不确定转子系统非参数建模与散度参数识别

刘彦旭; 刘保国; 张震; 冯伟; 张瑞丰

doi:10.13224/j.cnki.jasp.20230065

不确定转子系统非参数建模与散度参数识别

doi: 10.13224/j.cnki.jasp.20230065

刘彦旭^1,,
刘保国^{1, 2,*, ,},
张震¹,
冯伟^{1, 2},
张瑞丰¹

1.
河南工业大学机电工程学院，郑州 450001
2.
河南工业大学河南省超硬磨料磨削装备重点实验室，郑州 450001

基金项目: 国家自然科学基金（12072106）

详细信息

作者简介:
刘彦旭（1990-），男，博士生，主要从事转子动力学研究。E-mail：yanxuliu2010@sina.com

通讯作者:
刘保国（1962-），男，教授、博士生导师，博士，主要从事转子动力学、随机振动研究。E-mail：bgliu1978@sina.com

中图分类号: V233.1
计量
- 文章访问数: 497
- HTML浏览量: 218
- PDF量: 55
- 被引次数: 0
出版历程
- 收稿日期: 2023-02-09
- 网络出版日期: 2023-08-17

Nonparametric modeling and dispersion parameter identification for uncertain rotor systems

LIU Yanxu^1
,,
LIU Baoguo^{1, 2,*
, ,},
ZHANG Zhen¹,
FENG Wei^{1, 2},
ZHANG Ruifeng¹

1.
School of Electromechanical Engineering，Henan University of Technology，Zhengzhou 450001，China
2.
Henan Key Laboratory for Superabrasive Grinding Equipment，Henan University of Technology，Zhengzhou 450001，China

摘要

摘要:
针对具有不确定性的转子系统，提出了基于非参数建模和矩阵极分解理论的不确定动力学建模方法，并提出了适用于不确定转子系统非参数动力学模型散度参数识别的方法。利用所搭建的转子实验台对该方法进行了实验验证。结果表明：在转子系统的4个观测点处，转子转速不超过3 000 r/min时，非参数模型结果的均值和确定性模型几乎重合；但转速接近1阶临界转速时，采用非参数不确定动力学计算模型所得到的结果均值与实测结果更为接近。该研究可为研究具有模型不确定性的双转子或多转子系统的非参数建模方法及对应的散度参数识别方法研究提供参考。
- 非参数建模 /
- 模型不确定 /
- 转子系统 /
- 散度参数 /
- 振动响应
Abstract:
For rotor systems with uncertainty, an uncertain dynamic modeling method based on nonparametric modeling and matrix polar decomposition theory was proposed, and a method for identifying the dispersion parameters of the nonparametric dynamic model of the uncertain rotor system was also proposed. The nonparametric modeling method was verified by utilizing the rotor experimental platform. The results showed that at four observation points of the rotor system, when the rotor speed did not exceed 3 000 r/min, the mean value of the results of the nonparametric model almost coincided with the deterministic model. However, when the speed was close to the first critical speed, the mean value of the results obtained by the nonparametric uncertain dynamic calculation model was closer to the measured results. This study can provide a reference for the study of nonparametric modeling methods and corresponding dispersion parameter identification methods of two-rotor or multi-rotor systems with model uncertainty.
- nonparametric modeling /
- model uncertainty /
- rotor system /
- dispersion parameter /
- vibration response

HTML

图 1 转子-支承系统

Figure 1. System of the rotor-support

下载: 全尺寸图片幻灯片

图 2 转子-支承系统计算模型

Figure 2. Computational model of the system of rotor-support

下载: 全尺寸图片幻灯片

图 3 转子实验平台

Figure 3. Rotor experimental bench

下载: 全尺寸图片幻灯片

图 4 确定性动力学计算模型的坎贝尔图

Figure 4. Campbell diagram of the deterministic dynamic model

下载: 全尺寸图片幻灯片

图 5 确定性动力学计算模型的1阶振型

Figure 5. First order vibration mode of deterministic dynamic model

下载: 全尺寸图片幻灯片

图 6 转子系统的1阶振型

Figure 6. First order vibration mode of the rotor system

下载: 全尺寸图片幻灯片

图 7 不确定动力学计算模型振动响应预测

Figure 7. Vibration response prediction of the uncertain dynamic calculation model

下载: 全尺寸图片幻灯片

图 8 振动响应实测结果与非参数动力学模型预测的对比

Figure 8. Comparison between the measured results of vibration response and the prediction of nonparametric dynamic model

下载: 全尺寸图片幻灯片

表 1 转子实验台参数

Table 1. Parameters of the rotor experimental bench

参数	数值
转轴半径r/m	0.005
转轴弹性模量E/10¹¹ （N/m²）	2.060
轴长度l_i/m	0.408
各轮盘质量m_i/kg	0.670，0.500，0.340
各轮盘的直径d_i/m	0.039，0.039，0.020
支承刚度k₁/10⁷ （N/m）	6.0
支承刚度k₂/10⁷ （N/m）	6.0
各观测点距轴左端距离/m	0.058，0.193，0.278，0.343
盘2上的不平衡质量m_u/g	0.359
不平衡质量的偏心距e/m	0.03

下载: 导出CSV

参考文献(29)

[1]	雷冰龙,李超,何康,等. 共用支承-转子系统耦合振动分析及试验[J]. 航空动力学报,2020,35(11): 2293-2305. LEI Binglong,LI Chao,HE Kang,et al. Coupling vibration characteristics analysis and experiment of shared support-rotors system[J]. Journal of Aerospace Power,2020,35(11): 2293-2305. (in Chinese)
[2]	章健,张大义,王永锋,等. 共用支承-转子结构系统振动耦合特性分析[J]. 北京航空航天大学学报,2019,45(9): 1902-1910. ZHANG Jian,ZHANG Dayi,WANG Yongfeng,et al. Coupling vibration characteristics analysis of shared support-rotors system[J]. Journal of Beijing University of Aeronautics and Astronautics,2019,45(9): 1902-1910. (in Chinese)
[3]	CAPIEZ-LERNOUT E,SOIZE C. Nonlinear stochastic dynamics of detuned bladed-disks with uncertain mistuning and detuning optimization using a probabilistic machine learning tool[J]. International Journal of Non-Linear Mechanics,2022,143: 104023. doi: 10.1016/j.ijnonlinmec.2022.104023
[4]	CAPIEZ-LERNOUT E,SOIZE C. Nonparametric modeling of random uncertainties for dynamic response of mistuned bladed disks[J]. Journal of Engineering for Gas Turbines and Power,2004,126(3): 610-618. doi: 10.1115/1.1760527
[5]	SINHA A. Reduced-order model of a bladed rotor with geometric mistuning[J]. Journal of Turbomachinery,2009,131(3): 031007.1-031007.7.
[6]	MADDEN A,EPUREANU B I,FILIPPI S. Reduced-order modeling approach for blisks with large mass, stiffness, and geometric mistuning[J]. AIAA Journal,2012,50(2): 366-374. doi: 10.2514/1.J051140
[7]	GAN Chunbiao,WANG Yuehua,YANG Shixi. Nonparametric modeling on random uncertainty and reliability analysis of a dual-span rotor[J]. Journal of Zhejiang University: Science A (Applied Physics & Engineering),2018,19(3): 189-202. doi: 10.1631/jzus.A1600340
[8]	WANG Xiaojun,QIU Zhiping. Interval finite element analysis of wing flutter[J]. Chinese Journal of Aeronautics,2008,21(2): 134-140. doi: 10.1016/S1000-9361(08)60017-5
[9]	ZHANG Hongyan,BAI Changqing,MAO Yijun. Stochastic finite element modeling and response analysis of rotor systems with random properties under random loads[J]. Journal of Mechanical Science and Technology,2015,29(8): 3083-3090. doi: 10.1007/s12206-015-0706-9
[10]	刘保国,梁国珍,苏林林,等. 基于摄动法的随机参数转子系统动力响应的概率密度分析[J]. 机械强度,2013,35(4): 400-405. LIU Baoguo,LIANG Guozhen,SU Linlin,et al. Probability density analysis of the dynamic response of random parametricalrotor system based on the perturbation method[J]. Journal of Mechanical Strength,2013,35(4): 400-405. (in Chinese)
[11]	王存. 基于切比雪夫多项式展开的转子动力特性区间分析[J]. 航空动力学报,2020,35(4): 757-765. WANG Cun. Interval analysis of rotor dynamic characteristics based on Chebyshev polynomials expansion[J]. Journal of Aerospace Power,2020,35(4): 757-765. (in Chinese)
[12]	SOIZE C. Polynomial chaos expansion of a multimodal random vector[J]. ASA Journal on Uncertainty Quantification,2015,3(1): 34-60. doi: 10.1137/140968495
[13]	SNOUN C,BERGEOT B,BERGER S. Prediction of the dynamic behavior of an uncertain friction system coupled to nonlinear energy sinks using a multi-element generalized polynomial chaos approach[J]. European Journal of Mechanics:A Solids,2020,80: 103917. doi: 10.1016/j.euromechsol.2019.103917
[14]	LI Hongguang,LI Ming,ZHOU Shengtong,et al. Rotor dynamics behavior of turbo-expander involving droplet impact[J]. Mathematical and Computer Modelling of Dynamical Systems,2016,22(5): 444-462. doi: 10.1080/13873954.2016.1188830
[15]	YANG Yongfeng,WU Qinyu,WANG Yanlin,et al. Dynamic characteristics of cracked uncertain hollow-shaft[J]. Mechanical Systems and Signal Processing,2019,124: 36-48. doi: 10.1016/j.ymssp.2019.01.035
[16]	FU Chao,XU Yuandong,YANG Yongfeng,et al. Response analysis of an accelerating unbalanced rotating system with both random and interval variables[J]. Journal of Sound and Vibration,2020,466: 115047. doi: 10.1016/j.jsv.2019.115047
[17]	MA Yanhong,WANG Yongfeng,WANG Cun,et al. Nonlinear interval analysis of rotor response with joints under uncertainties[J]. Chinese Journal of Aeronautics,2020,33(1): 205-218. doi: 10.1016/j.cja.2019.09.021
[18]	MA Yanhong,WANG Yongfeng,WANG Cun,et al. Interval analysis of rotor dynamic response based on Chebyshev polynomials[J]. Chinese Journal of Aeronautics,2020,33(9): 2342-2356. doi: 10.1016/j.cja.2020.04.010
[19]	WEI Sha,HAN Qinkai,PENG Zhike,et al. Dynamic analysis of parametrically excited system under uncertainties and multi-frequency excitations[J]. Mechanical Systems and Signal Processing,2016,72/73: 762-784. doi: 10.1016/j.ymssp.2015.10.036
[20]	冯伟,刘保国,丁浩,等. 非参数不确定动力学建模研究综述[J]. 振动与冲击,2020,39(5): 1-9. FENG Wei,LIU Baoguo,DING Hao,et al. Review of uncertain nonparametric dynamic modeling[J]. Journal of Vibration and Shock,2020,39(5): 1-9. (in Chinese)
[21]	刘彦旭,刘保国,冯伟,等. 不确定双圆盘转子系统振动响应分析[J]. 航空动力学报,2021,36(3): 488-497. LIU Yanxu,LIU Baoguo,FENG Wei,et al. Vibration responses analysis for double disks rotor system with uncertainties[J]. Journal of Aerospace Power,2021,36(3): 488-497. (in Chinese)
[22]	SOIZE C. A nonparametric model of random uncertainties for reduced matrix models in structural dynamics[J]. Probabilistic Engineering Mechanics,2000,15(3): 277-294. doi: 10.1016/S0266-8920(99)00028-4
[23]	MURTHY R,MIGNOLET M P,EL-SHAFEI A. Nonparametric stochastic modeling of uncertainty in rotordynamics: Part Ⅰ formulation[J]. Journal of Engineering for Gas Turbines and Power,2010,132(9): 092501.1-092501.7.
[24]	GAN Chunbiao,GUO Shuangquan,LEI Hua,et al. Random uncertainty modeling and vibration analysis of a straight pipe conveying fluid[J]. Nonlinear Dynamics,2014,77(3): 503-519. doi: 10.1007/s11071-014-1313-5
[25]	陈佳. 半正定内积下的矩阵极分解研究[D]. 成都: 成都理工大学, 2021. CHEN Jia. Research on polar decomposition of matrices with respect to positive semi-definite inner product[D]. Chengdu: Chengdu University of Technology, 2021. (in Chinese)
[26]	MIGNOLET M P,SOIZE C. Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies[J]. Probabilistic Engineering Mechanics,2008,23(2/3): 267-278.
[27]	CAPIEZ-LERNOUT E,PELLISSETTI M,PRADLWARTER H,et al. Data and model uncertainties in complex aerospace engineering systems[J]. Journal of Sound and Vibration,2006,295(3/4/5): 923-938.
[28]	SOIZE C. A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics[J]. Journal of Sound and Vibration,2005,288(3): 623-652. doi: 10.1016/j.jsv.2005.07.009
[29]	PASCUAL B,ADHIKARI S. Combined parametric-nonparametric uncertainty quantification using random matrix theory and polynomial chaos expansion[J]. Computers & Structures,2012,112/113: 364-379.