A new method for the analysis of deformation and load in a ball bearing with variable contact angle

The contact angle of a ball in a ball bearing is conventionally assumed to be a constant value in the mechanism analysis: in reality, this is not true. This assumption is made for the purpose of simplifying calculations, but the real elastic deformation produced at the position of each ball due to the acting force varying with the contact angle is unable to be considered. This study tries to establish a simple, three-dimensional expression for the elastic deformation at different position angles in terms of the geometry of the contact surface at the inner and outer races. Simply using the Newton method when the bearing deformations in the radial and axial directions are available can solve the contact angle as a function of position angle. Several characteristics arising from the variable contact angle will be discussed.