Element Discretization of the Mechanical Subproblem. ............. 69
3.3.3. Boundary Treatment of the Mechanical Subproblem. ........................... 75
3.4. SUMMARY ...................................................................................................... 77
4. NUMERICAL SOLUTION SCHEMES FOR TIRE THERMOMECHANICAL
PROBLEM ............................................................................................................... 78
4.1. FULL DISCRETIZATION OF THE THERMAL SUBPROBLEM ................ 78
4.2. FULL DISCRETIZATION OF THE MECHANICAL SUBPROBLEM ........ 79
4.3. ERROR ESTIMATES FOR THE FINITE ELEMENT METHOD ................. 80
4.3.1. Convergence Rate Estimates of Thermomechanical FE Method. .......... 81
4.3.2. Realistic Simulation using the FE Package. ........................................... 84
4.4. SUMMARY ...................................................................................................... 85
5. TIRE MATERIAL, GEOMETRY, AND THERMOMECHANICAL FATIGUE
MODELING ............................................................................................................. 89
vii

5.1. TIRE MATERIAL CHARACTERIZATION................................................... 89
5.1.1. Rubber Material Hyperelasticity. ........................................................... 89
5.1.2. Rubber Material Viscoelasticity. ............................................................ 95
5.1.3. Rubber Material Fatigue Behavior. ...................................................... 110
5.1.3.1 Fully relaxing crack growth test. ..............................................111
5.1.3.2 Non-relaxing crack growth test. ................................................113
5.1.4. Thermal Material Properties. ................................................................ 118
5.2. THE 56/80R63 TIRE GEOMETRY MODELING IN ABAQUS .................. 120
5.3. TIRE THERMOMECHANICAL FATIGUE MODELING AND
ANALYSIS .................................................................................................... 125
5.3.1. Deformation Module. ........................................................................... 126
5.3.2. Thermal Module. .................................................................................. 126
5.3.3. Fatigue Module. .................................................................................... 127
5.3.3.1 Multiaxial fatigue life estimation. .............................................127
5.3.3.2 Rainflow counting procedure. ...................................................130
5.3.3.3 Initial crack size calibration. .....................................................132
5.3.3.4 Critical plane analysis. ..............................................................132
5.4. SUMMARY .................................................................................................... 134
6. MODEL VALIDATION, EXPERIMENTAL DESIGN, AND
EXPERIMENTATION .......................................................................................... 136
6.1. MESH CONVERGENCE STUDY ................................................................ 136
6.2. VERTICAL STIFFNESS VALIDATION ...................................................... 137
6.2.1. Field Measurement. .............................................................................. 137
6.2.2. Static Vertical Stiffness Analysis. ........................................................ 139
6.3. FOOTPRINT VALIDATION ......................................................................... 139
6.4. DESIGN OF EXPERIMENTS ....................................................................... 141
6.5. EXPERIMENTATION OF TIRE OPERATING VARIABLES .................... 145
6.5.1. Simulating the Effects of Inflation Pressure on Fatigue Life. .............. 145
6.5.2. Simulating the Effects of Axle Load on Fatigue Life. ......................... 146
6.5.3. Simulating the Effects of Speed on Fatigue Life. ................................ 146
6.6. SUMMARY .................................................................................................... 146
7. RESULTS AND DISCUSSIONS .......................................................................... 148
viii

7.1. TIRE DEFLECTION, FORCES, AND CONTACT PRESSURE ................. 148
7.2. TIRE ENERGY LOSS AND TEMPERATURE ............................................ 156
7.3. TIRE FATIGUE PERFORMANCE ............................................................... 164
7.3.1. Local Cracking Plane Loading Histories. ............................................. 164
7.3.2. Effect of SIC on Fatigue Life. .............................................................. 169
7.3.3. Effect of Thermal Loads on Fatigue Life. ............................................ 175
7.4. SUMMARY .................................................................................................... 179
8. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS ......................... 183
8.1. SUMMARY .................................................................................................... 183
8.2. CONCLUSIONS............................................................................................. 184
8.3. PHD RESEARCH CONTRIBUTIONS ......................................................... 187
8.4. RECOMMENDATION .................................................................................. 187
APPENDIX ......................................................................................................................189
BIBLIOGRAPHY ........................................................................................................... 192
VITA .............................................................................................................................. 203
ix

LIST OF ILLUSTRATIONS
Figure Page
1.1. U.S. Percent Share of World Nonfuel Mineral Production ......................................... 2
1.2. Average Price of a 40.00R57 Tire [4] .......................................................................... 3
1.3. Mechanical Separation in a 55/80R63 Tire [10] .......................................................... 5
1.4. Fatigue failure Forms Initiated by Rock Cuts in (a) Sidewall, and (b) Tread ............. 6
1.5. Tire Aspect Ratio ....................................................................................................... 13
2.1. Schematic of a Radial Tire Cross Section.................................................................. 18
2.2. Bias-ply and Radial Tire Constructions [25] ............................................................. 19
2.3. A Steel Cord Composition [37] ................................................................................. 22
2.4. Mullins Effect in Filled Rubber ................................................................................. 24
2.5. Tire Forces and Moments [21] ................................................................................... 25
3.1. Thermal Boundary Surfaces on Tire Geometry ......................................................... 64
4.1. Tire Axisymmetric Mesh ........................................................................................... 86
4.2. Temperature (in ℃) Solution of (a) Developed Thermal FE Model Package, (b)
MATLAB PDE Toolbox Solver, and (c) ABAQUS Thermal Analysis ................... 87
4.3. Displacement (in mm) Solution of Developed FE Model Package ........................... 88
4.4. Displacement (in mm) Solution of ABAQUS Coupled Temperature-
Displacement Analysis ............................................................................................... 88
5.1. Regions of Extracted Tire Specimens ........................................................................ 90
5.2. Skived 56/80R63 Tire Specimens .............................................................................. 91
5.3. A Typical Simple Tension Specimen Geometry ....................................................... 93
5.4. Simple Tension Test Results–All Compounds .......................................................... 96
5.5. Derived Planar Tension Results–All Compounds ..................................................... 97
5.6. Derived Equibiaxial Tension Results–All Compounds ............................................. 98
5.7. Comparison of Test and Ogden Model Results–All Compounds and Modes ........... 99
5.8. Stress Relaxation Test Results–All Compounds ..................................................... 101
5.9. ABAQUS Prony Series Fitting Results–All Compounds ........................................ 104
5.10. Nonlinear Viscoelastic Model [15] ........................................................................ 105
5.11. Unit Cube Model Boundary Conditions ................................................................ 109