Dynamic characteristics analysis of the complex rotor-blade system for the aero-turboshaft engine
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摘要:
基于赫兹接触理论与数理统计相结合的方法，构建了含有弹性、弹-塑性、完全塑性的3个变形过程在内的端齿等效接触动力学模型。针对航空涡轴转子系统复杂的结构特征，采用有限元和哈密顿变分原理建立了含有接触效应的端齿连接结构在内的航空发动机复杂转子-叶片耦合系统的动力学分析模型，并通过与有限元结果对比验证了模型的有效性。在此基础上，研究了不同预紧力作用下耦合系统的固有频率、稳态响应以及瞬态不平衡响应特性。研究结果表明预紧力对端齿连接结构的接触状态影响非常明显，在预紧松弛状态下，其连接界面滑移会引起有效接触界面的抗弯刚度和抗扭刚度的减少，从而引起端齿连接刚度下降，同时在耦合系统的轮盘处
x 方向，扭转振动与叶尖弯曲方向处的瞬态和稳态不平衡响应的幅值有明显放大现象，而当预紧力设计范围为2.0×104～2.0×105 N，此时端齿连接结构近似等效于刚性连接。本文研究结果可为含有端齿连接结构的航空涡轴发动机轴向预紧力的设计提供了定量的参考依据。-
关键词:
- 端齿预紧 /
- 接触模型 /
- 航空涡轴发动机 /
- 稳态和瞬态不平衡响应 /
- 动力学特性
Abstract:The equivalent contact model of the end-tooth connection including three stages such as the elastic, elastoplastic and plastic deformation was proposed using the Hertz contact theory in conjunction with the mathematical statistics method. In view of the complex structure of the aero-turboshaft engine, the general dynamic model of the complex rotor blade system, including the end tooth connection considering the contact effect, was established based on the finite element method and Hamilton's variance principle. The concrete finite element results demonstrated the validity and correctness of the analytical model. And on the basis, the effects of the pre-tightening forces on the natural frequencies, transient and steady unbalance responses were further investigated. The results showed that the effects of the pre-tightening forces had a significant effect on the contact state of the end-tooth connection. In the relaxation state of the pre-tightening force, the slippage of contact interface can reduce the bending and torsional stiffness of the end-tooth connection, leading to a decrease in the connection stiffness of the end-tooth connection. For the transient and steady-state unbalanced responses, there existed obvious amplitude amplification phenomena in the rotor vibration in
x direction, torsional direction and bending vibration of the blade tip. The saturation stage of the pre-tightening force was selected at the range of 2.0×104—2.0×105 N, the end tooth connection was approximately equivalent to the rigid connection. The results provide a quantitative reference for the design of the aero-turboshaft engine considering the end-tooth connection under the action of the pre-tightening forces. -
图 1 含有端齿连接结构的航空涡轴发动机复杂转子-叶片耦合系统示意图（单位：mm）
Figure 1. Schematic diagram of the complex turboshaft engine rotor blade system considering the end-tooth connection （unit: mm）
图 3 端齿连接结构的接触面积和刚度转换
Figure 3. Contact area and stiffness transformation of end-tooth connection
图 4 端齿连接结构的等效过程示意图（ANSYS模型）
Figure 4. Schematic diagram of equivalent progress of the end-tooth connection （ANSYS model）
图 8 阶梯轴-中心拉杆耦合简化示意图
Figure 8. Schematic diagram of the coupling relationship between the central tie rod and stepped shaft.
图 10 在预紧力160 kN作用下，航空涡轴发动机的耦合系统在Ω=0 r/min的振型图
Figure 10. Mode shapes from the coupling system for the turboshaft engine under F0=160 kN and Ω=0 r/min
图 11 预紧力对耦合系统中含有弯曲固有频率的影响
Figure 11. Effects of the pre-tightening forces on the bending natural frequencies of the coupling system
图 12 预紧力对耦合系统中含有扭转固有频率的影响
Figure 12. Effects of the pre-tightening forces on the torsional natural frequencies of the coupling system
图 13 不同预紧力作用下，耦合系统的稳态不平衡响应（转速为
3000 r/min）Figure 13. Effects of the pre-tightening forces on the steady-state vibration （rotating speed of
3000 r/min）
图 14 不同预紧力作用下，耦合系统的不平衡响应（转速为
6000 r/min）Figure 14. Effects of the pre-tightening forces on the steady-state vibration （rotating speed of
6000 r/min）
图 15 不同预紧力作用下，耦合系统在升速过程的瞬态不平衡响应
Figure 15. Effects of the pre-tightening forces on the transient vibration
表 1 在预紧力160 kN作用下,考虑端齿连接结构的耦合系统在Ω=0 r/min的固有频率
Table 1. Natural frequencies of the coupling system for the turboshaft engine under F0=160 kN and Ω=0 r/min
阶数 固有频率/ Hz 误差/% 振型描述 解析解 有限元解 f（n1） 93.02 92.06 0.26 1阶扭转 f（n2） 103.38 103.63 0.06 轴的轴向振动 f（n4） 173.21 171.08 0.31 平动与弯曲 f（n5） 478.90 472.56 0.33 俯仰振动 f（n7） 529.18 539.42 0.48 叶片与阶梯轴扭转
耦合（耦合反向）f（n8） 546.63 557.87 0.51 叶片弯曲 f（n15） 910.85 961.86 1.36 中心拉杆1阶弯曲 f（n17） 1117.90 1123.70 0.13 2阶扭转 f（n18） 1377.24 1364.80 0.23 转子1阶弯曲 注：耦合同向表示两个轮盘上的叶片弯曲模态方向相同，反之亦然。 
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