First Order Tire Dynamics

Abstract

For the dynamic simulation of road vehicles, the model-element’ tire/road’ is of special importance, according to its influence on the achievable results. In the interest of a balanced modeling, the precision of the complete vehicle model should stand in reasonable relation to the performance of the applied tire model. Fully nonlinear and dynamic tire models are very complex, [3]. Usually, they are used to investigate and evaluate the stochastic vehicle vibrations occurring during rough road rides and causing strength-relevant component loads. Comparatively lean tire models, like TMeasy [1] or the Magic Formula [2], are based on an analytical approximation of steady-state characteristics. They are widely used with multi-body system programs to investigate the handling properties of vehicles. This handling tire models are characterized by an useful compromise between user-friendliness, model-complexity and efficiency in computation time on the one hand, and precision in representation on the other hand.

Within the handling tire models simplified transient tire properties are used to approximate the low frequency tire dynamics. Usually, the dynamic forces and torques are generated by first order differential equations driven by the steady state tire forces and torques. It is a common practice to derive the time constants from so called tire relaxations lengths. However, measurements [4] show that the relaxations lengths cannot be considered as constant but will strongly depend on the wheel load and the slip quantities.

In this paper a method is presented where the first order tire dynamics is generated by a Taylor- Expansion of the steady state forces and torques. Thus, relaxations lengths which include the wheel load and slip dependencies are automatically generated from the steady state tire properties. Slight model modifications make it possible to simulate stick slip effects during parking maneuvers. The results of this simple but effective approach correspond quite well with measurements.