Modelling of pre-tightening force in rod-fastened rotors and it induced vibration localization
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摘要:
为探究拉杆转子在考虑接触面力学特性下预紧力失谐诱发振动的机理，从弹塑性理论及接触面微观角度，详细分析了单个微凸体在接触过程中的变形规律和力学特性，并通过高斯分布得到接触面宏观的力学接触模型。结合接触面力学特性，建立了一种保证其原始模型主要特征参数不变且能够确定其厚度的等效接触层；进一步通过这种等效接触层模型分析了拉杆预紧力降低和周向失谐时临界转速和固有频率的变化规律；利用波的传递揭示了预紧力周向失谐诱发拉杆转子振动模态局部化的机理。结果表明：预紧力减弱后，等效接触层刚度减小，临界转速和固有频率降低；随着预紧力失谐拉杆数量的增加，转子的临界转速和固有频率降低。当外部激励的频率处于拉杆转子的频率禁带时，振动能量无法传遍整体结构而积聚在局部区域，从而诱发了振动局部化现象。论文研究结果能够为复杂拉杆转子的动力学分析和优化设计提供参考方法。
Abstract:In order to explore the mechanism of the vibration induced by the pre-tightening mistune of the rod-fastened rotor considering the mechanical characteristics of the contact surface, and viewed from the elastoplastic theory and the microscopics of the contact surface, the deformation laws and mechanical characteristics of a single asperity in the contact process were analyzed in detail, and the macroscopic mechanical contact model of the contact surface was obtained through Gaussian distribution. First, an equivalent contact layer was established to ensure that the main characteristic parameters of the original model could be kept unchanged and its thickness was determined, based on the mechanical properties of the contact surface; then, the variation law of critical speed and natural frequency when the pre-tightening force was reduced and detuned in the circumferential direction was further analyzed by this equivalent contact layer model; finally, the mechanism of vibration mode localization of rod-fastened rotor induced by circumferential detuning of pre-tightening force was revealed by means of wave transmission. The results showed that the equivalent contact layer stiffness and the critical speed and natural frequency decreased as the pre-tightening reduced. Moreover, the critical speed and natural frequency of the rotor became lower, as the number of pre-tightening detuning rods increased. As the fluctuation frequency of the rod-fastened rotor was within the frequency stop-band, the vibration energy cannot be transmitted throughout the whole structure. The research results can provide a reference method for the dynamic analysis and optimal design of complex rod-fastened rotors.
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图 8 实际接触面积及刚度随预紧力变化
Figure 8. Real contact area and stiffness change with pre-tightening
图 14 轮盘-等效接触层应变能云图
Figure 14. Roulette-equivalent contact layer strain energy cloud diagram
图 16 固有频率为178.86 Hz时的主振型
Figure 16. Principal mode shape as the natural frequency is 178.86 Hz
图 17 固有频率为803.62 Hz时的主振型
Figure 17. Principle mode shape as the natural frequency is 803.62 Hz
表 1 接触面参数的变化
Table 1. Variation of contact surface parameters
预紧力/N 压强/GPa 刚度/（GN/m） 阶段 0.0001 0.1803 0.0002 弹性 $\vdots $ $\vdots $ $\vdots $ $\vdots $ 0.0065 0.6983 0.0006 弹性 0.0014 1.1536 0.0008 弹塑性 $\vdots $ $\vdots $ $\vdots $ $\vdots $ 4.6755 1.9583 0.0027 弹塑性 4.9260 1.96 0.0024 塑性 
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表 2 不同预紧力条件下4个接触面的参数
Table 2. Parameters of four contact surfaces with different pre-tightening
接触面
名称拉杆
预紧力/kN刚度/
（GN/m）弹性模量/
GPa泊松比 第1接触界面 300 90.8678 9.8642 0.0652 600 152.4454 15.9863 0.0732 第2接触界面 300 93.1667 9.0938 0.0700 600 157.1805 14.8537 0.0774 第3接触界面 300 95.0672 8.4074 0.0752 600 161.7066 13.8706 0.0820 第4接触界面 300 97.13077 7.8317 0.0807 600 165.5469 12.9716 0.0869
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表 3 不同预紧力下转子的临界转速和固有频率
Table 3. Critical speed and natural frequency of the rotor under different pre-tightening
模态
阶数临界转速/Hz 固有频率/Hz F =300 kN F =600 kN F =300 kN F =600 kN 1 2.85 3.56 1.42 1.78 2 22.44 27.54 11.28 13.87 3 24.22 29.73 11.31 13.89 4 356.18 363.82 179.65 182.94 5 671.63 709.51 367.69 388.88 6 791.31 828.24 367.7 388.89 7 998.85 1033.55 450.25 467.28 8 1484.2 1570.22 826.96 865.01 9 1684.1 1765.98 827.3 865.33
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表 4 6种预紧力失谐形式相应的临界转速和固有频率
Table 4. Critical speed and natural frequency of six types of pre-tightening detuning
模态 临界转速/Hz 固有频率/Hz Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ 1 2.36 2.36 2.36 2.36 2.36 2.36 1.18 1.18 1.18 1.18 1.18 1.18 2 24.22 23.77 23.32 22.86 22.39 22.14 12.32 12.19 11.96 11.73 11.50 11.26 3 25.99 25.52 25.04 24.55 24.04 23.76 12.41 12.20 11.97 11.74 11.51 11.27 4 353.06 352.43 351.89 351.35 350.61 349.88 179.32 179.11 178.86 178.61 178.24 177.93 5 721.99 721.41 720.3 719.92 718.96 717.82 382.13 381.41 380.69 380.45 379.8 379.09 6 764.77 764.38 763.72 762.35 762.38 759.99 382.65 382.27 381.78 380.85 380.71 379.2 7 974.76 974.5 974.12 973.77 973.61 972.81 463.9 463.03 462.6 462.21 461.95 461.13 8 1631.5 1630.9 1628.7 1627.6 1626.2 1624.4 806.77 805.23 803.62 803.05 801.87 801.16 9 1806.8 1805 1802.5 1799.2 1796.5 1791 809.31 808.1 807.39 805.72 804.8 801.7
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表 5 定量评估预紧力失谐下的振动局部化
Table 5. Quantitative assessment of vibration localization under preload detuning
失谐类型 无量纲位移/10−3 位移局部化因子/10−2 A 9.16 9.92 B 9.25 19.85 C 9.34 29.77 D 9.43 39.7 E 9.62 60.64 F 9.71 70.56
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