A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed.

Contact mechanics of rough surfaces in tribology: multiple asperity contact

A method is described to determine contact stresses and deformation using a combination of the finite element method and a surface integral form of the Bousinesq solution. Numerical examples of contacting hypoid gears are presented.

A combined surface integral and finite element solution for a three‐dimensional contact problem

A new numerical method for the analysis of elastic and elastic-plastic contacts of two rough surfaces has been developed. The method is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. The present variational approach guarantees the uniqueness of the solution of the contact problem and significantly reduces the computation time as compared with the conventional matrix inversion method, and thus, makes it feasible to solve 3-D contact problem with large number of contact points. The model is extended to elastic-perfectly plastic contacts. The model is used to predict contact statistics for computer generated surfaces.

A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle

This paper present a micro-contact model incorporating asperity interactions in elastic-plastic contact of rough surfaces. The effect of the asperity interactions on the local deformation behavior of a given micro-contact is first modeled based on the Saint-Venant's Principle and Love's Formula. The local contact interference is related in closed form to the local contact load, the global mean pressure and material parameters. This micro-contact model equation is then integrated into the elastic-plastic contact model developed in Zhao et al. (2000) to allow the asperity interactions and plastic deformation to be considered simultaneously. The effects of the asperity interactions on the mean surface separation, the real area of contact and the redistribution of the contact load among contacting asperities of different heights are studied. The results show that the asperity interactions can significantly affect the mean surface separation and microcontact load redistribution. The results also reveal that the effect of asperity interactions can be largely cancelled out by the effect of asperity plastic deformation.

A model of asperity interactions in elastic-plastic contact of rough surfaces

A computer program is developed to analyze the contact of a rigid smooth plane and computer-simulated elastic rough surfaces. The simulated surfaces have isotropic Gaussian height distribution and bilinear autocorrelation function. Results of two cases are presented: (1) dry contact between a square elastic rough punch and a rigid smooth plane; (2) dry contact between an elastic rough half-space and a rigid smooth plane. Force-compliance relationship is compared with hat derived by Bush, Gibson, and Thomas. Real contact area ratio Ar is found to be approximately proportional to nominal contact pressure in the range 0.025 < Ar < 0.3. Presented at the 39th Annual Meeting in Chicago, Illinois May 7—10, 1984

W. T. Lai

Papers

Computer Simulation of Elastic Rough Contacts