This paper proposes a model of concentrated parameters for a rolling bearing operating in dynamic conditions with and without localized defect. The rolling bearing is modeled as a Z + 2 df degree of freedom (DOF) system, where Z is the number of rolling elements. The radial displacement of these rolling elements is considered in this model. In the analytical formulation, the contact force between the balls and races is considered as non-linear spring-dampers, whose stiffnesses are obtained applying Hertzian elastic contact deformation theory. The equations of motion are formulated using Lagrange's equation, considering the characteristics of the individual components of a rolling bearing, such as rotor, rolling elements, and inner and outer race. The Runge-Kutta method is used to solve the non-linear differential equations of motion. The simulation is accomplished by MATLAB and SIMULINK. To validate the simulated model, we have designed a testbed to carry out. The frequency components of the signal generated by the model in simulation and the experimentally obtained signal are compared. The results achieved experimentally demonstrate the validity of the mathematical model presented here. The model provides a powerful tool to predict the satisfactory behavior of this system.
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