“…The ball-bearing contact trajectory has been presented as the all centre points of the Hertzian contact ellipse for the ball against both raceways during the movement, as illustrated in Figure 1. 26 Particularly, the contact trajectory for the race is more prominent than the ball. Figure 1.Contact wear for the ball bearing on both raceways: (a) for the outer race in the inertial system and (b) for the inner race in the body-fixed frame.…”
Section: Model and Methodsmentioning
confidence: 99%
“…These above transformation matrixes can be obtained by the three Euler angles technique given in literature. 20,26…”
Section: Model and Methodsmentioning
confidence: 99%
“…25 Xi et al. 26 recently developed dynamic contact trajectory for the ball bearing based on Gupta model, and running paths on both raceways for each ball against them are discussed in detail, but still requires further improvement for the practical application. The bearing failures and their causes given by the bearing manufacturer SKF 27 are mostly qualitative descriptions for path patterns under various conditions including the case of outer ring oval compression (can be considered as waviness order of 2).…”
A dynamic contact wear model of ball bearings consisting of wear degree and position distribution is proposed by integrating the developed contact wear model, multi-body dynamics and raceway waviness or ball diameter differences. Subsequently, the dynamic wear characteristics, not only for the ideal bearing under different axial and radial loads, but also for the bearing with above defects are analysed. The influences of load, typical waviness orders and amplitude on the wear of each ball against both raceways are evaluated and qualitatively validated. Finally, the dynamic characteristics of ball bearings with one ball larger are discussed, and then vibration frequency and wear rates distinction are verified by the experiment with working-surface roughness measurement as a way for wear rate assessment.
“…The ball-bearing contact trajectory has been presented as the all centre points of the Hertzian contact ellipse for the ball against both raceways during the movement, as illustrated in Figure 1. 26 Particularly, the contact trajectory for the race is more prominent than the ball. Figure 1.Contact wear for the ball bearing on both raceways: (a) for the outer race in the inertial system and (b) for the inner race in the body-fixed frame.…”
Section: Model and Methodsmentioning
confidence: 99%
“…These above transformation matrixes can be obtained by the three Euler angles technique given in literature. 20,26…”
Section: Model and Methodsmentioning
confidence: 99%
“…25 Xi et al. 26 recently developed dynamic contact trajectory for the ball bearing based on Gupta model, and running paths on both raceways for each ball against them are discussed in detail, but still requires further improvement for the practical application. The bearing failures and their causes given by the bearing manufacturer SKF 27 are mostly qualitative descriptions for path patterns under various conditions including the case of outer ring oval compression (can be considered as waviness order of 2).…”
A dynamic contact wear model of ball bearings consisting of wear degree and position distribution is proposed by integrating the developed contact wear model, multi-body dynamics and raceway waviness or ball diameter differences. Subsequently, the dynamic wear characteristics, not only for the ideal bearing under different axial and radial loads, but also for the bearing with above defects are analysed. The influences of load, typical waviness orders and amplitude on the wear of each ball against both raceways are evaluated and qualitatively validated. Finally, the dynamic characteristics of ball bearings with one ball larger are discussed, and then vibration frequency and wear rates distinction are verified by the experiment with working-surface roughness measurement as a way for wear rate assessment.
“…High-precision angular contact hybrid ceramic ball bearing is a typical rolling bearing, which is widely used in many rotating machinery, especially the electric spindles, because its dynamic contact capacity of each rolling body relative to the raceway can bear the radial and axial forces [1]. Therefore, the design and manufacturing level, assembly and service performance of the spindle bearings directly determine the machining capability of machine tool spindles.…”
High-precision spindle bearing is one of the most critical and vulnerable parts in a motorized spindle. Its unexpected failure may lead to production loss. Stochastic resonance (SR) is a weak signal detection method, which can obtain noise energy in strong background noise and enhance incipient fault characteristics of spindle bearing. Based on the fact that asymmetry can improve the enhancement ability of asymmetric bistable SR in weak feature extraction, we introduce an underdamped well-width asymmetric bistable SR (UABSR) method to the field of bearing fault diagnosis for the first time. However, the engineering application of UABSR can still be limited by two aspects. Firstly, the SNR index can take effect only when the actual fault frequency is obtained in advance, so the UABSR method is at high-cost in real practices. Secondly, an appropriate band-pass filter band range of the bearing faults can hardly be obtained due to the massive impulsive noise in operations. Here an improved UABSR method for spindle bearing fault diagnosis is proposed. Infogram method is used to process and analysis the original vibration signal for resisting the influence from the impulsive noise and obtaining more accurate frequency range of spindle bearing fault. In addition, time domain zero-crossing (TDZC) index, as the index of the improved UABSR method, can directly reflect the fault characteristics of spindle bearings without knowing the accurate fault characteristic frequency in advance. Besides, the Quantum Genetic Algorithms (QGAs) and the fourth-order Runge-Kutta algorithm are combined to simultaneously obtain the optimal system parameter, the asymmetric ratio, the damping factor and the rescaling factor of the improved UABSR model. Comparing the Infogram and original UABSR methods, the improved UABSR method performs better effect in incipient spindle bearing fault diagnosis. INDEX TERMS Spindle rolling bearing, fault diagnosis, underdamped asymmetric bistable stochastic resonance, vibration signal analysis, time domain zero-crossing index.
“…In this transfer process, the rolling elements are not equally loaded. This uneven load distribution is affected by the amplitude of the external load and the geometry of the rolling bearing [1] and plays a significant role on the operating characteristics of a bearing [2], such as the static carrying capacity [3,4], dynamic vibration [5][6][7][8], radial stiffness [5,[9][10][11][12] and fatigue life [1,3,[13][14][15]. To determine the radial load distribution, Stribeck [16] first derived an equation to calculate the maximum load on a rolling element of a ball bearing with zero radial clearance.…”
The radial load distribution integral is corrected for radial bearings. The error of Harris integral method for calculating the radial load distribution is analysed. The error is found absolutely caused by the inaccurate values of the radial load distribution integral given by Harris. Based on the extent of the load zone, the radial load distribution integral is corrected by three stages. The corrected radial load distribution integral is capable of calculating the load distribution of a bearing with a small load zone caused by a light external load or a great radial clearance. The corrected radial load distribution integral is found affected by the number of rolling elements. According to the variation of the number of rolling elements participating in the radial load transfer, the corrected radial load distribution integral can be divided into different phases. Some specific numerical examples are shown to illustrate the performance of the corrected radial load distribution integral. The comparison between the results obtained from the corrected radial load distribution integral and Harris integral shows the higher accuracy and superiority of the corrected radial load distribution integral.
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