转子系统的降维及非线性动力学研究
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摘要
随着旋转机械日益向高功率、高转速、高效率以及柔性化方向的发展,工程领域中许多振动故障都与系统的非线性因素紧密相关。转子系统的非线性动力学研究历来受到研究者的重视。本文应用非线性动力学理论与方法,研究了转子系统中的若干重要问题,其主要研究目标为:1、以工程应用为背景,研究大型旋转机械的非线性动力学降维问题以及连续转子系统的非线性油膜力/密封力耦合振动特性;2、研究浮环轴承/转子系统的非线性振动特性,揭示浮环轴承/刚性转子和悬臂转子的动力学演化规律;3、针对转子的轴向摩擦问题,分析不同参数影响下,转子摩擦程度以及丰富的非线性动力学行为。本文的主要研究工作和成果包含以下几个部分:
1、综述了动力系统的降维方法研究现状、应用及最新进展,阐明了转子非线性动力学的研究方法、研究现状和发展趋势。
2、研究连续转子系统的近似惯性流形与非线性Galerkin降维方法,与标准Galerkin方法进行对比分析,验证了非线性Galerkin方法应用在连续转子系统中的有效性,分析了连续转子/轴承/密封系统的非线性动力学演化规律。结果表明:在截断模态的数目相同情况下,非线性Galerkin优于标准Galerkin方法。连续转子系统的油膜/密封耦合系统中,转子的响应主要表现为同步周期运动与非同步的概周期运动形式,并且在概周期运动领域存在多周期运动窗口。
3、研究浮环轴承支撑的刚性转子和悬臂转子的动力学特性。通过改变不同的系统参数,揭示参数变化对系统稳定性的影响规律,并且利用非线性Galerkin方法的后处理格式,对连续悬臂转子系统进行分析。结果表明:浮环轴承转子系统的运动形式主要表现为周期运动,倍周期运动,概周期运动和混沌运动,并且浮环厚度、内外间隙比、润滑油粘度等参数对系统特性有重要的影响。对于考虑陀螺力矩下的连续悬臂转子系统,浮环轴承的运动规律也有所改变。
4、研究轴向摩擦转子系统的弯扭耦合振动。主要结论为:横向振动表现为由周期运动变成多周期甚至混沌运动,并且伴随着轴心轨迹逐渐放大。扭转运动相图逐渐变得混乱,频谱中出现许多复杂频率成分。由于耦合作用,扭转和横向振动中或多或少地都会出现相同的频率成分,并且单盘摩擦影响小于双盘摩擦。
Modern turbomachinery are increasingly designed in high power, high speed, high efficiency and high flexibility. A large number of vibration failures are closely related with the nonlinear factors of a rotor system in engineering fields. It has been attract to more attention of the researchers about the nonlinear dynamics of rotor system. Application the nonlinear dynamics theories and methods in this thesis, several important problems of the rotor system are researched. Merely purpose includes: 1. the study on the dimension reduce of the rotor dynamic system in the large turbo- machinery and the vibration characters of a continue rotor with nonlinear oil film forces and the seal fluid forces together. 2. It is revealed that the floating ring bearing-rigid rotor and the overhang rotor at the evolution of dynamics by researching the nonlinear vibration characters of floating ring bearing/rotor. 3. The friction degrees and the rich dynamic behaviors under the different system parameters for the rotor with the axial rubs. Several works and results included in the thesis are as follow:
1. The dimension reduction methods, application and latest developed are summarized. Besides, the research methods, status and further trends in rotor dynamics are indicated.
2. The approximately inertial manifold and nonlinear Galerkin method in a continue rotor system is studied. Comparing to the standard Galerkin method, the effectiveness is explained at the application of the nonlinear Galerkin method in a continue rotor system. Furthermore, the dynamic characters in a continue rotor/bearing/seal are analyzed. The investigation shows that the nonlinear Galerkin method has an advantage over the standard one with when the same order of truncations, transitions, or bifurcations, of the rotor whirl from being synchronous to non-synchronous as the unstable speed is exceeded. The non-synchronous oil/seal whirl is a quasi-periodic motion. In the regime of quasi-periodic motion, the“windows”of multi-periodic were found.
3. The rigid rotor and overhung rotor with floating ring bearing supporting is researched at the vibration characters. The influence discipline of system stability is revealed by adopting the varying parameters of rotor and floating ring. Furthermore, a continuous overhung rotor with gyroscopic moment is studied by the post-process version of nonlinear Galerkin method. The results show that the dynamic behaviors include periodic motion, double-periodic motion, quasi-periodic motion and chaos. Several parameters as the thickness of floating ring, the ratio of inner/outer oil gap, viscosity of lubricating oil are influence on the stability of system. The dynamical response is also revealed in an overhung rotor system with gyroscopic moment.
4. The study on lateral and torsional vibrations of a rotor system with axial rubs. The conclusions include that the lateral vibration of rotor experiences changes from being periodic to multi-periodic and chaotic eventually. At the same time the vibrational amplitude is also enlarged. The phase portrait of the torsional response becomes complex as many frequency components appear in amplitude-frequency spectrum. Due to the couple effect, more or less same frequency components appear both in the lateral and the torsional motions. The single disk contact/rubs have less influence to the rotor dynamics than the two disk rubs have.
1、综述了动力系统的降维方法研究现状、应用及最新进展,阐明了转子非线性动力学的研究方法、研究现状和发展趋势。
2、研究连续转子系统的近似惯性流形与非线性Galerkin降维方法,与标准Galerkin方法进行对比分析,验证了非线性Galerkin方法应用在连续转子系统中的有效性,分析了连续转子/轴承/密封系统的非线性动力学演化规律。结果表明:在截断模态的数目相同情况下,非线性Galerkin优于标准Galerkin方法。连续转子系统的油膜/密封耦合系统中,转子的响应主要表现为同步周期运动与非同步的概周期运动形式,并且在概周期运动领域存在多周期运动窗口。
3、研究浮环轴承支撑的刚性转子和悬臂转子的动力学特性。通过改变不同的系统参数,揭示参数变化对系统稳定性的影响规律,并且利用非线性Galerkin方法的后处理格式,对连续悬臂转子系统进行分析。结果表明:浮环轴承转子系统的运动形式主要表现为周期运动,倍周期运动,概周期运动和混沌运动,并且浮环厚度、内外间隙比、润滑油粘度等参数对系统特性有重要的影响。对于考虑陀螺力矩下的连续悬臂转子系统,浮环轴承的运动规律也有所改变。
4、研究轴向摩擦转子系统的弯扭耦合振动。主要结论为:横向振动表现为由周期运动变成多周期甚至混沌运动,并且伴随着轴心轨迹逐渐放大。扭转运动相图逐渐变得混乱,频谱中出现许多复杂频率成分。由于耦合作用,扭转和横向振动中或多或少地都会出现相同的频率成分,并且单盘摩擦影响小于双盘摩擦。
Modern turbomachinery are increasingly designed in high power, high speed, high efficiency and high flexibility. A large number of vibration failures are closely related with the nonlinear factors of a rotor system in engineering fields. It has been attract to more attention of the researchers about the nonlinear dynamics of rotor system. Application the nonlinear dynamics theories and methods in this thesis, several important problems of the rotor system are researched. Merely purpose includes: 1. the study on the dimension reduce of the rotor dynamic system in the large turbo- machinery and the vibration characters of a continue rotor with nonlinear oil film forces and the seal fluid forces together. 2. It is revealed that the floating ring bearing-rigid rotor and the overhang rotor at the evolution of dynamics by researching the nonlinear vibration characters of floating ring bearing/rotor. 3. The friction degrees and the rich dynamic behaviors under the different system parameters for the rotor with the axial rubs. Several works and results included in the thesis are as follow:
1. The dimension reduction methods, application and latest developed are summarized. Besides, the research methods, status and further trends in rotor dynamics are indicated.
2. The approximately inertial manifold and nonlinear Galerkin method in a continue rotor system is studied. Comparing to the standard Galerkin method, the effectiveness is explained at the application of the nonlinear Galerkin method in a continue rotor system. Furthermore, the dynamic characters in a continue rotor/bearing/seal are analyzed. The investigation shows that the nonlinear Galerkin method has an advantage over the standard one with when the same order of truncations, transitions, or bifurcations, of the rotor whirl from being synchronous to non-synchronous as the unstable speed is exceeded. The non-synchronous oil/seal whirl is a quasi-periodic motion. In the regime of quasi-periodic motion, the“windows”of multi-periodic were found.
3. The rigid rotor and overhung rotor with floating ring bearing supporting is researched at the vibration characters. The influence discipline of system stability is revealed by adopting the varying parameters of rotor and floating ring. Furthermore, a continuous overhung rotor with gyroscopic moment is studied by the post-process version of nonlinear Galerkin method. The results show that the dynamic behaviors include periodic motion, double-periodic motion, quasi-periodic motion and chaos. Several parameters as the thickness of floating ring, the ratio of inner/outer oil gap, viscosity of lubricating oil are influence on the stability of system. The dynamical response is also revealed in an overhung rotor system with gyroscopic moment.
4. The study on lateral and torsional vibrations of a rotor system with axial rubs. The conclusions include that the lateral vibration of rotor experiences changes from being periodic to multi-periodic and chaotic eventually. At the same time the vibrational amplitude is also enlarged. The phase portrait of the torsional response becomes complex as many frequency components appear in amplitude-frequency spectrum. Due to the couple effect, more or less same frequency components appear both in the lateral and the torsional motions. The single disk contact/rubs have less influence to the rotor dynamics than the two disk rubs have.
引文
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