Asymptotic analysis, regularisation and stable numerical solutions for heavily loaded line EHL contacts: Part 1. Asymptotic and numerical analysis of isothermal problems

摘要

A stable numerical approach is developed for solution of problems for heavily loaded line EHL problems and the asymptotic equations of the problem in the inlet and exit contact zones. The numerical approach is based on two ideas: (ⅰ) It uses the form of the original and asymptotic EHL equations resolved for pressure involved in the equations for the gap between the lubricated solids; and (ⅱ) It uses regularisation based on an asymptotic solution of the non-isothermal EHL problem. That allows for a stable solution of the EHL problem even for extremely high dimensionless pressure viscosity coefficients ranging from 0 to 40. Therefore, the paper consists of three parts: (ⅰ) Part 1 is devoted to development of an asymptotic approach to solution of heavily loaded EHL contacts and to numerical solution of these equations. This part is very essential as it paves the way to the asymptotic analysis of non-isothermal EHL problem and, consequently, to construction of a stable regularised numerical algorithm; (ⅱ) Part 2 is devoted to asymptotic and numerical analysis of non-isothermal EHL problem for heavily loaded contacts; and (ⅲ) Part 3 is devoted to development of regularised stable numerical solutions of the asymptotic and original equations for heavily loaded EHL contacts.