柔性旋转梁动力学特性理论与实验研究
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摘要
柔性旋转梁结构被广泛地应用于旋转机械和空间结构中。近年来,旋转梁结构越来越柔,越来越细长,转速越来越高,对旋转梁的研究提出了一系列新的研究课题。开展柔性旋转梁动态性能研究需要综合考虑梁理论、转子动力学、陀螺力学、非线性动力学等多门学科。
针对旋转梁线性动力学中普遍忽略离心力效应的现状,本文提出离心力效应也是陀螺效应中一种表现形式,推导了含有离心力效应项的旋转梁控制方程,并分析了旋转梁动力学分析中考虑离心力效应的必要性。通过解析法和有限单元法研究了旋转角速度、陀螺效应、转动惯量、长细比和重力等因素对旋转梁动态性能的影响。
针对von Karman非线性假设无法准确地描述柔性旋转梁振动过程中的大挠度变形这一问题,本文基于局部位移、Jaumann应力和应变度量,根据完全拉格朗日格式,建立了柔性旋转梁大挠度振动的几何非线性理论,实现了对柔性旋转梁大位移和大旋转的准确预测。通过对不同工况下柔性旋转梁的几何变形情况的数值模拟分析,证明该非线性模型具有良好的可适应性。通过理论预测结果和实验结果对比,验证了本文提出的非线性模型的准确性。
本文建立了用于结构大挠度振动测量的非接触式动态摄像测量理论。该测量方法通过静态标定和动态标定相结合的方法确定并优化系统参数。重点提出了对摄像测量系统精度影响较大的几个因素,如标定设备精度、摄像机排布以及数值计算中的奇异点问题等。借助于自行设计的小型圆柱形标靶,联合动态摄像测量系统,实现了对柔性旋转梁大挠度振动的准确测量。根据实验结果,发现随着激励速度增加,旋转梁运动过程存在着阶段性规律,可分为稳态运动阶段、混沌振荡阶段和成型阶段。
针对经验模态分解(EMD)法过程中产生的模态混叠现象,本文提出了一种半经验的信号补偿法对经验模态分解法进行了改进。改进后的经验模态分解法可以有效地抑制模态混叠问题的产生,且兼具噪音滤波的功能。基于改进后的经验模态分解法,分别采用希尔伯特-黄变换(HHT)和共轭对分解(CPD)法研究了柔性旋转梁实验振动信号的瞬时频率和瞬时振幅,进一步分析了柔性旋转梁的振动特性。
本文关于柔性旋转梁的研究,丰富并完善了旋转梁结构动力学的理论和实验研究,对旋转结构的设计和分析提供了一定的理论依据。
Flexible spinning beam-like structures are widely used in rotating machinary and space structures. Recently, spinning beams become more and more flexible and slender. And the spinning speed also increases rapidly. All of these changes bring new challenges to researchers. The researches on dynamics characteristics of flexible spinning beams synthetically involve several cross subjects: beam theory, rotor dynamics, gyro dynamics, nonlinear dynamics and geometrical nonlinearity. Hence, the studies on dynamics characteristics of flexible spinning beams are considerably important both in theoretical study and engineering application.
An important gyroscopic term due to centrifugal forces is missing in many reports in the spinning beam literature. In this thesis, the term due to centrifugal force is considered to belong to gyroscopic effects, and also proved to be indispensable for correct modeling and analysis of spinning beams. The influences of rotary inertia, spinning speed, gyroscopic effects, slenderness, and gravity on dynamic characteristics are investigated in detail using analytical and finite-element methods.
Geometrically nonlinear models of spinning beams usually only include von Karman or cubic nonlinearity in the literature. Base on local displacements, Jaumann stress and strain measures, and an exact coordinate transformation, a total Lagrangian geometrically exact nonlinear theory of spinning beams undergoing large deflection vibration is derived. The new geometrically exact theory can account for large displaces and large rotations of spinning beams. By analyzing the deformed geometries of flexible spinning beams under different working conditions using numerical methods, the nonlinear model is verified to be of powerful adaptability. The model is proved to be correct by comparing the numerical and experimental results.
A camera-based noncontact measurement theory for dynamic testing of structures that undergo large deflection is derived in this thesis. Static calibration is used to estimate system parameters at first. Then dynamic calibration is performed for refinement of estimated system parameters and establishment of a lens distortion model. Some key issues that are essential for measure accuracy are discussed, such as key devices, experimental set-up and singularity problem. The thesis also makes a preliminary study of using just one camera for accurate dynamic measurement. The small-sized cylindrical makers which are self-designed, combined with the camera-based measurement system, are used to realize the accurate measurement of large deflection vibration of flexible spinning beam. The paper also analyses the evolution mechanism.
A experience-based signal compensation method (SCM) is presented to reduce the mode mixing phenomenon. The empirical mode decomposition (EMD), combined with SCM, is proposed to avoid the mode mixing phenomenon. Furthermore, this method could also be used to do noise filtering effectively. Based on the new technique, the conjugate-pair decomposition (CPD) and Hilbert-Huang transform (HHT) are used to investigate the experimental vibration signal in order to obtain time-varying frequencies and amplitudes to reveal nonlinear dynamic characteristics of a spinning beam.
In this paper, the research on flexible spinning beams enriches the structure dynamics of spinning beams both theoretically and experimentally, and also provides theoretical basis for design and analysis of spinning structures.
针对旋转梁线性动力学中普遍忽略离心力效应的现状,本文提出离心力效应也是陀螺效应中一种表现形式,推导了含有离心力效应项的旋转梁控制方程,并分析了旋转梁动力学分析中考虑离心力效应的必要性。通过解析法和有限单元法研究了旋转角速度、陀螺效应、转动惯量、长细比和重力等因素对旋转梁动态性能的影响。
针对von Karman非线性假设无法准确地描述柔性旋转梁振动过程中的大挠度变形这一问题,本文基于局部位移、Jaumann应力和应变度量,根据完全拉格朗日格式,建立了柔性旋转梁大挠度振动的几何非线性理论,实现了对柔性旋转梁大位移和大旋转的准确预测。通过对不同工况下柔性旋转梁的几何变形情况的数值模拟分析,证明该非线性模型具有良好的可适应性。通过理论预测结果和实验结果对比,验证了本文提出的非线性模型的准确性。
本文建立了用于结构大挠度振动测量的非接触式动态摄像测量理论。该测量方法通过静态标定和动态标定相结合的方法确定并优化系统参数。重点提出了对摄像测量系统精度影响较大的几个因素,如标定设备精度、摄像机排布以及数值计算中的奇异点问题等。借助于自行设计的小型圆柱形标靶,联合动态摄像测量系统,实现了对柔性旋转梁大挠度振动的准确测量。根据实验结果,发现随着激励速度增加,旋转梁运动过程存在着阶段性规律,可分为稳态运动阶段、混沌振荡阶段和成型阶段。
针对经验模态分解(EMD)法过程中产生的模态混叠现象,本文提出了一种半经验的信号补偿法对经验模态分解法进行了改进。改进后的经验模态分解法可以有效地抑制模态混叠问题的产生,且兼具噪音滤波的功能。基于改进后的经验模态分解法,分别采用希尔伯特-黄变换(HHT)和共轭对分解(CPD)法研究了柔性旋转梁实验振动信号的瞬时频率和瞬时振幅,进一步分析了柔性旋转梁的振动特性。
本文关于柔性旋转梁的研究,丰富并完善了旋转梁结构动力学的理论和实验研究,对旋转结构的设计和分析提供了一定的理论依据。
Flexible spinning beam-like structures are widely used in rotating machinary and space structures. Recently, spinning beams become more and more flexible and slender. And the spinning speed also increases rapidly. All of these changes bring new challenges to researchers. The researches on dynamics characteristics of flexible spinning beams synthetically involve several cross subjects: beam theory, rotor dynamics, gyro dynamics, nonlinear dynamics and geometrical nonlinearity. Hence, the studies on dynamics characteristics of flexible spinning beams are considerably important both in theoretical study and engineering application.
An important gyroscopic term due to centrifugal forces is missing in many reports in the spinning beam literature. In this thesis, the term due to centrifugal force is considered to belong to gyroscopic effects, and also proved to be indispensable for correct modeling and analysis of spinning beams. The influences of rotary inertia, spinning speed, gyroscopic effects, slenderness, and gravity on dynamic characteristics are investigated in detail using analytical and finite-element methods.
Geometrically nonlinear models of spinning beams usually only include von Karman or cubic nonlinearity in the literature. Base on local displacements, Jaumann stress and strain measures, and an exact coordinate transformation, a total Lagrangian geometrically exact nonlinear theory of spinning beams undergoing large deflection vibration is derived. The new geometrically exact theory can account for large displaces and large rotations of spinning beams. By analyzing the deformed geometries of flexible spinning beams under different working conditions using numerical methods, the nonlinear model is verified to be of powerful adaptability. The model is proved to be correct by comparing the numerical and experimental results.
A camera-based noncontact measurement theory for dynamic testing of structures that undergo large deflection is derived in this thesis. Static calibration is used to estimate system parameters at first. Then dynamic calibration is performed for refinement of estimated system parameters and establishment of a lens distortion model. Some key issues that are essential for measure accuracy are discussed, such as key devices, experimental set-up and singularity problem. The thesis also makes a preliminary study of using just one camera for accurate dynamic measurement. The small-sized cylindrical makers which are self-designed, combined with the camera-based measurement system, are used to realize the accurate measurement of large deflection vibration of flexible spinning beam. The paper also analyses the evolution mechanism.
A experience-based signal compensation method (SCM) is presented to reduce the mode mixing phenomenon. The empirical mode decomposition (EMD), combined with SCM, is proposed to avoid the mode mixing phenomenon. Furthermore, this method could also be used to do noise filtering effectively. Based on the new technique, the conjugate-pair decomposition (CPD) and Hilbert-Huang transform (HHT) are used to investigate the experimental vibration signal in order to obtain time-varying frequencies and amplitudes to reveal nonlinear dynamic characteristics of a spinning beam.
In this paper, the research on flexible spinning beams enriches the structure dynamics of spinning beams both theoretically and experimentally, and also provides theoretical basis for design and analysis of spinning structures.
引文
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