球轴承振动的研究
摘要
根据球轴承的结构特点，从摩擦动力学观点出发，运用摩擦学和结构动力学的知识，在分析钢球—滚道接触副的载荷—变形特性和接触动力学特性的基础上，建立了润滑接触条件下同时考虑EHL卷吸和挤压运动的球轴承振动理论模型和运动微分方程，分析了几何参数，结构参数和工况条件对球轴承振动特性的影响，以钢球和滚道的表面波纹度为例，讨论了不同激励作用下球轴承振动的计算方法。建立了基于微机的数字化球轴承振动测量系统，设计和制作了专门的试验球轴承，以创新的固定式加速度计安装方式实现了球轴承振动真实信号的测量，通过试验验证了球轴承振动的理论模型，试验研究了包括润滑在内的摩擦学因素对球轴承振动特性的影响。球轴承振动信号的分析中，以基于时间序列的AR模型分析了正常的球轴承振动信号，以小波包变换分析了球轴承的异音，为球轴承的振动分析建立了简便可靠的分析技术。
理论分析和试验研究表明：
1)球轴承振动是钢球—滚道接触副中的各种摩擦学作用引起的，具有摩擦动力学的本质，任何对接触副的摩擦学特性有影响的因素都将对球轴承的振动和噪声特性产生影响；
2)中心轴向载荷作用下，载荷增大使球轴承的固有振动频率升高，载荷越大同样的载荷增幅引起的频率升幅减小，足够大的中心轴向载荷作用下载荷的变化对球轴承振动的频率特性不会产生明显的影响；
3)轴向和径向联合载荷作用下，径向载荷不大时球轴承振动的固有频率基本不变，但是可能引起变刚度激励的非线性振动，出现新的频峰，过大的径向载荷将使部分钢球脱离接触，使球轴承的振动和噪声呈现不稳定状态；
4)润滑对球轴承的振动和噪声特性有重要的影响，良好的润滑对振动有明显的抑制作用，润滑不充分时，振动和噪声的水平会有明显增高，一定条件下还会激发接触副中的谐振，发出啸声，造成接触表面的伤害，无润滑干接触时，短时的运转就会损伤接触副表面，使振动和噪声迅速增大，并随时可能引发严重的磨损和卡滞失效；
接触副润滑良好时，油膜的“刚化效应”使球轴承振动的固有频率有所提高，润滑剂中含有弥散性污浊时，振动的幅度总体升高，但弥散性污浊不会改变球轴承振动的频率特性；
浙江大学博士学位论文:球轴承振动的研究
5)低速时，球轴承振动的基本特征呈现不稳定状态，随着转速的提高，球轴
承振动的频率特性趋于稳定，固有频率频峰升高;
6)理论分析表明，干接触时钢球和滚道表面波纹度的某些谐波分量能激励球
轴承的振动，振动的幅值与谐波幅值成正比，实际球轴承中钢球的分布不可能完全
均匀，波纹度的激励作用会随时发生;润滑接触的分析表明，波纹度的任意谐波分
量均能激励球轴承的振动;
7)球轴承的几何和结构参数分析表明，球轴承尺寸越大，径向、轴向和角振
动的固有频率越低;钢球中心圆直径增大，球轴承的径向和轴向振动的固有频率基
本不变，角振动的固有频率有所上升，振动的幅频特性基本不变;径向游隙加大使
球轴承的径向振动固有频率降低，轴向和角振动的固有频率有所升高，径向振动幅
频特性的幅值升高，而轴向和角向降低;钢球的数量增多使球轴承振动的固有频率
上升，幅频特性的幅值下降，径向振动的幅值下降最为明显;外圈沟曲率半径系数
增大使球轴承径向振动的固有频率升高，轴向和角振动的固有频率降低，径向幅频
特性基本不变，轴向和角向幅频特性幅值升高;内圈沟曲率半径系数增大使径向、
轴向和角振动固有频率均下降，振动幅频特性的幅值均有升高;
8)试验对比表明，传感器采用探针式安装时，由于探针接触副接触特性的影
响，钡(量得到的球轴承振动信号有失真，采用专门设计和制作的试验球轴承，以固
定式安装加速度计，首次测量得到了球轴承振动的真实信号，通过对振动信号的分
析，验证了球轴承振动的理论模型;
9)基于时间序列分析的AR模型适用于大样本球轴承振动信号的分析，以样
本长度的均方根值作定阶上界，FPE做判阶准则，给出的AR谱光滑，频率分辨率
高，是球轴承振动分析的简便而可靠的手段;
10)以时频域分析的小波包变换分析球轴承异音信号能够比较好地定位和聚焦
异音发生的时间，时间间隔，频率范围，同样是球轴承振动分析的可靠的手段，可
用作球轴承故障诊断技术。
研究结果开辟了滚动轴承摩擦动力学研究的新途径，丰富和完善了滚动轴承的
振动理论，对低噪声轴承的设计和工程应用有重要的指导意义。
The vibration model and differential equation are constructed based on the structural characteristics of ball bearings, tribo-dynamics viewpoint of bearing vibration, theory of tribology and structural dynamics, and analysis of the characteristics of load - deformation and contact dynamics of contact pairs of balls and ring races. The effect of geometrical and structural parameters and working conditions on the vibration characteristics of ball bearings is analyzed and the exciting and response characteristics of waviness is discussed. The theoretical model of bearing vibration is verified experimentally by digital measurement system of bearing vibration and fixed measurement method of accelerometer. The effect of tribology factors on bearing vibration is studied experimentally. AR model and WPT are used to processing the normal arid abnormal signals. The results are as follows:
1. The vibration of ball bearings is caused by the tribology action of contact pairs of ball and ring races and has the essential of tribo-dynamics. Any factors affecting the tribology characteristics of contact pairs will affect vibration and noise of bearings consequently.
2. Vibration characteristics of bearing keep almostly unchanged with the increasing of axial load expecting the increasing of nature frequencies. When radial load increasing with axial load unchanged, nature frequencies keep unchanged but some new vibration peaks appears in the spectrum.
3. Vibration amplitudes are damped and nature frequency are enhanced with sufficient lubrication. Vibration and noise of bearings increase obviously and roar can happen and the contact surfaces scratch slightly under insufficient and unclean lubrication state. Bearing will be disabled in a few minutes without any lubrication.
4. Bearing vibration is unstable under low speed. With the speed increasing, the vibration become stable and natural frequencies increase slightly but the amplitudes increase apparently.
5. Bearing vibration can be excited only by some harmonics of
waviness without lubrication and by all harmonics with lubrication based on the theoretical analysis.
6. The nature frequencies of ball bearings decrease with the increasing sizes. When international clearance increasing, nature frequencies decrease in radial and increase in axial and angular and the amplitudes increase in radial and decrease in axial and angular. When the number of balls increasing, nature frequencies increase and amplitudes decrease. When the pitch diameter increasing, axial nature frequency increase and others nearly keep no change. When outer race groove curvature radius increasing, nature frequencies increase in radial and decrease in axial and angular and amplitudes keep no change in radial and increase in axial and angular. When inner race groove curvature radius increasing, nature frequencies decrease and amplitudes increase.
7. The distortion in amplitude and frequency components of bearing vibration signals picked up by the present probe measurement method is founded and right conclusions cannot be achieved by the signals. When accelerometer is rigidly screwed with steel stud onto a flat outer surface of a ball bearing, vibration signal can be got without distortion and the reliability of research on bearing vibration is assured.
8. AR model is suitable for large samples of bearing vibration signals, square root of length of samples can be used as the upper limitation of order determination and the FPE order selection criterion is effective. Many advantages of AR spectrum are founded over the classical based on FFT.
9. Time-Frequency analysis is necessary for abnormal noise of ball bearings. WPT overcomes the principle shortcomings of STFT and proved to be a best tool to process the abnormal signals.
The research results open a new study field of tribo-dynamics of vibration of rolling element bearings and have significances not only in perfecting and enriching the vibration and noise theory of rolling element bearings but also in gu
理论分析和试验研究表明：
1)球轴承振动是钢球—滚道接触副中的各种摩擦学作用引起的，具有摩擦动力学的本质，任何对接触副的摩擦学特性有影响的因素都将对球轴承的振动和噪声特性产生影响；
2)中心轴向载荷作用下，载荷增大使球轴承的固有振动频率升高，载荷越大同样的载荷增幅引起的频率升幅减小，足够大的中心轴向载荷作用下载荷的变化对球轴承振动的频率特性不会产生明显的影响；
3)轴向和径向联合载荷作用下，径向载荷不大时球轴承振动的固有频率基本不变，但是可能引起变刚度激励的非线性振动，出现新的频峰，过大的径向载荷将使部分钢球脱离接触，使球轴承的振动和噪声呈现不稳定状态；
4)润滑对球轴承的振动和噪声特性有重要的影响，良好的润滑对振动有明显的抑制作用，润滑不充分时，振动和噪声的水平会有明显增高，一定条件下还会激发接触副中的谐振，发出啸声，造成接触表面的伤害，无润滑干接触时，短时的运转就会损伤接触副表面，使振动和噪声迅速增大，并随时可能引发严重的磨损和卡滞失效；
接触副润滑良好时，油膜的“刚化效应”使球轴承振动的固有频率有所提高，润滑剂中含有弥散性污浊时，振动的幅度总体升高，但弥散性污浊不会改变球轴承振动的频率特性；
浙江大学博士学位论文:球轴承振动的研究
5)低速时，球轴承振动的基本特征呈现不稳定状态，随着转速的提高，球轴
承振动的频率特性趋于稳定，固有频率频峰升高;
6)理论分析表明，干接触时钢球和滚道表面波纹度的某些谐波分量能激励球
轴承的振动，振动的幅值与谐波幅值成正比，实际球轴承中钢球的分布不可能完全
均匀，波纹度的激励作用会随时发生;润滑接触的分析表明，波纹度的任意谐波分
量均能激励球轴承的振动;
7)球轴承的几何和结构参数分析表明，球轴承尺寸越大，径向、轴向和角振
动的固有频率越低;钢球中心圆直径增大，球轴承的径向和轴向振动的固有频率基
本不变，角振动的固有频率有所上升，振动的幅频特性基本不变;径向游隙加大使
球轴承的径向振动固有频率降低，轴向和角振动的固有频率有所升高，径向振动幅
频特性的幅值升高，而轴向和角向降低;钢球的数量增多使球轴承振动的固有频率
上升，幅频特性的幅值下降，径向振动的幅值下降最为明显;外圈沟曲率半径系数
增大使球轴承径向振动的固有频率升高，轴向和角振动的固有频率降低，径向幅频
特性基本不变，轴向和角向幅频特性幅值升高;内圈沟曲率半径系数增大使径向、
轴向和角振动固有频率均下降，振动幅频特性的幅值均有升高;
8)试验对比表明，传感器采用探针式安装时，由于探针接触副接触特性的影
响，钡(量得到的球轴承振动信号有失真，采用专门设计和制作的试验球轴承，以固
定式安装加速度计，首次测量得到了球轴承振动的真实信号，通过对振动信号的分
析，验证了球轴承振动的理论模型;
9)基于时间序列分析的AR模型适用于大样本球轴承振动信号的分析，以样
本长度的均方根值作定阶上界，FPE做判阶准则，给出的AR谱光滑，频率分辨率
高，是球轴承振动分析的简便而可靠的手段;
10)以时频域分析的小波包变换分析球轴承异音信号能够比较好地定位和聚焦
异音发生的时间，时间间隔，频率范围，同样是球轴承振动分析的可靠的手段，可
用作球轴承故障诊断技术。
研究结果开辟了滚动轴承摩擦动力学研究的新途径，丰富和完善了滚动轴承的
振动理论，对低噪声轴承的设计和工程应用有重要的指导意义。
The vibration model and differential equation are constructed based on the structural characteristics of ball bearings, tribo-dynamics viewpoint of bearing vibration, theory of tribology and structural dynamics, and analysis of the characteristics of load - deformation and contact dynamics of contact pairs of balls and ring races. The effect of geometrical and structural parameters and working conditions on the vibration characteristics of ball bearings is analyzed and the exciting and response characteristics of waviness is discussed. The theoretical model of bearing vibration is verified experimentally by digital measurement system of bearing vibration and fixed measurement method of accelerometer. The effect of tribology factors on bearing vibration is studied experimentally. AR model and WPT are used to processing the normal arid abnormal signals. The results are as follows:
1. The vibration of ball bearings is caused by the tribology action of contact pairs of ball and ring races and has the essential of tribo-dynamics. Any factors affecting the tribology characteristics of contact pairs will affect vibration and noise of bearings consequently.
2. Vibration characteristics of bearing keep almostly unchanged with the increasing of axial load expecting the increasing of nature frequencies. When radial load increasing with axial load unchanged, nature frequencies keep unchanged but some new vibration peaks appears in the spectrum.
3. Vibration amplitudes are damped and nature frequency are enhanced with sufficient lubrication. Vibration and noise of bearings increase obviously and roar can happen and the contact surfaces scratch slightly under insufficient and unclean lubrication state. Bearing will be disabled in a few minutes without any lubrication.
4. Bearing vibration is unstable under low speed. With the speed increasing, the vibration become stable and natural frequencies increase slightly but the amplitudes increase apparently.
5. Bearing vibration can be excited only by some harmonics of
waviness without lubrication and by all harmonics with lubrication based on the theoretical analysis.
6. The nature frequencies of ball bearings decrease with the increasing sizes. When international clearance increasing, nature frequencies decrease in radial and increase in axial and angular and the amplitudes increase in radial and decrease in axial and angular. When the number of balls increasing, nature frequencies increase and amplitudes decrease. When the pitch diameter increasing, axial nature frequency increase and others nearly keep no change. When outer race groove curvature radius increasing, nature frequencies increase in radial and decrease in axial and angular and amplitudes keep no change in radial and increase in axial and angular. When inner race groove curvature radius increasing, nature frequencies decrease and amplitudes increase.
7. The distortion in amplitude and frequency components of bearing vibration signals picked up by the present probe measurement method is founded and right conclusions cannot be achieved by the signals. When accelerometer is rigidly screwed with steel stud onto a flat outer surface of a ball bearing, vibration signal can be got without distortion and the reliability of research on bearing vibration is assured.
8. AR model is suitable for large samples of bearing vibration signals, square root of length of samples can be used as the upper limitation of order determination and the FPE order selection criterion is effective. Many advantages of AR spectrum are founded over the classical based on FFT.
9. Time-Frequency analysis is necessary for abnormal noise of ball bearings. WPT overcomes the principle shortcomings of STFT and proved to be a best tool to process the abnormal signals.
The research results open a new study field of tribo-dynamics of vibration of rolling element bearings and have significances not only in perfecting and enriching the vibration and noise theory of rolling element bearings but also in gu
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