Vibration modulation mechanism and features of an inter-shaft bearing with raceway damage
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摘要:
为了揭示中介轴承滚道损伤振动信号调制机理及包络谱特征，开展了双转子系统中介轴承故障振动建模、仿真和试验验证研究，分析了中介轴承在转子不平衡离心负载和转子自重负载复合作用下的承载特性，探究了负载对中介轴承故障振动幅值调制的影响规律。仿真和试验验证结果表明：当转子不平衡离心力远小于转子系统自重时，中介轴承承载区是传统的固定模式，此时中介轴承滚道损伤振动幅值调制主要来源于滚道损伤随转轴同步转动引起的位置调制，调制频率为轴转速频率。当转子不平衡离心负载与转子系统自重相当或大于转子系统自重时，中介轴承承载区会是一种移动的模式。此时，中介轴承移动承载区与滚道损伤区之间的“追逐”运动模式会引入更多的调制，调制频率包括高、低转子的转速以及它们的转速差。此外，在转子不平衡离心负载作用下，复杂的调制关系改变了包络谱的能量分布。
Abstract:To reveal the vibration modulation mechanism and envelope spectrum features of an inter-shaft bearing with raceway damage, the modeling, simulations and experimental validations of vibration in a dual-rotor system were conducted. Considering the concurrent action of the rotor unbalance centrifugal loading and the rotor dead weight, the amplitude modulation mechanism of the inter-shaft bearing fault vibration was explored. The results indicated that when the rotor unbalance centrifugal loading was much smaller than the rotor system dead weight, the loading zone of the inter-shaft bearing maintained a traditional fixed pattern. The amplitude modulation of vibration caused by the raceway damage was mainly originated from the change in damage position caused by raceway rotation. When the rotor unbalance centrifugal loading was equivalent to or greater than the rotor system dead weight, the loading zone of the inter-shaft bearing was in a moving pattern. In addition to the modulation due to shaft rotation, a more complex modulation relationship could be caused by the ‘chasing’ motion pattern between the moving loading zone and the raceway damage location. The modulation frequencies encompassed the rotation speeds of the high-pressure rotor, low-pressure rotor and their difference. Moreover, under the action of the rotor unbalance centrifugal loading, the complex modulation relationships altered the energy distribution of the envelope spectrum.
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Key words:
- dual-rotor system /
- inter-shaft bearing /
- rotor imbalance /
- raceway damage /
- amplitude modulation /
- envelope analysis
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图 4 外滚道损伤冲击响应包络谱
Figure 4. Envelope analysis of impact response induced by outer race damage
图 5 当$ {{f}_{\rm{l}}} = - 11\;{\text{Hz}}, {{f}_{{\mathrm{h}}}} = {17}\;{\text{Hz}} $，外滚道损伤冲击包络阶次谱局部放大图
Figure 5. When $ {{f}_{\rm{l}}} = - 11\;{\text{Hz}}, {{f}_{{\mathrm{h}}}} = {17}\;{\text{Hz}} $, zoom of impact response envelope spectrum induced by outer race damage
图 6 当$ {{f}_{\rm{l}}} = - {51}\;{\text{Hz}}, {{f}_{{\mathrm{h}}}} = {77}\;{\text{Hz}} $，外滚道损伤冲击包络阶次谱局部放大图
Figure 6. When $ {{f}_{\rm{l}}} = - {51}\;{\text{Hz}}, {{f}_{{\mathrm{h}}}} = {77}\;{\text{Hz}} $，zoom of impact response envelope spectrum induced by outer race damage
图 8 内滚道损伤冲击响应包络分析
Figure 8. Envelope analysis of impact response induced by inner race damage
图 9 当$ {{f}_{\rm{l}}} = - {11}\;{\text{Hz}}, {{f}_{{\mathrm{h}}}} = {17}\;{\text{Hz}} $，内滚道损伤冲击包络阶次谱局部放大图
Figure 9. when $ {{f}_{\rm{l}}} = - {11}\;{\text{Hz}}, {{f}_{{\mathrm{h}}}} = {17}\;{\text{Hz}} $，zoom of impact response envelope spectrum induced by inner race damage
图 10 当$ {{f}_{\rm{l}}} = - {51}\;{\text{Hz}}, {{f}_{{\mathrm{h}}}} = {77}\;{\text{Hz}} $，内滚道损伤冲击包络阶次谱局部放大图
Figure 10. When ${{f}_{\rm{l}}} = - {51}\;{\text{Hz}}, {{f}_{{\mathrm{h}}}} = {77}\;{\text{Hz}} $，zoom of impact response envelope spectrum induced by inner race damage
图 17 中介轴承外滚道损伤振动信号
Figure 17. Vibration response of inter-shaft bearing with outer race damage
图 18 滤波得到的冲击响应高频成分
Figure 18. Impact response high frequency components after band filter
图 19 外滚道损伤冲击响应高频成分包络谱
Figure 19. Envelope spectra of high frequency components induced by outer race damage
图 20 转速$ {f}_{{\mathrm{l}}}=-{8.6}\;\text{Hz}、{{f}}_{\text{h}}={15}\;\text{Hz} $，外滚道冲击响应包络谱局部图
Figure 20. When $ {f}_{{\mathrm{l}}}=-{8.6}\;\text{Hz},\;{{f}}_{\text{h}}={15}\;\text{Hz}$, zoom of envelope spectrum about outer race damage impact response
图 21 转速$ {f}_{{\mathrm{l}}}=-{21.4}\;\text{Hz}、{{f}}_{{\mathrm{h}}}={31.1}\;\text{Hz} $，外滚道冲击响应包络谱局部图
Figure 21. When $ {f}_{{\mathrm{l}}}=-{21.4}\;\text{Hz},\;{{f}}_{{\mathrm{h}}}={31.1}\;\text{Hz} $, zoom of envelope spectrum about outer race damage impact response
图 22 中介轴承内滚道损伤振动信号
Figure 22. Vibration response of inter-shaft bearing with inner race damage
图 23 带通滤波得到的冲击响应高频成分
Figure 23. Impact response high frequency components after band filter
图 24 内滚道损伤冲击响应高频成分包络谱
Figure 24. Envelope spectra of high frequency components induced by inner race damage
图 25 转速$ {f}_{{\mathrm{l}}}=-{5.9}\;\text{Hz}、{{f}}_{{\mathrm{h}}}=8.7\;\text{H}\text{z} $，内滚道冲击响应包络谱局部图
Figure 25. When$ {f}_{{\mathrm{l}}}=-{5.9}\;\text{Hz},\;{{f}}_{{\mathrm{h}}}=8.7\;\text{H}\text{z} $, zoom of envelope spectrum about inner race damage impact response
图 26 转速$ {f}_{{\mathrm{l}}}=-{25.5}\;\text{Hz}、{{f}}_{{\mathrm{h}}}={30.3}\;\text{Hz} $，外滚道冲击响应包络谱局部图
Figure 26. When${f}_{{\mathrm{l}}}=-{25.5}\;\text{Hz},\;{{f}}_{{\mathrm{h}}}={30.3}\;\text{Hz} $, zoom of envelope spectrum about inner race damage impact response
表 1 故障冲击仿真参数
Table 1. Simulation parameters of the impact response
参数 数值 高压转子质量$ {{m}_{{{\mathrm{hd}}}}} $/kg 22 低压转子质量$ {{m}_{\rm{ld}}} $/kg 17 不平衡加权系数$ {{\eta }_{{\mathrm{h}}}} = {{\eta }_{{\mathrm{l}}}} $ 0.05 自重加权系数$ {{\kappa }_{{\mathrm{h}}}} = {{\kappa }_{{\mathrm{l}}}} $ 0.1 结构共振频率$ {{f}_{{\mathrm{n}}}} $/Hz 8000 高压转子不平衡$ {{e}_{{\mathrm{h}}}} $/10−5 6.2 低压转子不平衡$ {{e}_{{\mathrm{l}}}} $/10−5 9.7 振动传递系数$ {{A}_{{\mathrm{m}}}} （{{a}_{0}}） $ 0.3（0.51） 冲击响应幅值系数$ {{A}_{{T_{\mathrm{r}}}}} $ 0.7 冲击衰减系数$ {2{\text{π}} }{{\zeta }_{{\mathrm{n}}}}{{f}_{{\mathrm{n}}}} $ 1000 
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表 2 中介轴承结构参数
Table 2. Structure parameters of the inter-shaft bearings
参数 数值 参数 数值 滚动体数量$ {{N}_{\rm{b}}} $ 9 滚动体缺陷特征阶次$ {{f}_{{{\mathrm{bsf}}}}} $ 4.644 轴承接触角$ {\alpha } $/rad 0 内滚道缺陷特征阶次$ {{f}_{{{\mathrm{bpfi}}}}} $ 5.428 外滚道缺陷特征阶次$ {{f}_{{{\mathrm{bpfo}}}}} $ 3.572 滚动体自转特征阶次$ {{f}_{{{\mathrm{re}}}}} $ 2.322 滚动体直径$ d $/mm 7.938 轴承节径$ {{D}_{{\mathrm{m}}}} $/mm 38.5 注：表中特征阶次是指特征频率与轴转速的比值。
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表 3 中介轴承滚道损伤诱发振动包络谱上的频率成分
Table 3. Frequency components in vibration envelope spectrum of the inter-shaft bearings raceway damage
同步基频 $ {{f}_{{\mathrm{l}}}} $ $ {{f}_{\rm{h}}} $ $ \left| {{{f}_{\rm{h}}} - {f_{\rm{l}}}} \right| $ 其他 特征分量 $ {l}{{f}_{{\mathrm{l}}}} $ $ {l}{{f}_{\rm{h}}} $ $ {l}{{f}_{{\mathrm{bpfi}}}} $；$ {l}{{f}_{{\mathrm{bpfo}}}} $；
$ {l}{{f}_{{\mathrm{bpfi}}}} \pm k\left| {{f_{\rm{h}}} - {f_{\rm{l}}}} \right| $；
$ {l}{{f}_{{\mathrm{bpfo}}}} \pm k\left| {{f_{\rm{h}}} - {f_{\rm{l}}}} \right| $
$ {l}{{f}_{{\mathrm{bpfi}}}} \pm m{f_{\rm{l}}} $；
$ {l}{{f}_{{\mathrm{bpfi}}}} \pm m{f_{\rm{h}}} $
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