A method for improving the capability of convergence of numerical lubrication simulation by using the PID controller

Numerically simulating lubricated components is a basic analysis method in tribology. Such kind of simulation usually requires solving a closed equation system. Iterative algorithm has been used to numerically solve it for many years. The convergence of the corresponding solution procedures is achieved by adjusting some initial parameters to satisfy the pre-defined convergence criteria. There is very little discussion about the method used to adjust the initial parameters, however it directly influence the convergence of the whole simulation. In this paper, the analogy between the solution procedures and the feedback loop was discussed. And based on such analogy, the widely used proportional-integral-derivative controller (PID controller) in the control of the feed-back loop could be also used to make the solution procedures of lubrication simulation converge. The mixed point contact EHL problem, which is rather difficult to converge in lubrication simulation, was chosen as the example to prove the validity and efficiency of using PID controller in the solution procedures. The results show that the PID controller can be easily implemented and simplify the code. And it really accelerates the convergent speed of the simulation. In some working conditions, the traditional way cannot lead to satisfied results but the PID controller can make it. The most attractive advantage of using PID controller is that it can automatically converge the solution procedure, no extra modification is needed once the simulation starts.