Higher-Order Multilevel Solvers for the EHL Line and Point Contact Problem

[+] Author and Article Information
C. H. Venner

University of Twente, 7500 AE Enschede, The Netherlands

J. Tribol 116(4), 741-750 (Oct 01, 1994) (10 pages) doi:10.1115/1.2927328 History: Received January 29, 1993; Revised January 20, 1994; Online June 05, 2008


This paper addresses the development of efficient numerical solvers for EHL problems from a rather fundamental point of view. A work-accuracy exchange criterion is derived, that can be interpreted as setting a limit to the price paid in terms of computing time for a solution of a given accuracy. The criterion can serve as a guideline when reviewing or selecting a numerical solver and a discretization. Earlier developed multilevel solvers for the EHL line and circular contact problem are tested against this criterion. This test shows that, to satisfy the criterion a second-order accurate solver is needed for the point contact problem whereas the solver developed earlier used a first-order discretization. This situation arises more often in numerical analysis, i.e., a higher order discretization is desired when a lower order solver already exists. It is explained how in such a case the multigrid methodology provides an easy and straightforward way to obtain the desired higher order of approximation. This higher order is obtained at almost negligible extra work and without loss of stability. The approach was tested out by raising an existing first order multilevel solver for the EHL line contact problem to second order. Subsequently, it was used to obtain a second-order solver for the EHL circular contact problem. Results for both the line and circular contact problem are presented.

Copyright © 1994 by The American Society of Mechanical Engineers
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