多级端齿连接的转子系统损伤评估及动力学分析

付杰; 李超; 武昌耀; 苗淏溟; 洪杰; 王永锋

doi:10.13224/j.cnki.jasp.20250244

多级端齿连接的转子系统损伤评估及动力学分析

doi: 10.13224/j.cnki.jasp.20250244

付杰^1,,
李超^2,*, ,,
武昌耀³,
苗淏溟²,
洪杰^{1, 2},
王永锋²

1.
北京航空航天大学能源与动力工程学院，北京 100191
2.
北京航空航天大学航空发动机研究院，北京 100191
3.
中国航发湖南动力机械研究所，湖南株洲 412002

基金项目: 国家科技重大专项（J2022-Ⅳ-0004-0021，J2022-Ⅶ-0001-0043）

详细信息

作者简介:
付杰（1998-），男，博士生，主要从事航空发动机整机结构动力学及安全性。E-mail：fujie0603@buaa.edu.cn

通讯作者:
李超（1977-），男，副研究员，博士，主要从事航空发动机整机结构动力学及安全性设计。E-mail：Lichao7715@163.com

中图分类号: V231.96
计量
- 文章访问数: 562
- HTML浏览量: 330
- PDF量: 61
- 被引次数: 0
出版历程
- 收稿日期: 2025-05-22
- 网络出版日期: 2025-08-29

Damage assessment and dynamic characteristics analysis of rotor systems with multi-stage curvic couplings connection

FU Jie^1
,,
LI Chao^{2,*
, ,},
WU Changyao³,
MIAO Haoming²,
HONG Jie^{1, 2},
WANG Yongfeng²

1.
School of Energy and Power Engineering，Beihang University，Beijing 100191，China
2.
Research Institute of Aero-Engine，Beihang University，Beijing 100191，China
3.
Hunan Aviation Powerplant Research Institute，Aero Engine Corporation of China，Zhuzhou Hunan 412002，China

摘要

摘要:
以典型多级端齿连接结构的燃气发生器转子为研究对象，分析了转子系统的动力学特性，并对转子及端齿在临界转速下的应变能分布特征进行了分析。对连接结构的界面损伤提出了界面损伤评估方法，采用界面接触状态系数、界面接触应力和摩擦功对装配状态下、起动状态下和工作状态下的转子结构系统的界面接触损伤进行了评估。最后对考虑界面损伤的转子动力学特性进行了分析。结果表明：端齿D的界面损伤较为严重，起动状态下端齿D的有效接触区域占比20%；工作状态下：在多重载荷（装配载荷、离心载荷、温度载荷）的作用下，端齿D的有效接触区域占比34.67%，有效接触区域相较起动状态有所改善，但端齿D的摩擦功增加了231.6%，端齿D左右端齿的相对径向变形较大，达0.23～0.25 mm，界面滑移较为严重，对转子的稳健性影响较大；考虑界面接触损伤，转子的1阶和2阶临界转速分别变化了3.11%和0.55%，弯曲临界转速降低了7.77%。
- 涡轴发动机 /
- 端齿连接结构 /
- 燃气发生器转子 /
- 损伤评估 /
- 动力学特性
Abstract:
Taking the typical multi-stage curvic couplings of a gas generator rotor as the research object, the dynamic characteristics of the rotor system were analyzed, and the strain energy distribution of the rotor and curvic couplings at critical speeds was examined. An interface damage assessment methodology was developed to evaluate the contact damage of the rotor structure system under different operational conditions, including the assembly state, start-up state, and working state. The evaluation incorporated parameters such as the interface contact state coefficient, interface contact stress, and friction work. Finally, the dynamic characteristics of the rotor considering interface damage were analyzed. The results indicated that the interface damage of curvic couplings D was relatively severe. During the start-up state, the effective contact area ratio of curvic couplings D was approximately 20%. Under working conditions subjected to multiple loads (assembly load, centrifugal load, and thermal load), the effective contact area ratio of curvic couplings D increased to 34.67%, representing an improvement compared with the start-up state. However, the friction work of curvic couplings D rose significantly by 231.6%, and the relative radial deformation between curvic couplings D and its adjacent teeth reached 0.23—0.25 mm, resulting in substantial interface sliding. This phenomenon had a considerable impact on the robustness of the rotor system. Furthermore, considering the effects of interface contact damage, the first and second critical speeds of the rotor changed by 3.11% and 0.55%, respectively, while the bending critical speed decreased by 7.77%.
- turboshaft engine /
- curvic couplings /
- gas generator rotor /
- damage assessment /
- dynamic characteristics

HTML

图 1 多级端齿连接的燃发器转子结构

Figure 1. Structure of the gas generator rotor with multi-stage curvic couplings

下载: 全尺寸图片幻灯片

图 2 端齿连接结构受力分析示意图

Figure 2. Diagram of force analysis for the curvic couplings

下载: 全尺寸图片幻灯片

图 3 燃发转子有限元模型

Figure 3. FEM model of the gas generator rotor

下载: 全尺寸图片幻灯片

图 4 燃发转子Campbell图

Figure 4. Campbell diagram of the gas generator rotor

下载: 全尺寸图片幻灯片

图 5 燃发转子各阶模态振型

Figure 5. Modal shapes of each order of the gas generator rotor

下载: 全尺寸图片幻灯片

图 6 连接结构接触界面迟滞回归曲线

Figure 6. Contact interface hysteresis regression curve

下载: 全尺寸图片幻灯片

图 7 离心载荷作用下各部件的变形

Figure 7. Deformation of each component under centrifugal load

下载: 全尺寸图片幻灯片

图 8 离心载荷作用下端齿连接结构径向位置变化

Figure 8. Radial position variation of the curvic couplings under centrifugal load

下载: 全尺寸图片幻灯片

图 9 燃发转子预紧力大小及施加位置

Figure 9. Magnitude and application position of the preload force of the gas generator rotor

下载: 全尺寸图片幻灯片

图 10 工作状态下转子温度分布

Figure 10. Rotor temperature distribution under working conditions

下载: 全尺寸图片幻灯片

图 11 不同状态下的界面接触状态

Figure 11. Interface contact states under different conditions

下载: 全尺寸图片幻灯片

图 12 工作状态下端齿连接结构径向位置变化

Figure 12. Radial position variation of the curvic couplings under working conditions

下载: 全尺寸图片幻灯片

图 13 燃发转子动力特性计算模型

Figure 13. Calculation model of dynamic characteristics of the gas generator rotor

下载: 全尺寸图片幻灯片

图 14 刚度修正模型与接触模型变形弹性线对比

Figure 14. Comparison of stiffness correction model and deformation elastic line of contact model

下载: 全尺寸图片幻灯片

图 15 考虑连接结构刚度损失时燃发转子Campbell图

Figure 15. Campbell diagram of the gas generator rotor considering the stiffness loss of the connection structure

下载: 全尺寸图片幻灯片

表 1 各阶临界转速振型下转子-支承应变能占比

Table 1. Proportion of strain energy of rotor-support under each critical speed mode %

振型	3#支承	4#支承	支承	转子
涡轮平动振型	30.06	55.33	85.39	14.61
压气机俯仰振型	48.53	31.85	80.38	19.62
转子1阶弯曲振型	3.17	1.49	4.66	95.34

下载: 导出CSV

表 2 各阶临界转速振型下端齿结构应变能占比

Table 2. Proportion of strain energy of the curvic couplings under each critical speed mode %

端齿编号	平动振型	俯仰振型	1阶弯曲振型
端齿A	0.13	0.57	0.15
端齿B	0.08	0.26	0.47
端齿C	0.40	0.32	4.62
端齿D	0.15	0.06	1.35
端齿E	0.11	0.03	0.50
端齿F	0.07	0.01	0.05
注：此处为端齿结构占整个转子-支承系统应变能的比例，包括支承。

下载: 导出CSV

表 3 各端齿连接结构接触界面轴向力变化情况分析

Table 3. Analysis of the axial force variation at the contact interface of the curvic couplings

端齿	装配接触力/N	起动接触力/N	工作接触力/N	起动差异率/%	工作差异率/%
A	314362	231259	231940	−26.44	−26.22
B	310478	239136	239406	−22.98	−22.89
C	307021	231808	232097	−24.50	−24.40
D	88917	51108	46793	−42.52	−47.37
E	84116	27641	26584	−67.14	−68.40
F	84664	32099	28402	−62.09	−66.45

下载: 导出CSV

表 4 各端齿连接结构最大接触应力分析

Table 4. Analysis of the maximum contact stress of curvic couplings MPa

端齿	装配状态	起动状态	工作状态
A	319.16	132.96	143.52
B	136.45	92.159	91.699
C	111.99	118.46	114.31
D	32.673	65.339	50.202
E	50.533	25.97	25.828
F	41.926	39.55	27.751

下载: 导出CSV

表 5 各端齿连接结构摩擦功分析

Table 5. Analysis of friction work of curvic couplings

端齿	起动状态		工作状态
端齿	滑移距离/ 10⁻² mm	摩擦功/ （kJ/m²）	滑移距离/ 10⁻² mm	摩擦功/ （kJ/m²）
A
B	7.797	26.73	7.667	26.16
C	8.465	29.86	7.987	29.39
D	10.225	5.32	25.342	17.64
E	4.616	2.94	4.763	3.00
F	3.840	2.66	4.685	2.90

下载: 导出CSV

表 6 端齿界面刚度损失修正

Table 6. Correction of stiffness loss at the curvic couplings interface

端齿	接触状态系数/%	刚度损失/%	原始刚度/ MPa	修正系数/%	修正刚度/ MPa
A	100		110		110
B	93.02	6.98	111	93.02	103.25
C	80.48	19.52	112	80.48	90.138
D	34.67	65.33	181	34.67	62.753
E	61.04	38.96	181	61.04	110.48
F	55.85	44.15	181	55.85	101.09

下载: 导出CSV

表 7 各阶临界转速振型下转子-支承应变能占比

Table 7. Strain energy proportion of rotor-support under each critical speed mode

模态振型	考虑刚度损失/%		无刚度损失/%
模态振型	支承应变能	转子应变能	支承应变能	转子应变能
涡轮平动	85.02	14.98	85.39	14.61
压气机俯仰	80.18	19.82	80.38	19.62
1阶弯曲	4.82	95.18	4.66	95.34

下载: 导出CSV

表 8 各阶临界转速振型下端齿结构应变能占比对比分析

Table 8. Comparison of proportion of strain energy of the curvic couplings under each critical speed mode %

端齿	平动振型		俯仰振型		1阶弯曲
端齿	无损	有损	无损	有损	无损	有损
A	0.13	0.13	0.57	0.56	0.15	0.13
B	0.08	0.09	0.26	0.28	0.47	0.46
C	0.40	0.47	0.32	0.38	4.62	5.21
D	0.15	0.38	0.06	0.16	1.35	3.46
E	0.11	0.16	0.03	0.04	0.50	0.78
F	0.07	0.12	0.01	0.02	0.05	0.08
注：此处为端齿结构占整个转子系统应变能的比例，包括支承。

下载: 导出CSV

参考文献(23)

[1]	陈光, 洪杰, 马艳红. 航空燃气涡轮发动机结构[M]. 北京: 北京航空航天大学出版社, 2010. CHEN Guang, HONG Jie, MA Yanhong. Aviation gas turbine engine structure[M]. Beijing: Beijing University of Aeronautics & Astronautics Press, 2010. (in Chinese CHEN Guang, HONG Jie, MA Yanhong. Aviation gas turbine engine structure[M]. Beijing: Beijing University of Aeronautics & Astronautics Press, 2010. (in Chinese)
[2]	洪杰, 马艳红. 航空燃气涡轮发动机结构与设计[M]. 北京: 科学出版社, 2021. HONG Jie, MA Yanhong. Structure and design of aircraft gas turbine engine[M]. Beijing: Science Press, 2021. (in Chinese HONG Jie, MA Yanhong. Structure and design of aircraft gas turbine engine[M]. Beijing: Science Press, 2021. (in Chinese)
[3]	马艳红, 陈雪骑, 王永锋, 等. 航空燃气轮机转子系统结构非连续性及稳健设计[M]. 北京: 北京航空航天大学出版社, 2023. MA Yanhong, CHEN Xueqi, WANG Yongfeng, et al. Structural discontinuity and robust design of aero gas turbine rotor system[M]. Beijing: Beijing University of Aeronautics & Astronautics Press, 2023. (in Chinese MA Yanhong, CHEN Xueqi, WANG Yongfeng, et al. Structural discontinuity and robust design of aero gas turbine rotor system[M]. Beijing: Beijing University of Aeronautics & Astronautics Press, 2023. (in Chinese)
[4]	尹泽勇, 欧圆霞, 李彦, 等. 端齿轴段刚度及其对转子动力特性的影响[J]. 振动工程学报, 1993, 6(1): 63-67. YIN Zeyong, OU Yuanxia, LI Yan, et al. Stiffness of a shaft section with curvic couplings and its effect on dynamic characteristic of a rotor[J]. Journal of Vibration Engineering, 1993, 6(1): 63-67. (in Chinese YIN Zeyong, OU Yuanxia, LI Yan, et al. Stiffness of a shaft section with curvic couplings and its effect on dynamic characteristic of a rotor[J]. Journal of Vibration Engineering, 1993, 6(1): 63-67. (in Chinese)
[5]	尹泽勇, 欧园霞, 胡柏安, 等. 端齿连接及变轴力的影响[J]. 航空动力学报, 1994, 9(2): 20-23. YIN Zeyong, OU Yuanxia, HU Baian, et al. End-tooth connection and influence of variable axial force[J]. Journal of Aerospace Power, 1994, 9(2): 20-23. (in Chinese YIN Zeyong, OU Yuanxia, HU Baian, et al. End-tooth connection and influence of variable axial force[J]. Journal of Aerospace Power, 1994, 9(2): 20-23. (in Chinese)
[6]	PISANI S R, RENCIS J J. Investigating CURVIC coupling behavior by utilizing two- and three-dimensional boundary and finite element methods[J]. Engineering Analysis with Boundary Elements, 2000, 24(3): 271-275. doi: 10.1016/S0955-7997(99)00057-0
[7]	KIM B J, OH J, PALAZZOLO A. An improved preloaded Curvic coupling model for rotordynamic analyses[J]. Journal of Sound and Vibration, 2023, 544: 117391. doi: 10.1016/j.jsv.2022.117391
[8]	王龙凯, 麻鹏伟, 王艾伦, 等. 考虑端齿连接的转子-滚动轴承系统非线性振动特性研究[J]. 机械强度, 2023, 45(5): 1036-1042. WANG Longkai, MA Pengwei, WANG Ailun, et al. Study on nonlinear vibration characteristics for the rotor-rolling bearing system with curvic couplings[J]. Journal of Mechanical Strength, 2023, 45(5): 1036-1042. (in Chinese WANG Longkai, MA Pengwei, WANG Ailun, et al. Study on nonlinear vibration characteristics for the rotor-rolling bearing system with curvic couplings[J]. Journal of Mechanical Strength, 2023, 45(5): 1036-1042. (in Chinese)
[9]	杨郑烈, 王艾伦, 张海彪, 等. 考虑接触效应的端齿连接转子动力学特性研究[J]. 机械强度, 2020, 42(6): 1489-1495. YANG Zhenglie, WANG Ailun, ZHANG Haibiao, et al. Study on dynamic characteristics of end-toothed connection rotor considering contact effect[J]. Journal of Mechanical Strength, 2020, 42(6): 1489-1495. (in Chinese YANG Zhenglie, WANG Ailun, ZHANG Haibiao, et al. Study on dynamic characteristics of end-toothed connection rotor considering contact effect[J]. Journal of Mechanical Strength, 2020, 42(6): 1489-1495. (in Chinese)
[10]	张帅. 拉杆转子端面齿刚度弱化对模态的影响及其验证[J]. 热力透平, 2023, 52(2): 126-129, 152. ZHANG Shuai. Influence and its verification of stiffness weakening of end teeth on modal characteristics of central Tie-rod rotor[J]. Thermal Turbine, 2023, 52(2): 126-129, 152. (in Chinese ZHANG Shuai. Influence and its verification of stiffness weakening of end teeth on modal characteristics of central Tie-rod rotor[J]. Thermal Turbine, 2023, 52(2): 126-129, 152. (in Chinese)
[11]	裘子剑, 刘继兴. 双排圆弧端齿连接结构对转子动力特性的影响[J]. 制造技术与机床, 2021(12): 96-101. QIU Zijian, LIU Jixing. Influence of double-row curvic couplings connected structure on rotor dynamic characteristics[J]. Manufacturing Technology & Machine Tool, 2021(12): 96-101. (in Chinese QIU Zijian, LIU Jixing. Influence of double-row curvic couplings connected structure on rotor dynamic characteristics[J]. Manufacturing Technology & Machine Tool, 2021(12): 96-101. (in Chinese)
[12]	JIN Miao. The nonlinear dynamic characteristics of the aero-turboshaft engine rotor blade casing rubbing system with the curvic couplings considering the elastoplastic stage[J]. Engineering Analysis with Boundary Elements, 2024, 161: 78-102. doi: 10.1016/j.enganabound.2024.01.007
[13]	YIN Yijun, HENG Xing, ZHANG Haibiao, et al. Modeling method and dynamic analysis of turboshaft engine combustor rotor with curvic couplings considering thermal contact resistance under temperature field influence[J]. Results in Engineering, 2025, 25: 103853. doi: 10.1016/j.rineng.2024.103853
[14]	WANG Chongyang, LI Zihang, WANG Haoze, et al. Nonlinear modeling and vibration response analysis of rod fastening rotor-bearing system with curvic coupling[J]. Tribology International, 2024, 199: 109984. doi: 10.1016/j.triboint.2024.109984
[15]	HENG Xing, WANG Ailun, ZHANG Haibiao, et al. Research on the dynamic variation law of the discontinuous characteristics of the curvic coupling of aero-engine rotors under working conditions[J]. Engineering Science and Technology, an International Journal, 2024, 59: 101870.
[16]	洪杰, 徐翕如, 苏志敏, 等. 高速转子连接结构刚度损失及振动特性[J]. 北京航空航天大学学报, 2019, 45(1): 18-25. HONG Jie, XU Xiru, SU Zhimin, et al. Joint stiffness loss and vibration characteristics of high-speed rotor[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(1): 18-25. (in Chinese HONG Jie, XU Xiru, SU Zhimin, et al. Joint stiffness loss and vibration characteristics of high-speed rotor[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(1): 18-25. (in Chinese)
[17]	马艳红, 倪耀宇, 陈雪骑, 等. 长拉杆-止口连接弯曲刚度损失及对转子系统振动响应影响[J]. 航空学报, 2021, 42(3): 223861. MA Yanhong, NI Yaoyu, CHEN Xueqi. Bending stiffness loss of rod-rabbet joints and its effect on vibration response of rotor systems[J] Acta Aeronautica et Astronautica Sinica, 2021, 42(3): 223861. (in Chinese MA Yanhong, NI Yaoyu, CHEN Xueqi. Bending stiffness loss of rod-rabbet joints and its effect on vibration response of rotor systems[J] Acta Aeronautica et Astronautica Sinica, 2021, 42(3): 223861. (in Chinese)
[18]	邱欣可, 曾武, 高庆, 等. 基于应变能理论的端齿弯曲刚度及其转子动力学特性影响研究[J]. 燃气轮机技术, 2022, 35(3): 19-26. QIU Xinke, ZENG Wu, GAO Qing, et al. Research of the bending stiffness of couplings and the effect of rotor dynamic characteristics based on strain energy theory[J]. Gas Turbine Technology, 2022, 35(3): 19-26. (in Chinese QIU Xinke, ZENG Wu, GAO Qing, et al. Research of the bending stiffness of couplings and the effect of rotor dynamic characteristics based on strain energy theory[J]. Gas Turbine Technology, 2022, 35(3): 19-26. (in Chinese)
[19]	雷冰龙, 李超, 洪杰, 等. 转子连接结构力学特性稳健设计[J]. 航空发动机, 2021, 47(2): 38-44. LEI Binglong, LI Chao, HONG Jie, et al. Robust design of mechanical properties of rotor connection structures[J]. Aviation Engine, 2021, 47(2): 38-44 (in Chinese LEI Binglong, LI Chao, HONG Jie, et al. Robust design of mechanical properties of rotor connection structures[J]. Aviation Engine, 2021, 47(2): 38-44 (in Chinese)
[20]	洪杰, 沈玉芃, 王永锋, 等. 动力涡轮转子结构系统力学特性稳健设计方法[J]. 北京航空航天大学学报, 2019, 45(3): 437-445. HONG Jie, SHEN Yupeng, WANG Yongfeng, et al. Robust design method for mechanical characteristics of power turbine rotor structural system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(3): 437-445. (in Chinese HONG Jie, SHEN Yupeng, WANG Yongfeng, et al. Robust design method for mechanical characteristics of power turbine rotor structural system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(3): 437-445. (in Chinese)
[21]	洪杰, 徐筱李, 梁天宇, 等. 转子结构系统界面失效分析及稳健设计方法[J]. 航空动力学报, 2018, 33(3): 649-656. HONG Jie, XU Xiaoli, LIANG Tianyu, et al. Interface failure analysis and robust design method in rotor structural system[J]. Journal of Aerospace Power, 2018, 33(3): 649-656. (in Chinese HONG Jie, XU Xiaoli, LIANG Tianyu, et al. Interface failure analysis and robust design method in rotor structural system[J]. Journal of Aerospace Power, 2018, 33(3): 649-656. (in Chinese)
[22]	顾家柳. 转子动力学[M]. 北京: 国防工业出版社, 1985. GU Jialiu. Rotor dynamics[M]. Beijing: National Defense Industry Press, 1985. (in Chinese GU Jialiu. Rotor dynamics[M]. Beijing: National Defense Industry Press, 1985. (in Chinese)
[23]	LIU, F, HONG, J, MA, Y, et al. Research on robustness analysis and evaluation method of inter-shaft bearing-rear journal of low press turbine system[C]//Proceedings of the ASME Turbo Expo: Turbomachinery Technical Conference and Exposition. Boston, Massachusetts, US: ASME, 2023: V11AT22A026.