Research On Vibrational Behavior And Extended Characterizing Method Of High-speed Ball Bearing

High-frequency spindle is the key high-performance functional product in the field of numerical control tools.JB/T 10801-2007 points out that spindle vibration is measured under the working speed.However,in GB/T 24610-2019,the default rotational speed is1 800 r/min which is much lower than the working speed of the high-frequency spindle.The nonlinear characteristics of the bearing caused by rotational speed make the individual ball bearing vibration measuring and characterizing method at 1 800 r/min unable to fully adapt to and characterize the bearing state under high speed.Therefore,theoretical and experimental studies on the vibration characteristics of an individual ball bearing covering low,medium,and high-speed ranges,and studies of the influence of ball bearing on the vibration characteristics of spindle vibration measuring system are of great significance to promote the development of rolling bearing vibration measuring standard in the bearing industry.For an individual ball bearing vibration measuring,the vibration analysis model of an individual ball bearing includes the influence of the rotational speed,axial load,and support stiffness and mass eccentricity of the drive mandrel.Bearing quasi-static analysis method and Lagrange equation derive the two order nonlinear differential equations of the high-speed ball bearing.The influence of the waviness of the races and balls,the localized defect on the outer raceway,bearing lubricating oil film are considered into these equations.On the basis of the individual ball bearing vibration analysis model,the two order nonlinear differential equations of the high speed rotor-ball bearing-bearing pedestal system are derived by the finite element method and Lagrange equation.For determining the frequency band range of the waviness information in the frequency domain characterizing method,the studies of the bearing vibration frequencies caused by waviness order are developed firstly.Results show that there is a clear mathematical relationship between the waviness order and particular bearing vibration frequencies.The amplitude of these frequencies will be affected by rotational speed,bearing lubricating oil film,and eccentricity of the driving mandrel.Then,the influence of waviness parameters on the response amplitude and frequency distribution characteristics of response spectrum of high-speed ball bearing vibration is studied.Results show that the frequency band range that contains a large amplitude in the bearing vibration response spectrum is less affected by the waviness parameters,and that waviness amplitude has the most significant effect on the amplitude of this frequency band.For determining the total analysis frequency band range in the frequency domain characterizing method,the studies of the influence of the rotational speed on the vibration characteristics of the high-speed ball bearing are developed.Results reveal that the frequency band whose amplitude root mean square almost coincides with the full frequency band amplitude root mean square is within a fixed range.This frequency band determines the total analysis frequency bandwidth and it is not affected by the rotational speed,axial load,and bearing lubricating oil film.The impact signal can be caused by the localized defect.The center frequency of the optimal sub-signal frequency band containing the impact signal generated by the localized defect in the bearing vibration response has a piecewise linear relationship with the rotational speed.This frequency affects the total analysis frequency band bandwidth.For determining the speed of the rolling bearing vibration extended measuring,the relationship between the vibration characteristics of the individual ball bearing and high speed rotor-ball bearing-bearing pedestal system is analyzed.Results show that rotor and bearing pedestal's vibration frequencies caused by bearing waviness identify with that of the individual ball bearing;The center frequency position of the optimal sub-signal frequency band containing the impact signal in the vibration response of the bearing pedestal is consistent with that of an individual ball bearing;At low and high speeds,the width of the localized defect required to extract the impact characteristics from the bearing pedestal vibration acceleration response is much larger than that of the individual ball bearing.The studies of ball bearing vibration test method at low,medium and high speed are carried out at the rolling bearing high-speed vibration measuring bench.The results show that the non-contact vibration measuring at high speed avoids the influence of the high multiple rotational frequencies of the mandrel,and that non-contact vibration measuring has more advantages than contact vibration measuring in reflecting the vibration characteristics of the bearing itself.The results also verify that the proposed vibration analysis model of individual ball bearing and spindle vibration system are rational,and that theoretical results are correct.On the basis of GB/T 24610-2019,rolling bearing high-speed vibration characterizing method is extended.In the time domain characterizing method,dimensional parameters are more conducive to characterizing the positive relationship between waviness amplitude and bearing vibration response amplitude than nondimensional parameters;In the frequency domain characterizing method,in accordance with the mathematical relationship between the waviness and bearing vibration frequency and the characteristics of bearing vibration energy distribution,the frequency bands based on the multiples of the speed is newly divided.The new analysis frequency bands reduce and locate the frequency band range and location of abnormal bearing vibration levels,which is of great significance to the development of the evaluation system of bearing vibration.