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# Elastohydrodynamic Analysis of Rolling Line Contact Using Boundary Element Method

## Citation

Onsa, Mahmoud Hassan (2001) Elastohydrodynamic Analysis of Rolling Line Contact Using Boundary Element Method. PhD thesis, Universiti Putra Malaysia.

## Abstract / Synopsis

This study aims at incorporating the use of the boundary element method (BEM) as an efficient and fast numerical method for the solution of the problem of the elastohydrodynamic (EHL) of hard rolling line contact. EHL of hard rolling is the dominant mode of lubrication in many critical, highly stressed machine elements such as gears, cams and followers, and bearings. The study of the stress concentration and deformation is important to predict the performance and the life expectancy against failures. These failures are manifested in wear, fatigue and scuffing. This fundamental study is based on isothermal, steady state, and smooth line contact EHL. The rolling of two cylindrical rollers was approximated by a roller and a plane. The hard rolling EHL relates to counter-formal contact elements made of high elastic modulus materials such as metals. The problem is to seek a solution, which reconciles the hydrodynamic equation represented by the Reynolds equation, and the elasticity equation while at the same time allowing for the variation of the lubricant properties with pressure. The resultant regime is highly non-linear. A hybrid solution is util ised to solve the elasticity problem using the BEM, and to solve the Reynolds equation for the pressure us ing the finite difference method (FDM) in a ful ly coupled solution. The BEM fundamental ly consists of the transformation of the partial differential equations, which describe the behaviour of the variables ins ide and on the boundary of the domain into integral equation relating to the boundary values, and the numerical solution of these equations. The boundary integral equation is formulated for the elasticity and solved using the BEM. The hydrodynam ic equation is solved using FDM. The coupled solution i s solved using Newton-Raphson iterative technique. The converged solut ion gives the pressure distibution and the l ubricant film thickness. The overa l l result of executi ng the hybrid BEM-FDM program gives a ful l agreement when compared to the program using FDM while resu lting i n reduction in the C PU time. The results also agree with other published numerical works. These veri fy the use of the developed method. To fu l ly uti l ize the advancement of the developed program, an extension of the models needs to include a non-Newtonian behaviour of l ubricant and the thermal effects.