Stochastic analysis for in-plane dynamic responses of low-speed uniformity of tires due to geometric defects

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Tire uniformity is defined as the dynamic mechanical characteristics of pneumatic tires due to the defects originating in tire components during manufacturing processes. These defects lead to deviations in the structural and material parameters of tires and, in turn, induce variations in the dynamic response. In this scenario, this paper proposes a probabilistic model of the low-speed uniformity analysis for predicting the impacts of the uncertainties in the geometric defects and the vertical load on the dynamic responses. The deterministic coupled rigid–flexible ring model, combined with the generalized polynomial chaos expansion theory, is developed to simulate the radial force variation due to radial run-out. In this approach, the non-uniform tire radius and the vertical load are selected as a set of random variables and are approximated by the generalized polynomial chaos expansions. The distributions of these input variables are identified from 200 measured tires by the Pearson model. A non-intrusive probabilistic collocation method is adopted to evaluate the coefficients of the generalized polynomial chaos expansions, and the selection of collocation points is also illustrated. Finally, the distributions of the radial force variation and its first harmonic due to the geometric defects and vertical loads are predicted in comparison with measurements. Moreover, the distributions of the dynamic response caused by each parameter and different variance levels are discussed and verified by the measurement data from 1130 tires.

Original languageEnglish
Article number110377
JournalMechanical Systems and Signal Processing
StatePublished - 15 Aug 2023


  • Generalized polynomial chaos
  • Radial force variation
  • Tire ring model
  • Tire uniformity
  • Uncertainty quantification


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