﻿ 连接界面变形对转子动力特性影响的力学模型<sup>*</sup>
 文章快速检索 高级检索

1. 北京航空航天大学 能源与动力工程学院, 北京 100083;
2. 中国航发沈阳发动机设计研究所, 沈阳 110015;
3. 先进航空发动机协同创新中心, 北京 100083

Mechanical models of influence of interface deformation on rotor dynamic characteristics
JIN Hai1,2, LIU Jixing1, ZHANG Dayi1, HONG Jie1,3
1. School of Energy and Power Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. AECC Shenyang Engine Design and Research Institute, Shenyang 110015, China;
3. Collaborative Innovation Center of Advanced Aero-Engine, Beijing 100083, China
Received: 2017-06-30; Accepted: 2017-09-08; Published online: 2017-10-18 17:07
Foundation item: National Natural Science Foundation of China (51575022, 51475021)
Corresponding author. ZHANG Dayi, E-mail:dayi@buaa.edu.cn
Abstract: In order to analyze the problems of vibration increasing and interface wear of aero engine during work, the dynamic models of rotor-bearing system with three disks were established on the basis of the structural feature analysis. A parametric description has been made to analyze the coaxial and parallelism deviation of contact interface, and the dynamic differential equation for rigid high pressure rotor system was obtained by the Lagrangian method considering the interface deformation. The results exhibit that the interface deformation will cause the additional excitation force in the rigid rotor system, where the amplitude of the additional excitation force caused by the coaxial deviation is proportional to the square of the speed, and only applies to the corresponding degree of freedom; the amplitude of the additional excitation force caused by the parallelism deviation is only related with the rigidity and the deviation magnitude regardless of the speed, and it also applies to the support freedom.
Key words: aero engine     interface deformation     Lagrangian method     additional excitation force     rigid rotor system

1 高压转子界面变形力学模型 1.1 典型高压转子系统结构特征

 图 1 高压转子系统结构简图 Fig. 1 Sketch of HP rotor system
 图 2 考虑螺栓连接结构的高压转子分析模型 Fig. 2 Analysis model of HP rotor considering bolted joints
1.2 螺栓连接结构界面变形模型

1.2.1 接触端面同轴度偏差

 图 3 接触界面滑移量周向分布不均示意图 Fig. 3 Schematic of skip circumferential maldistribution of contact interface

 (1)

1.2.2 接触端面平行度偏差

 图 4 接触界面平行度偏差示意图 Fig. 4 Schematic of contact interface parallelism deviation
1.3 界面变形对转子动力特性影响模型

1.3.1 接触端面同轴度偏差

 图 5 接触端面同轴度偏差对转子系统影响 Fig. 5 Impact of contact interface coaxial deviation on rotor system

 图 6 转子盘2形心偏移和倾斜示意图 Fig. 6 Schematic of centroid offset and skew of disk 2

 (2)

 (3)

 图 7 同轴度偏差导致的形心偏移和倾斜 Fig. 7 Centroid offset and skew caused by coaxial deviation

1.3.2 接触端面平行度偏差

 图 8 接触端面平行度偏差对转子系统影响 Fig. 8 Impact of contact interface parallelism deviation on rotor system

 (4)

 (5)

 (6)

2 Lagrange方法建立转子系统运动学方程 2.1 欧拉角坐标下的转子系统运动学描述

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

2.2 端面同轴度偏差对动力特性的影响

 (14)

 (15)

 (16)

 (17)

 (18)

2.3 端面平行度偏差对动力特性的影响

 (19)

 (20)

xOz平面内转子盘轴系统弹性势能V′dx

 (21)

 (22)

3 结论

1) 以典型航空发动机高压刚性转子为例，对界面变形模型进行分析，并对接触端面同轴度偏差以及平行度偏差的界面变形进行定量描述，建立了考虑界面变形的刚性转子系统力学模型。

2) 对典型航空发动机高压刚性转子系统采用Lagrange方法建立了考虑界面变形以及弹性支承的16自由度动力学方程，并推导了界面变形对系统动力学方程的影响。同轴度偏差将使得转子系统产生附加不平衡激振力和附加第1类初始倾斜激振力，激振力幅值均与转速平方成正比，且分别作用于平动和转动自由度，对支承自由度无影响；平行度偏差将产生附加初始弯曲激振力和第2类初始倾斜激振力，激振力幅值均与转速无关，仅与刚度和平行度偏差量有关，且该附加激振力在支承自由度方向有一定分量。

 [1] 付才高, 郑大平, 欧园霞. 航空发动机设计手册第19册:转子动力学及整机振动[M]. 北京: 航空工业出版社, 2000: 1-6. FU C G, ZHENG D P, OU Y X. Aero engine design manual 19th:Rotordynamics and whole engine vibration[M]. Beijing: Aviation Industry Press, 2000: 1-6. (in Chinese) [2] 洪杰, 马艳红, 张大义. 航空燃气轮机总体结构设计与动力学分析[M]. 北京: 北京航空航天大学出版社, 2014: 366-369. HONG J, MA Y H, ZHANG D Y. Structure design and dynamic analysis of aero gas turbine engines[M]. Beijing: Beihang University Press, 2014: 366-369. (in Chinese) [3] 陈萌, 马艳红, 刘书国, 等. 航空发动机整机有限元模型转子动力学分析[J]. 北京航空航天大学学报, 2007, 33 (9): 1013–1016. CHEN M, MA Y H, LIU S G, et al. Rotordynamics analysis of whole aero-engine models based on finite element method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33 (9): 1013–1016. (in Chinese) [4] BÖSWALD M, LINK M, SCHEDLINSKI C. Computational model updating and validation of aero-engine finite element models based on vibration test data[C]//International Forum on Aeroelasticity and Structural Dynamics, 2005: 1-17. [5] 李俊慧, 马艳红, 洪杰. 转子系统套齿结构动力学设计方法研究[J]. 航空发动机, 2009, 35 (4): 36–39. LI J H, MA Y H, HONG J. Dynamic design method of spline joint structure for rotor system[J]. Aero Engine, 2009, 35 (4): 36–39. (in Chinese) [6] 闻邦椿, 顾家柳. 高等转子动力学:理论、技术与应用[M]. 北京: 机械工业出版社, 1999: 77-82. WEN B C, GU J L. Advanced rotor dynamics-theory technology and application[M]. Beijing: China Machine Press, 1999: 77-82. (in Chinese) [7] ARUMUGAM P, SWARNAMANI S, PRABHU B S. Effects of coupling misalignment on the vibration characteristics of a two stage turbine rotor[C]//ASME Design Engineering Technical Conference. New York: ASME, 1995: 1049-1054. [8] LI J, HONG J, MA Y, et al. Modelling of misaligned rotor systems in aero-engines[C]//ASME 2012 International Mechanical Engineering Congress and Exposition. New York: ASME, 2012: 535-543. [9] 姚星宇, 王建军, 翟学. 航空发动机螺栓连接薄层单元建模方法[J]. 北京航空航天大学学报, 2015, 41 (12): 2269–2279. YAO X Y, WANG J J, ZHAI X. Modeling method of bolted joints of aero engine based on thin-layer element[J]. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41 (12): 2269–2279. (in Chinese) [10] 姚星宇, 王建军. 航空发动机螺栓连接载荷与结构参数对连接刚度影响规律[J]. 推进技术, 2017, 38 (2): 424–433. YAO X Y, WANG J J. Effects of load and structure parameters of aero engine bolted joints on joint stiffness[J]. Journal of Propulsion Technology, 2017, 38 (2): 424–433. (in Chinese) [11] QIN Z Y, HAN Q K, CHU F L. Analytical model of bolted disk-drum joints and its application to dynamic analysis of jointed rotor[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2014, 228 (4): 646–663. DOI:10.1177/0954406213489084 [12] QIN Z, HAN Q, CHU F. Bolt loosening at rotating joint interface and its influence on rotor dynamics[J]. Engineering Failure Analysis, 2016, 59 : 456–466. DOI:10.1016/j.engfailanal.2015.11.002 [13] LIU S, MA Y, ZHANG D, et al. Studies on dynamic characteristics of the joint in the aero-engine rotor system[J]. Mechanical Systems & Signal Processing, 2012, 29 (5): 120–136. [14] WANG C, ZHANG D, ZHU X, et al. Study on the stiffness loss and the dynamic influence on rotor system of the bolted flange joint[C]//ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. New York: ASME, 2014: 1-14. [15] 杨帆. 燃气轮机螺栓连接结构热蠕动及动力学特性研究[D]. 哈尔滨: 哈尔滨工业大学, 2016. YANG F. Gas turbine bolt connection structure thermal creep and dynamics research[D]. Harbin: Harbin Institute of Technology, 2016(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10213-1016774328.htm [16] YAMAMOTO T, ISHIDA Y. Linear and nonlinear rotordynamics:A modern treatment with applications[M]. New York: John Wiley & Sons, 2001: 35-39.

文章信息

JIN Hai, LIU Jixing, ZHANG Dayi, HONG Jie

Mechanical models of influence of interface deformation on rotor dynamic characteristics

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(6): 1294-1302
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0440