Extension of the multiphysical magic formula tire model for ride comfort applications

In the development of physical tire models, the complexity of the composite structure and the multiphysical variables require strongly nonlinear mathematical formulations to guarantee a desired degree of accuracy. The aim of the current work is to extend the applicability of the multiphysical magic formula-based tire model, already developed and presented by the authors, within a wider frequency range, interposing a rigid ring body between the contact patch and the wheel hub. The contact patch, varying in terms of size, shape, and relative position, is evaluated using instantaneous cams to define the effective plane. Here the advanced slip model, taking into account thermodynamic and wear effects, is then integrated. The adopted formulations have been mathematically and physically justified. They have been analytically compared to formulations related to the rigid-ring implementation available in the literature. Specific experimental activities concerning both the tire’s vertical kinematics and dynamics have been conducted to demonstrate the model’s improved physical consistency on small wavelength unevennesses.