FINITE ELEMENT ANALYSIS OF FRICTIONALLY EXCITED THERMOELASTIC INSTABILITY

Abstract

The frictional heat generated during braking causes thermoelastic distortion that modifies the contact pressure distribution. If the sliding speed is sufficiently high, this can lead to frictionalfy excited thermoelastic instability, characterized by major nonuniformi-ties in pressure and temperature. In automotive applications, a particular area of concern is the relation between thermoelasticalfy induced hot spots in the brake disks and noise and vibration in the brake system. The critical sliding speed can be found by examining the conditions under which a perturbation in the temperature and stress fields can grow in time. The growth has exponential character, and subject to certain restrictions, the growth rate b is found to be real. The critical speed then corresponds to a condition at which b = 0 and hence at which there is a steady-state solution involuing nonuniform contact pressure. We first treat the heat sources Q at the contact nodes as given and use standard finite element analysis (FEA) to determine the corresponding nodal contact forces P. The heat balance equation Q =fVP, where f is the coefficient of friction, then defines a linear eigenvalue problem for the critical speed V. The method is found to give good estimates for the critical speed in test cases with a relatively coarse mesh. It is generally better conditioned and more computationally efficient than a direct finite element simulation of the system in time. Results are presented for several examples related to automotive practice and show that theflexural rigidity of the friction pad assembly has a major effect on the critical speed.