Frictionally-excited thermoelastic contact of rough surfaces

Frictional sliding contact between two elastically similar half-planes, one of which has a sinusoidally wavy surface, is studied in the full-contact regime. The steady-state regime is evaluated, within the limits imposed by the well-known phenomenon of thermo-elastic instability (TEI). TEI gives a critical speed whose value depends on the wavelength of the perturbation, and above which the perturbation itself grows arbitrarily with time. It is found that the TEI critical speed, Vcr, is clearly identified by the steady-state solution only in the special and limiting case when the flat half-plane is non-conductor; in that case, Vcr is the speed for which the steady-state predicts infinite amplification. In all other cases, Vcr (appropriate to the wavelength of the profile) does not correspond to infinite amplification, nor to the maximum one, VM. In the limiting case of thermoelastically similar materials, not only the system is unconditionally stable (Vcr=∞) for f H1<0.5, where f is the friction coefficient and H1 a certain thermoelastic constant, but the regime at the maximum amplification is also always stable, and arbitrarily large amplification is obtained for f H1 tending to infinity. However, it is found that in most practical cases of braking systems, Vcr⪡VM, and so the limiting conditions are reached at Vcr. At this speed, the amplification is typically not extremely high.