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.
Tartary buckwheat tea (TBT) is the most popular and widely consumed buckwheat product in many countries. However, the perfect quality control standards for TBT were still lacking, and the content of heavy metals in TBT and their health risks to consumers were still unknown. In this research, the total phenolic content, total flavonoid content, and antioxidant capacity as well as six metal contents and their health risks in TBT were detected. The results showed that the total phenolic content, total flavonoid content, and antioxidant capacity varied significantly among different types of TBT. Meanwhile, six metal concentrations in TBT leaves and infusions decreased in the order of Zn, Cu, Cr, Ni, Pb, and Cd. Health risk assessment indicated that the heavy metal intake only from TBT would not cause a noncarcinogenic risk to consumers. However, a strong carcinogenic risk of Cr in TBT for consumers should be paid more attention.
Classical Mahalanobis distance is used as a method of detecting outliers, and is affected by outliers. Some robust Mahalanobis distance is proposed via the fast MCD estimator. However, the bias of the MCD estimator increases significantly as the dimension increases. In this paper, we propose the improved Mahalanobis distance based on a more robust Rocke estimator under high-dimensional data. The results of numerical simulation and empirical analysis show that our proposed method can better detect the outliers in the data than the above two methods when there are outliers in the data and the dimensions of data are very high.
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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