Non-smooth Models of Wheel-Road Interactions Based on Piecewise-Linear luz(…) and tar(…) Projections

Vehicle modeling is often practiced on the concept of partial models created independently to describe the dynamics of longitudinal movements (related to the drive and braking processes), the dynamics of lateral movements (related to the vehicle steering processes), the dynamics of vertical movements (related to the effects of road unevenness and suspension operation). The paper presents a set of three innovative non-smooth dynamical models describing the interaction of a pneumatic wheel with a road in terms of the longitudinal, lateral and vertical dynamics of the vehicle motion. They are based on a simple two-mass substitute physical model. The presented mathematical models use piecewise-linear luz(…) and tar(…) projections. Thanks to these projections and their mathematical apparatus, the developed models are useful for a simplified description and analysis of strong nonlinear non-smooth processes, including the most difficult ones related to wheel locking, sudden wheel slip, or wheel detachment from the road surface.