旋转柔性带冠叶片碰撞振动特征研究
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摘要
旋转柔性叶片是在高速旋转机械中，将热能转化为机械能的重要装置之一。为避免由于振动问题而造成的叶片失效，工程中常采用为叶片加装叶冠装置，通过叶冠之间的碰撞和摩擦作用消耗振动能量，从而达到减缓旋转柔性叶片振动的目的。由于柔性叶片的高速旋转，以及叶冠间的接触碰撞等因素，使其动力学系统具有动力刚化和非光滑特性，其非线性动力学行为十分复杂，常有叉形分岔、擦边分岔、倍周期分岔、阵发性混沌运动等夹杂发生的现象。这些因素对分析旋转柔性带冠叶片的碰撞减振机理和探索动力学行为及其演变规律提出了更高的要求。本文考虑高速旋转运动与带冠叶片弹性振动的强耦合关系，结合非光滑动力系统的分析方法对旋转柔性带冠叶片的碰撞振动机理开展研究，具体内容包括：
结合带冠叶片所处的高速旋转工作状态，计及动力刚化的影响，建立柔性旋转带冠叶片的动力学模型。应用Frobenius方法推导出受动力刚化影响的旋转带冠叶片横向振动的动频及动态振型函数的表达式，并证明了所得模态函数的正交性。结合这种模态函数，利用Galerkin方法对偏微分动力学方程进行离散，提出一种计算动态接触刚度的方法，并应用平均法计算尾流激励下旋转带冠叶片的碰撞振动主共振响应。将相邻叶冠间隙、激励力幅值、叶片宽度、厚度和长度作为可调参数，分析系统的非线性现象，研究旋转带冠叶片的碰撞减振机理以及结构特征参数对碰撞振动问题的影响。
考虑叶冠间隙非对称的情况，将叶冠质量对旋转柔性叶片固有特性的影响等效到边界条件中，研究动力刚化作用下的动频及相应的模态和动态接触刚度。采用近似解析方法求解非对称间隙旋转带冠叶片在主共振、亚谐波共振和超谐波共振情况下的非线性动力学响应，分析非对称间隙比等结构特征参数对系统幅频特性的影响规律，研究非对称间隙情况下旋转柔性带冠叶片的非线性动力学特性及碰撞减振机理。随后探讨了非对称间隙的参数设计对带冠叶片减振性能的影响。
根据旋转带冠叶片的动力学模型，采用与取前三阶模态进行离散的结果对比的方法，给出仅取最低阶模态离散的适用范围和精确程度。然后结合Floquet理论，获取系统特征值的解析表达式，提出一种带冠叶片碰撞振动系统的周期运动稳定性判定方法，进而对带冠叶片碰撞振动系统擦边分岔临界值的解析解法进行研究。数值仿真结果用于分析系统周期运动的擦边分岔、叉式分岔、倍周期分岔与混沌现象等，并研究了转子转速、相邻叶冠间隙等系统参数变化时对周期解稳定性造成的影响。
考虑到带冠叶片需要成组工作才能完成热能转化为机械能的任务，因此建立了成组带冠叶片的动力学模型，应用动量法来描述叶冠间的相互作用，并选取成组叶片的拓扑结构——第s和s+1个叶片来研究成组叶片的碰撞振动问题。然后，将解析和数值仿真方法相结合，分析系统周期运动的存在性和稳定性问题，研究系统发生擦边分岔、倍周期分岔、亚谐分岔等动力学行为。研究系统随结构特征参数变化时动力学行为的演变规律，为旋转柔性带冠叶片的优化设计提供理论依据。
The rotating flexible shrouded blades is widly used in high-speed rotatingmachinery, which transform heat energy into mechanical energy. In order to preventvibration failures of turbo-machinery blades, a blade shroud device used to beinstalled on the turbine blade in practical engineering. The vibration energy isabsorbed through the impact and friction between the adjacent blade shrouds toimprove the reliability of rotating flexible blades. Due to the high speed rotatingstate of the flexible blades and contact collision between blade shrouds, thedynamical model of a flexible blade has dynamic stiffening and non-smoothdynamical characteristics. The dynamic behavior for such a nonlinear system is verycomplex. Fork bifurcation, grazing bifurcation, period-doubling bifurcation andparoxysmal chaotic motion may appear mixedly. These factors make the study of thecollision damping mechanism for rotating flexible shrouded blades and study of thedynamic behavior evolution law become to be very difficult. In this dissertation,considering the strong coupling ralationship between elastic vibration andhigh-speed rotating motion of the shrouded blade and combining with the analysismethod of non-smooth dynamical systems, the impact vibration mechanism of theraotating flexible shrouded blade is investigated, the main contents include thefollowing aspects.
Accoding to the high-speed rotary working condition of the shrouded blades,the dynamic model is formulated for a flexible rotating shrouded blade in which thedynamic stiffening is considered. Then the Frobenius method is employed todetermine the dynamic frequencies and corresponding mode functions of theshrouded blade under the action of dynamic stiffness, and the orthogonality ofmodes is also proved. And then, combined with this modal function, the Galerkinmethod is employed to discretize the partial governing differential equation of therotating blade to a set of ordinary differential equations, and a equivalent method ofdynamic contact stiffness is proposed. Then the average method is applied to obtainthe primary resonant response of the system in the case of wake flow excitation.Taking the gap between adjacent blade shrouds, the amplitude of the external load,the width, thickness and length of the blade as adjustable parameters the nonlin eardynamical responses of the rotating blade are obtained and used to analyze thenonlinear behaviour of the system. In this way, the shock and vibration mechanismof the shrouded blade is revealed and the relationship between vibration suppressionand structure parameters of the blade shroud is studied.
For the case of asymmetric balde shroud gap, accounting the effect of shroudmass of rotating flexible blades on the natural property into the boundary condition,the dynamic frequency and the corresponding modal functions and dynamic contactstiffness under the action of dynamic stiffness are investigated. An approximateanalytical method is empolyed to obtain the dynamic responses of the primary, thesub-harmonic and the super-harmonic resonances of the shrouded blade. The effectof asymmetric gap ratio on amplitude-frequency characteristics is analysed. Thenonlinear dynamic characteristics and collision damping mechanism is investigatedfor the rotating flexible shrouded blades in the case of asymmetric gap. Then, theinfluence of the parametric design about the asymmetric gap on dampingperformance of shrouded blades is discussed.
Based on the dynamical model of the rotating shrouded blade, contrasting withthe results of the discreterized model with the first3modes, the scope and theaccuracy of the discriterized mode with the first mode only is given. The Floquettheory is employed to obtain the analytical expression of the system eigenvalues,and a method to determine the stability of the periodic motion of impact-vibrationsystem for a shrouded blades is proposed. Numerical simulation results are given toanalyze dynamic characteristics of grazing bifurcation, pitchfork bifurcation,period-doubling bifurcation and chaotic phenomena of the system. And the influenceof the system parameters such as rotor speed and blade shroud gap on the stability ofperiodic solutions studied is studied.
In order to complete the task of transforming thermal energy into mechanicalenergy, blades need to be assembled to a group. Thus, the dynamical model isestablished for a group of shrouded blades model. The momentum method is used todescribe the interaction between the balde shrouds. And the topology structure ofgroup blades(the s and s+1blades) is selected to study collision vibrations of groupblades. Then, a combination of analytical and numerical simulation method is usedto analyze the existence and stability for the periodic motion of the system. And thedynamic behavior is investigated for the system, such as grazing bifurcation,period-doubling bifurcation, and the subharmonic bifurcation phenomenon. Finally,the evolution law of the dynamic behavior of the system is analyzed with thevariation of structural characteristics parameters. And a theoretical basis is providedfor the optimized design of rotating flexible shrouded blades.
结合带冠叶片所处的高速旋转工作状态，计及动力刚化的影响，建立柔性旋转带冠叶片的动力学模型。应用Frobenius方法推导出受动力刚化影响的旋转带冠叶片横向振动的动频及动态振型函数的表达式，并证明了所得模态函数的正交性。结合这种模态函数，利用Galerkin方法对偏微分动力学方程进行离散，提出一种计算动态接触刚度的方法，并应用平均法计算尾流激励下旋转带冠叶片的碰撞振动主共振响应。将相邻叶冠间隙、激励力幅值、叶片宽度、厚度和长度作为可调参数，分析系统的非线性现象，研究旋转带冠叶片的碰撞减振机理以及结构特征参数对碰撞振动问题的影响。
考虑叶冠间隙非对称的情况，将叶冠质量对旋转柔性叶片固有特性的影响等效到边界条件中，研究动力刚化作用下的动频及相应的模态和动态接触刚度。采用近似解析方法求解非对称间隙旋转带冠叶片在主共振、亚谐波共振和超谐波共振情况下的非线性动力学响应，分析非对称间隙比等结构特征参数对系统幅频特性的影响规律，研究非对称间隙情况下旋转柔性带冠叶片的非线性动力学特性及碰撞减振机理。随后探讨了非对称间隙的参数设计对带冠叶片减振性能的影响。
根据旋转带冠叶片的动力学模型，采用与取前三阶模态进行离散的结果对比的方法，给出仅取最低阶模态离散的适用范围和精确程度。然后结合Floquet理论，获取系统特征值的解析表达式，提出一种带冠叶片碰撞振动系统的周期运动稳定性判定方法，进而对带冠叶片碰撞振动系统擦边分岔临界值的解析解法进行研究。数值仿真结果用于分析系统周期运动的擦边分岔、叉式分岔、倍周期分岔与混沌现象等，并研究了转子转速、相邻叶冠间隙等系统参数变化时对周期解稳定性造成的影响。
考虑到带冠叶片需要成组工作才能完成热能转化为机械能的任务，因此建立了成组带冠叶片的动力学模型，应用动量法来描述叶冠间的相互作用，并选取成组叶片的拓扑结构——第s和s+1个叶片来研究成组叶片的碰撞振动问题。然后，将解析和数值仿真方法相结合，分析系统周期运动的存在性和稳定性问题，研究系统发生擦边分岔、倍周期分岔、亚谐分岔等动力学行为。研究系统随结构特征参数变化时动力学行为的演变规律，为旋转柔性带冠叶片的优化设计提供理论依据。
The rotating flexible shrouded blades is widly used in high-speed rotatingmachinery, which transform heat energy into mechanical energy. In order to preventvibration failures of turbo-machinery blades, a blade shroud device used to beinstalled on the turbine blade in practical engineering. The vibration energy isabsorbed through the impact and friction between the adjacent blade shrouds toimprove the reliability of rotating flexible blades. Due to the high speed rotatingstate of the flexible blades and contact collision between blade shrouds, thedynamical model of a flexible blade has dynamic stiffening and non-smoothdynamical characteristics. The dynamic behavior for such a nonlinear system is verycomplex. Fork bifurcation, grazing bifurcation, period-doubling bifurcation andparoxysmal chaotic motion may appear mixedly. These factors make the study of thecollision damping mechanism for rotating flexible shrouded blades and study of thedynamic behavior evolution law become to be very difficult. In this dissertation,considering the strong coupling ralationship between elastic vibration andhigh-speed rotating motion of the shrouded blade and combining with the analysismethod of non-smooth dynamical systems, the impact vibration mechanism of theraotating flexible shrouded blade is investigated, the main contents include thefollowing aspects.
Accoding to the high-speed rotary working condition of the shrouded blades,the dynamic model is formulated for a flexible rotating shrouded blade in which thedynamic stiffening is considered. Then the Frobenius method is employed todetermine the dynamic frequencies and corresponding mode functions of theshrouded blade under the action of dynamic stiffness, and the orthogonality ofmodes is also proved. And then, combined with this modal function, the Galerkinmethod is employed to discretize the partial governing differential equation of therotating blade to a set of ordinary differential equations, and a equivalent method ofdynamic contact stiffness is proposed. Then the average method is applied to obtainthe primary resonant response of the system in the case of wake flow excitation.Taking the gap between adjacent blade shrouds, the amplitude of the external load,the width, thickness and length of the blade as adjustable parameters the nonlin eardynamical responses of the rotating blade are obtained and used to analyze thenonlinear behaviour of the system. In this way, the shock and vibration mechanismof the shrouded blade is revealed and the relationship between vibration suppressionand structure parameters of the blade shroud is studied.
For the case of asymmetric balde shroud gap, accounting the effect of shroudmass of rotating flexible blades on the natural property into the boundary condition,the dynamic frequency and the corresponding modal functions and dynamic contactstiffness under the action of dynamic stiffness are investigated. An approximateanalytical method is empolyed to obtain the dynamic responses of the primary, thesub-harmonic and the super-harmonic resonances of the shrouded blade. The effectof asymmetric gap ratio on amplitude-frequency characteristics is analysed. Thenonlinear dynamic characteristics and collision damping mechanism is investigatedfor the rotating flexible shrouded blades in the case of asymmetric gap. Then, theinfluence of the parametric design about the asymmetric gap on dampingperformance of shrouded blades is discussed.
Based on the dynamical model of the rotating shrouded blade, contrasting withthe results of the discreterized model with the first3modes, the scope and theaccuracy of the discriterized mode with the first mode only is given. The Floquettheory is employed to obtain the analytical expression of the system eigenvalues,and a method to determine the stability of the periodic motion of impact-vibrationsystem for a shrouded blades is proposed. Numerical simulation results are given toanalyze dynamic characteristics of grazing bifurcation, pitchfork bifurcation,period-doubling bifurcation and chaotic phenomena of the system. And the influenceof the system parameters such as rotor speed and blade shroud gap on the stability ofperiodic solutions studied is studied.
In order to complete the task of transforming thermal energy into mechanicalenergy, blades need to be assembled to a group. Thus, the dynamical model isestablished for a group of shrouded blades model. The momentum method is used todescribe the interaction between the balde shrouds. And the topology structure ofgroup blades(the s and s+1blades) is selected to study collision vibrations of groupblades. Then, a combination of analytical and numerical simulation method is usedto analyze the existence and stability for the periodic motion of the system. And thedynamic behavior is investigated for the system, such as grazing bifurcation,period-doubling bifurcation, and the subharmonic bifurcation phenomenon. Finally,the evolution law of the dynamic behavior of the system is analyzed with thevariation of structural characteristics parameters. And a theoretical basis is providedfor the optimized design of rotating flexible shrouded blades.
引文
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