Discrete convolution and FFT method with summation of influence coefficients (DCS–FFT) for three-dimensional contact of inhomogeneous materials

Abstract

Certain contact problems must be treated as three-dimensional (3D) axial periodic problems, such as the contact of cylinders with rough surfaces and/or inhomogeneities in the materials, whose structural features in contact are confined in a finite domain in one direction but extended infinitely in the other direction. A novel numerical model for simulating the contact of machined cylindrical components containing inhomogeneities is developed via extending the concept of the 3D line-contact fast Fourier transform (FFT) algorithms. Due to the stochastic similarity of asperity and inhomogeneity distributions in the length direction, the cylinder is divided into N segments in the length direction while taking the roughness and inhomogeneities in one of these segments as representatives. The periodic convolution and FFT is used in the length direction, together with superposing the influence coefficients (ICs) of the N segments, while the discrete (circular) convolution and fast Fourier transformation (DC–FFT) is used in the non-periodic direction; this is named the DCS–FFT algorithm. The accuracy of the DCS–FFT algorithm is examined by the comparison of the numerical results for a degenerated cylindrical contact with the corresponding analytical solution, and its efficiency is evaluated through the comparison of its execution speed with that of two other FFT-based algorithms. The developed method is implemented to study the influence of inhomogeneities on subsurface stress distributions with/without the periodic length direction extension and superposition of inhomogeneity ICs. A criterion is provided to decide whether the DCS procedure is needed for the contact analysis of inhomogeneity-containing cylinders.