Efficient Solution to the Cavitation Problem in Hydrodynamic Lubrication

Hydrodynamic lubrication is present in the majority of machinery where load is transmitted between two contacting surfaces in relative motion. Cavitation in liquid lubricating films is common and directly affects the pressure distribution and subsequently the load-carrying capacity and friction force transmitted across the contact. By reformulating the Elrod–Adams implementation of the Jakobsson–Floberg–Olsson cavitation conditions, we developed an efficient algorithm, called Fischer-Burmeister-Newton-Schur (FBNS), for calculating the pressure distribution that combines two attractive properties. First, the system of discretized equations arising from the reformulation is continuously differentiable and unconstrained, thus allowing for the use of gradient-based methods to solve it. Second, the computational cost of solving the system is similar to that when cavitation is not considered. With the new algorithm, the transient analysis and optimisation of contacts with complex shapes becomes computationally feasible. A comparison of the FBNS with the established algorithms and an application to the transient analysis of a hydrodynamic contact with surface texturing are reported. The results show that the FBNS yields roughly two orders of magnitude reduction in computational time when compared against other algorithms.