一种利用振动响应识别裂纹转子参数的方法
|
摘要
针对一类含裂纹的转子动力学特性及其参数识别,本文选取裂纹转子刚度模型——中性轴模型,提出适用于对中性轴模型的裂纹转子运动微分方程的求解方法,并研究了裂纹转子系统参数对动力学的影响。然后,采用反向求解思路,用龙格-库塔法拆分迭代裂纹转子运动微分方程,通过平均值法确定基因算法中的适应度函数,从而实现裂纹转子参数识别问题向求解动力学响应差异值最小化的最值优化问题的转化,最终使用基因算法对最值优化问题求解,并通过算例对该方法进行了验证,实现了低于0.6%相对误差的裂纹转子参数识别。
Aiming at dynamic characteristics and parameter identification of a kind of cracked rotor, the stiffness model of the cracked rotor-neutral axis model was choosed to propose a numerical solution method for differential equations of cracked rotor under neutral axis model and study on the influence of parameters on dynamic characteristics of cracked rotor system. Then follow the inverse problem solution, the motion differential equation of cracked rotor was dismantled and iterated by using the Runge-Kutta method. The fitness function in genetic algorithm was obtained by using the average value method. Thus the transformation from the parameter identification problem of crack rotor to the optimal problem solving the minimization of the dynamic response difference value so as to realize the cracked rotor parameter identification problem solving the dynamic response to the most value optimization problem of minimizing the value difference. Finally, the genetic algorithm was used to solve the optimal problem and the example was used to verify the method. The relative error from parameter identification of the cracked rotor was realized below 0.6%.
Aiming at dynamic characteristics and parameter identification of a kind of cracked rotor, the stiffness model of the cracked rotor-neutral axis model was choosed to propose a numerical solution method for differential equations of cracked rotor under neutral axis model and study on the influence of parameters on dynamic characteristics of cracked rotor system. Then follow the inverse problem solution, the motion differential equation of cracked rotor was dismantled and iterated by using the Runge-Kutta method. The fitness function in genetic algorithm was obtained by using the average value method. Thus the transformation from the parameter identification problem of crack rotor to the optimal problem solving the minimization of the dynamic response difference value so as to realize the cracked rotor parameter identification problem solving the dynamic response to the most value optimization problem of minimizing the value difference. Finally, the genetic algorithm was used to solve the optimal problem and the example was used to verify the method. The relative error from parameter identification of the cracked rotor was realized below 0.6%.
引文
[1]Wang CH,Brown MW.Life prediction techniques for variable amplitude multiaxial fatigue—Part 1:Theories[J].Journal of Engineering Materials&Technology,1996,118(3):367-370
[2]Belkheiri M,Rabhi A,Boudjema F,et al.Model Parameter Identification and Nonlinear Control of a Twin Rotor MIMO System-TRMS[J].IFAC Proceedings Volumes,2009,42(10):1487-1492
[3]Menshikov Y.Identification of Rotor Unbalance as Inverse Problem of Measurement[J].Advances in Pure Mathematics,2013,3(9A):20-25
[4]Kumar C,Rastogi V.A brief review on dynamics of a cracked rotor[J].International Journal of Rotating Machinery,2009,2009(2):1-6
[5]王宗勇,林伟,闻邦椿.开闭裂纹转轴刚度的解析研究[J].振动与冲击,2010,29(9):69-72
[6]高建,朱晓梅.转轴上裂纹开闭模型的研究[J].应用力学学报,1992(1):108-112
[7]郭超众.具有呼吸裂纹的转子动力学特征提取及预诊方法研究[D].哈尔滨:哈尔滨工业大学,2014:23-41
[8]朱厚军,赵玫,王德洋.Jeffcott裂纹转子动力特性的研究[J].振动与冲击,2001,20(1):1-4
[9]杨丹,甘春标,杨世锡,等.含横向裂纹Jeffcott转子刚度及动力学特性研究[J].振动与冲击,2012,31(15):121-126
[10]Ishikawa T,Nakayama K.Topology Optimization of Rotor Structure in Brushless DC Motor With Concentrated Windings Using Genetic Algorithm Combined With Cluster of Material[J].IEEE Transactions on Magnetics,2012,48(2):899-902
[11]Hamdan M.Optimization of Small Wind Turbines using Genetic Algorithms[J].International Journal of Applied Metaheuristic Computing,2016,7(4):50-65
[2]Belkheiri M,Rabhi A,Boudjema F,et al.Model Parameter Identification and Nonlinear Control of a Twin Rotor MIMO System-TRMS[J].IFAC Proceedings Volumes,2009,42(10):1487-1492
[3]Menshikov Y.Identification of Rotor Unbalance as Inverse Problem of Measurement[J].Advances in Pure Mathematics,2013,3(9A):20-25
[4]Kumar C,Rastogi V.A brief review on dynamics of a cracked rotor[J].International Journal of Rotating Machinery,2009,2009(2):1-6
[5]王宗勇,林伟,闻邦椿.开闭裂纹转轴刚度的解析研究[J].振动与冲击,2010,29(9):69-72
[6]高建,朱晓梅.转轴上裂纹开闭模型的研究[J].应用力学学报,1992(1):108-112
[7]郭超众.具有呼吸裂纹的转子动力学特征提取及预诊方法研究[D].哈尔滨:哈尔滨工业大学,2014:23-41
[8]朱厚军,赵玫,王德洋.Jeffcott裂纹转子动力特性的研究[J].振动与冲击,2001,20(1):1-4
[9]杨丹,甘春标,杨世锡,等.含横向裂纹Jeffcott转子刚度及动力学特性研究[J].振动与冲击,2012,31(15):121-126
[10]Ishikawa T,Nakayama K.Topology Optimization of Rotor Structure in Brushless DC Motor With Concentrated Windings Using Genetic Algorithm Combined With Cluster of Material[J].IEEE Transactions on Magnetics,2012,48(2):899-902
[11]Hamdan M.Optimization of Small Wind Turbines using Genetic Algorithms[J].International Journal of Applied Metaheuristic Computing,2016,7(4):50-65