Inverse approach for estimating pressure and viscosity in the elastohydrodynamic lubrication of circular contacts

Abstract

The film thickness under steady state conditions can be measured by using an optical interferometer. An inverse approach is proposed for estimating the pressure distribution on the basis of film thickness measurement in elastohydrodynamic lubrication (EHL) circular contacts. This approach is constructed from the approximated model of elastic deformation and force balance equations. To obtain an accurate pressure, it is necessary to divide the domain into a few regions on account of the singularity at the pressure spike. The principle of measuring point selection is proposed, and the problem of pressure fluctuation is overcome. On the basis of the smoothed pressure distribution, the apparent viscosity of the film can be obtained from the Reynolds equation. The least-squares method is used to compute the optimum value of the pressure-viscosity index. Results show that the best region for estimating the pressure-viscosity index is along the x axis because the Poiseuille term becomes zero in the Reynolds equation on account of the symmetry. In this region, the estimated pressure-viscosity index shows very good agreement with the exact value when measurement errors are neglected. When measurement errors are taken into account, the close agreement shows the potential of the proposed approach in estimating accurate values of the pressure-viscosity index. Generally, the error in estimating the pressure-viscosity index increases with increasing standard deviation of the measurement error, load, speed, material parameter and absolute error of the measured film thickness. The inverse approach can also be used to estimate the pressure distribution on a film thickness map obtained from an optical EHL tester. Moreover, the agreement between the actual and the estimated values of z is quite good.