Effects of preload and number of balls on nonlinear dynamic behavior of ball bearing system

In this paper, the radial and axial vibrations of rigid shaft supported by ball bearings are analyzed. In analytical formulation, the contacts between the balls and races are considered as nonlinear springs, whose stiffness is obtained by using Hertzian elastic contact deformation theory. The governing differential equations of motion are obtained using Lagrange's equations. The implicit type numerical integration technique Newmark-beta with Newton-Raphson method is used to solve the nonlinear differential equations iteratively. The effects of two important parameters viz., preload and the number of balls are investigated in perfect bearings.