Numerical methods for contact between two joined quarter spaces and a rigid sphere

Abstract

a b s t r a c tQuarter space problems have many useful applications wherever an edge is involved, and solution to the related contact problem requires extension to the classical Hertz theory. However, theoretical exploration of such a problem is limited, due to the complexity of the involved boundary conditions. The present study proposes a novel numerical approach to compute the elastic field of two quarter spaces, joined so that their top surfaces occupy the same plane, and indented by a rigid sphere with friction. In view of the equivalent inclusion method, the joined quarter spaces may be converted to a homogeneous half space with properly established eigenstrains, which are analyzed by our recent half space-inclusion solution using a three-dimensional fast Fourier transform algorithm. Benchmarked with finite element analysis the present method of solution demonstrates both accuracy and efficiency. A number of interesting parametric studies are also provided to illustrate the effects of material combinations, contact location and friction coefficient showing the deviation of the solution from Hertz theory.

Contact Calculation for Rolling Bearings in Quarter-Spaces

“…5 is the same as that shown in Fig. 4 (b) in reference [8]. As the distance d increases, the pressure profile moves to the edge of quarter-space, and the maximum contact pressure decreases.…”

“…In order to verify the contact program, the same contact model as reference [8] is established. The radius of the sphere is equal to R. The applied load is equal to W. The distance d between the center of the sphere and the edge varies.…”

An Efficient Numerical Method With a Parallel Computational Strategy for Solving Arbitrarily Shaped Inclusions in Elastoplastic Contact Problems

“…By using the influence coefficients, a numerical implementation based on 3D-FFT could be employed to speed up the computation, and the elastic field caused by arbitrarily shaped inclusions calculated. This method has been successfully used to analyze the contact involving joined quarter spaces [18]. The analytical solutions of influence coefficients can bypass the additional complexity of surface domain truncation but requires more computational time than the Zhou et al [16] since four 3D-FFT schemes must be used.…”

Interfacial mechanics investigation of transmission components under non-Newtonian lubrication conditions

“…Literature Review 2011b) or a half-space (Zhou et al, 2011a;Zhou, 2012). Furthermore, Wang et al (2012) applied this approach to solve the contact between a sphere and two joined quarter spaces by treating one of them as an inclusion. Wang et al (2014a) investigated the contact between a flat-ended punch and a half-space embedded with inhomogeneities.…”