Multiscale modeling of rubber hysteretic friction on rough rigid surfaces

Abstract

The performance of car tires on road tracks is strongly affected by hysteretic friction. In order to optimize driving characteristics, like minimizing fuel consumption, improving skid resistance, increasing tire durability, and increasing vehicle controllability during steering and braking, the rolling friction coefficient should be predicted properly. The accurate and efficient modeling and prediction of the hysteretic friction is still a challenge. In the past decade, two different modeling frameworks have attracted significant attention. They are the viscoelastic half-space (VHS)-based contact mechanics model, based on linear kinematics and implemented with the boundary element method (BEM), and the viscoelastic contact model in the finite deformation framework implemented with the finite element method (FEM). The first one has the ability to model all involved length scales at once with a reduced computational cost under the assumption of a flat geometry of the rough surface and small deformations. The second one does not have these limitations and is able to predict the friction coefficient accurately in the finite deformation framework, but at much higher computational cost. It is not able to investigate all involved length scales at once since it needs an extremely fine mesh refinement, which leads to an impractically slow simulation. This work has two major aims. The first goal is to study the accuracy of geometrical and rheological linearity assumptions in evaluation of rolling friction coefficient. This is done by comparing the simulation results of tire tread block in contact with a sinusoidal road track surface using the linear VHS-based model and the finite deformation model in terms of rolling friction coefficient, contact area, and pressure distributions. It has been found that accurate rolling friction predictions can be obtained through the linear VHS-based model within Reynolds assumption for moderate values of root mean square slopes, whereas finite deformation computations should be adopted for large root mean square slopes. The contact area is much more sensitive to the geometrical and rheological nonlinearities than the rolling friction coefficient. The second goal of the thesis is to establish a new hybrid (nonlinear FEM/linear BEM) multiscale method which combines the advantages of both methods. The presented hybrid multiscale approach has proven to be a suitable tool to study rolling-friction coefficient within a plausible degree of accuracy for relative large contact area and low sliding velocities. It allows a more faster calculation of friction coefficient than the finite deformation model.