Comparison of FFT-MLMI for Elastic Deformation Calculations

Abstract

Numerical simulation of contact problems requires the calculation of the surface displacement of the contacting bodies. This is true for the lubricated contact, i.e., for elastohydrodynamic lubrication (EHL) as well as for the dry contact. The background of the method, the elastic theory, can be found in Johnson 4. In a wide range of tribological situations, the elastic-half plane assumption is valid. Consequently, the surface displacement can be written as an integral of the elastic kernel times the pressure function. Unfortunately, this equation does not have, in the real domain, an analytical solution under realistic conditions and thus numerical techniques have to be used. Note that the Integral Fourier Transformation (IFT) can be used to obtain an analytical solution in the frequency domain, see Ling 6, Westergaard 16, or Newland 9; the remaining problem is to obtain the analytical solution, through the reverse transformation, in the real domain. Note also that this integral can be regarded as a convolution product.