Prediction of response intervals for misalignment faults in uncertain rotor systems
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摘要:
针对区间不确定性对航空发动机转子系统的影响，运用一种基于Chebyshev正交多项式的非嵌入式区间分析方法对含参数不确定性的转子系统动力学特性进行分析。将叶盘不平衡量、联轴器不对中量以及联轴器套齿质量等关键参数的不确定性纳入考虑，建立含不对中故障的转子系统动力学模型。在此基础上，通过数值仿真的方式研究不确定性系统振动响应及其参数影响规律，分析了转子系统振动响应在不同转速下对不同不确定性参数的敏感程度。同时，通过与传统Monte Carlo模拟对比验证了方法的有效性。结果表明:转子系统的振动响应在不确定性区间参数的影响下呈现出区间形式，且对于不同不确定性参数的影响表现出明显差异。在多源不确定性参数共同作用下，系统所表现出的区间现象更为明显，甚至对系统的临界转速也造成了一定的影响。研究结果可为含不对中故障的复杂转子系统的不确定性响应预测提供一定的理论参考。
Abstract:Considering the effect of interval uncertainty on aero-engine rotor systems, a non-embedded interval analysis method based on Chebyshev orthogonal polynomials was applied to analyze the dynamics of rotor systems with parameter uncertainties. The uncertainties of the key parameters, such as the amount of blade disk unevenness, the amount of coupling misalignment, and the mass of coupling sleeve teeth, were taken into account to establish a dynamic model of the rotor system with misalignment faults. On this basis, the vibration response of the uncertain system and the influence of its parameters were investigated by numerical simulation, and the sensitivity of the vibration response of the rotor system to different uncertain parameters at different rotational speeds was analyzed. Meanwhile, the effectiveness of the method was verified by comparing with the traditional Monte Carlo simulation. The results showed that the vibration response of the rotor system presented an interval form under the influence of the uncertainty interval parameters, and the effects of different uncertainty parameters showed obvious differences. Under the combined effect of multiple sources of uncertainty parameters, the interval phenomenon of the system was more obvious, and even the critical speed of the system was also affected. The results of this study can provide a theoretical reference for prediction of the uncertainty response of complex rotor systems with misaligned faults.
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Key words:
- rotor system /
- misalignment fault /
- parameter uncertainty /
- interval analysis /
- vibration response
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图 1 含不对中故障的转子结构示意图
Figure 1. Schematic diagram of rotor structure with misalignment fault
图 2 不确定性转子系统稳态响应计算流程图
Figure 2. Flow chart of steady state response calculation of uncertain rotor system
图 3 确定性转子系统横向响应幅频曲线
Figure 3. Amplitude frequency curve of lateral response of deterministic rotor system
图 4 确定性转子系统竖向响应幅频曲线
Figure 4. Amplitude frequency curve of vertical response of deterministic rotor system
图 5 联轴器不对中程度呈参数不确定性时，转子系统横向响应幅频曲线
Figure 5. Amplitude frequency curve of lateral response of rotor system in the condition of uncertain misalignment of gear coupling
图 6 联轴器质量呈参数不确定性时，转子系统横向响应幅频曲线
Figure 6. Amplitude frequency curve of lateral response of rotor system in the condition of uncertain mass of coupling
图 7 叶盘不平衡呈参数不确定性时，转子系统横向响应幅频曲线
Figure 7. Amplitude frequency curve of lateral response of rotor system in the condition of uncertain disc eccentricity
图 8 多源不确定性参数影响下系统横向响应幅频曲线
Figure 8. Amplitude frequency curve of lateral response of rotor system in the condition of multi-source uncertain parameters
图 9 转速为$ \omega = 400\;{\text{rad/s}} $时，含多源不确定性参数的转子系统时间历程曲线
Figure 9. Time histories curve of rotor system with multi-source uncertain parameters at the rotational speed $ \omega = 400\;{\text{rad/s}} $
图 10 转速为$ \omega = 800\;{\text{rad/s}} $时，含多源不确定性参数的转子系统时间历程曲线
Figure 10. Time histories curve of rotor system with multi-source uncertain parameters at the rotational speed $ \omega = 800\;{\text{rad/s}} $
图 11 转速为$ \omega = 400\;{\text{rad/s}} $时，含多源不确定性参数的转子系统轴心轨迹图
Figure 11. Whirling orbit diagram of rotor system with multi-source uncertain parameters at the rotational speed $ \omega = 400\;{\text{rad/s}} $
图 12 转速为$ \omega = 800\;{\text{rad/s}} $时，含多源不确定性参数的转子系统轴心轨迹图
Figure 12. Whirling orbit diagram of rotor system with multi-source uncertain parameters at the rotational speed $ \omega = 800\;{\text{rad/s}} $
图 13 转速为$ \omega = 400\;{\text{rad/s}} $时，不同不确定性工况下转子系统横向响应区间波动
Figure 13. Interval fluctuation of lateral response of rotor system with different uncertainty conditions at the rotational speed $ \omega = 400\;{\text{rad/s}} $
图 14 转速为$ \omega = 800\;{\text{rad/s}} $时，不同不确定性工况下转子系统横向响应区间波动
Figure 14. Interval fluctuation of lateral response of rotor system with different uncertainty conditions at the rotational speed $ \omega = 800\;{\text{rad/s}} $
表 1 转子系统结构参数
Table 1. Structural parameters of rotor system
参数描述 数值 叶盘等效质量$ {m_{\text{d}}} $/kg 32.1 左轴承处等效质量$ {m_{\text{l}}} $/kg 4 右轴承处等效质量$ {m_{\text{r}}} $/kg 4 联轴器质量$ {m_{\text{c}}} $/kg 2.61 弹性轴刚度$ {k_{\text{d}}} $/107 （N/m） 2.5 左端轴承刚度$ {k_{\text{l}}} $/107 （N/m） 2.0 右端轴承刚度$ {k_{\text{r}}} $/107 （N/m） 2.0 叶盘阻尼系数$ {c_{\text{d}}} $/103 （N·s/m） 2.1 轴承处阻尼系数$ {c_{\text{l}}} $和$ {c_{\text{r}}} $/103 （N·s/m） 1.05 叶盘不平衡$ e $/mm 0.01 联轴器不对中量$ \Delta E $/mm 0.2/0.4/0.6 
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表 2 转子系统不确定性参数
Table 2. Uncertain parameters of rotor system
参数类型 ΔE/mm mc/kg e/mm 确定性 0.2 2.61 0.01 不确定性 [0.2, 0.6] [2, 3] [0.005, 0.015]
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