考虑模型形式误差的转子动力学修正及确认
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摘要
研究考虑模型形式误差的轴承-转子系统工作转速下的动力学模型修正和确认方法。首先,介绍了模型形式误差以及基于复模态特征值灵敏度的模型修正理论;然后,在此基础上以轴承-柔性转子系统为仿真算例,考虑模型形式误差,使用系统在恒定工作转速下的涡动频率和阻尼参数,同时对轴承的支承刚度、支承阻尼和转盘的直径转动惯量参数进行修正;最后,通过不平衡响应结果对修正模型进行了确认。仿真结果显示,考虑模型形式误差时的修正参数最大误差仍有-10.1%,而修正后特征值实部最大误差为0.95%,特征值虚部最大误差为-1.15%,修正后不平衡响应与目标模型基本重合。研究表明,考虑模型形式误差时轴承-转子系统的修正方法是稳健的,也是有效可行的。
Structure dynamical model updating and validation for bearing-rotor system at working speed considering model-form error is presented.The theory of model-form error,model updating based on complex eigenvalue sensitivity analysis is successfully accomplished in this piece of work.The updating for simulation example about flexible rotor-bearing system at working speed,considering model-form error,is performed to bearing stiffness,bearing damping and diameter moment of inertia parameters using wheel frequency and damping as objective residues.The updated model is validated through unbalance response prediction.The simulation results show that the maximum residual errors of updated parameter is still -10.1%,but the maximum residual errors for the real part of updated eigenvalue is 0.95% and for the imaginary part is -1.15% even taking into 2% model-form error account in model updating.The unbalance response prediction of the updated model matches the target model unbalance response quite well.The results,in no doubt,proved the effectiveness and robustness of the model updating method considering model-form error using wheel frequency and damping for bearing-rotor system at working speed.
Structure dynamical model updating and validation for bearing-rotor system at working speed considering model-form error is presented.The theory of model-form error,model updating based on complex eigenvalue sensitivity analysis is successfully accomplished in this piece of work.The updating for simulation example about flexible rotor-bearing system at working speed,considering model-form error,is performed to bearing stiffness,bearing damping and diameter moment of inertia parameters using wheel frequency and damping as objective residues.The updated model is validated through unbalance response prediction.The simulation results show that the maximum residual errors of updated parameter is still -10.1%,but the maximum residual errors for the real part of updated eigenvalue is 0.95% and for the imaginary part is -1.15% even taking into 2% model-form error account in model updating.The unbalance response prediction of the updated model matches the target model unbalance response quite well.The results,in no doubt,proved the effectiveness and robustness of the model updating method considering model-form error using wheel frequency and damping for bearing-rotor system at working speed.
引文
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[23]Adhikari S.Rates of change of eigenvalues and eigenvectors in damped dynamic system[J].American Institute of Aeronautics and Astronautics Journal,1999,37(11):1452-1458.
[24]Chouchane M,Guedria N,Smaoui H.Eigensensitivity computation of asymmetric damped systems using an algebraic approach[J].Mechanical Systems and Signal Processing,2007,21(7):2761-2776.
[2]廖明夫,谭大力,耿建明,等.航空发动机高压转子的结构动力学设计方法[J].航空动力学报,2014,29(7):1505-1519.Liao Mingfu,Tan Dali,Geng Jianming,et al.Structure dynamics design method of aero-engine high pressure rotor[J].Journal of Aerospace Power,2014,29(7):1505-1519.(in Chinese)
[3]Mottershead J E,Link M,Friswell M I.The sensitivity method in finite element model updating:a tutorial[J].Mechanical Systems and Signal Processing,2011,25(7):2275-2296.
[4]张保强,陈国平,郭勤涛.使用有效模态质量和遗传算法的有限元模型修正[J].振动、测试与诊断,2012,32(4):577-580.Zhang Baoqiang,Chen Guoping,Guo Qintao.The finite element model updating using effective modal mass and genetic algorithm[J].Journal of Vibration,Measurement&Diagnosis,2012,32(4):577-580.(in Chinese)
[5]常涛,郭勤涛,张保强.应用模型修正方法的印制电路板参数识别[J].振动、测试与诊断,2013,33(3):509-513.Chang Tao,Guo Qintao,Zhang Baoqiang.Parameter identification of printed circuit board using model correction method[J].Journal of Vibration,Measurement&Diagnosis,2013,33(3):509-513.(in Chinese)
[6]Cortés F,Elejabarrieta M J.Computational methods for complex eigenproblems in finite element analysis of structural systems with viscoelastic damping treatments[J].Computer Methods in Applied Mechanics and Engineering,2006,195(44):6448-6462.
[7]Elbeheiry E M.On eigenproblem solution of damped vibrations associated with gyroscopic moments[J].Journal of Sound and Vibration,2009,320(3):691-704.
[8]Arora V,Singh S P,Kundra T K.Damped model updating using complex updating parameters[J].Journal of Sound and Vibration,2009,320(1):438-451.
[9]冯文贤,陈新.基于试验复模态参数的有限元模型修正[J].航空学报,1999,20(1):11-16.Feng Wenxian,Chen Xin.Updating design parameters of finite element model by using test complex modal data[J].Acta Aeronautica et Astronautica Sinica,1999,20(1):11-16.(in Chinese)
[10]Lu Yong,Yu Zhenguo.A two-level neural network approach for dynamic FE model updating including damping[J].Journal of Sound and Vibration,2004,275(3):931-952.
[11]蒋家尚,袁永新.基于复模态试验数据的粘性阻尼矩阵的修正[J].振动与冲击,2007,26(5):74-80.Jiang Jiashang,Yuan Yongxin.Vicious damping matrix updating from complex modal testing[J].Journal of Vibration and Shock,2007,26(5):74-80.(in Chinese)
[12]Datta B N,Deng S,Sokolov V O,et al.An optimization technique for damped model updating with measured data satisfying quadratic orthogonality constraint[J].Mechanical Systems and Signal Processing,2009,23(6):1759-1772.
[13]Yuan Yongxin,Guo Yongqiang.A direct updating method for damped gyroscopic systems using measured modal data[J].Applied Mathematical Modelling,2010,34(6):1450-1457.
[14]赵斌,陈果.转子-支承耦合结构的模型修正研究[J].航空计算技术,2014,44(5):86-91.Zhao Bin,Chen Guo.Study on model updating of a rotor-support coupling structure[J].Aeronautical Computing Technique,2014,44(5):86-91.(in Chinese)
[15]Miao Hui,Zang Chaoping,Friswell M.Model updating and validation of a dual-rotor system[C]∥Proceedings of the 26th International Conference on Noise and Vibration Engineering(ISMA2014).Leuven,Belgium:Catholic University of Louvain,2014:2723-2738.
[16]张保强,郭勤涛,陈国平,等.基于复模态模型修正方法的磁悬浮轴承支承参数识别[J].南京航空航天大学学报,2010,42(6):748-752.Zhang Baoqiang,Guo Qintao,Chen Guoping,et al.Parameter identification of active magnetic bering support based on finite element model updating using complex modal data[J].Journal of Nanjing University of Aeronautics&Astronautics,2010,42(6):748-752.(in Chinese)
[17]Xu Yuanping,Zhou Jin,Di Long,et al.Active magnetic bearing rotor model updating using resonance and MAC error[J].Shock and Vibration,2015,2015(2):1-9.
[18]Chouksey M,Dutt J K,Modak S V.Model updating of rotors supported on journal bearings[J].Mechanism and Machine Theory,2014,71(1):52-63.
[19]Cavalini Jr A A,Lobato F S,Koroishi E H,et al.Model updating of a rotating machine using the self-adaptive differential evolution algorithm[J].Inverse Problems in Science and Engineering,2016,24(3):504-523.
[20]丁继锋,马兴瑞,韩增尧,等.结构动力学模型修正的三步策略及其实践[J].航空学报,2010,31(3):546-552.Ding Jifeng,Ma Xingrui,Han Zengyao,et al.Three step model updating method in structure dynamics and its application[J].Acta Aeronautica Et Astronautica Sinica,2010,31(3):546-552.(in Chinese)
[21]Oberkampf W L,Helton J C,Joslyn C A,et al.Challenge problems:uncertainty in system response given uncertain parameters[J].Reliability Engineering and System Safety,2004,85(1):11-19.
[22]Oberkampf W L,Roy C J.Verification and validation in scientific computing[M].New York,USA:Cambridge University Press,2010:572-575.
[23]Adhikari S.Rates of change of eigenvalues and eigenvectors in damped dynamic system[J].American Institute of Aeronautics and Astronautics Journal,1999,37(11):1452-1458.
[24]Chouchane M,Guedria N,Smaoui H.Eigensensitivity computation of asymmetric damped systems using an algebraic approach[J].Mechanical Systems and Signal Processing,2007,21(7):2761-2776.