Tire Modeling by Finite Elements

Abstract

Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

An approach for large-scale gyroscopic eigenvalue problems with application to high-frequency response of rolling tires

“…Finite element simulations are well established in tire industries for the product development with special focus on stationary rolling properties [2,8,17,29]. For these stationary rolling analysis the relative kinematic Arbitrary Lagrangian Eulerian (ALE) description has been established, and the theoretical foundations are summarized in [19].…”

The simulation of in-plane tyre modal behaviour: a broad modal range comparison between analytical and discretised modelling approaches

“…A non-linear sidewall element is described in [35], while a model focused on the simulation of the contact is presented in [36]. A detailed discussion on discretized modelling approaches can be found in [37,38].…”

Dynamics and Stability of Rolling Viscoelastic Tires

“…Many previous works [22,4,24,26,19,12,20,27,14] use a change of variables X = R(t)X, where R(t) is the rotation matrix describing the rotation of the tire up to time t. The equations of motion are then reformulated with this change of variables, and the steady state solution to the spinning tire becomes a static problem, i.e. the transformed motion of the tire under this change of variables, φ, satisfies φ( X, t) = φ( X, 0) for all time.…”

“…We show below that z 0 satisfying ∂ t F(z 0 , 0) = 0 are steady state solutions. We follow a common approach in the literature for solving the steady state problem (see [4,24,26,19,12,20,27,14]) and introduce a new spatial variable X defined by…”

“…Due to the complex geometry involved, the finite element method is preferred. The problem is often formulated using a change of variables that allows a time-independent computation of the steady state stresses of the rolling tire [22,4,24,26,19,12,20,27,14]. This problem is well studied, but the literature only addresses tires with tread patterns that are invariant with the respect to rotation of the tire, while in practice, tread patterns are more complex.…”