Stochastic analysis for simple and computationally efficient models for tire non-uniformity investigation

The aim of this work is to propose, using a probabilistic approach, an uncertainty model to predict the influence of the tire parameters variability (stiffness and density variations due to non-uniformity) upon its dynamic response to a rotating force. Non-uniformity in tires can be described as imperfections that can be originated either in the elements that compose the tire or in the manufacturing process. A circular ring model using Euler-Bernoulli circular beam spectral elements is submitted to a rotating force simulating the one generated by the rolling movement. It is numerically created in the model as a triangular pulse applied out-of-phase at the different nodes of the ring. This deterministic model is an efficient way to compute the hub forces considering the non-uniformity and using a stochastic approach. In this approach, the non-uniformity is concentrated and modeled trough distinct radial stiffness and mass density, which are considered uncertain. This dynamic model is used to analyze comfort criteria based on the radial component of the resultant hub force. In order to assess the validity of the proposed modeling, a Maximum Likelihood Estimator (MLE) is used to verify if one can fit the same probability distribution for both experimentally and numerically obtained for a given the comfort criterion. Finally, a reliability analysis is performed comparing numerical with experimental results.