A new universal approximate model for conformal contact and non-conformal contact of spherical surfaces

Elastic spherical contact, especially conformal contact, is a widely encountered problem in mechanical design and wear analysis, but corresponding universal methods do not exist. A new approximate universal solution for the normal contact between frictionless spherical surfaces is established by combining analytical and numerical methods. The proposed model is not limited to an elastic half-space and can be universally used to calculate the pressure distribution of conformal and non-conformal contact. The validity and universality of the model were verified by a large number of three-dimensional finite element analyses of different materials and structures. With the new model, users can investigate the complex relationships between key parameters, such as maximum contact pressure, radius of contact region, normal load radii, and radial clearance, and apply this understanding in design and wear analysis of products with spherical contact surfaces, such as bearings.