The application of asymptotic solutions to contact problems characterised by logarithmic singularities

We give the contact pressure distribution near a contacting wedge having a slightly rounded form adjacent to a discontinuity in surface profile. It is shown that, well away from the rounding the pressure is logarithmic in form, just as it is near the apex of a sharp wedge. This pair of solutions may then be used to ‘patch in’ a roundness correction relevant to any punch having a discontinuous gradient. Further, it is noted that the multiplier on the logarithm term is pre-determined by the change in gradient. This process is applied to a finite, slightly blunt wedge, where the exact answer is known, and to a wheel having a worn flat. The agreement with the exact solution in the former case is seen to be very good.