带冠涡轮叶片振动特性的子区间组合分析方法

推进技术 ›› 2017, Vol. 38 ›› Issue (10): 2323-2330.

带冠涡轮叶片振动特性的子区间组合分析方法

刘继兴¹,张大义¹,王存¹,洪杰^1,2

北京航空航天大学能源与动力工程学院，北京 100191,北京航空航天大学能源与动力工程学院，北京 100191,北京航空航天大学能源与动力工程学院，北京 100191,北京航空航天大学能源与动力工程学院，北京 100191; 先进航空发动机协同创新中心，北京 100191

发布日期:2021-08-15
作者简介:刘继兴，男，硕士生，研究领域为航空发动机振动控制。E-mail: jixing_liu@163.com 通讯作者:张大义，男，博士，副教授，研究领域为航空发动机结构强度振动。
基金资助:
国家自然科学基金面上项目(51575022)。

Sub-Interval Combination Method for Dynamical Characteristics of Shrouded Turbine Blades

School of Energy and Power Engineering，Beihang University，Beijing 100191，China,School of Energy and Power Engineering，Beihang University，Beijing 100191，China,School of Energy and Power Engineering，Beihang University，Beijing 100191，China and School of Energy and Power Engineering，Beihang University，Beijing 100191，China; Collaborative Innovation Center of Advanced Aero-Engine，Beijing 100191，China

Published:2021-08-15

摘要/Abstract

摘要： 为准确计算分析带冠涡轮叶片振动特性的非确定性问题，将区间组合法与有限元法相结合，发展了适用于复杂结构振动特性的区间求解方法，并建立了基于商用有限元软件的区间振动特性求解流程。考虑工况温度、叶冠接触状态和榫头约束角刚度的分散性，对带冠涡轮叶片的模态特性和振动响应进行了求解，研究得到了典型结构、载荷等非确定性参数对叶片振动特性的影响规律。研究结果表明，与蒙特卡洛法相比，该方法可使计算效率提高10倍以上，计算结果的相对误差不大于50%，获得振动特性的区间结果更为可靠，并且该方法无需对非确定性参数的概率分布进行假设，具有良好的工程应用前景。

关键词: 叶片；非确定性；区间方法；有限元法；振动特性

Abstract: In order to analysis the uncertain problems of dynamical characteristics of shrouded turbine blades accurately， an interval method for complex structures combined by interval theory and finite element method has been presented. The solution procedure for the interval dynamical characteristics is given based on the commercial finite element software. Taking the dispersion of operation temperature， contact status of the shrouds and angular stiffness of firtree root into account， the modal characteristics and vibration response of a shrouded turbine blade are studied， and as a consequence the effects of typical uncertain parameters of structures and loads on the vibration characteristics of blade are obtained. The results show that the computational efficiency can be improved more than 10 times， and the relative error of the calculated results is less than 50% compared with Monte Carlo method， in particular the results obtained by the interval method are more reliable. Moreover it is not necessary to get the information about the probability distribution characteristics for the uncertain parameters by this developed method， which indicates a better engineering application prospect compared to most probabilistic methods.

Key words: Blades；Uncertainty；Interval method；Finite element method；Dynamical characteristics

刘继兴,张大义,王存,洪杰. 带冠涡轮叶片振动特性的子区间组合分析方法[J]. 推进技术, 2017, 38(10): 2323-2330.

LIU Ji-xing¹,ZHANG Da-yi¹,WANG Cun¹,HONG Jie^1,2. Sub-Interval Combination Method for Dynamical Characteristics of Shrouded Turbine Blades[J]. Journal of Propulsion Technology, 2017, 38(10): 2323-2330.

参考文献

[1] Srinivasan AV. Flutter and Resonant Vibration Characteristics of Engine Blades[J]. Engineering for Gas Turbines and Power, 1997, 119(4): 742-775.
[2] Dianyin Hu, Jianxing Mao, Rongqiao Wang, et al. Optimization Strategy for a Shrouded Turbine Blade Using Variable-Complexity Modeling Methodology[J]. AIAA Journal, 2016, 54(9): 2808-2818.
[3] 陈璐璐, 张大义, 文敏, 等. 带凸肩风扇叶片振动特性及设计方法研究[J]. 推进技术, 2015, 36(9):1389-1394. (CHEN Lu-lu, ZHANG Da-yi, WEN Min, et al. Dynamical Effects of Shrouds on Fan Blade Vibration and Its Corresponding Design Method[J]. Journal of Propulsion Technology, 2015, 36(9): 1389-1394.)
[4] 马艳红, 张大义, 洪杰, 等. 气流激励下叶片的高周疲劳概率寿命预估[J]. 推进技术, 2009, 30(4):462-467. (MA Yan-hong, ZHANG Da-yi, HONG Jie, et al. Prediction on High-Cycle Life of Blades Using Probability Method[J]. Journal of Propulsion Technology, 2009, 30(4): 462-467.)
[5] 航空发动机设计手册第18册, 叶片轮盘及主轴强度分析 [M]. 北京:航空工业出版社, 2001.
[6] Zhang D, Hong J, Ma Y, et al. A Probability Method for Prediction on High Cycle Fatigue of Blades Caused by Aerodynamic Loads[J]. Advances in Engineering Software, 42(12): 1059-1073.
[7] 徐可君, 江龙平, 陈景亮, 等. 叶片振动的非概率可靠性研究[J]. 机械工程学报, 2002, 38(10): 17-19.
[8] 杨鑫. 带冠涡轮叶片动力响应设计技术研究[D]. 北京:北京航空航天大学, 2008.
[9] 杨鑫, 马艳红, 洪杰. 基于接触状态的叶冠预扭设计和磨损分析[J]. 燃气涡轮试验与研究, 2008, 21(3): 35-39.
[10] Kaminski M. Perturbation Based on Stochastic Finite Element Method Homogenization of Two-Phaseelastic Composites[J]. Computers & Structures, 2000, 78(6): 811-826.
[11] Li Chen, Rao S S. Fuzzy Finite-Element Approach for the Vibration Analysis[J]. Finite Elements in Analysis and Design, 1997, 27(1): 69-83.
[12] 邱志平. 非概率集合理论凸方法及其应用[M]. 北京: 国防工业出版社, 2005.
[13] 陈萌. 航空发动机转子系统动力学特性区间分析理论与方法研究[D]. 北京:北京航空航天大学, 2010.
[14] Ma Y, Liang Z, Chen M, et al. Interval Analysis of Rotor Dynamic Response with Uncertain Parameters[J]. Journal of Sound & Vibration, 2013, 332(16): 3869-3880.
[15] Wang X, Qiu Z. Interval Finite Element Analysis of Wing Flutter[J]. Chinese Journal of Aeronautics, 2008, 21(2): 134-140.
[16] Rao S S, BerkeL. Analysis of Uncertain Structural System Using Interval Analysis[J]. AIAA Journal,1997, 35(4): 725-735.
[17] Stewart Mc William. Anti-Optimisation of Uncertain Structures Using Interval Analysis[J]. Computers and Structures, 2001, 79(4): 421-430.
[18] 郭书祥, 吕震宙. 线性区间有限元静力控制方程的组合解法[J]. 计算力学学报, 2003, 20(1): 34-38.
[19] 张建国, 陈建军, 马孝松, 等. 不确定结构动力特征值区间分析的一种算法[J]. 应用力学学报, 2006, 23(1): 96-100.
[20] Moore R E, Kearfott R B, Cloud M J. Introduction to Interval Analysis[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2009.
[21] 洪杰, 杨鑫, 陈璐璐, 等. 基于接触状态分析的叶冠阻尼评估与改进设计[J]. 北京航空航天大学学报, 2012, 38(5): 681-687.
[22] Mindlin R D. Compliance of Elastic Bodies in Contact[J]. Journal of Applied Mech. ASME, 1949, 16.(编辑:梅瑛)　　　　　　　　　　　　　*　收稿日期:2016-10-01；修订日期:2016-12-28。基金项目:国家自然科学基金面上项目(51575022)。作者简介:刘继兴,男,硕士生,研究领域为航空发动机振动控制。E-mail: jixing_liu@163.com通讯作者:张大义,男,博士,副教授,研究领域为航空发动机结构强度振动。E-mail: dayi@buaa.edu.cn