Inverse approach for calculating pressure and viscosity in elastohydrodynamic lubrication of line contacts

Abstract

This paper proposes an inverse approach which generates a smoothed pressure distribution based upon a small number of measuring points of the film thickness and overcomes the problems of pressure fluctuations. The Reynolds equation of line contacts is then employed to determine the value of the pressure–viscosity index. To investigate the sensitivity of the results to measurement errors, different errors are deliberately implemented in the numerical calculations. Results show that the traditional direct inverse method requires many measuring points of film thickness to establish the amplitude and location of the pressure spike, but the inverse approach can obtain accurate results using just 29 measuring points. When errors in the film thickness measurements, it is found that the inverse approach still yields a reasonably smooth curve for the pressure profile. When film thickness measurement errors are excluded, the proposed approach is very close to the exact value of the pressure–viscosity index. Even when errors in the film thickness are deliberately introduced, the inverse approach still provides a satisfactory value of the pressure–viscosity index. The resulting apparent viscosity errors are much smaller than those generated when using the direct method. The implemented errors in load and effective elastic modulus have a significant effect on the accuracy of the results, but that the influence of errors in average velocity and in the viscosity at ambient pressure is insignificant. In these implemented errors, the resolution of the film thickness measurement plays the most important role in determining the accuracy of the apparent viscosity.