碰摩转子动力学行为及融合相空间特征研究
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摘要
转子系统的碰摩故障是一种强非线性现象,具有复杂的非线性动力学行为。随着转子转速和载荷的不断提高以及新型材料的日益推广使用,系统的非线性将更加突出,表现出混沌特性。从理论和实验两方面识别碰摩转子的复杂动力学现象,认识其非线性规律,对于转子系统的设计、使用及故障诊断具有重要的意义。
本文以碰摩转子为主要研究对象,从两方面对碰摩转子的非线性问题展开研究。其一是基于非线性转子动力学理论对碰摩转子系统非线性动力学行为进行分析;其二是基于融合相空间重构技术提取碰摩转子实验数据中的混沌特征量。概述地说,围绕上述问题所开展的具体研究内容包括以下方面:
1.碰摩转子系统非线性动力学模型的建立。在考虑非线性油膜力、非线性刚度和非线性摩擦力对碰摩转子影响的基础上,建立了非对称油膜力作用下碰摩转子系统非线性动力学微分方程。
2.碰摩转子系统非线性动力学行为研究。应用数值分析方法研究了碰摩转子系统复杂的动力学行为,并利用分岔图、Poincare截面图、时域波形图、轴心轨迹图、相图及频谱图详细分析了碰摩转子系统混沌运动的演化规律。重点研究了转速、偏心量、非线性刚度比、定子刚度及速度影响因数对转子系统分岔和混沌行为的影响。研究结果表明,非对称油膜力、非线性刚度和非线性摩擦力对系统动力学行为的影响与转速有很大关系。
3.碰摩转子系统相空间重构参数选择方法研究。针对嵌入维数计算过程中存在主观性强、计算速度慢等缺点,提出基于IMF分量数的嵌入维数计算方法,该方法物理意义明确、简单有效,在计算过程中不需要先验知识,并且延迟时间对嵌入维数的计算精度没有影响。
4.碰摩转子系统相空间重构方法研究。通过对重构后混沌吸引子的形状进行对比分析,指出基于单变量时间序列的相空间重构方法中存在信息不完备等弊端,为了解决这一问题,提出基于Bayes估计的融合相空间重构方法。将相空间重构和数据融合相结合,针对各个单变量时间序列重构出的吸引子与原系统真实吸引子之间存在的偏差,在相空间中利用Bayes估计将各个单变量相点进行最优融合,得到更为理想的融合相空间。并将所提出的方法应用到典型混沌系统和碰摩转子系统中。分析结果表明,融合相空间能够更完整地复现碰摩转子系统的主要特征信息。
5.碰摩转子系统混沌特征量的提取方法研究。为了保证故障信息的完整性,提出在融合相空间中计算混沌吸引子的特征量—最大Lyapunov指数和关联维数,给出相应的算法。分析结果表明,利用相点融合技术得到的多变量时间序列的最大Lyapunov指数和关联维数更真实、精确。最大Lyapunov指数和关联维数这两个量化指数对系统故障辨识是行之有效的,其有效性在典型混沌系统仿真以及碰摩转子系统的三种故障分类与辨识中获得证实。
6.碰摩转子系统的实验研究。设计出转子系统局部碰摩装置,在RK4转子实验台上测取碰摩转子系统三种典型故障数据,包括油膜失稳、碰摩以及碰摩和油膜失稳耦合故障数据。
Rub-impact fault of rotor system is seriously non-linear phenomenon, and it shows strong nonlinear dynamical behavior. With the increasing of rotation speed and load as well as the use of new type material for rotor system, its nonlinearity is outstanding and shows chaotic characteristic. Complicated vibration phenomenon could be idetified in theory and experiment, and nonlinear rule could be understood, which plays an important part in design, use, and fault diganosis for rotor system.
Rub-impact rotor is regarded as the primary research object in this paper, and from two aspects nonlinear characteristic of rotor system is analyzed. Firstly, nonlinear dynamic behavior of rub-impact rotor system is analyzed based nonlinear rotor dynamic theory. Secondly, chaotic characteristic parameters are extracted from the experiment data of rub-impact rotor based on technology of phase space fused. Summarily speaking, the detailed research content based on problem above is as follows:
1.The establishment of nonlinear dynamical model for rub-impact rotor system. Considering the effect of nonlinear film force, nonlinear stiffness and nonlinear friction force, a nonlinear dynamical differential equation of rotor system with non-symmetry film force.
2.The research of nonlinear dynamical behavior for rub-impact rotor system. The complicated dynamical behavior of rub-impact rotor system is researched by numerical analysis method. The evolutive rule of chaotic motion for rub-impact rotor system is comprehensively analyzed by bifurcation diagram, Poicnare section diagram, time domain wave diagram, axle center trail, phase diagram and frequency spectrum diagram. In addition, the effect of some system parameters (rotation speed, eccentricity, nonlinear stiffness ratio, stator stiffness and speed effect factor) on bifuration and chaotic behavior is principally researched. The analysis results show the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force on dynamical behavior of rotor system has serious smething with rotation speed.
3.The research of phase space reconstruction parameters for rub-impact rotor system. As for the subjectivity and computation in determination of embedding dimension, a new method of embedding dimension determined by the number of intrinsic mode functions is presented. The physics meaning of this method is clear, and its computation process is simple. Above all, this method dosen’t need prescient knowledge, and delay time dosen’t affect the computation precision of embedding dimension.
4.The research of phase space reconstruction for rub-impact rotor system. Through the analysis of chaotic attractor of univariate time series, the information reconstructed from univariate time series is imperfect, which is the abuse of phase space reconstruction from univariate time series. Then the method of phase space reconstruction based on Bayes estimate theory is presented. As for the difference between attractor reconstruted from univariate and the one reconstructed from multivariate, this method combine phase space reconstruction with data fusion, and the phase points of any univariate is fused in phase space by Bayes estimate theory, then, a new phase space fused could be obtained. And this method is applied to typical chaotic system and rub-impact rotor system, then the analysis results show the information reconstructed from multivariate includes the main characters of all univariate and represents the comprehensive information of system attractor, which makes phase space reconstructed more abundant.
5.The research of chaotic characteristic extraction method for rub-impact rotor system. To ensure the integrality of fault information, maximum Lyapunov exponent and correlation dimension could be extracted in phase space fused. The analysis results show maximum Lyapunov exponent and correlation dimension for multivariate time series based phase point fused is more true and accurate. The typical chaotic system simulation of maximum Lyapunov exponent and correlation dimension and the fault diagnosis of three typical fault for rub-impact rotor system show maximum Lyapunov exponent and correlation dimension is effective in fault diagnosis.
6.The experiment research of rub-impact rotor system. Auocal rub-impact equipment of rotor system is designed. Three typical fault (oil film instability, rub-impact and coupled fault) data are obtained from RK4 rotor experiment-bed.
本文以碰摩转子为主要研究对象,从两方面对碰摩转子的非线性问题展开研究。其一是基于非线性转子动力学理论对碰摩转子系统非线性动力学行为进行分析;其二是基于融合相空间重构技术提取碰摩转子实验数据中的混沌特征量。概述地说,围绕上述问题所开展的具体研究内容包括以下方面:
1.碰摩转子系统非线性动力学模型的建立。在考虑非线性油膜力、非线性刚度和非线性摩擦力对碰摩转子影响的基础上,建立了非对称油膜力作用下碰摩转子系统非线性动力学微分方程。
2.碰摩转子系统非线性动力学行为研究。应用数值分析方法研究了碰摩转子系统复杂的动力学行为,并利用分岔图、Poincare截面图、时域波形图、轴心轨迹图、相图及频谱图详细分析了碰摩转子系统混沌运动的演化规律。重点研究了转速、偏心量、非线性刚度比、定子刚度及速度影响因数对转子系统分岔和混沌行为的影响。研究结果表明,非对称油膜力、非线性刚度和非线性摩擦力对系统动力学行为的影响与转速有很大关系。
3.碰摩转子系统相空间重构参数选择方法研究。针对嵌入维数计算过程中存在主观性强、计算速度慢等缺点,提出基于IMF分量数的嵌入维数计算方法,该方法物理意义明确、简单有效,在计算过程中不需要先验知识,并且延迟时间对嵌入维数的计算精度没有影响。
4.碰摩转子系统相空间重构方法研究。通过对重构后混沌吸引子的形状进行对比分析,指出基于单变量时间序列的相空间重构方法中存在信息不完备等弊端,为了解决这一问题,提出基于Bayes估计的融合相空间重构方法。将相空间重构和数据融合相结合,针对各个单变量时间序列重构出的吸引子与原系统真实吸引子之间存在的偏差,在相空间中利用Bayes估计将各个单变量相点进行最优融合,得到更为理想的融合相空间。并将所提出的方法应用到典型混沌系统和碰摩转子系统中。分析结果表明,融合相空间能够更完整地复现碰摩转子系统的主要特征信息。
5.碰摩转子系统混沌特征量的提取方法研究。为了保证故障信息的完整性,提出在融合相空间中计算混沌吸引子的特征量—最大Lyapunov指数和关联维数,给出相应的算法。分析结果表明,利用相点融合技术得到的多变量时间序列的最大Lyapunov指数和关联维数更真实、精确。最大Lyapunov指数和关联维数这两个量化指数对系统故障辨识是行之有效的,其有效性在典型混沌系统仿真以及碰摩转子系统的三种故障分类与辨识中获得证实。
6.碰摩转子系统的实验研究。设计出转子系统局部碰摩装置,在RK4转子实验台上测取碰摩转子系统三种典型故障数据,包括油膜失稳、碰摩以及碰摩和油膜失稳耦合故障数据。
Rub-impact fault of rotor system is seriously non-linear phenomenon, and it shows strong nonlinear dynamical behavior. With the increasing of rotation speed and load as well as the use of new type material for rotor system, its nonlinearity is outstanding and shows chaotic characteristic. Complicated vibration phenomenon could be idetified in theory and experiment, and nonlinear rule could be understood, which plays an important part in design, use, and fault diganosis for rotor system.
Rub-impact rotor is regarded as the primary research object in this paper, and from two aspects nonlinear characteristic of rotor system is analyzed. Firstly, nonlinear dynamic behavior of rub-impact rotor system is analyzed based nonlinear rotor dynamic theory. Secondly, chaotic characteristic parameters are extracted from the experiment data of rub-impact rotor based on technology of phase space fused. Summarily speaking, the detailed research content based on problem above is as follows:
1.The establishment of nonlinear dynamical model for rub-impact rotor system. Considering the effect of nonlinear film force, nonlinear stiffness and nonlinear friction force, a nonlinear dynamical differential equation of rotor system with non-symmetry film force.
2.The research of nonlinear dynamical behavior for rub-impact rotor system. The complicated dynamical behavior of rub-impact rotor system is researched by numerical analysis method. The evolutive rule of chaotic motion for rub-impact rotor system is comprehensively analyzed by bifurcation diagram, Poicnare section diagram, time domain wave diagram, axle center trail, phase diagram and frequency spectrum diagram. In addition, the effect of some system parameters (rotation speed, eccentricity, nonlinear stiffness ratio, stator stiffness and speed effect factor) on bifuration and chaotic behavior is principally researched. The analysis results show the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force on dynamical behavior of rotor system has serious smething with rotation speed.
3.The research of phase space reconstruction parameters for rub-impact rotor system. As for the subjectivity and computation in determination of embedding dimension, a new method of embedding dimension determined by the number of intrinsic mode functions is presented. The physics meaning of this method is clear, and its computation process is simple. Above all, this method dosen’t need prescient knowledge, and delay time dosen’t affect the computation precision of embedding dimension.
4.The research of phase space reconstruction for rub-impact rotor system. Through the analysis of chaotic attractor of univariate time series, the information reconstructed from univariate time series is imperfect, which is the abuse of phase space reconstruction from univariate time series. Then the method of phase space reconstruction based on Bayes estimate theory is presented. As for the difference between attractor reconstruted from univariate and the one reconstructed from multivariate, this method combine phase space reconstruction with data fusion, and the phase points of any univariate is fused in phase space by Bayes estimate theory, then, a new phase space fused could be obtained. And this method is applied to typical chaotic system and rub-impact rotor system, then the analysis results show the information reconstructed from multivariate includes the main characters of all univariate and represents the comprehensive information of system attractor, which makes phase space reconstructed more abundant.
5.The research of chaotic characteristic extraction method for rub-impact rotor system. To ensure the integrality of fault information, maximum Lyapunov exponent and correlation dimension could be extracted in phase space fused. The analysis results show maximum Lyapunov exponent and correlation dimension for multivariate time series based phase point fused is more true and accurate. The typical chaotic system simulation of maximum Lyapunov exponent and correlation dimension and the fault diagnosis of three typical fault for rub-impact rotor system show maximum Lyapunov exponent and correlation dimension is effective in fault diagnosis.
6.The experiment research of rub-impact rotor system. Auocal rub-impact equipment of rotor system is designed. Three typical fault (oil film instability, rub-impact and coupled fault) data are obtained from RK4 rotor experiment-bed.
引文
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