Mechanism analysis for aero-elastic stability improvement of intentional mistuned bladed disk
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摘要:
理解人为失谐提升叶盘气动弹性稳定性的机理，有助于提高航空发动机叶盘的结构设计水平。首先，通过将失谐叶盘的气弹耦合模态投影到谐调模态张成的线性空间中，获得了以谐调叶盘气动阻尼比线性叠加表示的失谐叶盘气动阻尼比的解析表达式。从理论上证明了：失谐气弹耦合模态振型中包含多个彼此独立的谐调叶盘模态振型的贡献；气动阻尼比水平较高的谐调叶盘模态的参与提高了失谐叶盘的气弹稳定性。接着，提出了失谐叶盘气弹稳定性的预测方法，在计算过程中先分别分析失谐和气弹耦合的模态特性，再相互结合预测失谐叶盘的气动阻尼比水平。该方法只需进行一次气弹耦合分析，一是在实际设计中可降低对失谐设计叶盘气弹稳定性实验测量需求，二是降低仿真过程中的计算量，加快失谐模式寻优过程。最后，采用具有NASA-Rotor37叶型的叶盘作为研究对象，在多种失谐模式和失谐强度下验证了上述理论的正确性。结果表明：解析表达式误差小于0.1%；预测方法对稳定边界有一定的高估且误差在5%以内，对于总体影响规律的预测与精确解一致。
Abstract:By projecting the aero-elastic modes of the mistuned bladed disk to the modal space spanned by the tuned modes, a closed-form expression of the mistuned aerodynamic damping ratio as a linear superposition of the tuned damping was obtained. It was theoretically demonstrated that: a mistuned aero-elastic mode was constructed by several tuned and independent modes; and the contribution of the tuned modes with high aeroelastic damping can increase the aeroelastic damping of the mistuned mode. A method to predict the aerodynamic damping ratio of the mistuned bladed disk was proposed. It started with respective analysis of aero-elastic coupling and mistuning, and the aerodynamic damping ratio of the mistuned modes can be predicted. A single-time aeroelastic analysis was required for two significant benefits. One is reducing the experimental measurements and the other is decreasing the calculation cost to accelerate the optimization process of mistuning pattern. The bladed disk with NASA-Rotor37 blade profile was considered, and several typical mistuning patterns were applied with different levels of mistuning strength. Results showed that the closed-form expression had an error lower than 0.1%. The prediction method would overrate the stability boundary with error lower than 5%, so it is capable to capture the overall trends of the accurate results.
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图 3 叶盘第1阶模态族二节径振型（图2（b）蓝色圈出）
Figure 3. Modal shape of the blisk 1st modal family with 2 nodal diameter （blue circled in Fig.2（b））
图 8 参考叶片不同振幅下气动影响系数幅值
Figure 8. Amplitude of the aerodynamic influence coefficient with different maximum vibration amplitudes of the reference blade
图 9 谐调叶盘一弯模态族气动阻尼比分布
Figure 9. Distribution of the aerodynamic damping ratio of the tuned blisk with blade 1st bending deformation
图 11 气动阻尼比准确值与近似值对比（h=6）
Figure 11. Comparison between the reference value and the approximate value of the aerodynamic damping ratio (h=6)
图 12 气动阻尼比准确值与近似值对比（h=18）
Figure 12. Comparison between the reference value and the approximate value of the aerodynamic damping ratio (h=18)
图 13 不同谐波人为失谐叶盘最小气动阻尼比准确值与近似值对比
Figure 13. Comparation between the reference value and the approximate value of the minimum aerodynamic damping ratio of the harmonic intentional mistuned blisk with different orders
图 14 失谐强度为0.8%的叶盘最小气动阻尼比分布（准确值与近似值对比）
Figure 14. Distribution of the minimum aerodynamic damping ratio of the mistuned blisk with 0.8% mistuning level (comparison between the reference values and the approximate values)
图 15 失谐强度为0.8%的叶盘最小气动阻尼比具体值（准确值与近似值对比）
Figure 15. Values of the minimum aerodynamic damping ratio of the mistuned blisk with 0.8% mistuning level (comparison between the reference values and the approximate values)
图 16 谐调叶盘模态对人为失谐叶盘最小气动阻尼比贡献度
Figure 16. Contributions of the tuned blisk modes to the minimum aerodynamic damping ratio of the intentional mistuned blisk
图 17 不同谐波人为失谐叶盘最小气动阻尼比预测值与准确值对比
Figure 17. Comparison between the predicted minimum aerodynamic damping ratio and the reference minimum aerodynamic damping ratio of the different orders harmonic intentional mistuned blisk
图 18 不同随机失谐强度下叶盘最小气动阻尼比准确值与预测值分布对比
Figure 18. Distribution comparison of the predicted minimum aerodynamic damping ratio and reference minimum aerodynamic damping ratio of the random mistuned blisk with different mistuning levels
图 19 随机失谐强度为0.8%的叶盘最小气动阻尼比对比（准确值和预测值）
Figure 19. Comparison of the random mistuned blisk with 0.8% mistuning level (between the reference minimum aerodynamic damping ratio and predicted minimum aerodynamic damping ratio)
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