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, 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 = ∞) for fH₁ < 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 fH₁ tending to infinity. However, it is found that in most practical cases of braking systems, V_cr ≪ V_M, and so the limiting conditions are reached at V_cr. At this speed, the amplification is typically not extremely high.