More often than not, in studies involving dynamics and vibration of rotor systems, the bearings within a rotor system are treated as linear components. However, it is well understood that bearing systems are nonlinear due to both their geometrical properties and Hertzian contact between their components. This paper develops a linear formulation to approximate the vibration behavior of rolling bearings. A study of the approximation in the linear representation for rolling bearings is presented in which the effects of preload, lubricant viscosity and outer ring mass on the accuracy of the linear representation are determined.

The equations of motion governing the vibrations of rolling element bearing are found to be a set of second-order, nonlinear ordinary differential equations with position periodic coefficients. These equations are linearized about nominal values of the position vectors of the rolling element and the outer ring center. The linearized equations of motion are solved to obtain the small perturbations (displacements) from the nominal positions.

The results show that the linear model representation is applicable for bearings with preload. Existence of damping and/or greater outer ring mass enhance the approximation provided by the linear model. Most importantly, the linear representation provides a conservative estimate of the rolling element motion and very accurate estimate of the outer ring motion.

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