Non-smooth models and simulation studies of the suspension system dynamics basing on piecewise linear luz(…) and tar(…) projections

Abstract

Strongly nonlinear phenomena are attributes of suspension system dynamics of vehicles operated at high dynamic loads and high speeds. The causes of these phenomena are backlasches and dry friction in the mechanisms, detachments of the wheel from the roadway, impacts on the bumper elements, etc. It is well known that modelling of strong nonlinear phenomena can be based on a piecewise linear approach. To simplify the mathematical description of such phenomena, Żardecki developed special luz(…) and tar(…) projections. These piecewise-linear projections have a surprisingly simple mathematical apparatus that enables analytical operations (eg. reductions) for differential and algebraic equations and inclusions with non-smooth nonlinearities, and simplifies numerical simulations. The application of this method to model and simulation studies of the dynamics of the car steering system (including freeplay and stick-slip processes) have been reported in several authorial articles. This article presents examples related to suspension system dynamics.