Sliding thermoelastodynamic instability

Abstract

Numerous mechanisms can give rise to instabilities and vibrations in sliding systems. These can generally be characterized as either elastodynamic (e.g. ‘brake squeal’) or thermoelastic. The time-scales of these processes differ considerably, so it is usual to neglect coupling between them, i.e. to neglect thermal effects in elastodynamic analyses and to use the quasi-static approximation in thermoelastic analyses. In the present paper, we consider the potential coupling between them in the simplest possible context—a thermoelastodynamic layer sliding against a rigid plane and constrained to one-dimensional displacements. The results show that although the coupling is extremely weak, it has a destabilizing effect on the natural elastodynamic vibration of the layer at arbitrarily low sliding speeds. A numerical solution of the transient equations below the quasi-static critical speed shows that an initial disturbance grows exponentially until periods of separation develop, after which the system approaches asymptotically to a steady state involving periods of contact and separation alternating at the lowest natural frequency of the elastodynamic system. With increasing sliding speed, the proportion of the cycle spent in contact is reduced and the maximum contact pressure increases. It is important to note that neither a quasi-static thermoelastic analysis, nor an elastodynamic analysis neglecting thermal expansion would predict instability in this speed range. Similar instabilities due to thermoelastodynamic coupling are almost certain to occur in more complex practical sliding systems such as brakes and clutches, implying the need for the incorporation of these effects in commercial analysis software. The proposed mechanism might also provide an explanation of reported experimental observations of vibrations normal to the contact interface during frictional sliding.