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1 International Journal of Applied Mechanics and Engineering

1 2008

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Stability analysis of ball bearings due to the effect of off-size balls

Purohit R. K., Purohit K.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 4

987-1002

In this paper, the radial vibrations of a rigid shaft supported by radial ball bearings is studied. The mathematical formulation takes into account the sources of nonlinearity such as the Hertzian contact force, ball waviness and ball size variation. The contacts between the balls and races are treated as nonlinear springs and the springs act only in compression to simulate the contact deformation and the resulting force. The nonlinear stiffness is obtained using the Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark-ß with Newton-Raphson method is used to solve the nonlinear differential equations iteratively. A computer program was developed to simulate the effect of ball size variation. Results presented in the form of Fast Fourier Transformation and Poincare maps agree with the results of various authors. All results show that the off sized balls in the bearing cause vibrations at the cage speed and its harmonics.