带冠涡轮叶片干摩擦非线性响应分析方法

高世民; 陶凯航; 叶航; 林聚强; 李海旺

doi:10.13224/j.cnki.jasp.20240517

带冠涡轮叶片干摩擦非线性响应分析方法

doi: 10.13224/j.cnki.jasp.20240517

高世民^{1, 2,},
陶凯航^{1, 2},
叶航³,
林聚强¹,
李海旺^{1, 2}

1.
天目山实验室绿色民用航空发动机一体化设计中心，杭州 310023
2.
北京航空航天大学航空发动机研究院，北京 102206
3.
成都航利（集团）实业有限公司，成都 611936

基金项目: 中国博士后科学基金（2024M764086）

详细信息

作者简介:
高世民（1991-），男，博士，主要从事转子叶盘结构强度研究。E-mail：gaoshimin@buaa.edu.cn

中图分类号: V231.92
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- 被引次数: 0
出版历程
- 收稿日期: 2024-07-29
- 网络出版日期: 2024-12-09

Nonlinear dynamic forced response method with dry friction applied to shrouded turbine blades

GAO Shimin^{1, 2
,},
TAO Kaihang^{1, 2},
YE Hang³,
LIN Juqiang¹,
LI Haiwang^{1, 2}

1.
Green Civil Aero-engine Integrated Design Center，Tianmushan Laboratory，Hangzhou 310023，China
2.
Research Institute of Aero-Engine，Beihang University，Beijing 102206，China
3.
Chengdu Holy Industry and Commerce Corporation，Limited，Chengdu 611936，China

摘要

摘要:
带冠涡轮叶片减振分析中为获得与高循环疲劳相关的应力结果，通过模型减缩，采用谐波平衡法和时频转换法，结合谐响应分析，求解考虑干摩擦作用的非线性稳态强迫应力响应，形成适用于工程设计的带冠涡轮叶片干摩擦非线性应力响应分析方法。针对锯齿冠涡轮叶片，获得了不同激振力下不同初始正压力下的位移和应力共振响应。结果表明：初始正压力的增加，将引起幅频响应曲线典型的“歪头”特征和软特性；在相同激振力下，共振位移幅值随初始正压力的增大呈现先减小后增大的趋势；在相同正压力下，随激振力增大，位移响应幅值呈现先快速增长后趋于稳定的趋势；1阶模态参与系数远大于其他阶次，说明叶片振动主要是单阶模态；叶身在指定载荷下的最大振动应力为118.94 MPa。
- 带冠涡轮叶片 /
- 干摩擦阻尼 /
- 减振设计 /
- 减缩模型 /
- 非线性动力学响应
Abstract:
To obtain the stress results related to high cycle fatigue in the vibration-suppression design of shrouded turbine blades, a design method for the dry friction nonlinear stress response analysis of shrouded turbine blades was built by solving the nonlinear steady-state forced response with dry friction through reduced order model, harmonic balance method and alternating frequency-time method. The resonant responses under different initial normal forces and excitations were obtained for the zig-zag shroud turbine blade. The results indicated that an increase in initial normal force could cause typical "tilting" and soft characteristics in amplitude frequency response function. Under the same exciting force, the resonance amplitude showed a trend of first decreasing and then increasing with the increase of initial normal force. Under the same normal force, as the exciting force increased, the response amplitude showed a trend of first rapidly growing and then stabilizing. The first-order mode participation coefficient was much higher than the others, indicating that the vibration of shrouded blades was mainly represented by the first-order mode. Maximum resonance stress with nonlinear contact forces of shrouded turbine blade body was 118.94 MPa.
- shrouded turbine blades /
- dry friction damping /
- vibration suppression design /
- reduced order model /
- nonlinear dynamic response

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图 1 带冠涡轮叶片及其干摩擦非线性响应问题

Figure 1. Shrouded turbine blades and dry friction nonlinear response problem

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图 2 一维切向相对位移-变正压力接触模型

Figure 2. One-dimensional tangential relative displacement-variable normal force contact model

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图 3 减缩模型

Figure 3. Reduced order model

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图 4 时频转换法

Figure 4. Alternating frequency-time

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图 5 相邻扇区的全局坐标系和局部接触坐标系

Figure 5. Global and local contact coordinate systems of adjacent sectors

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图 6 弧长延拓的预报-校正格式

Figure 6. Predictor-corrector of arc-length continuation

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图 7 干摩擦非线性强迫响应计算流程

Figure 7. Calculation process for nonlinear forced response of dry friction

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图 8 带冠涡轮叶片干摩擦振动应力求解流程

Figure 8. Flow chart of solving vibration stress of shrouded turbine blade with dry friction

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图 9 锯齿冠涡轮转子叶片有限元模型

Figure 9. Finite element model of zig-zag shrouded turbine blade

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图 10 叶冠自由状态一弯振型

Figure 10. First bending modal shape with free shroud

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图 11 不同初始正压力下幅频特性曲线

Figure 11. Amplitude frequency response curves with different initial normal forces

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图 12 135 N和360 N初始正压力下幅频特性曲线

Figure 12. Amplitude frequency response curves with 135 N and 360 N initial normal forces

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图 13 幅频特性曲线（局部放大图）

Figure 13. Amplitude frequency response curves （zoomed view）

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图 14 不同激振力下共振幅值随初始正压力的变化

Figure 14. Resonance amplitude variation with initial normal force for different exciting forces

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图 15 不同初始正压力下共振幅值随激振力的变化

Figure 15. Resonance amplitude variation with exciting force for different initial normal forces

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图 16 带冠涡轮叶片干摩擦共振振动位移分布

Figure 16. Resonance displacement distribution of shrouded turbine blade with dry friction

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图 17 带冠涡轮叶片干摩擦共振振动应力（Von Mises）分布

Figure 17. Resonance stress （Von Mises） distribution of shrouded turbine blade with dry friction

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图 18 带冠涡轮叶身干摩擦共振振动应力（Von Mises）分布

Figure 18. Resonance stress （Von Mises） distribution of shrouded turbine blade body with dry friction

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表 1 干摩擦响应分析所需接触模型参数

Table 1. Contact parameters required for dry friction response analysis

参数	数值
摩擦因数	0.3
初始接触正压力/N	0～450
接触刚度k_t /10⁶ （N/m）	1

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表 2 锯齿冠叶片无减缩与减缩模型固有频率

Table 2. Natural frequencies of whole and reduced order models for shrouded blade

阶次	固有频率/Hz		频率差/%
阶次	无减缩模型	减缩模型	频率差/%
1	519.44	519.55	0.02
2	1394.40	1395.52	0.08
3	1962.90	1966.43	0.18
4	2469.50	2474.86	0.22
5	4095.40	4106.96	0.28
6	5544.50	5588.02	0.78
7	7234.90	7278.30	0.60
8	7978.90	8065.40	1.08
9	11075.00	11307.70	2.10
10	11978.00	12149.39	1.43

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表 3 不同初始正压力共振时的归一化主模态坐标

Table 3. Normalized modal coordinates for different initial normal forces %

主模态阶次	初始正压力/N
主模态阶次	9	135	450
1	100	100	100
2	4.02	2.71	4.02
3	6.89	6.95	6.89
4	5.31	5.06	5.31
5	2.81	3.12	2.81
6	2.08	1.99	1.99
7	0.89	0.98	0.98
8	0.83	0.79	0.79
9	0.24	0.26	0.25
10	0.04	0.05	0.06

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