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

Abstract

PurposeThe 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/approachOnce 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.FindingsThis 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/valueThe 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.