The influence of surface roughness in elliptical contacts

The influence of surface roughness on contact behaviour is of great importance in many tribological situations. In the last decade several methods to calculate the pressure distribution and the real contact area in contacts between rough surfaces have been described. A problem arising for slender elliptical contacts, such as between gear teeth, roller and raceway, cam and follower, etc., is that the size of the contact is much greater than the size of the asperities. Accordingly the number of contact nodes necessary for an accurate solution to the problem becomes excessively large. This paper describes a method to calculate the influence of three-dimensional surface roughness in contacts that are very long in one direction. The method is based on restricting the calculations to a subpart of the real contact area, while the rest of the contact is taken into account by mirroring techniques. The results show that the real contact area is very sensitive to the amplitude of the roughness, while the waviness is less important. An equation is suggested from which the real area can be calculated if the smooth case contact parameters and two roughness parameters are known.