Frictionally-excited thermoelastic contact of rough surfaces

Frictional sliding contact between two elastically similar half-planes, one of which has a sinuisoidally 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 deqends on the wavelength of the perturbation, and above which the perturbation itself grows arbitrarily with time. It is found that the TEI critical speed, V-cr, 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, V-cr is the speed for which the steady-state predicts infinite amplification. In all other cases, V-cr (appropriate to the wavelength of the profile) does not correspond to infinite amplification, nor to the maximum one, V-M. In the limiting case of thermoelastically similar materials, not only the system is unconditionally stable (V-cr = infinity) for fH(1) < 0.5, where f is the friction coefficient and H-1 a certain thermoelastic constant, but the regime at the maximum amplification is also always stable, and arbitrarily large amplification is obtained for fH(1) tending to infinity. However, it is found that in most practical cases of braking systems, V-cr much less than V-M, and so the limiting conditions are reached at V-cr. At this speed, the amplification is typically not extremely high. (C) 2000 Elsevier Science Ltd. All rights reserved.