Thermo-mechanical investigation of a friction oscillator under high-frequency excitation

Abstract

The frictional behavior, temperature evolution, and system dynamics in tribological systems are closely coupled. However, in many cases, at least one of the mentioned phenomena is neglected or not modeled consistently. This paper presents a model of a thermo-mechanically coupled oscillator, where the reduction of friction force due to high-frequency excitation is analyzed. The oscillator’s equation of motion, the impulse balance, and the heat equation for the thermo-mechanical continuum are evaluated so that a set of nonlinear equations describes the coupled system. Using specific mathematical procedures like Laplace-transformation and a particular transformation ansatz for integral equations, the system can be transformed into a set of ordinary differential equations, enabling efficient simulation. Based on this equation set, an averaging method is applied to eliminate the fast time scale of the mechanical oscillation due to high-frequency excitation so that only the averaged influence of the motion goes into the heat evolution. This procedure leads to concise expressions to determine the stationary state of the system, and the quantities of interest can be calculated conveniently. These equations yield parameter combinations where the friction force can be reduced due to the high-frequency excitation, even though thermal expansion is considered. However, there are also parameter regions where the excitation yields a significantly larger friction force.