The Numerical Solution of Dynamically Loaded Elastohydrodynamic Contact as a Nonlinear Complementarity Problem

Abstract

A numerical method has been developed for solving the nonlinear differential equation which arises in the elastohydrodynamic contact of bearing surfaces. This method is based upon the finite element approximation of the governing field equation, the Newton-Raphson algorithm for solving nonlinear systems, and the complementarity formulation of free-boundary problems. The lubricated contact between a sphere and a semi-infinite half-space under dynamic loading is analyzed as an illustrative problem.

Transient analysis of isothermal elastohydrodynamic circular point contacts

“…Furthermore, this paper provides solutions that conform well with the optical interferometric studies under oscillating conditions reported by Ren et al [15]. Even better agreement is obtained with the numerical results of Oh [16].…”

“…To obtain a veri®cation for the numerical method presented here for the ®rst time under non-steady conditions, a comparison is made between the present analysis and the ®ndings by Oh [16], who considered a sinusoidal variation in contact load according to the relationship WˆW 0 …1 ‡ e sin !t †, where the chosen value for e Oh's [16] ®nite element results serve a useful purpose for the comparison with the ®nite diVerence approach employed in this paper. The data for the analysis are provided in Table 2.…”

Transient effects in lubricated textured bearings

“…In particular a number of studies have formulated the cavitation problem in terms of variational inequalities [18][19][20][21], while a parallel group of studies focused on the use of complementarity [22][23][24][25]. In these studies the problem of determining the cavitated area was solved using complementarity; however, these methods do not inherently ensure the conservation of mass.…”

Transient analysis of isothermal elastohydrodynamic circular point contacts

“…The agreement between the various numerical techniques is highlighted later by a comparison between the method employed here and that reported by Oh [16], using ®nite element analysis. Figure 5 shows the corresponding central pressure pro®les in the direction of entraining motion for the various ®lm thickness pro®les shown in Fig.…”

“…Close agreement is observed for most of the load cycle. A small divergence is observed between the two sets of results around the maximum load region of the cycle, probably owing to the relatively coarse ®nite element mesh employed by Oh [16].…”