A novel theoretical model of tire in-plane dynamics on uneven roads and its experimental validation

Zhe Liu, Feng Wang, Zhixing Cai, Yintao Wei, Steffen Marburg

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The dynamic response of tires directly affects the handling stability and ride comfort of a vehicle, which in turn determines the vehicle ride, handling, and driver perception. Modeling and simulation of tire dynamics typically require a reasonable computational cost while ensuring proper accuracy. In this study, a novel theoretical model, the coupled rigid–flexible ring model, is presented to analyze the characteristics of the in-plane dynamic responses of tires on uneven road surfaces. The proposed new method consists of three primary sub-models: an elastic contact algorithm featured by a flexible ring model, rolling/vibration dynamics represented by a rigid ring model, and an internal-force transmission algorithm linking the rigid and flexible ring models. In this way, the proposed new method has the merits of both high accuracy up to 150 Hz and low computing cost. A contact algorithm based on the two-dimensional flexible ring provides a pressure distribution on the tire–road contact patch and the length of the footprint under different vertical loads. The transient dynamic response is then estimated by combining the rigid ring model with the flexible ring model. The accuracy of the contact algorithm and the transient responses are validated against experimental radial stiffness and the over-cleat tests respectively. The results show that the in-plane dynamics of the tire can be predicted well. In addition, this model is extended to the analysis of the low-speed uniformity of tires with geometric defects and is validated experimentally. It indicates that the novel proposed model offers many application scenarios and extension possibilities.

Original languageEnglish
Article number109854
JournalMechanical Systems and Signal Processing
StatePublished - 1 Mar 2023


  • Contact algorithm
  • Low-speed uniformity test
  • Over-cleat
  • Tire model
  • Tire uniformity


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