Abstract

The objective of this study is to conduct a numerical investigation to examine the temperatures in off-the-road (OTR) tires under operating conditions at mine sites. To achieve this, a new mathematical equation was developed based on a modified Mooney–Rivlin (MR) strain energy function, the pseudo-elasticity theory, and the inverse analysis method. This equation was used to determine the internal heat generation rates of tire rubbers. With heat generation rates, the governing equation of heat conduction and the mathematical expression of boundary conditions were further generated to describe the heat transfer in tire rubbers. Based on these equations, a novel finite element (FE) OTR tire thermal (OTRTire-T) model was developed. This OTRTire-T model was used to numerically investigate temperatures in OTR tires at vertical loads from 0.34 to 1.04 MN, hauling speeds from 5 to 30 km/h, and ambient temperatures from −30 to 40 °C. The results showed that a large vertical load (e.g., 1.04 MN) increased the tire rubber temperatures considerably. Tire rubber temperature also increased with an increase in hauling speeds, and the increase became more significant at larger vertical loads (e.g., 1.04 MN). The OTRTire-T model identified an inverse proportional relationship between the rubber temperature increments and the ambient temperatures from −30 to 40 °C. Nonetheless, the rubber temperature in the OTR tire increased relatively rapidly with an increase in ambient temperatures.

References

1.
Oil Sands Discovery Center
,
2016
, “
Facts about Alberta’s Oil Sands and Its Industry
,” https://open.alberta.ca/publications/facts-about-alberta-s-oil-sands-and-its-industry, Accessed October 12, 2020.
2.
Meech
,
J.
, and
Parreira
,
J.
,
2013
, “
Predicting Wear and Temperature of Autonomous Haulage Truck Tires
,”
IFAC Proc.
,
46
(
16
), pp.
142
147
.
3.
Parreira
,
J.
,
2013
, “
An Interactive Simulation Model to Compare an Autonomous Haulage Truck System With a Manually-Operated System
,”
Ph.D. thesis
,
University of British Columbia
,
Canada
.
4.
Kerr
,
C. L.
,
2017
, “
Load G-Level as a Truck-Ground KPI
,”
Master’s thesis
,
University of Alberta
,
Canada
.
5.
Li
,
Y.
,
Liu
,
W. Y.
, and
Frimpong
,
S.
,
2012
, “
Effect of Ambient Temperature on Stress, Deformation and Temperature of Dump Truck Tire
,”
Eng. Fail. Anal.
,
23
, pp.
55
62
.
6.
Nyaaba
,
W.
,
2017
, “
Thermomechanical Fatigue Life Investigation of an Ultra-Large Mining Dump Truck Tire
,”
Dissertation
,
Missouri University of Science and Technology
,
Rolla, MI
.
7.
Alberta Agriculture and Forestry
,
218
, “
Current and Historical Alberta Weather Station Data Viewer
,” https://acis.alberta.ca/weather-data-viewer.jsp, Accessed March 16, 2021.
8.
Ta
,
C.
,
2018
, “
Operation Truck Data
,” Report,
Syncrude Canada Ltd.
,
Canada
.
9.
He
,
Y.
,
2005
, “
Study of the Unsteady Temperature Field of Tire
,”
Ph.D. thesis
,
Huazhong University of Science and Technology
,
China
.
10.
Anzabi
,
R. V.
,
Nobes
,
D. S.
, and
Lipsett
,
M. G.
,
2012
, “
Haul Truck Tire Dynamics Due to Tire Condition
,”
J. Phys. Conf. Ser.
,
364
(
1
), p.
12005
.
11.
Anzabi
,
R. V.
,
2015
, “
Haul Truck Tire Reliability and Condition Monitoring
,”
Ph.D. thesis
,
University of Alberta
,
Canada
.
12.
Allouis
,
C.
,
Farroni
,
F.
,
Sakhnevych
,
A.
, and
Timpone
,
F.
,
2016
, “
Tire Thermal Characterization: Test Procedure and Model Parameters Evaluation
,”
Proceedings of the World Congress on Engineering
,
London, UK
,
June 29–July 4
, Vol. 2224, pp.
1199
1204
.
13.
Farroni
,
F.
,
Sakhnevych
,
A.
, and
Timpone
,
F.
,
2017
, “
Physical Modelling of Tire Wear for the Analysis of the Influence of Thermal and Frictional Effects on Vehicle Performance
,”
Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl.
,
231
(
1–2
), pp.
151
161
.
14.
Wu
,
W.
,
2017
, “
Simulation Analysis of Tire Temperature Field
,”
Master’s thesis
,
Jilin University
,
China
.
15.
Nyaaba
,
W.
,
Bolarinwa
,
E. O.
, and
Frimpong
,
S.
,
2019
, “
Durability Prediction of an Ultra-Large Mining Truck Tire Using an Enhanced Finite Element Method
,”
Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
,
233
(
1
), pp.
161
169
.
16.
Nyaaba
,
W.
,
Frimpong
,
S.
, and
Anani
,
A.
,
2019
, “
Fatigue Damage Investigation of Ultra-Large Tire Components
,”
Int. J. Fatigue
,
119
, pp.
247
260
.
17.
Michelin
,
2016
, “
Technical Data—Earthmover Tires
,” https://www.otrusa.com/wp-content/uploads/2017/07/Michelin-Technical-Data-6.pdf, Accessed September 20, 2020.
18.
Golbakhshi
,
H.
,
Namjoo
,
M.
, and
Mohammadi
,
M.
,
2014
, “
Evaluating the Effect of Dissipated Viscous Energy of a Rolling Tire on Stress, Strain and Deformation Fields Using an Efficient 2D FE Analysis
,”
Int. J. Automot. Eng.
,
16
(
5.9
), pp.
3
7
.
19.
Marais
,
J.
, and
Venter
,
G.
,
2018
, “
Numerical Modelling of the Temperature Distribution in the Cross-Section of an Earthmover Tyre
,”
Appl. Math. Model.
,
57
, pp.
360
375
.
20.
Ma
,
S.
,
Guo
,
Y.
, and
Liu
,
W. V.
,
2022
, “
An Analytical Solution to Predict Temperatures of Dumbbell-Shaped Rubber Specimens Under Cyclic Deformation
,”
Heat Transfer Eng.
21.
Liu
,
M.
,
2010
, “
Constitutive Equations for the Dynamic Response of Rubber
,”
Ph.D. thesis
,
University of Akron
,
Akron, OH
.
22.
Liu
,
M.
, and
Fatt
,
M. S. H.
,
2011
, “
A Constitutive Equation for Filled Rubber Under Cyclic Loading
,”
Int. J. Non Linear. Mech.
,
46
(
2
), pp.
446
456
.
23.
Zhi
,
J.
,
Lu
,
H.
,
Wang
,
H.
,
Wang
,
S.
,
Lin
,
W.
,
Qiao
,
C.
, and
Jia
,
Y.
,
2016
, “
Analysis on Dynamic Compression Performance of Tire Rubber Based on Generalized Maxwell Model
,”
Acta Polym. Sin.
,
20
(
7
), pp.
887
894
.
24.
Ma
,
S.
,
Huang
,
G.
,
Obaia
,
K.
,
Moon
,
S. W.
, and
Liu
,
W. V.
,
2022
, “
Hysteresis Loss of Ultra-Large off-the-Road Tire Rubber Compounds Based on Operating Conditions at Mine Sites
,”
Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
,
236
(
2–3
), pp.
439
450
.
25.
Marais
,
J.
,
2017
, “
Numerical Modelling and Evaluation of the Temperature Distribution in an Earthmover Tyre: Establishing a Safe Operating Envelope
,”
Dissertation
,
Stellenbosch University
,
South Africa
.
26.
Dodge
,
Y.
,
2008
,
The Concise Encyclopedia of Statistics
,
Springer Science & Business Media
,
Berlin/Heidelberg, Germany
.
27.
Zwillinger
,
D.
,
2018
,
CRC Standard Mathematical Tables and Formulas
,
Chapman and Hall/CRC
,
Boca Raton, FL
.
28.
Xia
,
K.
,
2011
, “
Finite Element Modeling of Tire/Terrain Interaction: Application to Predicting Soil Compaction and Tire Mobility
,”
J. Terramech.
,
48
(
2
), pp.
113
123
.
29.
Smith
,
R. E.
,
Tang
,
T.
,
Johnson
,
D.
,
Ledbury
,
E.
,
Goddette
,
T.
, and
Felicelli
,
S. D.
,
2012
, “
Simulation of Thermal Signature of Tires and Tracks
,” Report,
Mississippi State Univ Mississippi State Center for Advanced Vehicular Systems
,
MS
.
30.
Tang
,
T.
,
Johnson
,
D.
,
Smith
,
R. E.
, and
Felicelli
,
S. D.
,
2014
, “
Numerical Evaluation of the Temperature Field of Steady-State Rolling Tires
,”
Appl. Math. Model.
,
38
(
5–6
), pp.
1622
1637
.
31.
Kim
,
B.
,
Lee
,
S. B.
,
Lee
,
J.
,
Cho
,
S.
,
Park
,
H.
,
Yeom
,
S.
, and
Park
,
S. H.
,
2012
, “
A Comparison among Neo-Hookean Model, Mooney-Rivlin Model, and Ogden Model for Chloroprene Rubber
,”
Int. J. Precis. Eng. Manuf.
,
13
(
5
), pp.
759
764
.
32.
Kumar
,
N.
, and
Rao
,
V. V.
,
2016
, “
Hyperelastic Mooney-Rivlin Model: Determination and Physical Interpretation of Material Constants
,”
Parameters
,
2
(
10
), p.
1
.
33.
Cho
,
J. R.
,
Lee
,
H. W.
,
Jeong
,
W. B.
,
Jeong
,
K. M.
, and
Kim
,
K. W.
,
2013
, “
Numerical Estimation of Rolling Resistance and Temperature Distribution of 3-D Periodic Patterned Tire
,”
Int. J. Solids Struct.
,
50
(
1
), pp.
86
96
.
34.
Nyaaba
,
W.
,
Frimpong
,
S.
,
Somua-Gyimah
,
G.
, and
Galecki
,
G.
,
2016
, “
FEA Prediction of Off-Road Tire Temperature Distribution
,”
Science in the Age of Experience
,
Boston, MA
,
May 23–25
, pp.
1
14
35.
Liang
,
C.
,
Ji
,
L.
,
Mousavi
,
H.
, and
Sandu
,
C.
,
2019
, “Evaluation of Tire Traction Performance on Dry Surface Based on Tire-Road Contact Stress,”
SIAR International Congress of Automotive and Transport Engineering: Science and Management of Automotive and Transportation Engineering
,
I.
Dumitru
,
D.
Covaciu
,
L.
Racila
, and
A.
Rosca
, eds.,
Springer
,
New York
, pp.
138
152
.
36.
Neves
,
R. R. V.
,
Micheli
,
G. B.
, and
Alves
,
M.
,
2010
, “
An Experimental and Numerical Investigation on Tyre Impact
,”
Int. J. Impact Eng.
,
37
(
6
), pp.
685
693
.
37.
Wang
,
W.
,
Yan
,
S.
, and
Zhao
,
S.
,
2013
, “
Experimental Verification and Finite Element Modeling of Radial Truck Tire Under Static Loading
,”
J. Reinf. Plast. Compos.
,
32
(
7
), pp.
490
498
.
38.
Zhou
,
H.
,
Wang
,
G.
,
Ding
,
Y.
,
Yang
,
J.
,
Liang
,
C.
, and
Fu
,
J.
,
2015
, “
Effect of Friction Model and Tire Maneuvering on Tire-Pavement Contact Stress
,”
Adv. Mater. Sci. Eng.
,
2015
, pp.
1
15
.
39.
Hu
,
X.
,
Liu
,
X.
,
Shan
,
Y.
, and
He
,
T.
,
2021
, “
Simulation and Experimental Validation of Sound Field in a Rotating Tire Cavity Arising From Acoustic Cavity Resonance
,”
Appl. Sci.
,
11
(
3
), p.
1121
.
40.
Lin
,
Y. J.
, and
Hwang
,
S. J.
,
2004
, “
Temperature Prediction of Rolling Tires by Computer Simulation
,”
Math. Comput. Simul.
,
67
(
3
), pp.
235
249
.
41.
Li
,
F.
,
Liu
,
F.
,
Liu
,
J.
,
Gao
,
Y.
,
Lu
,
Y.
,
Chen
,
J.
,
Yang
,
H.
, and
Zhang
,
L.
,
2018
, “
Thermo-Mechanical Coupling Analysis of Transient Temperature and Rolling Resistance for Solid Rubber Tire: Numerical Simulation and Experimental Verification
,”
Compos. Sci. Technol.
,
167
, pp.
404
410
.
42.
Mooney
,
M.
,
1940
, “
A Theory of Large Elastic Deformation
,”
J. Appl. Phys.
,
11
(
9
), pp.
582
592
.
43.
Rivlin
,
R. S.
,
1948
, “
Large Elastic Deformations of Isotropic Materials. I. Fundamental Concepts
,”
Philos. Trans. R. Soc. London, Ser. A
,
240
(
822
), pp.
459
490
.
44.
Ma
,
S.
,
Huang
,
G.
,
Obaia
,
K.
,
Moon
,
S.
, and
Liu
,
W. V.
,
2021
, “
A Novel Phenomenological Model for Predicting Hysteresis Loss of Rubber Compounds Obtained From Ultra-Large Off-the-Road Tires
,”
Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
45.
Liu
,
M.
,
2007
, “
A Three-Dimensional Hyper-Viscoelasticity Constitutive Model for the Dynamic Response of Rubber
,”
PhD thesis
,
University of Akron
,
Akron, OH
.
46.
Österlöf
,
R.
,
Kari
,
L.
, and
Wentzel
,
H.
,
2015
, “
Temperature Dependency of a Viscoplastic Constitutive Model for Rubber with Reinforcing Fillers
,”
9th European Conference on Constitutive Models for Rubbers, ECCMR 2015
,
Sept. 1–4
,
CRC Press/Balkema
, pp.
149
156
.
47.
Österlöf
,
R.
,
Wentzel
,
H.
, and
Kari
,
L.
,
2016
, “
A Finite Strain Viscoplastic Constitutive Model for Rubber With Reinforcing Fillers
,”
Int. J. Plast.
,
87
, pp.
1
14
.
48.
Carleo
,
F.
,
Barbieri
,
E.
,
Whear
,
R.
, and
Busfield
,
J. J. C.
,
2018
, “
Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates
,”
Polymers (Basel)
,
10
(
9
), p.
988
.
49.
Hurtado
,
J.
,
Lapczyk
,
I.
, and
Govindarajan
,
S.
,
2013
, “
Parallel Rheological Framework to Model Non-Linear Viscoelasticity, Permanent Set, and Mullins Effect in Elastomers
,”
Const. Models Rubber
,
8
, pp.
95
100
.
50.
Kießling
,
R.
,
Landgraf
,
R.
,
Scherzer
,
R.
, and
Ihlemann
,
J.
,
2016
, “
Introducing the Concept of Directly Connected Rheological Elements by Reviewing Rheological Models at Large Strains
,”
Int. J. Solids Struct.
,
97
, pp.
650
667
.
51.
Ogden
,
R. W.
, and
Roxburgh
,
D. G.
,
1999
, “
A Pseudo–Elastic Model for the Mullins Effect in Filled Rubber
,”
Proc. R. Soc. A
,
455
(
1988
), pp.
2861
2877
.
52.
Huang
,
L.
,
Yang
,
X.
, and
Gao
,
J.
,
2019
, “
Pseudo-Elastic Analysis with Permanent Set in Carbon-Filled Rubber
,”
Adv. Polym. Technol.
,
2019
, pp.
1
8
.
53.
Dorfmann
,
A.
, and
Ogden
,
R. W.
,
2004
, “
A Constitutive Model for the Mullins Effect With Permanent Set in Particle-Reinforced Rubber
,”
Int. J. Solids Struct.
,
41
(
7
), pp.
1855
1878
.
54.
Wineman
,
A.
,
2005
, “
Some Results for Generalized Neo-Hookean Elastic Materials
,”
Int. J. Non Linear. Mech.
,
40
(
2–3
), pp.
271
279
.
55.
Bergman
,
T. L.
,
Lavine
,
A. S.
,
Incropera
,
F. P.
, and
DeWitt
,
D. P.
,
2011
,
Introduction to Heat Transfer
,
John Wiley & Sons
,
Hoboken, NJ
.
56.
Disk
,
H.
,
2018
, “
Hot Disk Thermal Constants Analyser Instruction Manual
,” https://www.hotdiskinstruments.com/content/uploads/2017/04/TPS-500-S.pdf, Accessed August 1, 2021.
57.
Cebeci
,
T.
, and
Bradshaw
,
P.
,
2012
,
Physical and Computational Aspects of Convective Heat Transfer
,
Springer Science & Business Media
,
Berlin/Heidelberg, Germany
.
58.
Jiji
,
L. M.
,
2009
,
Heat Convection
,
Springer Science & Business Media
,
Berlin/Heidelberg, Germany
.
59.
Baker
,
C. R.
,
Cohanier
,
B.
, and
Gibassier
,
D.
,
2018
, “
Environmental Management Controls at Michelin–How Do They Link to Sustainability?
,”
Soc. Environ. Account. J.
,
38
(
1
), pp.
75
96
.
60.
Carter
,
R. A.
,
2020
, “
Data and Design Drive OTR Tire Improvements
,”
Eng. Min. J.
,
221
(
4
), pp.
38
41
.
61.
Caterpillar
,
2018
, “
Caterpillar Performance Handbook
,” https://wheelercat.com/wp-content/uploads/2018/07/SEBD0351_ED48.pdf, Accessed September 25, 2020.
62.
Narasimha Rao
,
K. V.
,
Kumar
,
R. K.
, and
Bohara
,
P. C.
,
2006
, “
A Sensitivity Analysis of Design Attributes and Operating Conditions on Tyre Operating Temperatures and Rolling Resistance Using Finite Element Analysis
,”
Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
,
220
(
5
), pp.
501
517
.
63.
Li
,
X.
,
2012
, “
Study on the Reinforcement and Blend Dependence of Hyperelasticity of Tire Rubbers Under the Moderate Finite Deformation
,”
Ph.D. thesis
,
University of Science and Technology of China
,
China
.
64.
Li
,
X.
,
Dong
,
Y.
,
Li
,
Z.
, and
Xia
,
Y.
,
2011
, “
Experimental Study on the Temperature Dependence of Hyperelastic Behavior of Tire Rubbers Under Moderate Finite Deformation
,”
Rubber Chem. Technol.
,
84
(
2
), pp.
215
228
.
65.
Xia
,
Y.
,
Li
,
W.
, and
Xia
,
Y.
,
2004
, “
Test and Characterization for the Incompressible Hyperelastic Properties of Conditioned Rubbers Under Moderate Finite Deformation
,”
Acta Mech. Solida Sin.
,
4
(
17
), pp.
307
314
.
66.
Sokolov
,
S. L.
,
2009
, “
Analysis of the Heat State of Pneumatic Tires by the Finite Element Method
,”
J. Mach. Manuf. Reliab.
,
38
(
3
), pp.
310
314
.
67.
He
,
Y.
,
Liu
,
L.
,
Ma
,
L.
, and
Sun
,
X.
,
2006
, “
Dependence of Heat Build-up of Tire on Temperature and Frequency
,”
Tire Ind.
,
6
, pp.
323
328
.
68.
Kerschbaumer
,
R. C.
,
Stieger
,
S.
,
Gschwandl
,
M.
,
Hutterer
,
T.
,
Fasching
,
M.
,
Lechner
,
B.
,
Meinhart
,
L.
, et al
,
2019
, “
Comparison of Steady-State and Transient Thermal Conductivity Testing Methods Using Different Industrial Rubber Compounds
,”
Polym. Test.
,
80
, p.
106121
.
69.
Wang
,
G.
,
Xu
,
H.
,
Liang
,
C.
,
Zhou
,
H.
, and
Sun
,
Y.
,
2017
, “
Research on the Influence of Thermophysical Parameters of Tire Compound on Temperature Field
,”
Rubber Ind.
,
(7)
, pp.
435
440
.
70.
Golbakhshi
,
H.
, and
Namjoo
,
M.
,
2014
, “
Finite Element Analysis for Estimating the Effect of Various Working Conditions on the Temperature Gradients Created Inside a Rolling Tire
,”
Int. J. Eng.
,
27
(
12
), pp.
1920
1927
.
71.
Lindeque
,
G. C.
,
2016
, “
A Critical Investigation Into Tyre Life on an Iron Ore Haulage System
,”
J. South. Afr. Inst. Min. Metall.
,
116
(
4
), pp.
317
322
.
72.
Jin
,
Z.
, and
Cui
,
Z.
,
2010
, “
Investigation on Strain Dependence of Dynamic Recrystallization Behavior Using an Inverse Analysis Method
,”
Mater. Sci. Eng. A
,
527
(
13–14
), pp.
3111
3119
.
73.
Lei
,
F.
, and
Szeri
,
A. Z.
,
2007
, “
Inverse Analysis of Constitutive Models: Biological Soft Tissues
,”
J. Biomech.
,
40
(
4
), pp.
936
940
.
74.
Li
,
F.
,
Liu
,
J.
,
Lu
,
Y.
,
Zhang
,
L.
, and
Yang
,
H.
,
2017
, “
Modeling on Constitutive Behaviors of Filled Rubber Compounds for Cyclic Loading Path
,”
Rubber Chem. Technol.
,
64
(
6
), pp.
79
83
.
You do not currently have access to this content.