Abstract
The objective of this study is to propose an analytical solution that can predict the temperatures of dumbbell-shaped rubber specimens under cyclic deformation. Initially, a new mathematical equation was formulated by modifying the Mooney–Rivlin strain energy function, using the pseudo-elasticity theory and the inverse analysis method. This equation was utilized to calculate the internal heat generation rates of rubber compounds. With heat generation rates, the governing equation of heat conduction and the mathematical expression of boundary conditions were created to describe the heat transfer that occurs within the rubber compounds. By having these equations, a novel analytical solution was developed—the RTDS solution (a solution to predict Rubber Temperatures in Dumbbell-shaped Specimens). This RTDS solution was used to predict rubber temperatures in dumbbell-shaped specimens under cyclic deformation. The results showed that the RTDS solution took 11.9 s to derive the rubber temperature results with an average mean absolute percent error (MAPE) of 9.2% compared with lab recordings. The RTDS solution identified a logarithmic increase in rubber temperatures at rising strain levels, and it also identified an increase in rubber temperatures with the rising strain rates. According to the RTDS solution, there was an inverse correlation between the increases in rubber temperature and the ambient temperatures.
Issue Section:
Research Papers
References
1.
Duffy
, O. C.
, and Wright
, G.
, 2015
, Fundamentals of Medium/Heavy Duty Commercial Vehicle Systems: 2014 NATEF Edition
, Jones & Bartlett Publishers
, Burlington, MA
.2.
Gent
, A. N.
, and Walter
, J. D.
, 2006
, Pneumatic Tire
, Department of Transportation, National Highway Traffic Safety Administration
, Washington, DC
.3.
Michelin
, 2016
, “Technical Data—Earthmover Tires
,” https://www.otrusa.com/wp-content/uploads/2017/07/Michelin-Technical-Data-6.pdf, Accessed December 20, 2022.4.
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
. 5.
Hu
, X.
, He
, R.
, Huang
, Y.
, Yin
, B.
, and Luo
, W.
, 2019
, “A Method to Predict the Dynamical Behaviors of Carbon Black Filled Natural Rubber at Different Temperatures
,” Polym. Test.
, 79
, p. 106067
. 6.
Marais
, J.
, 2017
, “Numerical Modelling and Evaluation of the Temperature Distribution in an Earthmover Tyre: Establishing a Safe Operating Envelope
,” Ph.D. thesis
, Stellenbosch University
, South Africa
.7.
Nyaaba
, W.
, 2017
, “Thermomechanical Fatigue Life Investigation of an Ultra-Large Mining Dump Truck Tire
,” Ph.D. thesis
, Missouri University of Science and Technology
, MO
.8.
Yang
, Y. L.
, Qiao
, L.
, Wang
, C.
, Lu
, F.
, and Kang
, X. H.
, 2014
, “Effect Analysis of Temperature on the Rubber Material Stress-Strain Relationship
,” Adv. Mater. Res.
, 977
, pp. 116
–119
. 9.
Luo
, W.
, Huang
, Y.
, Yin
, B.
, Jiang
, X.
, and Hu
, X.
, 2020
, “Fatigue Life Assessment of Filled Rubber by Hysteresis Induced Self-Heating Temperature
,” Polymers (Basel)
, 12
(4
), p. 846
. 10.
Luo
, W.
, Li
, M.
, Huang
, Y.
, Yin
, B.
, and Hu
, X.
, 2019
, “Effect of Temperature on the Tear Fracture and Fatigue Life of Carbon-Black-Filled Rubber
,” Polymers (Basel)
, 11
(5
), p. 768
. 11.
Zhang
, J.
, Xue
, F.
, Wang
, Y.
, Zhang
, X.
, and Han
, S.
, 2018
, “Strain Energy-Based Rubber Fatigue Life Prediction Under the Influence of Temperature
,” R. Soc. Open Sci.
, 5
(10
), p. 180951
. 12.
Ghoreishy
, M. H. R.
, Alimardani
, M.
, Mehrabian
, R. Z.
, and Gangali
, S. T.
, 2013
, “Modeling the Hyperviscoelastic Behavior of a Tire Tread Compound Reinforced by Silica and Carbon Black
,” J. Appl. Polym. Sci.
, 128
(3
), pp. 1725
–1731
. 13.
Kocjan
, T.
, Nagode
, M.
, Klemenc
, J.
, and Oman
, S.
, 2022
, “Prediction of Actual Fatigue Test Temperature and Isothermal Fatigue Life Curves for Non-Crystallising Rubber Under Fully Relaxing Uni-Axial Loading Conditions
,” Int. J. Fatigue
, 157
, p. 106622
. 14.
Brieu
, M.
, Diani
, J.
, Mignot
, C.
, and Moriceau
, C.
, 2010
, “Response of a Carbon-Black Filled SBR Under Large Strain Cyclic Uniaxial Tension
,” Int. J. Fatigue
, 32
(12
), pp. 1921
–1927
. 15.
Rangarajan
, S. E.
, and Ramarathnam
, K. K.
, 2021
, “Viscoelastic Properties of Natural Rubber With Fatigue Damage
,” Int. J. Fatigue
, 150
, p. 106344
. 16.
Behnke
, R.
, Kaliske
, M.
, and Klüppel
, M.
, 2016
, “Thermo-Mechanical Analysis of Cyclically Loaded Particle-Reinforced Elastomer Components: Experiment and Finite Element Simulation
,” Rubber Chem. Technol.
, 89
(1
), pp. 154
–176
. 17.
Guo
, Q.
, Zaïri
, F.
, Ovalle Rodas
, C.
, and Guo
, X.
, 2018
, “Constitutive Modeling of the Cyclic Dissipation in Thin and Thick Rubber Specimens
,” ZAMM-J. Appl. Math. Mech. für Angew. Math. und Mech.
, 98
(10
), pp. 1878
–1899
. 18.
Rodas
, C. O.
, Zaïri
, F.
, Naït-Abdelaziz
, M.
, and Charrier
, P.
, 2016
, “A Thermo-Visco-Hyperelastic Model for the Heat Build-Up During Low-Cycle Fatigue of Filled Rubbers: Formulation, Implementation and Experimental Verification
,” Int. J. Plast.
, 79
, pp. 217
–236
. 19.
Schieppati
, J.
, Schrittesser
, B.
, Wondracek
, A.
, Robin
, A. H. S.
, and Pinter
, G.
, 2019
, “Heat Build-Up of Rubbers During Cyclic Loading
,” Proceeding of 2019 European Conference on Constitutive Models for Rubber-ECCMR
, Nantes, France
, June 25–27
, pp. 25
–27
.20.
Benkahla
, J.
, Baranger
, T. N.
, and Issartel
, J.
, 2013
, “Fatigue Life Estimation for an NBR Rubber and an Expanded Polyurethane
,” Exp. Mech.
, 53
(8
), pp. 1383
–1393
. 21.
Zine
, A.
, Benseddiq
, N.
, and Abdelaziz
, M. N.
, 2011
, “Rubber Fatigue Life Under Multiaxial Loading: Numerical and Experimental Investigations
,” Int. J. Fatigue
, 33
(10
), pp. 1360
–1368
. 22.
Martinez
, J. R. S.
, Le Cam
, J.-B.
, Balandraud
, X.
, Toussaint
, E.
, and Caillard
, J.
, 2013
, “Mechanisms of Deformation in Crystallizable Natural Rubber. Part 1: Thermal Characterization
,” Polymer (Guildf)
, 54
(11
), pp. 2717
–2726
. 23.
Wang
, M.
, Liao
, Y.
, and Chen
, D.
, 2013
, “Study on the Thermal Effects of Rubbers During Loading–Unloading Cycles by Infrared Thermography
,” Polym. Bull.
, 70
(1
), pp. 171
–180
. 24.
Weng
, G.
, Huang
, G.
, Lei
, H.
, Qu
, L.
, Nie
, Y.
, and Wu
, J.
, 2011
, “Crack Initiation and Evolution in Vulcanized Natural Rubber Under High Temperature Fatigue
,” Polym. Degrad. Stab.
, 96
(12
), pp. 2221
–2228
. 25.
Mars
, W. V.
, and Fatemi
, A.
, 2002
, “A Literature Survey on Fatigue Analysis Approaches for Rubber
,” Int. J. Fatigue
, 24
(9
), pp. 949
–961
. 26.
Mars
, W. V.
, and Fatemi
, A.
, 2003
, “Fatigue Crack Nucleation and Growth in Filled Natural Rubber
,” Fatigue Fract. Eng. Mater. Struct.
, 26
(9
), pp. 779
–789
. 27.
Fernandes
, A. P.
, Sousa
, P. F. B.
, Borges
, V. L.
, and Guimaraes
, G.
, 2010
, “Use of 3D-Transient Analytical Solution Based on Green’s Function to Reduce Computational Time in Inverse Heat Conduction Problems
,” Appl. Math. Model.
, 34
(12
), pp. 4040
–4049
. 28.
Flint
, T. F.
, Francis
, J. A.
, Smith
, M. C.
, and Vasileiou
, A. N.
, 2018
, “Semi-Analytical Solutions for the Transient Temperature Fields Induced by a Moving Heat Source in an Orthogonal Domain
,” Int. J. Therm. Sci.
, 123
, pp. 140
–150
. 29.
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
. 30.
ASTM D412-16: 2016
, 2016
, “Standard Test Methods for Vulcanized Rubber and Thermoplastic Elastomers—Tension
,” ASTM International, West Conshohocken, PA.31.
Dodge
, Y.
, 2008
, The Concise Encyclopedia of Statistics
, Springer Science & Business Media
, Berlin/Heidelberg, Germany
.32.
Zwillinger
, D.
, 2018
, CRC Standard Mathematical Tables and Formulas
, Chapman and Hall/CRC
, Boca Raton, FL
.33.
Minaei
, A.
, and Safikhani
, H.
, 2021
, “A New Transient Analytical Model for Heat Transfer of Earth-to-Air Heat Exchangers
,” J. Build. Eng.
, 33
, p. 101560
. 34.
Luo
, W.
, Yin
, B.
, Hu
, X.
, Zhou
, Z.
, Deng
, Y.
, and Song
, K.
, 2018
, “Modeling of the Heat Build-Up of Carbon Black Filled Rubber
,” Polym. Test.
, 69
, pp. 116
–124
. 35.
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
. 36.
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
. 37.
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
. 38.
Banić
, M. S.
, Stamenković
, D. S.
, Miltenović
, V.
, Milošević
, M. S.
, Miltenović
, A. V.
, Đekić
, P. S.
, and Rackov
, M. J.
, 2012
, “Prediction of Heat Generation in Rubber or Rubber-Metal Springs
,” Therm. Sci.
, 16
(S2
), pp. 527
–539
. 39.
Mooney
, M.
, 1940
, “A Theory of Large Elastic Deformation
,” J. Appl. Phys.
, 11
(9
), pp. 582
–592
. 40.
Rivlin
, R.
, 1948
, “Large Elastic Deformations of Isotropic Materials. I. Fundamental Concepts
,” Philos. Trans. R. Soc. London. Ser. A, Math. Phys. Sci.
, 240
(822
), pp. 459
–490
. 41.
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
. 42.
Kumar
, N.
, and Rao
, V. V.
, 2016
, “Hyperelastic Mooney-Rivlin Model: Determination and Physical Interpretation of Material Constants
,” Parameters
, 2
(10
), p. 1
. 43.
Pang
, B.-J.
, Yang
, Z.-Q.
, Wang
, L.-W.
, and Chi
, R.-Q.
, 2011
, “Dynamic Compression Properties and Constitutive Model With Strain Rate Effect of Rubber Material
,” Chin. J. High Press. Phys.
, 25
(5
), pp. 407
–415
. http://dx.doi.org/CNKI:SUN:GYWL.0.2011-05-00644.
Ma
, S.
, Huang
, G.
, Obaia
, K.
, Moon
, S. W.
, 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.
, 237
(1
), pp. 207
–223
. 45.
Ogden
, R. W.
, and Roxburgh
, D. G.
, 1999
, “A Pseudo–Elastic Model for the Mullins Effect in Filled Rubber
,” Proc. R. Soc. London. Ser. A Math. Phys. Eng. Sci.
, 455
(1988
), pp. 2861
–2877
. 46.
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
. 47.
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
. 48.
Wineman
, A.
, 2005
, “Some Results for Generalized Neo-Hookean Elastic Materials
,” Int. J. Non. Linear. Mech.
, 40
(2–3
), pp. 271
–279
. 49.
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
. 50.
Lei
, F.
, and Szeri
, A. Z.
, 2007
, “Inverse Analysis of Constitutive Models: Biological Soft Tissues
,” J. Biomech.
, 40
(4
), pp. 936
–940
. 51.
Li
, F.
, Liu
, J.
, Lu
, Y.
, Zhang
, L.
, and Yang
, H.
, 2017
, “Modeling on Constitutive Behaviors of Filled Rubber Compounds for Cyclic Loading Path
,” Chin. Rubber Ind.
, 64
, pp. 79
–83
. http://dx.doi.org/CNKI:SUN:XJGY.0.2017-02-00752.
Bergman
, T. L.
, Lavine
, A. S.
, Incropera
, F. P.
, and DeWitt
, D. P.
, 2011
, Introduction to Heat Transfer
, John Wiley & Sons
, Hoboken, NJ
.53.
Bengtson
, H. H.
, 2010
, “Convection Heat Transfer Coefficient Estimation
,” https://s3.amazonaws.com/suncam/docs/119.pdf, Accessed May 12, 2021.54.
Jiji
, L. M.
, 2009
, Heat Convection
, Springer Science & Business Media
, Berlin/Heidelberg, Germany
.55.
Cebeci
, T.
, and Bradshaw
, P.
, 2012
, Physical and Computational Aspects of Convective Heat Transfer
, Springer Science & Business Media
, Berlin/Heidelberg, Germany
.56.
Greenberg
, M. D.
, 2015
, Applications of Green’s Functions in Science and Engineering
, Courier Dover Publications
, Mineola, NY
.57.
Cole
, K.
, Beck
, J.
, Haji-Sheikh
, A.
, and Litkouhi
, B.
, 2010
, Heat Conduction Using Greens Functions
, CRC Press
, Boca Raton, FL
.58.
Duffy
, D. G.
, 2015
, Green’s Functions With Applications
, Chapman and Hall/CRC
, Boca Raton, FL
.59.
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, 2021.60.
Cheheb
, Z.
, Mousseau
, P.
, Sarda
, A.
, and Deterre
, R.
, 2012
, “Thermal Conductivity of Rubber Compounds Versus the State of Cure
,” Macromol. Mater. Eng.
, 297
(3
), pp. 228
–236
. 61.
Gschwandl
, M.
, Kerschbaumer
, R. C.
, Schrittesser
, B.
, Fuchs
, P. F.
, Stieger
, S.
, and Meinhart
, L.
, 2019
, “Thermal Conductivity Measurement of Industrial Rubber Compounds Using Laser Flash Analysis: Applicability, Comparison and Evaluation
,” AIP Conference Proceedings
, College Park, MD
, Feb. 5
, AIP Publishing LLC, p. 030041
.62.
MTS
, 2006
, “MTS 810 & 858 Material Testing Systems
,” https://rihof.org/wp-content/uploads/2019/11/MTS-810-Brochure.pdf, Accessed October 15, 2020.63.
Wang
, X.
, and Wang
, W.
, 2021
, “Numerical Simulation and Experimental Study on Dynamic Heat Build-Up of Rubber
,” ACTA Polym. Sin.
, 52
(7
), pp. 787
–795
.64.
FLIR
, 2018
, “FLIR Exx-Series Building Brochure
,” https://www.testequipmentdepot.com/flir/pdf/exx-series-building_brochure.pdf, Accessed July 10, 2021.65.
Ma
, S.
, Wu
, L.
, and Liu
, W. V.
, 2023
, “Numerical Investigation of Temperatures in Ultra-Large Off-the-Road Tires Under Operating Conditions at Mine Sites
,” ASME J. Therm. Sci. Eng. Appl.
, 15
(2
), p. 021010
. 66.
Ma
, S.
, Fan
, C.
, and Liu
, W. V.
, 2023
, “Effects of Site Operating Conditions on Real Site TKPH (Tonne-Kilometer-per-Hour) of Ultra-Large Off-the-Road Tires
,” Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
67.
Zhi
, J.
, Wang
, S.
, Zhang
, M.
, Wang
, H.
, Lu
, H.
, Lin
, W.
, Qiao
, C.
, Hu
, C.
, and Jia
, Y.
, 2019
, “Numerical Analysis of the Dependence of Rubber Hysteresis Loss and Heat Generation on Temperature and Frequency
,” Mech. Time-Dependent Mater.
, 23
(4
), pp. 427
–442
. 68.
Rodrigues
, M. K.
, da Silva Brum
, R.
, Vaz
, J.
, Rocha
, L. A. O.
, dos Santos
, E. D.
, and Isoldi
, L. A.
, 2015
, “Numerical Investigation About the Improvement of the Thermal Potential of an Earth-Air Heat Exchanger (EAHE) Employing the Constructal Design Method
,” Renewable Energy
, 80
, pp. 538
–551
. 69.
Tye-Gingras
, M.
, and Gosselin
, L.
, 2014
, “Generic Ground Response Functions for Ground Exchangers in the Presence of Groundwater Flow
,” Renewable Energy
, 72
, pp. 354
–366
. 70.
Su
, B.
, Wu
, J.
, Cui
, Z.
, and Wang
, Y.
, 2015
, “Modeling of Truck Tire Curing Process by an Experimental and Numerical Method
,” Iran. Polym. J.
, 24
(7
), pp. 583
–593
. 71.
Systèmes
, D.
, 2013
, “Abaqus 6.13 Documentation
,” Google Scholar, http://130.149.89.49:2080/v6.13/index.html, Accessed June 10, 2021.72.
Yu
, H.
, Cai
, C.
, Bobet
, A.
, Zhao
, X.
, and Yuan
, Y.
, 2019
, “Analytical Solution for Longitudinal Bending Stiffness of Shield Tunnels
,” Tunn. Undergr. Sp. Technol.
, 83
, pp. 27
–34
. 73.
Yu
, H.
, Zhang
, Z.
, Chen
, J.
, Bobet
, A.
, Zhao
, M.
, and Yuan
, Y.
, 2018
, “Analytical Solution for Longitudinal Seismic Response of Tunnel Liners With Sharp Stiffness Transition
,” Tunn. Undergr. Space Technol.
, 77
, pp. 103
–114
. 74.
Li
, F.
, Liu
, J.
, Yang
, H.
, Lu
, Y.
, and Zhang
, L.
, 2016
, “Numerical Simulation and Experimental Verification of Heat Build-Up for Rubber Compounds
,” Polymer (Guildf)
, 101
, pp. 199
–207
. 75.
Haghpanahi
, M.
, Salimi
, S.
, Bahemmat
, P.
, and Sima
, S.
, 2013
, “3-D Transient Analytical Solution Based on Green’s Function to Temperature Field in Friction Stir Welding
,” Appl. Math. Model.
, 37
(24
), pp. 9865
–9884
. 76.
ISO
, 2017
, ISO 37:2017 Rubber, Vulcanized or Thermoplastic—Determination of Tensile Stress-Strain Properties
, International Organization for Standardization
, Geneva, Switzerland
.77.
ISO
, 2017
, ISO 6943:2017 Rubber, Vulcanized—Determination of Tension Fatigue
, International Organization for Standardization
, Geneva, Switzerland
.78.
Bazkiaei
, A. K.
, Shirazi
, K. H.
, and Shishesaz
, M.
, 2021
, “Thermo-Hyper-Viscoelastic Analysis of a Rubber Cylinder Under Cyclic Deformation
,” J. Rubber Res.
, 24
(1
), pp. 13
–26
. 79.
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
. 80.
Van Blommestein
, W. B.
, 2016
, “Experimentally Determined Material Parameters for Temperature Prediction of an Automobile Tire Using Finite Element Analysis
,” Ph.D. thesis
, Stellenbosch University
, South Africa
.81.
Goyanes
, S.
, Lopez
, C. C.
, Rubiolo
, G. H.
, Quasso
, F.
, and Marzocca
, A. J.
, 2008
, “Thermal Properties in Cured Natural Rubber/Styrene Butadiene Rubber Blends
,” Eur. Polym. J.
, 44
(5
), pp. 1525
–1534
. 82.
Huang
, J.
, 2016
, “Study of Thermomechanical Coupling Issue of Radial Truck Tire
,” Ph.D. thesis
, Qingdao University of Science and Technology
, China
.83.
Mu
, Q.
, Feng
, S.
, and Diao
, G.
, 2007
, “Thermal Conductivity of Silicone Rubber Filled With ZnO
,” Polym. Compos.
, 28
(2
), pp. 125
–130
. 84.
Kerschbaumer
, R. C.
, Stieger
, S.
, Gschwandl
, M.
, Hutterer
, T.
, Fasching
, M.
, Lechner
, B.
, Meinhart
, L.
, Hildenbrandt
, J.
, Schrittesser
, B.
, and Fuchs
, P. F.
, 2019
, “Comparison of Steady-State and Transient Thermal Conductivity Testing Methods Using Different Industrial Rubber Compounds
,” Polym. Test.
, 80
, p. 106121
. 85.
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
.86.
Alberta Agriculture and Forestry
, 2018
, “Current and Historical Alberta Weather Station Data Viewer
,” https://acis.alberta.ca/weather-data-viewer.jsp, Accessed December 16, 2022.87.
He
, Y.
, 2005
, “Study of the Unsteady Temperature Field of Tire
,” Ph.D. thesis
, Huazhong University of Science and Technology
, China
.88.
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
. http://dx.doi.org/CNKI:SUN:LTGY.0.2006-06-00089.
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
. 90.
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
. 91.
Zhao
, Z.
, Wang
, Q.
, Li
, J.
, Li
, Y.
, and Chu
, L.
, 2001
, “Steady State Thermal Analysis on Temperature Field of Tire Based on Rolling Stat
,” Chin. J. Mech. Eng.
, 37
(5
), pp. 30
–34
. 92.
Smith
, R. E.
, Tang
, T.
, Johnson
, D.
, Ledbury
, E.
, Goddette
, T.
, and Felicelli
, S. D.
, 2012
, “Simulation of Thermal Signature of Tires and Tracks
,” Mississippi State University Mississippi State Center for Advanced Vehicular Systems
, MI
, Report No. 0704-0188..Copyright © 2023 by ASME
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