Dynamic analysis of ball bearings with effect of preload and number of balls

In this paper, the radial and axial vibrations of rigid shaft supported ball bearings are studied. In the analytical formulation the contacts between the balls and the races are considered as nonlinear springs, whose stiffness are obtained by using the Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark- with Newton-Raphson method is used to solve the nonlinear differential equations iteratively. The effect on vibrations of varying preload and the number of balls in the bearings is investigated for prefect bearings. For perfect bearings, vibrations occur at the ball passage frequency. The amplitudes of these vibrations are shown to be considerably reduced if the preload and number of balls are correctly selected. All results are presented in the form of Fast Fourier Transformations (FFT).