Torsional coupled vibration characteristics of multi-stage blade disc-shaft system of aeroengine
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摘要: 针对多级叶盘转子结构, 考虑多级叶片弯曲变形和轴扭转变形耦合作用, 引入叶片离心刚化作用, 建立了包含多叶片、2级叶盘和轴的耦合振动模型; 应用哈密顿原理推导了多级叶盘-轴耦合振动微分方程组, 通过数值积分方法得到了系统质量矩阵与刚度矩阵, 进而求解出系统耦合模态; 研究了叶盘固有频率、叶片长度、叶盘间距、叶片扭转角对振动特征的影响。研究结果表明: 2级叶盘-轴系耦合振动包含3类耦合模态, 各阶模态频率以叶盘固有频率为边界相互分离; 叶片长度小于1 m时, 耦合第1、2阶频率受轴半径的影响较大, 叶片长度超过1 m后, 耦合第1、2阶频率受叶片长度的影响较大; 在系统转速为2 000 rad·s-1时, 在不同叶盘间距下, 耦合的3阶模态频率变化幅度分别降低5、3、7 Hz; 转速-频率曲线存在明显的频率转向特征, 叶片扭转角增加60°, 转向区域提高500 rad·s-1; 2级叶盘系统会产生不同于单级叶盘的耦合模态, 短叶片与长叶片均会对耦合频率产生显著影响; 叶片扭转角与叶盘间距的变化会使耦合区域移动, 从而降低可能发生的危险共振。Abstract: Aiming at the multi-stage blade disc rotor structure, the coupling effect of multi-stage blade bending deformation and shaft torsional deformation was taken into account, the centrifugal rigidity of blade was lead in, and the coupling vibration model containing multi-stage blades, two-stage blade discs and shaft was established. The differential equations of multi-stage blade disc-shaft coupling vibration were derived by using Hamilton principle, the system mass matrix and stiffness matrix were obtained by using numerical integration method, and then the coupled modes of the system were solved. The effects of natural frequency of blade disc, blade length, blade disc spacing and blade twist angle on vibration characteristics were studied. Analysis result shows that the two-stage blade disc-shaft coupling vibration includes 3 types of coupling modes, and the natural frequency of each order is separated from each other at the boundary of blade disc natural frequencies. When the blade length is less than 1 m, the first and second order coupling frequencies are greatly affected by the radius of shaft. When the blade length exceeds 1 m, the first and second order coupling frequencies are greatly affected by the blade length. When the system rotation speed is 2 000 rad·s-1, the variation amplitudes of 1-3 order coupling mode frequencies decrease by 5, 3 and 7 Hz under the influence of blade disc spacing, respectively. The speed-frequency curve has obvious frequency steering characteristics, the blade twist angle increases by 60°, and the steering area increases by 500 rad·s-1. The two-stage blade disc system will produce coupling modes different from the single-stage blade disc system, and the coupling frequency will be significantly affected by both short blade and long blade. The changes of blade twist angle and blade disc spacing will make the coupling area move, which reduces the risk of resonance that may occur.
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图 6 归一化2级叶盘-轴系耦合振型
Figure 6. Normalized coupling vibration mode of two-stage blade disc-shaft system
图 7 耦合频率随1号叶盘固有频率变化规律
Figure 7. Variation laws of coupling frequency with natural frequency of 1st blade disc
图 8 耦合频率随1号叶盘叶片长度变化规律
Figure 8. Variation laws of coupling frequency with blade length of 1st blade disc
表 1 模型参数
Table 1. Model parameters
参数 取值 轴半径/m 0.4 轴长度/m 1 叶片厚度/m 0.01 叶片宽度/m 0.2 叶片长度/m 1 叶盘半径/m 0.5 叶盘厚度/m 0.2 叶盘间距/m 0.6 弹性模量/GPa 200 材料密度/ (kg·m-3) 7 800 叶片数 25 叶盘级数 2 叶片扭转角/ (°) 15 切变模量/GPa 75 
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表 2 模态频率与振型
Table 2. Frequencies and shapes of modes
阶次 模态频率/Hz 模态振型 1 25.59 耦合第1阶模态 2~51 28.77 叶片1阶模态 52 35.78 耦合第2阶模态 53 59.66 耦合第3阶模态 54~103 66.82 叶片2阶模态
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表 3 本文方法与有限元方法比较
Table 3. Comparison between proposed method and FEM
阶次 有限元方法的模态频率/Hz 本文方法的模态频率/Hz 误差/% 1 25.47 25.69 0.86 2~51 28.42~28.63 28.77 0.75 52 35.47 35.78 0.92 53 59.32 59.96 1.07 54~103 66.06~66.37 66.82 0.68
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