Prediction of the Leakage Threshold for Hertzian Contact Seals: A Cellular Automata Model

The prediction and evaluation of leakage and leak tightness is an important issue in a multitude of high-pressure applications, such as valves, flanges or threaded connections. Through the use of finite element techniques it is in general possible to determine the local contact conditions at the seal on a macroscopic level (to wit the extent of the contact area and the contact pressure in this area). However, the leak tightness of a contact area depends also on the surface topology, which is a microscopic characteristic. Therefore the assessment of leak tightness requires an evaluation criterion relating both scales. Over the years a lot of empirical evaluation criteria have been developed, each with their own application domain. However, in terms of modelling the leakage a big step forwards was made only in the last decades. The Persson method models the contact area microscopically using contact models developed in the field of tribology. This contact evaluation is then combined with results from percolation theory, which state that for a sufficiently large contact area and a uniform contact pressure leakage will occur beyond a well-specified threshold. This has yielded a potent way of evaluating leakage, but the application is limited by the requirement that the contact pressure be uniform. In many applications, such as valves or O-ring seals, the contact is Hertzian and the contact pressure distribution is not uniform but parabolic. This paper will report the first results of an effort to extent such models to Hertzian contact seals. A set of samples for leakage experiments was produced with varying surface topology. The surface of these samples is measured and the leakage behaviour under high pressure is evaluated. At the same time a cellular automata model was built and used to model percolation under non-uniform contact pressures in an effort to adapt the Persson model. Finally the experiments and the modelling results are brought together via a finite element model and compared to each other. This paper will focus on the development of the cellular automata model and the obtained simulation results.