Numerical techniques for computing nonlinear dynamic characteristic of rotor-seal system

A transient CFD procedure to compute the nonlinear dynamic characteristic of the coupled rotor-seal system was presented in this study. In each time step, the displacement diffusion model was implemented to govern the mesh deformation, and the URANS (Unsteady Reynolds averaged Navier-Stokes) equations were solved to obtain the transient fluid force on the rotor surface for the free vibrations. With the obtained fluid force from the CFD solver, the nonlinear equations of motion for a simplified rotor-seal system were numerically solved on the basis of external user defined routines. During each transient time step, the computed fluid force from the CFD solver and the rotor motion from the user defined routines were transferred to each other timely. The rotor center trajectories, frequency spectrum and projection of Poincaré section were calculated to investigate the nonlinear dynamic performance of the single disk rotor-seal system. The effects of the rotational speed and pressure ratio on the vibration characteristic of the rotor-seal system were analyzed by the bifurcation theorem. The results show that the coupled rotor-seal system experiences a period-one motion, resonance, periodic-doubling motion, quasi-periodic motion, and finally possible chaotic motion as the rotor speed increases. The pressure ratio has pronounced effect on the frequency response of the first-order critical speed; however, it has little influence on the motion state as well as the frequency response of the rotating speed. Although a constant-clearance annular smooth stator seal was selected as the research object in the current paper, the presented transient CFD method is still available for other complex annular seals, such as labyrinth seal, honeycomb seal, pocket damper seal, etc.     

A novel nonlinear model of rotor/bearing/seal system and numerical analysis

A novel nonlinear model of rotor/bearing/seal system based on the Hamilton principle is proposed for steam turbine systems in power plants. The Musznyska model and unsteady bearing oil-film force model were applied to describe the nonlinear steam excitation force and oil-film force. The Runge-Kutta method was used to solve the motion equation of the rotor/seal/bearing system. The dynamic characteristics of the rotor/bearing/seal system were analyzed with bifurcation diagrams, time-history diagrams, trajectory diagrams, Poincare maps and frequency spectrums. The numerical analysis indicates that the seal force and the oil-film force influence the nonlinear dynamic characteristics of the rotor system. With the increase of rotation speed, the rotor system exhibits rich forms of periodic, double-periodic, multi-periodic, quasi-periodic and chaotic motion. The combined impact of steam excitation force and bearing oil-film force may cause a severe vibration which seriously affects the safety and stability of the rotor. The presented model provides a theoretic foundation for further research on the ultra-supercritical steam turbines.     

三维转子密封系统气流激振的研究

提出了分析三维转子密封系统气流激振流固耦合作用的数值计算方法。首先建立三维转子密封流固耦合模型,然后直接数值求解密封流场的非线性气动力,形成了考虑流固耦合效应的转子密封气流激振问题的分析方法。数值计算表明,对应于不同的转速、压比和预旋,转子振动的各个频率成分的幅值不同,但始终存在着转子一阶临界转速频率成分,而且该成分的幅值随着转速、气流进口压力和正向进气预旋的增高而增大,与工程和试验中的密封气流激振现象有较好的一致性,捕捉到了密封气流激振的基本特性。     

Experimental identification of fluid-induced force in labyrinth seals

The seal force is an important factor in turbomachineries. Therefore, the current paper puts forward an expanded seal force identification model. A seal test rig consisting of several sets of seals was prepared. Using the double-plane unbalance force identification theory in rotordynamics, the distributed seal force in the cylinder became equivalent to two selected planes. Considering the complex cylinder vibration with increasing rotating speed and inlet pressure, the cylinder was regarded as a vibration system with 4 degrees of freedom. The 4×4 impedance matrix was tested at the two selected planes using a shaker in two orthogonal directions. The equivalent seal force can be obtained by multiplying the impedance matrix with the measured change in the cylinder vibration. In the seal rig, tests were performed on the influence of inlet pressure, rotating speed, eccentricity ratio, rotor vibration, and clearance. The seal force increases almost linearly with the increasing inlet pressure, eccentricity ratio, and vibration amplitude. Furthermore, the seal force is strongly sensitive to the change in clearance between the cylinder and the rotating rotor. The phase difference between the seal force and the vibration influences the work done. If the phase difference is nearly 90°, then the work is at maximum. Moreover, the seal force applies positive force on the cylinder and negative force on the rotor.     

Nonlinear coupled dynamics of flexible blade-rotor-bearing systems

The nonlinear dynamic behavior of a rotor-bearing system with interaction between blades and rotor is addressed in this paper. Using the Lagrange equation, a time-dependent nonlinear model of a flexible blade-rotor-bearing system is established, in which the rotor is supported by journal bearings and the blades are modeled as pendulums in order to analyze the dynamic coupling between the elastic blades and the flexible shaft. To emphasize the gyroscopic effect of the rotor, the disk is assumed to be located at an arbitrary position of the shaft. Employing the orthogonal transformations, the 1-nodal diameter equations of motion of the blades, which are coupled with the dynamic equations of the rotor, are decoupled with other equations of the blades. Then the parametric excitation terms in the blade-rotor-bearing system are simplified in terms of periodic transformations. The dynamic equations with nonlinear oil-film forces are numerically solved using the Runge-Kutta method. Bifurcation diagrams, three-dimension spectral plots, and Poincaré maps are employed to analyze the dynamic behavior of the system. The numerical results show that the nonlinear dynamic behavior of the system varies with the increase of the rotational speed. And the effect of the nonlinear vibration of the rotor on the blade vibration is discussed.     

永磁同步型磨削电主轴偏心振动分析及实验*

电主轴是将旋转主轴与电机转子集成为一体的主轴单元,结构复杂,由于加工或装配误差等原因,电主轴转子会存在着一定的偏心量,为探求由于电主轴偏心所导致的转子振动特性,建立了电主轴转子偏心模型,采用Maxwell应力张量法计算了偏心造成的不平衡磁拉力(UMP),将UMP解析式代入Jeffcott转子模型,得到了转子偏心振动方程。以某磨床的永磁同步电主轴为研究对象,利用有限元方法分析了UMP,发现作用于转子的UMP始终指向气隙最小的方向,研究了不同转速下转子在质量偏心离心力和UMP作用下的振动响应。研究结果表明,电主轴在低速运行时,UMP为转子振动的主要来源;随着转速的增加,质量偏心离心力对转子振动的影响更加明显,而UMP大小保持不变,其频率随转速增加而增大,对转子振动的作用随之减弱。对某机床厂所研发永磁同步型磨削电主轴在试运行时产生的振动问题进行了实验,对主轴振动频谱分析后判断实验电主轴存在静态偏心,测得主轴轴心轨迹对前述分析进行了验证。     

On fault induced nonlinear rotary response and instability

Results of applying instantaneous frequency to the interpretation and characterization of bifurcation and evolution of instability are presented for a comprehensive rotor-journal bearing model incorporating translational and rotational inertia, bending stiffness, gyroscopic moments, shear deformation and disk imbalance. By designating rotor speed and the relative flexibility embodying the extent of surface crack development as the two controlled parameters, rich and complex nonlinear behaviors are observed as the model subjected to the combined exertion of slow crack breathing and bearing film pressure. Among them are that sub-harmonics attributable to the oil-film force are seen disappeared with crack opening and that the model system fails from one of the three possible scenarios: super-harmonic bifurcation, prolonged chaotic response, and large vibration amplitudes accompanied by no bifurcation. As a result of the investigation, a dynamic failure curve differentiating zones of stability and bifurcated instability from zones of dynamic failure is constructed and proposed as an alternative to the traditional stability chart.     

油气两相柔性丝刷封传热性能数值分析及试验研究*

为解决大过盈结构的柔性丝刷封局部过热、过多热量传至下游从而影响设备性能等问题,针对轴承腔处油气两相的密封环境和柔性丝刷封大过盈的结构特点,建立油气两相柔性丝刷封传热模型并进行数值计算;试验测量柔性丝刷封挡板的实时温度及刷封的温度变化,研究油气两相介质下柔性丝刷封的温度场分布和传热性能,分析工况参数和结构参数对其传热性能的影响。结果表明：最高温度出现在转子与轴向段刷丝束接触处,轴向段刷丝区存在局部〖JP2〗高温,径向段刷丝无明显温度变化,解释了大过盈结构的柔性丝刷封的传热机制;增大压差、转速和介质油气比均会导致刷封出口热流量增加,压差对出口热流量影响最显著,可设置多级刷封密封装置降低出口热流量以适应高压差的密封环境。以降低出口热流量为目标,得到了结构参数的较优取值范围,可为其传热性能的提升和结构优化提供参考。     

含内阻的拉杆组合转子双稳态振动特性

为揭示含内阻组合转子复杂的双稳态振动特性,基于拉格朗日方程推导了含轮盘接触、非线性油膜力及内阻的组合转子非线性运动控制方程。采用升速和降速相结合的方法研究了组合转子跨2阶临界转速的非线性动力学行为及内阻机理。研究结果表明：组合转子双稳态振动特征显著,内阻导致出现双稳态现象的转速区间明显向低转速方向移动,在分析组合转子振动特性时应考虑内阻效应,以有效预测双稳态现象的出现。     

Frequency characteristics of non-contact ultrasonic motor with motion error correction

The purpose of this research is to achieve real time motion error correction of the rotor in a non-contact ultrasonic motor (non-contact USM). The rotor is installed in a cylindrical stator with a small gap and designed so that it has a resonant frequency of 22.2 kHz, the 8th flexural mode of vibration. The multi-layered piezoelectric actuators excite the flexural wave traveling in the circumference direction. The ultrasonic vibration produces a sound field that levitates the rotor, and the traveling wave induces a near-boundary streaming to rotate the rotor by viscous force. In this paper, we describe an experimental test of the performance of a non-contact USM. When the flexural vibration amplitude was 0.3 μm, the rotational speed was 4 rpm. The rotational speed and starting torque was proportional to the vibration amplitude. The starting performance to attain rotational speed had a time constant of 2 s for several different amplitudes hence the rotational torque is independent of the rotational speed and the resistance force on the rotor is governed by viscosity. In addition, the non-contact USM has the capability of contact-free micro positioning of the rotor by controlling the deformation of the piezoelectric actuators. The PI controller was constructed to correct the detected motion error of the rotor in the radial direction. As a consequence, a motion error of 0.8 μm for one rotor revolution was reduced to 0.1 μm.     

非线性裂纹转子密封系统的耦合振动分析

随着旋转机械结构参数的提高,作用在转子上的密封中的气流激振力将显著增大。本文针对裂纹转子密封系统进行了研究。应用Muszynska非线性密封力模型,建立了在密封中的气流激振力作用下的裂纹转子系统耦合动力学方程,分析了在非线性密封力作用下的裂纹转子运动特性,并着重讨论了迷宫密封的物理和结构参数对裂纹转子运动特性的影响。研究结果表明,系统具有非常丰富的非线性动力学行为,密封中的气流激振力对裂纹转子的周期运动有明显的抑制作用,密封结构的各主要参数对系统稳定性有很大影响,故可以通过调整密封参数来改善系统的动态稳定性,这为旋转机械的理论设计和故障动态监测提供了理论依据。     

基于叶轮转子系统下的干气密封轴向振动分析*

为探究基于叶轮转子系统下干气密封轴向振动特性,基于干气密封结构特性,建立叶轮转子-轴承-干气密封系统轴向振动模型,采用待定系数法进行求解,推导得出静环轴向振动幅值表达式;建立叶轮转子-轴承-干气密封系统几何模型,运用ANSYS Workbench软件进行模拟仿真计算,分析气膜刚度和激振力对轴向振动的影响。结果表明:气膜刚度对动、静环振动幅值的影响不大;动、静环振动频率相同、振动幅值相同,说明动、静环的追随性高,其间隙稳定,从而保证干气密封的稳定运行;动、静环位振动幅值与激振力成正比关系,说明激振力严重影响干气密封的稳定性,为提高干气密封的稳定性,应平衡好叶轮的轴向激振力。     

转子-轴承-密封耦合系统的非线性振动特性研究

结合短轴承非线性油膜力模型和Muszynska密封力模型,运用数值积分方法分析了转子-轴承-密封耦合系统的非线性动力学特性,针对转速对耦合系统动态响应的影响进行了仿真计算,并利用转子中心分岔图、轨迹图、Poincare映射图、功率谱图分析了耦合系统的非线性动力学特性.理论分析表明:随着转速的变化,耦合系统呈现复杂的动力学行为,产生了包括单周期、3倍周期、拟周期等振动现象.     

双盘悬臂转子—轴承—机匣耦合系统碰摩故障分析

针对航空发动机转子系统的质量主要集中于压气机及涡轮部分的工程实际,将航空发动机转子系统简化为双盘悬臂连续体转子系统。建立含碰摩故障的双盘悬臂连续体转子—轴承—机匣耦合动力学模型,导出双盘悬臂连续体转子的四阶偏微分运动方程。运用变步长四阶龙格库塔法模拟系统的碰摩故障响应,分析转速与偏心量对系统碰摩故障响应的影响,发现该模型在发生碰摩故障时的一些非线性动力特性,为解决工程实际问题提供一定的理论依据。通过所建模型与单盘转子模型振动特性的比较,验证建立模型的必要性与工程意义。     

压缩机梳齿密封内部流场及激振力研究

以某大型压缩机转子振动试验台的平衡盘梳齿密封为研究对象,采用CFD方法,分析了转轴在不同相对偏心距下,定转速变压差和定压差变转速时的三维梳齿密封内部流场,总结了流场内部压力、速度和温度的变化规律。确定了由转轴偏心引起的密封激振力,转速升高、相对偏心距及压差增大均会导致激振力增大。     

Robust modal vibration suppression of a flexible rotor

This study deals with active robust modal vibration control of rotor systems supported by magnetic bearings. The inherent divergent rigid body modes are suppressed by using a dual-level control approach. Finite element method is applied to formulate the rotor model. The Timoshenko beam theory, including the effects of shearing deformations and rotary inertia, is considered in this work. Because practical control systems are often limited by its sensing, hardware, and computation speed capabilities, the reduced order approach is often used for a control system design. This study applies the independent modal space control (IMSC) approach to extract the accurate lower modes from the complex rotor systems with the gyroscopic effect considered. In practice, it is extremely difficult to model the complete dynamic characteristics of a rotor system. The model may contain unmodelled dynamics and parameter changes, which can be viewed as uncertainties of a system. As opposed to the conventional control approach, which requires fixed and accurate system parameters, this study considers robust control approach to design a controller capable of tolerating external disturbance and model uncertainties. It is demonstrated that the proposed approach is effective for vibration suppression when the system is subjected to impulsive or step loading, speed variation, and sudden loss of disk mass.     

液体动静压球轴承轴心运动轨迹研究

为研究外载荷对轴承转子系统稳定性的影响,以小孔节流的液体动静压球轴承转子系统为研究对象,建立液体动静压球轴承转子系统动力学模型。通过求解轴承润滑数学模型获得非线性油膜力,分析转子所受到的外载荷,采用欧拉算法预测出轴心下一个时刻位移、速度和加速度,并分析转子系统质量、不平衡载荷和阶跃载荷对转子回转精度的影响。结果表明：随着转子系统质量的增加,所需平衡的油膜力增加,轴心振动幅度增加,从而导致转子回转精度降低;相对于不考虑不平衡载荷,考虑不平衡载荷后其振动形态为椭圆且振动幅值增大,减小不平衡值将减小振幅并提高旋转精度;随着阶跃载荷的增加,达到平衡所需的时间也增加。     

含柔性转子的齿轮-轴承系统动态特性分析

为了分析齿轮系统动力学中的全耦合振动,提出采用虚拟样机建模的方法,将柔性转子引入到啮合耦合系统中,考虑齿轮时变啮合刚度、齿侧间隙和轴承间隙的影响,建立齿轮-柔性转子-轴承系统虚拟样机模型,通过求解模型的动力学方程得到系统的非线性动力学响应。仿真结果表明:考虑柔性转子的耦合系统,啮合冲击峰值下降明显;转子柔性增加,齿轮低频扭转振动出现"拍"现象;高速轻载时啮合振动非线性特性增强;轴承间隙增大使啮合力振动幅值显著增大。     

磁悬浮高速转子基于位移刚度力超前前馈补偿的高精度自动平衡方法

磁悬浮转子高速旋转时产生与转速同频的不平衡振动,向外界传递振动力,干扰外部动力学环境。为消除同频不平衡振动力(即自动平衡),可采用消除同频电流与补偿位移刚度力相结合的轴承力消除方法,但磁轴承功放环节的低通特性使位移刚度力补偿存在误差,并降低系统稳定性,且上述影响随转速升高而显著增大。为增强自动平衡效果,提出一种基于位移刚度力超前前馈补偿的高精度自动平衡方法,在消除同频电流的同时,采用不平衡量—电流前馈以补偿同频位移刚度力,并引入功放的简化逆模型对前馈量进行超前校正,消除功放低通特性的影响。对该方法进行仿真和试验验证,仿真结果同频轴承力减小到无超前校正时的20%,试验结果同频振动加速度减小到无超前校正时的28%,验证了该方法的有效性。     

UNBALANCE RESPONSE AND TOUCH-RUBBING THRESHOLD SPEED OF ROTOR SUBJECTED TO NONLINEAR MAGNETIC FORCES

Because of the effect of unbalance excitation and nonlinear magnetic force, the large vibration of the rotor supported by active magnetic bearing（AMB） will go beyond the radial gap of the bearing, even causing mechanical touch-rubbing when the system works at an operational speed closer to the critical speed. In order to investigate this problem, the linear model and nonlinear model of the single mass symmetric rigid rotor system supported by AMB are established respectively and the corresponding transfer functions of close-loop system are given. To pass through the numerical calculation by using MATLAB/Simulink, the effect of both the unbalance response and threshold speed of touch-rubbing of the system subjected to nonlinear magnetic forces and nonlinear output current of power amplifier are studied. Furthermore, threshold speed of touch-rubbing of the rotor-bearing system is defined and the results of numerical simulation are presented. Finally, based on above studies, two methods of increasing the touch-rubbing threshold speed are discussed.