International Journal of Automotive Technology

, Volume 20, Issue 4, pp 801–812 | Cite as

Proper Radial Spokes of Non-Pneumatic Tire for Vertical Load Supporting by Finite Element Analysis

  • Ravivat Rugsaj
  • Chakrit SuvanjumratEmail author


This research aimed to develop the 3D finite element model of non-pneumatic tire (NPT) for designing the proper radial spoke. The NPT was cut using waterjet cutting technique to prepare the appropriate test specimens. The hyperelastic constitutive models were used to model the deformation behavior of these NPT components. The rebar elements were used to model steel belt layers of the non-pneumatic tire, while the tying equation was used to tie the degree of freedom between belt layers and rubber elements. The NPT model was assigned to contact the rigid surface at the load of 14, 16, 18, 20 and 22 kN. The deformation analysis result of NPT model was compared with the physical experiment which obtained the average error of 9.29 %. The vertical stiffness of the NPT model was 810.66 N/mm; therefore the error was 6.81 % when it was compared to the experimental result. The validated NPT model was then used to search for the proper spoke thickness. The spoke thickness of 5 mm was found to be the proper thickness which given the identical vertical stiffness as the pneumatic tire.

Key words

Finite element method Hyperelastic Non-pneumatic tire Vertical stiffness testing 


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This work was financial supported by Rubber Technology Research Center (RTEC), Mahidol University and the Thailand Research Fund (TRF) under the TRF Research Grant No. RDG60T0140.


  1. Bathe, K. J. (1997). Finite Element Procedures. Prentice Hall. London, UK.zbMATHGoogle Scholar
  2. Gasmi, A., Joseph, P. F., Rhyne, T. B. and Cron, S. M. (2012). Development of a two-dimensional model of a compliant non-pneumatic tire. Int. J. Solids and Structures 49, 13, 1723–1740.CrossRefGoogle Scholar
  3. Gent, A. N. and Watler, J. D. (2006). The Pneumatic Tire. National Highway Traffic Safety Administration. Washington DC, USA.Google Scholar
  4. Helnwein, P., Liu, C. H., Meschke, G. and Mang, H. A. (1993). A new 3-D finite element model for cord-reinforced rubber composites — Applications to analysis of automobile tires. Finite Elements in Analysis and Design 14, 1, 1–16.CrossRefzbMATHGoogle Scholar
  5. Ingrole, A., Hao, A. and Liang, R. (2017). Design and modeling of auxetic and hybrid honeycomb structures for in-plane property enhancement. Materials & Design, 117, 72–83.CrossRefGoogle Scholar
  6. Jang, I. G., Sung, Y. H., Yoo, E. J. and Kwak, B. M. (2012). Pattern design of a non-pneumatic tyre for stiffness using topology optimization. Engineering Optimization 44, 2, 119–131.CrossRefGoogle Scholar
  7. Jin, X., Hou, C., Fan, X., Sun, Y., Lu, J. and Lu, C. (2018). Investigation on the static and dynamic behaviors of non-pneumatic tires with honeycomb spokes. Composite Structures, 187, 27–35.CrossRefGoogle Scholar
  8. Ju, J., Kim, D.-M. and Kim, K. (2012). Flexible cellular solid spokes of a non-pneumatic tire. Composite Structures 94, 8, 2285–2295.CrossRefGoogle Scholar
  9. Ju, J., Veeramurthy, M., Summers, J. D. and Thompson, L. (2013). Rolling resistance of a nonpneumatic tire having a porous elastomer composite shear band. Tire Science and Technology 41, 3, 154–173.Google Scholar
  10. Kim, K., Heo, H., Uddin, M. S., Ju, J. and Kim, D.-M. (2015). Optimization of nonpneumatic tire with hexagonal lattice spokes for reducing rolling resistance. SAE Paper No. 2015-01-1515.Google Scholar
  11. Kumar, N. and Rao, V. V. (2016). Hyperelastic mooney-rivlin model: Determination and physical interpretation of material constants. MIT Int. J. Mechanical Engineering 6, 1, 43–46.Google Scholar
  12. MSC. Software Corporation (2010). Marc 2010 Volume A: Theory and User Information. User Guide.Google Scholar
  13. Rhyne, T. B. and Cron, S. M. (2006). Development of a non-pneumatic wheel. Tire Science and Technology 34, 3, 150–169.CrossRefGoogle Scholar
  14. Rhyne, T. B., Cron, S. M. and Pompier, J. P. (2006). Compliant Wheel. Patent No. US7013939.Google Scholar
  15. Veeramurthy, M., Ju, J., Thompson, L. L. and Summers, J. D. (2014). Optimisation of geometry and material properties of a non-pneumatic tyre for reducing rolling resistance. Int. J. Vehicle Design 66, 2, 193–216.CrossRefGoogle Scholar

Copyright information

© KSAE 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringMahidol UniversityNakhon PathomThailand
  2. 2.Laboratory of Computer Mechanics for Design (LCMD), Department of Mechanical Engineering, Faculty of EngineeringMahidol UniversityNakhon PathomThailand

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