任意斜裂纹转子的耦合振动研究

对包含不同类型裂纹(横裂纹、横-斜裂纹以及任意斜裂纹)的转子的耦合振动进行研究,以揭示裂纹转子在不同方向上刚度参数的变化规律及其交叉耦合机理,特别是由此引发的振动特征. 对于包含不同类型裂纹的转子轴段,采用六自由度Timoshenko梁单元模型对其进行单元建模,并基于应变能理论推导计算柔度参数和刚度矩阵. 在此基础上, 采用纽马克-$\beta$数值算法求解裂纹转子的运动方程,获得裂纹转子在单故障或多故障激励(不平衡激励、扭转激励或不平衡激励加扭转激励)作用下的耦合振动响应,进而分析耦合振动谱特征. 与横裂纹和横-斜裂纹相比,任意斜裂纹使转子刚度矩阵的交叉耦合效应更显著,导致转子发生更强烈的弯-扭耦合甚至是纵-弯-扭耦合振动.无论是在不平衡激励还是扭转激励作用下, 弯曲振动与扭转振动幅度都更大. 而且,包含不同类型裂纹的转子的耦合振动特征频率,例如旋转基频与二倍频、扭转激励频率及其边带成分的幅值,对裂纹面方向角具有不同的敏感性. 所得的这些研究结果,可以为转子裂纹的特征参数辨识与诊断提供理论依据.      

转子扭转-纵向耦合振动分析

针对某转子的模型,分析了扭转-纵向耦合振动.计算结果表明:设置转子预应力与旋转时的离心力相对应,其扭转振动频率将随预应力的增大而增大.转子纵向振动频率不受该预应力的影响,这是因为转子旋转时预应力的方向与轴线垂直.随着转子旋转时预应力的变化,扭转振动频率接近纵向振动频率,出现扭转-纵向耦合振动.     

Sommerfeld effect in a gyroscopic overhung rotor-disk system

Deflection of a rotor-disk at the free end of a flexible overhung rotor-shaft causes rotation about diametral axis and consequently leads to a strong gyroscopic coupling in a spinning overhung rotor system. When the rotor is spun up about its axis, the unbalance in the rotor-disk causes transverse and rotational vibrations to increase as the spin speed approaches the critical speed of the rotor. These transverse and rotational vibrations dissipate a lot of energy, and if the rotor is driven through a non-ideal drive, i.e., a motor which can supply a limited amount of power, then the entire motor power may be spent to account for the energy dissipation. As a result, the rotor speed may get stuck in resonance at the critical speed or jump through the critical speed to a much higher speed with lower transverse and rotational vibration levels. These symptoms, normally referred to as the Sommerfeld effect, occur due to the intrinsic energetic coupling between the drive and the driven systems and are important design considerations for development of various rotating machinery with flexible rotor-shafts or supports (bearings). Sommerfeld effect in a strongly gyroscopic rotor dynamic system is studied in this article. The dynamics of an overhung rotor system near the regimes of Sommerfeld effect is studied by using a discrete and a continuous shaft-rotor model coupled with the model of the non-ideal motor drive. The models are developed using multi-energy domain modeling approach in bond graph model form. A steady-state analysis of power transfer mechanism is used to postulate the ideal characteristics of Sommerfeld effect in the neighborhood of the critical speed, and thereafter, full transient analysis is performed with aid of the bond graph model-generated coupled equations of motion to validate the postulated characteristics of the Sommerfeld effect.     

电动机-弹性连杆机构系统的动态方程及其响应

针对三相交流电机转子振动偏心时不均匀气隙的气隙磁场,分析其实际运行状态的机电耦合关系．建立以电机横振、扭振为节点位移的电机单元,应用有限单元法建立含电机电磁参数和弹性连杆机构结构参数的系统动态方程,并根据该方程对系统的动态响应进行仿真计算和分析,且通过实验进行验征,表明所建方程较好地反映丁系统动态性能与其电磁参数、结构参数之间的关系．     

电磁作用激发的水电机组转子轴系振动研究

水轮发电机组的振动问题是长期困扰广大科研工作者的一个难题,也一直是学术界研究的热点.本文针对某大型水轮发电机转子轴系,首先建立了轴系扭振的微分方程组,给出了轴系整体扭振零频的计算公式,并计算了零频数值.接着在考虑了转子静偏心、振动偏心和转动偏心的综合影响后,求得了气隙磁场能量和单边电磁拉力的表达式,并应用机电耦联系统的能量法,求得了系统由电磁力激发的组合强迫共振响应的一次近似解.最后并应用奇异性理论对分岔方程进行了分析,求得了分岔集、滞后集、双极限集和转迁集的参数区间,给出了普适开折平面和物理参数平面上的分岔图,求得了机组稳定运行区域的电磁参数.本文所得结论对水电机组的工程设计人员具有重要的指导意义.     

大型转子—基础—土壤系统的动力分析

本文对大型汽轮发电机组-基础-土壤系统采用模态综合技术进行了动力分析.用弹性半空间理论建立土壤的模型,基础底板则通过弹性薄板的李兹(Ritz)函数近似解的形式来描述.用三维梁单元来建立基础底板以上的框架结构和转子系统的运动方程.此外,还用模态应变能的相对大小,在这种复杂机械结构系统存在的众多固有频率中,区分出哪些是属于主要为转子系统的固有频率,称为“重要振动固有频率”,以确定系统的临界转速.最后,对引进的一台500MW汽轮发电机组的动力特性进行了分析.     

旋转运动中弹性梁耦合振动的辛方法

研究旋转梁结构的弹性耦合振动问题。通过引入对偶体系，建立了解决该类问题的辛方法。在辛体系中描述旋转梁纵向和横向耦合振动控制方程，即哈密顿正则方程。进一步求解得到结构的固有振动频率及相应的振动模态，发现固有振动频率随转动角速度先升后降以及模态之间的某种转化规律。     

考虑弯扭耦合作用的转子-挤压油膜阻尼器系统的碰摩响应特性分析

研究了支承在挤压油膜阻尼器上的Jeffcott转子系统的转静件碰摩的弯扭耦合振动特性。建立了系统运动方程，分析了各参数对系统响应的影响。仿真计算结果表明碰摩刚度对系统响应的影响十分明显，增大碰摩刚度更容易使系统响应的周期解失稳；不平衡参数增大，导致系统响应的振动幅度增大，系统更容易出现碰摩现象，进而导致系统周期解失稳；随着扭转刚度的增大，扭转角度变化幅度与快慢均发生变化，在刚度较低时，扭转角变化幅度随时间变化较慢；随着扭转刚度的增大，扭转角幅度变化明显加快；当扭转刚度继续增大，扭转角的幅度变化反而变慢。研究发现，系统响应具有两条通向混沌的道路，即阵发性通向混沌的道路和拟周期通向混沌的道路。     

风机塔筒结构横向振动特性的快速计算方法

本文提出了一种风机塔筒结构横向振动特性的快速计算方法．将机舱和叶片整体、连接法兰盘分别简化为集中质量,塔筒简化为非均匀悬臂梁,建立风机塔筒结构横向振动方程．给出了用假设模态法计算塔筒结构固有频率和模态函数的过程．通过与文献及有限元数值结果比较验证了方法的有效性．本文方法仅需给出结构的基本参数,如截面半径变化规律、法兰盘位置和质量、机舱及叶片质量,便可快速求解其频率和模态,无需建立其复杂的力学模型．     

基于电磁感应的扭转振动测量方法

设计了一种基于电磁感应效应的转子扭转振动测量方法.该方法的思路是使线圈与永磁体做相对运动,根据线圈切割磁感应线的速度与感应电动势正相关的原理,由线圈两端的电压变化量计算各点的瞬时速度变化量,进而积分求出扭振信息.算法上采用半周期插值以及与标准信号进行对应点比较,保证了瞬时速度变化量的精确度.装置设计方面通过适当的空间布局,在一定程度上消除了轴向振动和部分横振的影响.实测验证表明,该方法得出了与输入载荷一致的扭振信息,具有精确性良好,安装简易,操作方便的特点.     

Free vibration analysis of functionally graded material beams based on Levinson beam theory

Free vibration response of functionally graded material (FGM) beams is studied based on the Levinson beam theory (LBT). Equations of motion of an FGM beam are derived by directly integrating the stress-form equations of elasticity along the beam depth with the inertial resultant forces related to the included coupling and higherorder shear strain. Assuming harmonic response, governing equations of the free vibration of the FGM beam are reduced to a standard system of second-order ordinary differential equations associated with boundary conditions in terms of shape functions related to axial and transverse displacements and the rotational angle. By a shooting method to solve the two-point boundary value problem of the three coupled ordinary differential equations, free vibration response of thick FGM beams is obtained numerically. Particularly, for a beam with simply supported edges, the natural frequency of an FGM Levinson beam is analytically derived in terms of the natural frequency of a corresponding homogenous Euler-Bernoulli beam. As the material properties are assumed to vary through the depth according to the power-law functions, the numerical results of frequencies are presented to examine the effects of the material gradient parameter, the length-to-depth ratio, and the boundary conditions on the vibration response.     

两种典型螺栓连接结构的刚度特性比较研究

针对法兰对接和径向套接两种典型舱段螺栓连接形式,基于有限元静刚度计算、动力学简化建模、冲击响应特性分析及结构冲击试验,系统研究了两种连接形式的轴向刚度特性及其对动力学冲击响应的影响.有限元静刚度分析揭示了法兰对接与径向套接的轴向拉压刚度分别是非对称的和对称的,而法兰对接的平均刚度更大.之后,为两种连接形式建立了统一的动力学模型,证明非对称的轴向拉压刚度导致结构在受到横向载荷作用时会产生附加的耦合轴向振动,并且利用高精度幂函数拟合刚度跳变,得到耦合轴向振动频率是弯曲振动频率的二倍的结论.最后,通过冲击动力学试验证明了法兰对接存在二倍频的耦合轴向振动,而径向套接则不存在该耦合振动.径向套接虽然一阶频率较低,但阻尼效果更好.     

The transverse and torsional vibrations of A.C. motors in the starting process

According to the electromagnetic field theory, a set of differential equations is derived for coupling of the transient process for an electrical machine and transverse and torsional vibrations for the rotor by a unified method. A non-dimensional constant coefficient state equation is obtained by transformation. Computation is done. Rules of the change are obtained for transverse and torsional vibration, unilateral magnetic pull, electrical torque, and so on in the starting process. The theoretical results are shown to be in good agreement with the experimental results. The mathematical model verified by the experiment is used to analyse the effect of electromagnetic and mechanical parameters on electromagnetic force and vibration.     

Radial and torsional vibration characteristics of a rub rotor

The nonlinear dynamics characteristics of a vertical Jeffcott rotor with radial rub-impact are investigated in this paper. Considering the influence of speed whirling, the radial-torsional coupling model of the rub rotor in polar coordinate system is established. With the improved model, the dynamics characteristics of radial vibration, whirl and torsional vibration are analyzed under no rub, full annual rub and partial rub conditions. The radial harmonic frequency is obtained by the harmonic balance method. The torsional vibration has the harmonic frequency component similar to the radial vibration. The new harmonic frequency is useful to help diagnose the occurrence of rub fault. A reasonable explanation of backward whirl instability is presented in this paper. With development of partial rub, the backward whirl will occur. When the backward whirling frequency is near the natural frequency, the instability is observed. The numerical method gives the quantitative results and reveals the backward whirl instability process of rub.     

Analysis of Coupled Vibration Characteristics of Wind Turbine Blade Based on Green's Functions

This paper presents the analysis of dynamic characteristics of horizontal axis wind turbine blade, where the mode coupling among axial extension, flap vibration(out-of-plane bending), lead/lag vibration(in-plane bending) and torsion is emphasized. By using the Bernoulli-Euler beam to describe the slender blade which is mounted on rigid hub and subjected to unsteady aerodynamic force, the governing equation and characteristic equation of the coupled vibration of the blade are obtained. Due to the combined influences of mode coupling, centrifugal effect, and the non-uniform distribution of mass and stiffness, the explicit solution of characteristic equation is impossible to obtain. An equivalent transformation based on Green's functions is taken for the characteristic equation, and then a system of integrodifferential equations is derived. The numerical difference methods are adopted to solve the integrodifferential equations to get natural frequencies and mode shapes. The influences of mode coupling, centrifugal effect, and rotational speed on natural frequencies and mode shapes are analyzed. Results show that:(1) the influence of bending-torsion coupling on natural frequency is tiny;(2) rotation has dramatic influence on bending frequency but little influence on torsion frequency;(3) the influence of bending-bending coupling on dynamic characteristics is notable at high rotational speed;(4) the effect of rotational speed on bending mode is tiny.     

Nonlinear and parametric coupled vibrations of the rotor-shaft system as fault identification symptom using stochastic methods

In the paper several stochastic methods for detection and identification of cracks in the shafts of rotating machines are proposed. All these methods are based on the Monte Carlo simulations of the rotor-shaft lateral-torsional-longitudinal vibrations mutually coupled by transverse cracks of randomly selected depths and locations on the shaft. For this purpose there is applied a structural hybrid model of a real cracked rotor-shaft. This model is characterized by a high practical reliability and great computational efficiency, so important for hundreds of thousands numerical simulations necessary to build databases used in solving the inverse problem, i.e. crack parameter identifications. In order to ensure a good identification accuracy, for creating the Monte Carlo samples of data points there are proposed special probability density functions for locations and depths of the crack. Such an approach helps in enhancing databases corresponding to the most probable faults of the rotor-shaft system of the considered rotor machine. In the presented study six different database sizes are considered to compare identification efficiency and accuracy of considered methods. A sufficiently large database enables us to estimate almost immediately (usually in less than one second) the crack parameters with precision that is in most of the cases acceptable in practice. Then, as a next stage, one of the proposed fast improvement algorithms can be applied to refine identification results in a reasonable time. The proposed methods seem to provide very convenient diagnostic tools for industrial applications.     

透平转子的可靠性设计

介绍透平转子的可靠性设计方法。该方法以传统的转子强度和振动的设计方法为基础,把透平转子的静应力、材料静强度、应力幅、尺寸系数、表面加工系数、应力集中系数、材料疲劳极限、热疲劳累积损伤程度、材料低周疲劳程度、蠕变寿命、固有频率、激振力频率、不平衡响应等处理为随机变量,使用机械概率设计法确定转子设计的可靠度。文中给出了透平转子静强度、疲劳强度、热疲劳、蠕变寿命、避开弯曲共振、避开扭转共振和限制不平稳响     

RELIABILITY SENSITIVITY STUDY OF THE BENDING VIBRATION OF THE COMPRESSOR ROTOR

以转子系统H858 型离心式压缩机为研究对象,利用MSC.Patran&Nastran 软件对该转子系统弯曲振动情况下的固有频率进行分析,定义了系统振动问题的频率可靠性模式,并以此为基础,应用随机摄动技术、可靠性理论和灵敏度方法,推导出参数为正态随机变量时频率可靠性灵敏度的计算公式,并应用于转子系统弯曲振动情况下的频率可靠性灵敏度研究中,同时将理论分析结果与基于Nessus软件的有限元分析结果进行比较,进一步验证了所提方法的有效性.     

Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.     

Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh's quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.