Elasto-hydrodynamic lubrication: A non-linear complementarity problem

The classical problem of elasto-hydrodynamic lubrication of cylinders in line contact is formulated as a non-linear complementarity problem. A direct algorithm is applied to the approximation obtained by finite differences. Implementation considerations are emphasized. The new method provides reliable and automatic location of the previously troublesome lubricant free boundary. Numerical results reveal the qualitative behaviour of the pressure distribution and the lubricant film thickness under variation of key physical parameters.

[1]  D. Christopherson,et al.  A New Mathematical Method for the Solution of Film Lubrication Problems , 1941 .

[2]  D. Dowson,et al.  A Numerical Solution to the Elasto-Hydrodynamic Problem , 1959 .

[3]  A Direct Solution of the Elasto-Hydrodynamic Lubrication Problem , 1962 .

[4]  B. Sternlicht,et al.  A Numerical Solution for the Pressure, Temperature, and Film Thickness Between Two Infinitely Long, Lubricated Rolling and Sliding Cylinders, Under Heavy Loads , 1965 .

[5]  K. Herrebrugh,et al.  Solving the Incompressible and Isothermal Problem in Elastohydrodynamic Lubrication Through an Integral Equation , 1968 .

[6]  C. E. Lemke,et al.  Recent results in complementarity problems , 1970 .

[7]  C. Cryer.  The Solution of a Quadratic Programming Problem Using Systematic Overrelaxation , 1971 .

[8]  C. Cryer.  The method of Christopherson for solving free boundary problems for infinite journal bearings by means of finite differences , 1971 .

[9]  M. Z. Nashed,et al.  A nonlinear complementarity problem in mathematical programming in Banach space , 1972 .

[10]  C. Taylor,et al.  A Numerical Solution of the Elastohydrodynamic Lubrication Problem Using Finite Elements , 1972 .

[11]  A. Seireg,et al.  A Mathematical Programming Technique for the Evaluation of Load Distribution and Optimal Modifications for Gear Systems , 1973 .

[12]  K. P. Oh,et al.  A unified treatment of thick and thin film elastohydrodynamic problems by using higher order element methods , 1975, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[13]  M. Kostreva,et al.  On a Direct Algorithm for Nonlinear Complementarity Problems , 1978 .

[14]  Michael A. H. Dempster,et al.  Equivalence of Linear Complementarity Problems and Linear Programs in Vector Lattice Hilbert Spaces , 1980 .