Non-smooth Problems in Vehicle Systems Dynamics

The vehicle systems are modelled mathematically as parameter dependent multi-body systems. The connections between the elements are formulated either as dynamical equations or algebraic, or transcendental or tabulated constraint relations. The connections can rarely be modelled by analytic functions, and the missing analyticity can arise from non-uniqueness or discontinuities in the functions themselves or in their derivatives of any order. In vehicle systems the contact between the vehicle and its support (road or rail) is an important source of missing analyticity. The suspension systems of the vehicles consist of passive and active elements such as springs, dampers and actuators, and their characteristics are only analytic functions within certain intervals of operation. Unilateral contacts in the suspension systems may give rise to changes of the degrees of freedom of the system during operation, and cause impacts or sliding contact during the operation. 1 General Vehicle Model Figure 1 shows a typical 4-axle railway passenger car. The car body rests on two 2-axle carriages called bogies (bougies) or in USA trucks. The entire suspension system is built into the bogies. Fig. 1 A railway passenger car with a car body on two bogies H. True (B) DTU Informatics, The Technical University of Denmark, Kgs.Lyngby, Denmark e-mail: ht@imm.dtu.dk P.G. Thomsen, H. True (eds.), Non-smooth Problems in Vehicle Systems Dynamics, DOI 10.1007/978-3-642-01356-0 1, C © Springer-Verlag Berlin Heidelberg 2010 3