Inverse approach for calculating temperature in EHL of line contacts

This paper proposes a thermal elastohydrodynamic lubrication (TEHL) inverse approach to estimate the pressure, temperature rise, and apparent viscosity distributions in an EHL line contact. Once the film shape is measured, the pressure and estimated film thickness distributions can be calculated from force balance and elastic deformation theories. By using these smoothing pressure and film thickness distributions, the Gauss–Seidel iteration is employed to calculate the temperature rise distribution from energy, surface temperature, and rheology equations. This approach overcomes the problems of pressure and temperature rise fluctuations, and generates accurate results of pressure and temperature rise distribution from a small number of measured points of film thickness, which also saves computing time. Results show that the direct inverse method requires a lot of measured points to establish the amplitude and location of the pressure and temperature rise spikes, whereas the inverse approach can obtain the accuracy results with only 31 measured points. With the error from the resolution in the film thickness measurements, this approach also presents a smooth curve of the pressure and temperature rise distributions with a small error. Furthermore, this approach still provides a good solution in apparent viscosity, whereas the direct method provides a much larger error in apparent viscosity.