An analytical model is developed for studying in-plane structural vibrations in rolling element bearings. A lumped parameter approach is employed in developing the model. The mass and moment of inertia of the components comprising the bearing are lumped at their respective centers of mass. The localized stiffnesses due to contact deformation phenomenon are treated as nonlinear springs. The variable spring rates are obtained by application of Hertz equation for elastic contact deformation.
Effects of preload, ball rotational speed, and damping are studied using the formulation. An interesting observation is made as to the influence of preload. It is found that in the presence of preload, irrespective of the load magnitude, contact is maintained with both the inner and the outer races. Hence, responses obtained with and without the check for ball/inner race and ball/outer race interferences are identical. In addition, no appreciable change is observed in the responses when the preload value is varied from 10 N to 1N. At high speed of operation, the balls are found to maintain contact with the outer ring, whereas intermittent contact with the inner ring occurs for brief periods of time. Introduction of lubricant is found to dampen the oscillations considerably.