Dynamic modeling and response analysis of the loose supports in rotor systems
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摘要:
针对转子系统轴承支承件的松动问题，基于松动支承件的几何特征建立了轴承碰撞过程的数学表征，通过Lankarani-Nikaravesh模型对松动端轴承力进行计算。利用牛顿定律建立了转子系统轴承支承件松动的动力学模型，采用Runge-Kutta法对系统动力学方程进行求解，分析了松动程度、工作转速和系统阻尼对转子系统输出特性的影响。研究结果表明：支承件松动的转子系统在其频谱图上会出现
f s、3f s和5f s等奇数倍频信号；支承件松动会在增大轴承力幅值和增大载荷交变次数这两个方面显著降低轴承的使用寿命；转子系统会随着松动程度的加剧、运行转速升高以及系统阻尼减小而越不稳定。研究结果为轴承支承件松动故障影响分析工作提供了参考，也可以作为轴承座松动故障诊断的依据。Abstract:In view of the looseness of bearing supports in rotor systems, the mathematical representation of bearing impact process was established based on the geometric characteristics of loose supports. The bearing force of the loose end was calculated by Lankarani-Nikaravesh model. By using Newton's law, the dynamic model of the rotor system with bearing support looseness was established. The Runge-Kutta method was adopted to solve the dynamic equations. The influences of the factors, such as looseness degree, and working speed and damping, on the dynamic performance of the rotor system with bearing support looseness were studied. The results showed that: when the support of the rotor system was loose, the odd frequencies, such as
f s, 3f s and 5f s etc., could show up on its spectrum. Besides, the service life of the bearing could be significantly reduced by the increase of the bearing force and the frequency of load alternation caused by the looseness of the support. With the looseness being heavier, the accuracy of the rotor system in the looseness direction decreased gradually. The rotor system might become more unstable as the degree of looseness increased, the operating speed increased, and the system damping decreased. The research results can provide a reference for the fault analysis of the bearing support looseness. It also can be applied into the looseness diagnosis of bearing pedestal.-
Key words:
- looseness /
- rub and impact /
- roller bearing /
- rotor system /
- bearing /
- accuracy /
- bearing pedestal
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图 2 正常端轴承与轴承座接触模型
Figure 2. Contact model of bearing and bearing pedestal at normal end
图 4 松动端轴承与轴承座接触模型
Figure 4. Contact model of bearing and bearing pedestal at loose end
图 5 $ \overset{\frown} {{P}_{\text{1}}{P}_{\text{2}}} $段几何关系
Figure 5. Geometric relation of $ \overset{\frown} {{P}_{\text{1}}{P}_{\text{2}}} $
图 6 $ \overset{\frown} {{P}_{\text{4}}{P}_{1}} $段几何分析
Figure 6. Geometric analysis of $ \overset{\frown} {{P}_{\text{4}}{P}_{1}} $
图 8 不同松动程度下松动端轴承力
Figure 8. Bearing force at loose end under different looseness clearances
图 9 不同松动程度下松动端轴承力频谱
Figure 9. Bearing force frequency spectrum at loose end under different looseness clearances
图 10 不同松动程度下转盘Z向振动波形
Figure 10. Z-direction vibration waveform of the disc under different looseness clearances
图 12 不同工作转速下松动端轴承力
Figure 12. Bearing force at loose end under different working speeds
图 13 不同工作转速下松动端轴承力频谱
Figure 13. Bearing force frequency spectrum at loose end under different working speeds
图 14 不同工作转速下转盘Z向振动波形
Figure 14. Z-direction vibration waveform of the disc under different working speeds
图 17 不同阻尼环境下松动端轴承力频谱
Figure 17. Bearing force frequency spectrum at loose end under different damping
图 18 不同阻尼环境下转盘Z向振动波形
Figure 18. Z-direction vibration waveform of the disc under different damping
表 1 SKF6205-2RS轴承参数
Table 1. Bearing parameters of SKF6205-2RS
参数 数值 轴承内滚道半径ri/mm 15.25 轴承外滚道半径ro/mm 23.25 轴承外圈半径R/mm 26 滚珠数量Nb 9 弹性模量E/105 MPa 2.06 泊松比υ 0.3 
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表 2 本文模型结果与有限元结果对比
Table 2. Comparisons of the proposed model and finite element analysis
载荷/N 位移/mm 相对误差/% 本模型 有限元法 500 0.0143 0.0138 3.62 2000 0.0370 0.0367 0.82
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表 3 转子系统参数
Table 3. Parameters of rotor system
参数 数值 转盘质量m/kg 32.1 转盘偏心距e/mm 1.5 转轴刚度k/107 （N/m） 2.5 轴承质量mb/kg 4 恢复系数ce 0.9
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