Inverse approach for the pressure, temperature, and pressure-viscosity index determination in TEHL of line contacts

Purpose ‐ The purpose of this paper is to describe an inverse approach to estimate the pressure distribution, temperature distribution, and pressure-viscosity index (z) in a thermal elastohydrodynamic lubrication (TEHL) line contact. Design/methodology/approach ‐ Once the film thickness is given, the pressure distribution can be calculated using the inverse approach. Subsequently, thermal expansivity and temperature-viscosity coefficient of lubricant are given, and then the z is guessed initially. The Gauss-Seidel iteration is employed to calculate the temperature distribution from the rheology, energy, and surface temperature equations. In order to increase the algorithm stability, the least-squares method must be employed to calculate the optimum value of the z in the computational domain. Furthermore, the pressure-viscosity index must be updated by the iteration method to calculate accurate temperature distribution and apparent viscosity until convergence. Findings ‐ This approach presents a smooth curve of the pressure and temperature distributions with the measurement error from the resolution in the film thickness measurement and z value. Furthermore, this approach still provides a superior solution in apparent viscosity, whereas the direct method provides a much larger error in apparent viscosity. Originality/value ‐ The paper describes an inverse approach to estimate the pressure distribution, temperature distribution, and pressure-viscosity index in a TEHL line contact. This approach overcomes the problems of pressure and temperature rise fluctuations and generates accurate results of pressure and temperature distribution from a small number of measured points of film thickness, which also saves computing time. Furthermore, this approach still provides a superior solution in apparent viscosity.