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A dynamic model is developed to investigate vibrations o f high speed rolling ball bear ings with localized surface defects on raceways. In this model, each bearing component (i.e., inner raceway, outer raceway and rolling ball) has six degrees o f freedom (DOFs) to completely describe its dynamic characteristics in three-dimensional space. Gyro scopic moment, centrifugal force, lubrication traction!slip between bearing component are included owing to high speed effects. Moreover, local defects are modeled accurately and completely with consideration o f additional deflection due to material absence, changes o f Hertzian contact coefficient and changes o f contact force directions due to raceway curvature variations. The obtained equations o f motion are solved numerically using the fourth order Runge-Kutta-Fehlberg scheme with step-changing criterion. Vibration responses o f a defective bearing with localized surface defects are simulated and analyzed in both time domain and frequency domain, and the effectiveness o f fault feature extraction techniques is also discussed. An experiment is carried out on an aero space bearing test rig. By comparing the simulation results with experiments, it is con firmed that the proposed model is capable o f predicting vibration responses o f defective high speed rolling ball bearings effectively.

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Bearing defects are one of the most important mechanical sources for vibration and noise generation in machine tool spindles. In this study, an integrated finite element (FE) model is proposed to predict the vibration responses of a spindle bearing system with localized bearing defects and then the sensor placement for better detection of bearing faults is optimized. A nonlinear bearing model is developed based on Jones' bearing theory, while the drawbar, shaft and housing are modeled as Timoshenko's beam. The bearing model is then integrated into the FE model of drawbar/shaft/housing by assembling equations of motion. The Newmark time integration method is used to solve the vibration responses numerically. The FE model of the spindle-bearing system was verified by conducting dynamic tests. Then, the localized bearing defects were modeled and vibration responses generated by the outer ring defect were simulated as an illustration. The optimization scheme of the sensor placement was carried out on the test spindle. The results proved that, the optimal sensor placement depends on the vibration modes under different boundary conditions and the transfer path between the excitation and the response.

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