Simulation of friction and wear using the method of dimensionality reduction

Tribology focuses on the study and application of friction, wear and lubrication of interacting surfaces. In the present work, three areas of tribological applications are studied: (a) elastomer friction, (b) mixed and boundary lubrication, and (c) fretting wear. In analyzing above problems, we make use of the Method of Dimensionality Reduction (MDR), which enables to essentially simplify the theoretical and numerical analysis of tribological problems by mapping three-dimensional problems to one-dimensional ones. (a) Elastomer friction. The friction between an elastomer and a hard rough substrate can be attributed to energy dissipation in the elastomer due to internal friction in the material. In the present work, the elastomer is modeled as a simple Kelvin body and the rigid surface as a plane or curved surface with a superimposed self-affine fractal roughness having a Hurst exponent in the range from 0 to 1. The resulting frictional force as a function of velocity always shows a typical structure: it first increases linearly, achieves a plateau and finally drops to another constant level. The coefficient of friction on the plateau depends only weakly on the normal force. At lower velocities, the coefficient of friction depends on two dimensionless combinations of normal force, sliding velocity, shear modulus, viscosity, rms roughness, rms surface gradient, the linear size of the system and its shape, as well as the Hurst exponent of roughness. The physical nature of different regions of the law of friction is discussed and an analytical relation is suggested to describe the coefficient of friction in a wide range of loading conditions. Based on the obtained analytical relations, a master curve procedure is suggested, allowing to “construct” the complete dependence of the coefficient of friction on velocity and normal force on the basis of partial empirical data. Furthermore, a study of the kinetics of the coefficient of friction of an elastomer due to abrupt changes of sliding velocity is presented. Numerical simulations reveal the same qualitative behavior which has been observed experimentally on different classes of materials: the coefficient of friction first jumps and then relaxes to a new stationary value. Parameters of the jump of the coefficient of friction and the relaxation time are determined as functions of material and loading parameters. Depending on velocity and the Hurst exponent, relaxation of friction with characteristic length or characteristic time is observed. (b) Mixed lubrication. A new model of mixed and boundary lubrication is proposed in the framework of the MDR. The dynamic lubricated rolling contact with creep between rough surfaces is simulated based on the equations of elastohydrodynamic lubrication (EHL). In order to account for the breakthrough of the boundary layer in micro contacts, an additional criterion is imposed. For comparison, a twin-disc test rig is set up to measure the electrical resistance between two lubricated rolling surfaces under different normal forces, rotation speeds and temperatures. We investigate the probability of IV Abstract boundary layer breakthrough for both experiment and simulation and find good agreement. (c) Fretting wear. We investigate fretting wear of rotationally symmetric profiles. Proceeding from the recently suggested exact method to simulate wear within the MDR ([1] Dimaki et. al., Int. J. of Solids and Structures, 2014), we suggest an even faster numerical method which speeds up the calculation of wear by further several orders of magnitude.