A theoretical study on the response of a point elasto-hydrodynamic lubrication contact to a normal harmonic vibration under thermal and non-Newtonian conditions

Abstract

Time-dependent thermal and non-Newtonian elastohydrodynamic lubrication of an elliptical point contact subjected to a normal harmonic vibration was studied numerically in this work. The contact was idealized as between an infinite plane and a spherical roller. The normal vibration of the roller was described by specifying the centre of the spherical roller to the infinite plane (without deformation) as a cyclic function of time. The shear-thinning rheological property of the lubricant was described by the Eyring model. The time-dependent numerical solution was achieved instant after instant in each period of a vibration. The periodic errors were checked at the end of each vibration cycle until the responses of variables such as pressure, film thickness, and temperature were all periodic functions with the same frequency of the roller's vibration. At each instant, the pressure field was solved with a multi-grid method, the surface deflection produced by pressure was determined with a multi-level multi-integration technique, the non-Newtonian flow of the lubricant was considered by using the equivalent viscosity calculated according to the shear-strain rate along the entrainment direction only, and the temperature field was evaluated with a finite-difference scheme through a column-by-column relaxation process. The computing time for a cyclic solution was 12–15 h on a personal computer with a 3.0 GHz central processing unit. The effects of both the amplitude and the frequency of the vibration were investigated. It was shown that the time-dependent solution is significantly different from the steady-state solution, especially when the amplitude of vibration is large and the frequency of vibration is high. Corresponding to a typical thermal and non-Newtonian case, numerical solutions were also obtained under isothermal and Newtonian, isothermal and non-Newtonian, and thermal and Newtonian conditions. Comparisons between these solutions indicate that, under time-dependent conditions, the effects of thermal and non-Newtonian flow are similar to those under steady-state conditions.