Inverse approach for calculating pressure and viscosity in pure squeeze EHL motion of circular contacts

The inverse approach is proposed to the pure squeeze EHL motion of circular contact problems, where the pressure is approximated by polynomial form in terms of the radial coordinate and time to provide a smoothing algorithm in calculating pressure from the elasticity equation. The least-squares method is used to calculate the optimum value of the pressure–viscosity index from the transient Reynolds equation. Results show that the estimated pressure can be obtained accurately with a few measuring film thickness points, but it is hard to obtain the correct viscosity for the direct inverse method. By using the inverse approach, even though the measurement error in the film thickness is present, the fluctuations in the pressure can be overcome, and it predicts the pressure–viscosity index with very good accuracy. The post-impact high-pressure condition for the constant load case is suitable to evaluate the pressure–viscosity index in a wide range along the radial axis with very good accuracy. Subsequently the inverse approach is successfully used to estimate the pressure distribution resulting from the film thickness map from the interferometry measurements. The agreement between the actual value of the test fluid and the estimated value is quite good.