基于双重极值响应面法的叶盘联动可靠性分析

推进技术 ›› 2016, Vol. 37 ›› Issue (6): 1158-1164.

基于双重极值响应面法的叶盘联动可靠性分析

张春宜¹,路成¹,费成巍²,宋鲁凯¹,魏文龙¹

哈尔滨理工大学机械动力工程学院，黑龙江哈尔滨 150080,哈尔滨理工大学机械动力工程学院，黑龙江哈尔滨 150080,北京航空航天大学计算机学院，北京 100191,哈尔滨理工大学机械动力工程学院，黑龙江哈尔滨 150080,哈尔滨理工大学机械动力工程学院，黑龙江哈尔滨 150080

发布日期:2021-08-15
作者简介:张春宜，男，博士，教授，研究领域为机械设计、可靠性工程及优化设计。
基金资助:
国家自然科学基金(51275138)。

Linked Reliability Analysis of Aeroengine Blisk with Dual Extreme Response Surface Method

School of Mechanical and Power Engineering，Harbin University of Science and Technology，Harbin 150080，China,School of Mechanical and Power Engineering，Harbin University of Science and Technology，Harbin 150080，China,School of Computer Science and Engineering，Beijing University of Aeronautics and Astronautics，Beijing 100191，China,School of Mechanical and Power Engineering，Harbin University of Science and Technology，Harbin 150080，China and School of Mechanical and Power Engineering，Harbin University of Science and Technology，Harbin 150080，China

Published:2021-08-15

摘要/Abstract

摘要： 为了更准确地研究变形和应力对航空发动机叶盘性能的影响，在湍流模型理论和叶盘流场模型的基础上，提出了一种可靠性分析方法即双重极值响应面法(Dual Extremum Response Surface Method，DERSM)。在分析中考虑气体压力和离心力作用，合理选取随机输入变量，得到叶盘结构的总体最大变形和最大应力，并作为输出响应；对随机变量进行抽样，通过抽样点拟合各自的极值响应面方程；结合蒙特卡洛法对两个极值响应面模型进行联动抽样，计算出了航空发动机叶盘的可靠性概率。实例仿真表明:当叶盘最大允许变形量为4.2mm，最大许用应力为7.5×102MPa时，其可靠性概率为98.61%。与极值响应面法(Extremum Response Surface Method，ERSM)相比，DERSM在保证计算精度的前提下，计算效率提高23.52%，验证了DERSM在叶盘可靠性分析方面的有效性。

关键词: 可靠性分析；双重极值响应面法；叶盘；航空发动机；流-固耦合

Abstract: In order to more accurately predict the effects of deformation and stress on the performance of aeroengine blisk，a method of reliability analysis called DERSM (Dual Extremum Response Surface Method) was proposed based on the theory of turbulence model and the fluid field model of aeroengine blisk. Considering gas pressure and centrifugal force，the maximum deformation and stress were taken as the objects of blisk reliability analysis with respect to the reasonable random input variables. Extreme response surface equation is respectively fitted to the sample data acquired by extracting the random variables. The reliability probability of aeroengine blisk was obtained by using Monte Carlo method and linkage sampling to two extreme response surfaces. The simulation results show that the reliability degree is 98.61% when the maximum allowable deformation of bladed disk is 4.2mm and the maximum allowable stress is 7.5×102MPa. Compared with ERSM (Extremum Response Surface Method)，it is demonstrated that the computational efficiency of DERSM increased by 23.52% while keeping the calculation precision. The validity of reliability analysis of blisk based on DERSM is verified.

Key words: Reliability analysis；Dual extreme response surface method；Blisk；Aero-engine；Fluid-solid interaction

张春宜,路成,费成巍,宋鲁凯,魏文龙. 基于双重极值响应面法的叶盘联动可靠性分析[J]. 推进技术, 2016, 37(6): 1158-1164.

ZHANG Chun-yi¹,LU Cheng¹,FEI Cheng-wei²,SONG Lu-kai¹,WEI Wen-long¹. Linked Reliability Analysis of Aeroengine Blisk with Dual Extreme Response Surface Method[J]. Journal of Propulsion Technology, 2016, 37(6): 1158-1164.

参考文献

[1] 刘大响, 陈光. 航空发动机—飞机的心脏[M]. 北京:航空工业出版社, 2010.
[2] 白斌, 白广忱, 童小晨, 等. 航空发动机叶盘结构应力和变形的概率分析[J]. 航空发动机, 2014, 40(2): 38-46.
[3] 费成巍, 白广忱. 航空发动机涡轮叶片径向变形的概率分析[J]. 航空发动机, 2012, 38(1): 17-20.
[4] 王建军, 姚建尧, 李其汉. 刚度随机失谐叶盘结构概率模态特性分析[J]. 航空动力学报, 2008, 23(2): 256-262.
[5] Rossi M R, Feiner D M, Griffin J H. Experimental Study of the Fundamental Mistuning Model for Probabilistic Analysis[C]. Reno-Tahoe: ASME Turbo Expo, 2005.
[6] Han Xu, Jiang Chao, Liu Li-Xin, et al. Response-Surface-Based Structural Reliability Analysis with Random and Interval Mixed Uncertainties[J]. Science China Technological Sciences, 2014, 57(7): 1322-1334.
[7] 薛亮, 韩万金, 黄家骅, 等. 基于试验设计和响应面模型的风扇转子启动优化设计[J]. 推进技术, 2009, 30(3): 308-313. (XUE Liang, HAN Wan-Jin, HUANG Jia-hua, et al. Dynamic Optimization of a Fan Rotor Based on Design of Experiment and Response Surface Model[J]. Journal of Propulsion Technology, 2009, 30(3): 308-313.)
[8] Chen Jian-Yun, Xu Qiang, Li Jing, et al. Improved Response Surface Method for Anti-Slide Reliability Analysis of Gravity Dam Based on Weighted Regression[J]. Journal of Zhejiang University: Science A, 2010, 11(6): 432-439.
[9] Zhang Chun-Yi, Bai Guang-Chen. Extremum Response Surface Method of Reliability Analysis on Two-Link Flexible Robot Manipulator[J]. Journal of Central South University of Technology, 2012, 19(1): 101-107.
[10] 王桂华, 费成巍, 白广忱. 基于ERSM涡轮盘径向变形的非线性动态概率分析[J]. 推进技术, 2013, 34(4):529-536. (WANG Gui-hua, FEI Cheng-wei, BAI Guang-chen. Nonlinear Dynamic Probabilistic Analysis of Turbine Disk Radial Deformation Based on ERSM[J]. Journal of Propulsion Technology, 2013, 34(4):529-536.)
[11] Bai Guang-Chen, Fei Cheng-Wei. Distributed Collaborative Response Surface Method for Mechanical Dynamic Assembly Reliability Design[J]. Chinese Journal of Mechanical Engineering, 2013, 26(6): 1160-1168.
[12] LIAO Chuan-jun, HUANG Wei-feng, WANG Yu-ming, et al. Fluid-Solid Interaction Model for Hydraulic Reciprocating O-Ring Seals[J]. Chinese Journal of Mechanical Engineering (English Edition), 2013, 26(1):85-94.
[13] HUA Cheng, FANG Chao. Simulation of Fluid-Solid Interaction on Water Ditching of an Airplane by ALE Method[J]. Science Direct Journal of Hydrodynamics, 2011, 23(5): 637-642.
[14] 肖若富, 朱文若, 杨魏, 等. 基于双向流固耦合水轮机转轮应力特性分析[J]. 排灌机械工程学报, 2013, 31(10): 862-866.
[15] 李惠彬, 周鹂磷, 孙恬恬, 等. 涡轮增压器叶轮流场耦合模态分析[J]. 振动、测试与诊断, 2008, 28(3):252-255.
[16] 侯晓春, 季鹤鸣, 刘庆国, 等. 高性能航空燃气轮机燃烧技术[M]. 北京:国防工业出版社, 2002.
[17] 曾攀. 有限元分析及应用[M]. 北京:清华大学出版社, 2004.
[18] 秦权, 林道锦, 梅刚. 结构可靠度随机有限元—理论及工程应用[M]. 北京:清华大学出版社, 2006.
[19] 费成巍, 白广忱. 基于DCRSM的HPT叶尖径向运行间隙可靠性分析[J]. 航空学报, 2013, 34(9):2141-2149.
[20] 隋允康, 宇惠平. 响应面方法的改进及其对工程优化的应用[M]. 北京:科学出版社, 2010.
[21] 张志红, 何桢, 郭伟. 在响应曲面方法中三类中心复合设计的比较研究[J]. 沈阳航空学报, 2007, 24(1): 87-91.
[22] 刘志平, 石林英. 最小二乘法原理及其MATLAB实现[J]. 中国西部科技, 2008, 7(17): 33-34.
[23] 李建保, 张铁, 孙宝京, 等. 基于正交多项式最小二乘分段拟合的气象探测数据处理方法[C]. 绵阳:2011中国决策与控制会议, 2011.
[24] LI Zhong-mu, HAN Zhan-wen. Fitting Formulae for the Effects of Binary Interactions on Lick Indices and Colors of Stellar Populations[J]. Research in Astronomy and Astrophyscis, 2009, 9(2): 191-204.
[25] 张书刚, 郭迎清, 陈小磊. 航空发动机故障诊断系统性能评价与仿真验证[J]. 推进技术, 2013, 34(8):1121-1127. (ZHANG Shu-gang, GUO Ying-qing, CHEN Xiao-lei. Performance Evaluation and Simulation Validation of Fault Diagnosis System for Aircraft Engine[J]. Journal of Propulsion Technology, 2013, 34(8):1121-1127.)
[26] Jahani Ehsan, Shayanfar Mohsen A, Barkhordari Mohammad A. A New Adaptive Importance Sampling Monte Carlo Method for Structural Reliability[J]. KSCE Journal of Civil Engineering, 2013, 17(1): 210-215.
[27] 王芳, 侯朝帧. 一种估计网络可靠性的蒙特卡洛方法[J]. 计算机工程, 2004, 30(18): 13-15.
[28] FEI Cheng-wei. BAI Guang-chen. Nonlinear Dynamic Probabilistic Analysis for Turbine Casing Radial Deformation Using Extremum Response Surface Method Based on Support Vector Machine[J]. Journal of Computational and Nonlinear Dynamics, 2013, 8: 1-8
[29] 费成巍, 白广忱, 范觉超, 等. 涡轮转子多尺寸装配可靠性优化分析[J]. 推进技术, 2013, 34(1): 15-18. (FEI Cheng-wei, BAI Guang-chen, FAN Jue-chao, et al. Optimization and Analysis for Multi-Dimensions Assembly Reliability of Turbine Rotor[J]. Journal of Propulsion Technology, 2013, 34(1): 15-18.)
[30] WANG Jin-hui, CHU Guan-quan, LI Kai-yuan. Study on the Uncertainty of the Available Time Under Ship Fire Based on Monte Carlo Sampling Method[J]. China Ocean Engineering, 2013, 27(1): 131-140.(编辑:朱立影)　　　　　　　　　　　　　*　收稿日期:2015-01-20；修订日期:2015-02-24。基金项目:国家自然科学基金(51275138)。作者简介:张春宜,男,博士,教授,研究领域为机械设计、可靠性工程及优化设计。E-mail: zhangchunyi@hrbust.edu.cn