STUDY ON THE COUPLED ELECTROMECHANICAL DYNAMICS OF ROTOR SYSTEM EQUIPPED WITH MAGNETIC BEARINGS

The influences of thrust magnetic bearing and journal tilt on dynamic characteristics of rotor system are studied mainly. The outcome shows that the influences of coupling effects of thrust magnetic bearing and tilt of journal on critical rotational speeds of system are very large, and the stability of system reduces greatly. That shows it is important that the influence of coupling effects of thrust and radial magnetic bearings due to the rotor tilting must be considered in the study of rotor-magnetic bearings system dynamic characteristics, and also shows it is important that the rotor is mounted and debugged in ideal alignment of magnetic bearings.     

Effects of semi-floating ring bearing outer clearance on the subsynchronous oscillation of turbocharger rotor

Semi-floating ring bearing(SFRB) is developed to control the vibration of turbocharger rotor. The outer clearance of SFRB affects the magnitude and frequency of nonlinear whirl motion, which is significant for the design of turbocharger. In order to explore the effects of outer clearance, a transient finite element analysis program for rotor and oil film bearing is built and validated by a published experimental case. The nonlinear dynamic behaviors of rotor-SFRB system are simulated. According to the simulation results,two representative subsynchronous oscillations excited by the two bearings respectively are discovered. As the outer clearance of SFRB increases from 24 μm to 60 μm, the low-frequency subsynchronous oscillation experiences three steps, including a strong start, a gradual recession and a combination with the other one. At the same time, the high-frequency subsynchronous oscillation starts to appear gradually, then strengthens, and finally combines. If gravity and unbalance are neglected, the combination will start starts from high rotor speed and extents to low rotor speed, just like a "zipper". It is found from the quantitative analysis that when the outer clearance increases, the vibration amplitude experiences large value firstly, then reduction, and suddenly increasing after combination. A useful design principle of SFRB outer clearance for minimum vibration amplitude is proposed: the outer clearance value should be chosen to keep the frequency of two subsynchronous oscillations clearly separated and their amplitudes close.     

Dynamic Control of a Flexible Shaft Mounted in Adaptive or Active Bearing

The dynamic behavior of rotors is highly influenced by bearing characteristics. In previous works, the authors have shown that it may be beneficial to adapt the bearing behavior to the shaft behavior. Several adaptive and active components will be developed in this paper in order to control the shaft dynamical amplitude. Different models of hydrodynamic bearings behavior are described. The Reynolds equation resolution may be done by numerical or analytical solutions. A physical analysis of the equation of thin films will identify the most sensitive parameters. The shaft flexibility is taking into account by a modal approach. The fluid-structure coupling process is a simulation, step by step, of the rotor behavior. At each step, the nonlinear fluid force is numerically calculated to obtain the unbalanced shaft response. The results, presented in this paper, concern the dynamic response of unbalanced shaft mounted in adaptive or active bearings： bearings with variable clearance, variable viscosity or variable housing speed. It is shown that the fluid bearing parameters must be adapted to the rotor speed （in particular near or far a critical speed）. Then, the paper presents a new kind of active bearing. It works with a mechanical control of the housing position. Several parameters are tested and compared. The robustness of the dynamic control parameters is presented. In conclusion, the bearing adaptation could be very useful to control the shaft dynamic. This limits the effect of the critical speed, in particular by diminishing the shaft amplitude and the dynamic forces transmitted to the housing.     

CONTROL SYSTEM OF MAGNETIC BEARINGS BASED ON LINEAR QUADRATIC METHOD OF OPTIMAL CONTROL STRATEGY

A state equation for radical 4-degree-of-freedom active magnetic bearings is built, and the approach on how to use linear quadratic method of optical control theory to design a centralized and decentralized parameters control system is introduced, and also Matlab language is used to simulate and analyze. The simulation results have proved that the differences are small between centralized parameters and decentralized parameters control system. The conclusions of experiments have shown that decentralized controllers designed from optimal state feedback theory meet the requirements of active magnetic bearing system. The vibration amplitude of the rotor is about 20 μm when the speed of the rotor runs between 0 to 60 000 r/min. This method may be used in the study and design of controllers of magnetic bearings.     

Bifurcation and chaos analysis of nonlinear rotor system with axial-grooved gas-lubricated journal bearing support

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-0-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar6 map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.     

CAD/CAE OF THE WORKING CHARACTERISTICS OF A NEW TYPE OF FLUID COUPLING SHOCK ABSORBER

For purpose of simulation of the working characteristics of a new type of fluid coupling shock absorber for vibration protection of sensitive equipment, a physical model is presented by analyzing the internal fluid dynamic phenomenon with respect to the coupling shock absorber and implemented in MATLAB software package. Using the model it is possible to evaluate the importance of different factors for design of the shock absorber. In the meantime, the key-model machine is designed for coupling dynamic test. Comparisons with experimental results confirm the validity of the model. So the CAD/CAE software has been developed in MATLAB for design and experimental test of the new coupling shock absorber.     

SIMULATION STUDY OF GENERALIZED MINIMUM VARIANCE CONTROL FOR AN EXTRACTION TURBINE

In an extraction turbine, pressure of the extracted steam and rotate speed of the rotor are twoimportant controlled quantities. The traditional linear state feedback control method is not perfectenough to control the two quantities accuraely because of existence of nonlinearity and coupling. Ageneralized minimum variance control method is studied for an extraction turbine. Firstly, a nonlinearmathematical model of the control system about the two quantities is transformed into a linear systemwith two white noises. Secondly a generalized minimum variance control law is applied to the system.A comparative simulation is done. The simulation results indicate that precision and dynamic qualityof the regulating system under the new control law are both bcher than those under the state feedbackcontrol law.     

VIBRATION MEASUREMENT OF DOUBLE-ENDED TUNING FORKS RESONATOR

To enhance the coherence and reliability of the double-ended tuning fork (DETF) resonator, a measurement system of resonator vibration is presented to check its dynamic characteristics. Laser Doppler techniques are utilized and the relation between DETF vibration velocity and output current of photodetector is obtained. Resonator vibration equation is also analyzed and its driving power only depends on the direct current bias voltage and the amplitude of alternative voltage. Furthermore, a special resonator driving control circuit based on measurement is designed. The amplitude and frequency of circuit is controlled by a computer so that highly stable and strong driving signal can be output. Experiments on driving and measuring double-ended tuning fork have been done. The frequency of driving signal is 8 kHz and the peak-to-peak value of driving voltage is 140 V. Experimental results indicate resonator can be drived stably by driving control circuit and dynamic characteristics of DETF may be measured in real time.     

NONLINEAR DYNAMIC CHARACTERISTICS OF HYDRODYNAMIC JOURNAL BEARING-FLEXIBLE ROTOR SYSTEM

The nonlinear dynamic behaviors of flexible rotor system with hydrodynamic bearing supports are analyzed. The shaft is modeled by using the finite element method that takes the effect of inertia and shear into consideration. According to the nonlinearity of the hydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique with free-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system. According to physical character of oil film, variational constrain approach is introduced to continuously revise the variational form of Reynolds equation at every step of dynamic integration and iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametric finite element method without the increasing of computing efforts. Nonlinear oil film forces and their Jacobians are simultaneously calculated and their compatible accuracy is obtained. The periodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A meth     

Unbalance vibratory displacement compensation for active magnetic bearings

As the dynamic stiffness of radial magnetic bearings is not big enough,when the rotor spins at high speed,unbalance displacement vibration phenomenon will be produced.The most effective way for reducing the displacement vibration is to enhance the radial magnetic bearing stiffness through increasing the control currents,but the suitable control currents are not easy to be provided,especially,to be provided in real time.To implement real time unbalance displacement vibration compensation,through analyzing active magnetic bearings(AMB) mathematical model,the existence of radial displacement runout is demonstrated.To restrain the runout,a new control scheme-adaptive iterative learning control(AILC) is proposed in view of rotor frequency periodic uncertainties during the startup process.The previous error signal is added into AILC learning law to enhance the convergence speed,and an impacting factor influenced by the rotor rotating frequency is introduced as learning output coefficient to improve the rotor control effects.As a feed-forward compensation controller,AILC can provide one unknown and perfect compensatory signal to make the rotor rotate around its geometric axis through power amplifier and radial magnetic bearings.To improve AMB closed-loop control system robust stability,one kind of incomplete differential PID feedback controller is adopted.The correctness of the AILC algorithm is validated by the simulation of AMB mathematical model adding AILC compensation algorithm through MATLAB soft.And the compensation for fixed rotational frequency is implemented in the actual AMB system.The simulation and experiment results show that the compensation scheme based on AILC algorithm as feed-forward compensation and PID algorithm as close-loop control can realize AMB system displacement minimum compensation at one fixed frequency,and improve the stability of the control system.The proposed research provides a new adaptive iterative learning control algorithm and control strategy for AMB displacement minimum compensation,and provides some references for time-varied displacement minimum compensation.     

弹性支承高速喷漆涡轮系统动态特性研究

将一类高速喷漆涡轮系统机架与转子间精密滚动球轴承用约束矩阵来描述,进而将涡轮系统考虑成柔性、耦合双弹性梁,运用模态综合法建立其动力学模型.考虑转子前后两端喷杯及底盘偏心,建立双面离心力作用下的转子子系统强迫力模型.据此,研究了耦合系统固有频率、主模态等动特性,分析了转子末端动态响应.     

Dynamic characteristics of spindle with water-lubricated hydrostatic bearings for ultra-precision machine tools

A key component of ultra-precision machine tools is the spindle. The motivation for this study was to improve machining accuracies in precision cutting and grinding by pursuing improvements in the spindle characteristics by designing a sophisticated spindle with water-lubricated hydrostatic bearings. The static bearing stiffness of the developed spindle was investigated in previous studies. In addition to the static bearing stiffness, the dynamic characteristics regarding bearing stiffness also affect significantly on the machining results. In this study, dynamic characteristics of the developed spindle with water-lubricated hydrostatic bearings were investigated via simulations and experiments. Not only bearing dynamics but also rotor dynamics were considered in this study.In the simulation studies, the spindle dynamic characteristics were analysed based on the transfer matrix method. A spindle rotor supported with hydrostatic bearings was represented by discrete sections of the rotor. The mathematical model of transverse linear vibrations of the spindle rotor was derived with distributed parameters for these discretized rotor sections. As a result of the analysis on the amplitude-frequency characteristic, radial displacements of the rotor due to bearing displacement and bending deformation were defined. Then, the frequency characteristics were represented with Nyquist plots. Resonant frequencies and amplitudes formation in the transverse vibration of the rotor were determined. The influence of rotor bending deformations on spindle compliance was assessed. Furthermore, the study examined the influences of the supply pressure of the lubricating fluid, radial clearance and journal diameter of the hydrostatic bearings on the amplitude of the rotor vibration, and the resonance frequency of the system.Furthermore, the dynamic characteristics of the spindle were examined experimentally. The simulation results were in good agreement with the actual spindle dynamics obtained experimentally. The influence of the structural parameters of the rotor and the operating parameters of the bearings on the spindle dynamic characteristics was also determined. It was verified that the amplitude of the vibration of the rotor overhang part was dominantly affected not by bearing stiffness but by bending stiffness of the bearing journal of the front bearing and the length of the rotor overhang.Then it was verified that the resultant displacement of the rotor in the radial direction due to the influence of the bearing characteristics and the structural effect of the rotor is significantly small. Practical recommendations to improve the spindle design in terms of the dynamic characteristics of the spindle with water-lubricated hydrostatic bearings were also derived.     

基于显式有限元的转子不平衡与轴承故障耦合分析

为分析转子不平衡与轴承故障耦合振动特征及产生机理,在对转子不平衡与轴承故障耦合状态下受力分析的基础上,基于虚位移原理的增广拉格朗日法建立轴承运动控制方程,运用LS-DYNA建立转子-轴承系统二维显式动力学有限元模型,分析了故障耦合状态下轴承振动加速度、转子轴心运动轨迹,探明了转子不平衡-轴承缺陷耦合故障冲击响应特征及转子轴心运动轨迹突变机理,并通过试验进行了验证。结果表明:转子不平衡与轴承外圈故障耦合状态下,轴承座测点位置故障特征频率被转频调制,冲击幅值随转频变化;转子轴心轨迹呈椭圆形,且缺陷位于轴承承载区时,转子轴心轨迹存在突变。     

数控平面磨床主轴动力耦合系统减振方法

将一类平面磨床主轴系统简化为耦合双弹性梁结构 ,用模态综合法建立其动力学模型。据此 ,考虑实际工况 ,设计主轴系统动力减振器。模拟仿真和试验结果表明 ,在系统加入动力减振器后 ,主轴末端振动幅值可得到有效减小。     

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。     

轴承--转子--齿轮联轴器系统的振动研究

利用六个动力系数来刻划半联轴器的力学行为,建立了轴承—转子—齿轮联轴器系统的弯扭振动力学模型。最后进行了数值计算,结果表明在计算、设计轴承—转子—齿轮联轴器系统时必须考虑联轴器的影响。     

SFD作用下故障转子系统动力学特性及混沌控制

考虑挤压油膜阻尼器(squeeze film damper,简称SFD)作用,研究碰摩故障及不对中-碰摩耦合故障下系统动力学特性及SFD对系统混沌运动控制。基于Lagrange方程,建立不对中-碰摩耦合故障下SFD-转子-滚动轴承系统动力学模型,采用龙格库塔法对模型求解,并利用分岔图、Poincaré图、频谱图等进行对比分析。研究结果表明:合理油膜间隙下的SFD能有效抑制系统非协调响应以及振动幅值,使故障转子系统的混沌运动控制在稳定周期轨道上;过小的油膜间隙会形成很强的非线性油膜支反力,产生非协调频率成分,使稳定周期系统重返混沌状态;随着油膜间隙减小,SFD对不对中故障产生的典型2 X,3 X,4 X和5 X频幅值具有不同影响,其中2 X频幅值变化明显,3 X和4 X频幅值变化微弱,5 X频幅值基本不变。     

两种载荷下掘进机截割头转子系统动力学分析

为了研究不同截齿载荷条件下（锐利截齿和磨钝截齿）掘进机截割头和悬臂系统的动力学特性，建立了掘进机截割头-转子-轴承系统的弯扭耦合非线性动力学模型。考虑截割头和转轴之间的花键啮合间隙、滚动轴承接触的非线性因素影响下，推导了掘进机截割头转子系统的动力学微分方程。然后对受到时变载荷下的截割头转子系统动态响应特性进行了分析:在锐利截齿条件下，截割头转子系统在低转速n∈［15，20］时处于混沌和拟周期运动状态，提高转速后系统处于周期运动状态;在截齿磨钝条件下，截割头转子系统的振动明显加剧，混沌运动范围增大，频率幅值波动明显。结果表明：在给定截割煤层硬度、切削厚度等前提下，随着截割转速的升高，系统由混沌运动向周期运动转变。动态分析结果为掘进机的减振和动态设计提供了理论依据。     

轴承载荷对转子系统各支承的耦合振动分析

以多支承转子 轴承 弹性基础系统为研究对象,对多支承转子系统某支承处轴承载荷变化引起不同支承点处轴及轴承的耦合振动响应进行了研究。首先,建立了多支承转子系统支承间的耦合振动模型,并进行了仿真和试验,耦合振动模型考虑了每个支承处的油膜耦合效应,通过轴承载荷敏感度矩阵得到各支承耦合力;然后,利用龙格库塔法对油膜刚度为定刚度和动刚度两种情况下的转子系统进行了数值分析及仿真;最后,在8支承转子试验台上进行试验,采取改变某一支承处的位移来得到轴承载荷的变化,并提取各支承处的振动信号。结果表明,轴承位置在稳态和瞬态两种情况下改变时振动响应明显不同,油膜刚度为动刚度的分析结果更为合理。     

液下硫磺泵的转子动力学分析

为减少长轴液下硫磺泵转子系统的振动,基于转子动力学对液下硫磺泵进行研究,以转子体、轴承、轴承座以及联轴器构成转子系统,运用ANSYS模拟转子系统的临界转速、转子不平衡引起的同步振动响应。结果表明:转子系统在第一阶临界转速下运行,为刚性转子;在前四阶临界转速下,轴承处的变形都较小;在加载了不平衡量的谐响应分析中,轴承与叶轮都在前四阶固有频率下产生共振现象,两叶轮振幅接近,各轴承最大振幅也远小于标准要求。液下泵转子系统的动力学研究对预防转子破坏引起的故障具有重要意义。