Solving the Incompressible and Isothermal Problem in Elastohydrodynamic Lubrication Through an Integral Equation

Abstract

It will be shown that the hydrodynamic and elasticity equations in elastohydrodynamic lubrication can be coupled to one single integral equation of the following form: H(x) = f(x) − T ab K(x, ξ)F{H(ξ)}dξ in which f(x) and K(x, ξ) are both known analytic functions inside [a, b], and F(H) is in general a nonlinear function of the dimensionless film thickness. A numerical solution of this integral equation for constant viscosity is presented for a large range of loading conditions.