To study the vibration mechanism of ball bearings with localized defects, a vibration model of a ball bearing based on the Hertzian contact stress distribution is proposed to predict the contact force and vibration response caused by a localized defect. The calculation of the ball-raceway contact force when the ball passes over the defect is key to establishing a defect vibration model. Hertzian contact theory indicates that the contact area between the ball and the raceway is an elliptical contact surface; therefore, a new approach is used to calculate the ball-raceway contact force in the defect area based on the stress distribution and the contact area. The relative motion between the inner ring, the outer ring, and the balls is considered in the proposed model, and the Runge-Kutta algorithm is used to solve the vibration equations. In addition, vibration experiments of a bearing with an outer ring defect under different loads are performed. The numerical signals and experimental signals are compared in the time and frequency domains, and good correspondence between the numerical and experimental results is observed. Comparisons between the traditional model and the proposed model reveal that the proposed model provides more reasonable results.

The gearbox is an important component in industrial drives, providing safe and reliable operation for industrial production. Wavelet packet transform (WPT) analysis was used to extract fault features in the vibration signals generated by a gearbox. The extracted features from the WPT were used as input in a rough set (RS) for attribute reduction and then combined with a genetic algorithm to obtain global optimal attribute reduction results. The fault features gained after the attribute reductions were used to generate decision rules. The unknown gear status signal attributes were used as input to match the generated decision rules for fault diagnosis purposes. Gearbox vibration signals contain a significant amount of gear status information; a WPT has an acute portion-locked ability to extract attribute information from the vibration signals. However, WPT frequency aliasing would lead to the generation of spurious frequency components, affecting gear fault diagnosis. In this paper, we introduce an improved WPT to eliminate frequency aliasing, thus improving the accuracy of fault diagnosis. This paper studies the use of wavelet packet for feature extraction and the RS for classification; the results demonstrate that this method can accurately and reliably detect failure modes in a gearbox.

This article presents a dynamic model of ball bearings with a localised defect on the outer raceway to analyse the effect of damping variation on the vibration response of defective bearings. First, a dynamic model is built based on the Hertzian contact theory, the interaction between the bearing inner ring, outer ring, and rolling element; the effect of damping and stiffness is considered; and the vibration equation of the bearing system is solved by the fourth-order Runge-Kutta algorithm. Then, the damping ratios of the experimental bearings using different types of viscosity lubricating grease are measured and compared with the damping ratios of the dynamic model; in addition, the viscous damping coefficient of the experimental bearings are calculated. Finally, the numerical analysis and experimental results show that the grease with a different level of viscosity affects the vibration signal of the defective bearing.

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