Nonsmooth model order reduction for transient tire–road dynamics of frictional contact with ALE formulations

Dynamic simulation of fictional contact between vehicle tires and road surfaces necessitates fine meshes both in spatial and temporal scales, leading to high computational costs. Herein, the method of nonsmooth model order reduction is proposed to predict efficiently the transient tire–road contact dynamics with friction. The Arbitrary Lagrangian–Eulerian description based on the absolute nodal coordinate formulation for modeling the tire motion and the nonsmooth approach based on the cone complementarity problem for computing the frictional contact are merged into the reduction process. These approaches ensure the prediction efficiency and accuracy of frictional contact dynamics of tires during transient events. Then, the linearization procedures based on the Craig-Bampton modal reduction are performed successively within the separated time intervals to reduce the nonlinear dynamics equations of the nonsmooth multibody system to the low-dimensional modal spaces. And the map between the modal coordinates from a prior time interval to a subsequent time interval is fulfilled via the velocity transformation at their shared time node. Finally, five numerical examples and an experiment are presented to verify the accuracy and efficacy of the nonsmooth ALE reduced-order models of cable or tire systems. The nonlinear dynamics with large rotations, large deformations and nonsmoothness can be analyzed accurately with the reduced-order models. And the proposed method achieves a 50% reduction of computation time for the simulation of a single tire and a 30% reduction of computation time for that of an entire car with four wheels while maintaining the same computational accuracy.