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The objective of this study is to develop a mathematical model to aid in predicting the onset of instability in automotive disk brakes and clutches when using viscoelastic friction materials. The model is derived from and expands upon the fundamental of Burton’s model for thermoelasticity in pure elastic materials. In this investigation, three physical material parameters are considered: relaxation time, elasticity, and thermal conductivity. Prior to this parametric study, the effects of these material properties in relation to thermoelasticity were yet to be fully understood. Therefore, a finite element analysis is developed and used to validate the mathematical model by comparing the variation of the critical speed as a function of thermal conductivity. The results reveal that an increase in the relaxation time significantly reduces the critical sliding speed. Changing the elastic parameter further increases the effect of relaxation time by also reducing the critical sliding speed. However, increasing the thermal conductivity parameter dampens the effect of the elastic parameter and relaxation time on the critical speed. The study concludes there is a critical value of the relaxation time and elastic parameter above which the system stability is improved, meanwhile thermal conductivity attempts to counter the stability gained from other material properties. The study is instrumental in understanding the influence of viscoelastic parameters in sliding systems and provides an intuitive means of predicting the onset of thermomechanical instability.

Thermomechanical instability of viscoelastic friction materials in automotive disk clutches and brake pads