汽轮机自带围带叶片动力特性有限元分析
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摘要
本文研究大型汽轮机自带围带叶片的振动特性,着重论述自带围带叶片的减振机理、影响减振效果的因素及其在运行过程中形成整圈自锁的条件。作为工程实例,将国产1029mm叶顶自由叶片改型为自带围带叶片,以三维实体单元模化复杂叶型,采用三维有限元方法,对改型叶片及整圈自锁叶片的动静力特性进行了理论分析和数值计算。
在集中参数模型分析方面,建立了单自由度模型,在该模型中考虑了围带接触面正压力N_0、接触刚度k d、摩擦系数μ、与周向的夹角α、激振力幅值F_0对自带围带叶片减振特性的影响。其中,参数α的考虑是对已有模型的重要改进。参数α对阻尼围带的减振效果具有较大影响,合理地选取参数α可使阻尼围带的减振效果达到最佳。
在叶片建模方面,针对叶片变截面、大扭曲度、各特征截面型线为复杂曲线,不能用常规的初等曲线来描述的特点,提出了基于NURBS造型理论的叶片三维实体造型方法,对实例叶片进行了三维实体造型,利用三维实体模型并借助有限元方法来分析长叶片的动静力特性,改进了长叶片动静力特性分析方法。
在叶片动静力特性有限元分析方面,借助有限元分析软件ALGOR,研究了转速、围带工作面间初始间隙δ、与周向的夹角α对叶片扭转恢复角及围带接触紧度的影响;对自由叶片、整圈自锁叶片的固有频率、振型进行了计算分析,绘制了共振转速图(Campbell图),并考核了整圈自锁叶片在2850~3090r/min范围内是否存在节径数m≤6的“三重点”共振,对机组的安全运行具有实际的指导意义;提出改进的摩擦模型解决计算过程中收敛困难的问题,研究了自带围带叶片的动态响应,得出围带间存在最佳初始间隙,并确定了关键参数的取值范围,为自带围带叶片的优化设计提供了依据与可借鉴的方法。本文研究成果为汽轮机叶片动静力特性的研究提供了有效的数值方法,对我国汽轮机自带围带叶片的研制和改型设计有着重要的工程应用价值。
In this thesis, dynamic characteristics of integrally shrouded blade(ISB)of larger set steam turbine are investigated, mechanism and its influence factors of damping vibration of integrally shrouded blades are mainly presented, as well as the condition of interlocked of integrally shrouded blades which are in operation. For instance of engineering, the Chinese-built 1029mm freestanding blade is remodeled to interlocked blade with integral shroud, and theoretical analysis and numerical calculation have been done for dynamic-static characteristics of remodeled blades and its interlocked blades by using of three-dimensional solid unit to describe the blades and three-dimensional finite element method.
As for the study of analytical model of lumped-parameter, a single degree of freedom analytical model and calculation method is established. In the model, the effect of factors, such as normal force N_0, tangent rigidity k_d, angle of shroud interfaceα, excitation force F_0 and friction coefficientμof shroud interface, on the vibration damping of blades are quantitatively considered. Considering the parameterαis mainly improved to the foregone models. And the parameterαhas an obvious effect on vibration damping of damped shroud, so selecting the parameterαreasonably can achieve optimal effect.
With respect to the finite element model of blade, According to the characteristics of the sections change along with radial direction, great twist, the model curve of character sections are complicated curve and are unable to describe with elementary curve, the three dimension solid model method is presented based on model theory of Non-Uniform Rational B-Splines (NURBS). Three dimension solid modeling have been done for the example blades. The analytical method on dynamic-static characteristics of long blades is improved by using the three dimension model and finite element method.
As for the study of the dynamic-static characteristics of blade, with the aid of FEA software ALGOR, the influence of factors, such as rotating speed n , original clearanceδand the angleαof shroud interface to the direction of circle, to the angle of twist-back of blade and contact tightness between adjacent shrouds are researched; the natural vibration frequency and modal shape of free blade and interlocked blades system are calculated and analyzed, and also the resonant rotation speed chart (Campbell chart) of the free blade and interlocked blade is presented. The interlocked blades are examined for the“3-coincide point”resonance under nodal diameter number m≤6 within rotation speed range of 2850~3090 rpm, and there have an actual guidance for the operation security of steam turbine. In order to solve the difficulty of convergence during the calculation, the Coulomb frictional model is replaced by the regularization frictional model based on the investigations of blade vibration characteristics, and the dynamic response of integrally shrouded blade with dry frictional damping is studied, the optimal original clearanceδexisted and the range of the key parameters are determined. The achievements have provided quantitative basis and practicable method for optimal designing integrally shrouded blades.
The study results have provided a variety of effective numerical methods for the study on the dynamic-static characteristics of steam turbine blade, and will find important engineering application in development and modification design and optimization of the steam turbine integrally shrouded blade.
在集中参数模型分析方面,建立了单自由度模型,在该模型中考虑了围带接触面正压力N_0、接触刚度k d、摩擦系数μ、与周向的夹角α、激振力幅值F_0对自带围带叶片减振特性的影响。其中,参数α的考虑是对已有模型的重要改进。参数α对阻尼围带的减振效果具有较大影响,合理地选取参数α可使阻尼围带的减振效果达到最佳。
在叶片建模方面,针对叶片变截面、大扭曲度、各特征截面型线为复杂曲线,不能用常规的初等曲线来描述的特点,提出了基于NURBS造型理论的叶片三维实体造型方法,对实例叶片进行了三维实体造型,利用三维实体模型并借助有限元方法来分析长叶片的动静力特性,改进了长叶片动静力特性分析方法。
在叶片动静力特性有限元分析方面,借助有限元分析软件ALGOR,研究了转速、围带工作面间初始间隙δ、与周向的夹角α对叶片扭转恢复角及围带接触紧度的影响;对自由叶片、整圈自锁叶片的固有频率、振型进行了计算分析,绘制了共振转速图(Campbell图),并考核了整圈自锁叶片在2850~3090r/min范围内是否存在节径数m≤6的“三重点”共振,对机组的安全运行具有实际的指导意义;提出改进的摩擦模型解决计算过程中收敛困难的问题,研究了自带围带叶片的动态响应,得出围带间存在最佳初始间隙,并确定了关键参数的取值范围,为自带围带叶片的优化设计提供了依据与可借鉴的方法。本文研究成果为汽轮机叶片动静力特性的研究提供了有效的数值方法,对我国汽轮机自带围带叶片的研制和改型设计有着重要的工程应用价值。
In this thesis, dynamic characteristics of integrally shrouded blade(ISB)of larger set steam turbine are investigated, mechanism and its influence factors of damping vibration of integrally shrouded blades are mainly presented, as well as the condition of interlocked of integrally shrouded blades which are in operation. For instance of engineering, the Chinese-built 1029mm freestanding blade is remodeled to interlocked blade with integral shroud, and theoretical analysis and numerical calculation have been done for dynamic-static characteristics of remodeled blades and its interlocked blades by using of three-dimensional solid unit to describe the blades and three-dimensional finite element method.
As for the study of analytical model of lumped-parameter, a single degree of freedom analytical model and calculation method is established. In the model, the effect of factors, such as normal force N_0, tangent rigidity k_d, angle of shroud interfaceα, excitation force F_0 and friction coefficientμof shroud interface, on the vibration damping of blades are quantitatively considered. Considering the parameterαis mainly improved to the foregone models. And the parameterαhas an obvious effect on vibration damping of damped shroud, so selecting the parameterαreasonably can achieve optimal effect.
With respect to the finite element model of blade, According to the characteristics of the sections change along with radial direction, great twist, the model curve of character sections are complicated curve and are unable to describe with elementary curve, the three dimension solid model method is presented based on model theory of Non-Uniform Rational B-Splines (NURBS). Three dimension solid modeling have been done for the example blades. The analytical method on dynamic-static characteristics of long blades is improved by using the three dimension model and finite element method.
As for the study of the dynamic-static characteristics of blade, with the aid of FEA software ALGOR, the influence of factors, such as rotating speed n , original clearanceδand the angleαof shroud interface to the direction of circle, to the angle of twist-back of blade and contact tightness between adjacent shrouds are researched; the natural vibration frequency and modal shape of free blade and interlocked blades system are calculated and analyzed, and also the resonant rotation speed chart (Campbell chart) of the free blade and interlocked blade is presented. The interlocked blades are examined for the“3-coincide point”resonance under nodal diameter number m≤6 within rotation speed range of 2850~3090 rpm, and there have an actual guidance for the operation security of steam turbine. In order to solve the difficulty of convergence during the calculation, the Coulomb frictional model is replaced by the regularization frictional model based on the investigations of blade vibration characteristics, and the dynamic response of integrally shrouded blade with dry frictional damping is studied, the optimal original clearanceδexisted and the range of the key parameters are determined. The achievements have provided quantitative basis and practicable method for optimal designing integrally shrouded blades.
The study results have provided a variety of effective numerical methods for the study on the dynamic-static characteristics of steam turbine blade, and will find important engineering application in development and modification design and optimization of the steam turbine integrally shrouded blade.
引文
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