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Vibration Signature Analysis of High-Speed Unbalanced Rotors Supported by Rolling-Element Bearings due to Off-Sized Rolling Elements

In this paper an analytical model has been developed to investigate the nonlinear dynamic behavior of an unbalanced rotor-bearing system due to ball size variation of the rolling elements. Two cases of ball-size variation were considered: variations of 0.2 micron and 2 microns. In the analytical formulation, the contact between rolling elements and inner/outer races was considered a nonlinear spring, which became stiff using the Hertzian elastic deformation theory. A detailed contact-damping model reflecting the influences of the surface profiles and the speeds of both contacting elements was developed and applied in the rolling-element bearing model. The mathematical formulation accounted for the sources of nonlinearity, such as the Hertzian contact force, varying speed, and radial internal clearance. The equations of motion of a rolling-element bearing were formulated in generalized coordinates, using Lagrange’s equations that consider the vibration characteristics of the individual constituents, such as inner race, outer race, rolling elements, and shaft, in order to investigate the structural vibration of the bearing. All results have been presented in form of Fast Fourier Transformations (FFT) and Poincare maps. The highest radial vibrations due to ball-size variation were at a speed of the number of balls multiplied by the cage speed (ω = kωcage Hz). The other vibrations due to ball-size variation occurred at V C ± kωcage, where k was a constant. The current study provides a powerful tool for design and health monitoring of machine systems.