Optimization of the tire ice traction using combined Levenberg–Marquardt (LM) algorithm and neural network

  • Jingwei GaoEmail author
  • Yuanchao Zhang
  • Yonghao Du
  • Qiao Li
Technical Paper


In order to overcome prediction defects of the current tire friction mechanism model on ice surface, this paper puts forward a tire–rubber–ice surface traction prediction model by integrating the Levenberg–Marquardt (LM) optimizing algorithm with the neural network. With 125 groups of experimental data of different influencing factors as training samples, the LM optimizing algorithm is adopted to optimize the network model thus built. Meanwhile, the trained model is tested and compared with the other algorithms. Results suggest that the tire friction coefficient on different ice surfaces obtained by the algorithm proposed in this paper is the closest to the practical value with its overall error below 0.1%. Thus, the algorithm put forward in this paper can be directly applied to efficiently and accurately predict the friction characteristics between the tire and the ice surface and lay a solid foundation for the study of cars driving on the ice surface at a high speed.


Tire Ice Friction coefficient LM optimizing algorithm Neural network 



This paper is sponsored by Chinese National Natural Science Foundation (No. 51605483), National Key Research and Development Program (No. 2017YFB1300900) and Science Foundation of National University of Defense Technology (No. ZK16-03-14, No. ZK17-03-02).


  1. 1.
    Sheng D, Feng S, Li H (2012) Research on effect of torque characteristic of friction lining limited slip differential on vehicle handling stability. Automob Technol 295(5553):336–338. CrossRefGoogle Scholar
  2. 2.
    Rosu I, Elias-Birembaux H, Lebon F (2016) Experimental and numerical simulation of the dynamic frictional contact between an aircraft tire rubber and a rough surface. Lubricants 4(3):29. CrossRefGoogle Scholar
  3. 3.
    Han K, Hwang Y, Lee E (2016) Robust estimation of maximum tire-road friction coefficient considering road surface irregularity. Int J Automot Technol 17(3):415–425. CrossRefGoogle Scholar
  4. 4.
    Anudeep K, Bhoopalam Corina Sandu, Taheri Saied (2015) Experimental investigation of pneumatic tire performance on ice: part 1—indoor study. J Terramech 60(2015):43–54. CrossRefGoogle Scholar
  5. 5.
    Anudeep K, Bhoopalam Corina Sandu, Taheri Saied (2015) Experimental investigation of pneumatic tire performance on ice: part 2—outdoor study. J Terramech 60(2015):55–62. CrossRefGoogle Scholar
  6. 6.
    Shimizu K, Ikeya C (1989) Indoor test of ice and snow tires on iced drum-development of tester and characteristics of coated ice for test. SAE technical paper 890004.
  7. 7.
    Nordström O (1993) The VTI flat bed tyre test facility—a new tool for testing commercial tyre characteristics. SAE technical paper 933006.
  8. 8.
    Peng X, Xie Y, Guo K (2000) A new method for determining tire traction on ice. SAE technical paper 2000-01-1640.
  9. 9.
    Sandu C, Taylor B, Biggans J, Ahmadian M (2008) Building an infrastructure for indoor terramechanics studies: the development of a Terramechanics Rig at Virginia Tech. In: Proceedings of the 16th international conference of the international society for terrain vehicle system (ISTVS), Turin, Italy, vol 30, p 9Google Scholar
  10. 10.
    Ripka S, Lind H, Wangenheim M, Wallaschek J, Wiese K, Wies B (2012) Investigation of friction mechanisms of siped tire tread blocks on snowy and icy surfaces. Tire Sci Technol 40(1):1–24. CrossRefGoogle Scholar
  11. 11.
    Hunter J (1993) Reconstructing collision involving ice and slippery surfaces. SAE technical paper 930896.
  12. 12.
    Coutermarsh B, Shoop S (2009) Tire slip-angle force measurements on winter surfaces. J Terramech 46(4):157–163. CrossRefGoogle Scholar
  13. 13.
    Bhoopalam Anudeep Kishore, Sandu Corina (2014) Review of the state of the art in experimental studies and mathematical modeling of tire performance on ice. J Terramech 53(2014):19–35. CrossRefGoogle Scholar
  14. 14.
    ASTM F1572-08. Standard test methods for tire performance testing on snow and ice surfaces.
  15. 15.
    ASTM F1572-08. Standard test methods for single wheel driving traction in a straight line on snow and ice-covered surfaces.
  16. 16.
    Pottinger M, McIntyre J, Kempainen A, Pelz W (2000)Truck tire force and moment in cornering—braking—driving on ice, snow, and dry surfaces. SAE technical paper 2000-01-3431.
  17. 17.
    Padmanaban S, Pawar PR (2015) Estimation of tire friction potential characteristics by slip based on-road test using WFT. SAE Tech Pap 64(8):947–957. CrossRefGoogle Scholar
  18. 18.
    Hayhoe GF, Sahpley CG (1989) Tire force generation on ice. SAE Tech Pap 890028:199–207. CrossRefGoogle Scholar
  19. 19.
    Klapproth C, Kessel TM, Wiese K (2016) An advanced viscous model for rubber–ice-friction. Tribol Int 99:169–181. CrossRefGoogle Scholar
  20. 20.
    Lahayne O, Pichler B, Reihsner R (2016) Rubber friction on ice: experiments and modeling. Tribol Lett 62(2):17. CrossRefGoogle Scholar
  21. 21.
    Bowden FP, Hughes TP (1939) The mechanism of sliding on ice and snow. Proc R Soc Lond Ser A Math Phys Sci 172:0280–0298. CrossRefGoogle Scholar
  22. 22.
    Grosch KA (1963) Relation between the friction and visco-elastic properties of rubber. Nature 197:858. CrossRefGoogle Scholar
  23. 23.
    Liu Xujun, Wang Haiqing, Xingyang Wu (2014) Effect of the rubber components on the mechanical properties and braking performance of organic friction materials. J Macromol Sci Part B 53(4):707–720. CrossRefGoogle Scholar
  24. 24.
    Ojala N, Valtonen K, Kivikytö-Reponen P (2015) High speed slurry-pot erosion wear testing with large abrasive particles. Tribol Finn J Tribol 33(1):36–44Google Scholar
  25. 25.
    Chiroma H, Abdulkareem S, Herawan T (2015) Evolutionary neural network model for West Texas intermediate crude oil price prediction. Appl Energy 142:266–273. CrossRefGoogle Scholar
  26. 26.
    Deo RC, Şahin M (2015) Application of the artificial neural network model for prediction of monthly standardized precipitation and evapotranspiration index using hydrometeorological parameters and climate indices in eastern Australia. Atmos Res S161–162:65–81. CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.College of Aerospace Science and EngineeringNational University of Defense TechnologyChangshaChina

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