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.     

基于双频Bode图的磁悬浮控制力矩陀螺转子弹性自激振动抑制用陷波器设计

由于强陀螺效应和控制系统的高频滞后,磁悬浮控制力矩陀螺转子存在高频弹性自激振动,需要采用陷波器（Notch Filter－NF）进行相位校正和抑制,但是目前仍然缺乏有效的NF参数设计方法。本文提出一种基于双频Bode图的NF参数设计方法,采用双频Bode图分析转子弹性模态稳定性,得出不同转子转速下对NF相位校正角的要求,然后在保证转子章动稳定性的前提下优化设计NF参数。采用该方法设计的NF有效抑制了转子的弹性自激振动,使所研制的磁悬浮控制力矩陀螺稳定升速到20000r/min,验证了该方法的实用性和有效性。     

电磁轴承及其系统设计方法

电磁轴承是磁悬浮原理在机械领域中的一个应用实例,其工作机理是依靠电磁力使转子非接触地“支承”于轴承体内,有运动阻力小、无接触摩擦和磨损、功耗低以及寿命长等优点。国外在这方面已有成熟的产品应用于生产实际。介绍了电磁轴承及其系统设计的特点、系统控制器的设计方法、刚性转子系统的设计方法和柔性转子系统的动力学设计方法,并提供了几个实际设计的数据和部分试验结果。     

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.     

具有外部扰动的参数未知漂浮基柔性空间机械臂的对角递归神经网络控制

讨论载体位置和姿态均不受控情况下,存在外部扰动的参数未知漂浮基柔性空间机械臂系统关节运动的动力学控制问题。由假设模态法,利用拉格朗日方法建立漂浮基柔性空间机械臂的系统动力学方程。以此为基础,针对存在外部扰动和系统参数未知的情况,利用对角递归神经网络逼近柔性空间机械臂系统的逆动力学模型,设计基于对角递归神经网络的控制方案,以控制柔性空间机械臂的关节铰跟踪在关节空间的期望运动轨迹,同时能抑制柔性杆的振动。该方案由于没有专门设计主动控制器抑制柔性振动,因此不需要测量、反馈柔性振动模态,大大简化控制器的结构;无需预知控制对象的精确模型和系统参数,且能克服外部扰动的影响。计算机数值仿真证实所提方案的有效性和可行性。     

带弹性环保护轴承的动力学特性

提出在传统保护轴承外圈加弹性环来提高其在主动磁悬浮轴承(Active magnetic bearing,AMB)系统中的工作性能。为完善转子跌落仿真模型,得到AMB失效前转子准确的运动状态,理论推导得到AMB的支撑动刚度曲线,进而基于有限元分析方法得到转子在其支撑下的模态,并与试验结果进行对比,验证所得刚度曲线的正确性。在刚性转子理论基础上,建立转子在AMB系统中的动力学模型。基于Hertz接触理论,分别建立AMB失效后转子与保护轴承内圈之间的碰撞模型和保护轴承的实时动刚度模型。根据所建立的模型,对不同弹性环支撑刚度阻尼在不同初始转速下跌落后的动力学响应进行仿真计算,并与无弹性环状态下跌落结果进行对比。仿真分析结果表明,选用合适的弹性环有利于降低转子跌落后的振动幅值和碰撞力。分别在不同初始状态下进行跌落试验研究,试验结果与理论分析结果基本相符。     

含转子不平衡的磁轴承建模与同频电流抑制

为实现含转子不平衡的磁轴承系统动力学建模与同频电流抑制,分析了同频电流、力和力矩的产生机理,即转子不平衡（含静不平衡和动不平衡）经控制器、功放系统、感应电动势在磁轴承线圈中引起同频电流,进而与电流刚度和位移刚度相互作用产生力和力矩,完成了径向4自由度全主动磁轴承系统的建模。对该模型进行了数学求解和验证,提出了一种基于相移通用陷波反馈控制的同频电流抑制方法,可有效抑制控制器、功放系统和感应电动势产生的同频电流。仿真和实验验证了该方法的有效性,与传统的控制器串联陷波器方法相比,基于相移通用陷波反馈控制的同频电流抑制方法还可减少感应电动势引起的同频电流,同频电流进一步衰减了8.8dB。     

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.     

基于ANSYS的磁悬浮轴承转子系统的动力学特性研究

针对一个实际应用的磁悬浮支承柔性转子系统,进行多组参数条件下的有限元模态分析,分别得到系统的前8阶临界转速与模态振型。将有限元计算结果与试验结果进行对比分析,验证了有限元分析的正确性。通过对该磁悬浮转子系统的有限元分析表明:"轴承主导型"的低阶临界转速及振动模态是由轴承控制器各控制通道决定的;而"转子主导型"的高阶临界转速及振动模态符合传统的轴承转子系统动力学特性普遍规律。     

Optimal control of structural vibrations using a mixed-mode magnetorheological fluid mount

In this work, a mixed-mode magnetorheological (MR) mount is proposed and applied to the vibration control of a flexible beam structure subjected to external disturbances. On the basis of non-dimensional Bingham number, an appropriate size of the MR mount is designed and manufactured. After experimentally evaluating the field-dependent damping force of the MR mount, a structural system consisting of a flexible beam and vibrating rigid mass is established. The governing equation of motion of the system is derived and expressed as a state space control model. A linear quadratic Gaussian (LQG) controller is then designed in order to attenuate the vibration of the structural system. The controller is empirically realized and control responses such as acceleration and displacement of the structural system are evaluated and presented in frequency domain.     

System modeling and robust control of an AMB spindle : part II a robust controller design and its implementation

This paper discusses an entire procedure for a robust controller design and its implementation of an AMB (active magnetic bearing) spindle, which is part II of the papers presenting details of system modeling and robust control of an AMB spindle. Since there are various uncertainties in an AMB system and reliability is the most important factor for applications, robust control naturally gains attentions in this field. However, tight evaluations of various uncertainties based on experimental data and appropriate performance weightings for an AMB spindle are still ongoing research topics. In addition, there are few publications on experimental justification of a designed robust controller. In this paper, uncertainties for the AMB spindle are classified and described based on the measurement and identification results of part I, and an appropriate performance weighting scheme for the AMB spindle is developed. Then, a robust control is designed through the mixedμ synthesis based on the validated accurate nominal model of part I, and the robust controller is reduced considering its closed loop performance. The reduced robust controller is implemented and confirmed with measurements of closed-loop responses. The AMB spindle is operated up to 57,600 rpm and performance of the designed controller is compared with a benchmark PID controller through experiments. Experiments show that the robust controller offers higher stiffness and more efficient control of rigid modes than the benchmark PID controller.     

Modeling and control of a flexible rotor system with AMB-based sustentation

In this work the modeling and basic control design process of a rotary flexible spindle hovered by Active Magnetic Bearings (AMB) whose good capabilities for machine-tool industry extensively treated in the literature is presented. The modeling takes into account the three main behavioral characteristics of such magnetically-levitated rotor: the rigid dynamics, the flexible dynamics and the rotating unbalanced motion. Besides, the gyroscopic coupling is also studied proving that in this case, its effects are not significant and can be neglected. Using this model, a stabilizing controller based on symmetry properties is successfully designed for the system and a complete experimental analysis of its performance is carried out. Also, the predictions of the model are compared with the actual measured experimental results on a laboratory set-up based on the MBC500 Rotor Dynamics. Afterwards, a brief study about some nonlinear behavior observed in the system and its effect over the system stability at the critical speed is included.     

Dynamic characteristics of multi-degrees of freedom system rotor-bearing system with coupling faults of rub-impact and crack

Extensive studies on rotor systems with single or coupled multiple faults have been carried out. However these studies are limited to single-span rotor systems. A finite element model for a complex rotor-bearing system with coupled faults is presented. The dynamic responses of the rotor-bearing system are obtained by using the rotor dynamics theory and the modern nonlinear dynamics theory in connection with the continuation-shooting algorithm（commonly used for obtaining a periodic solution for a nonlinear system） for a range of rub-impact clearances and crack depths. The stability and Hopf instability of the periodic motion of the rotor-bearing system with coupled faults are analyzed by using the procedure described. The results indicate that the finite element method is an effective way for determining the dynamic responses of such complex rotor-bearing systems. Further for a rotor system with rub-impact and crack faults, the influences of the clearances are significantly different for different rub-impact stiffness. On the contrary, the influence of crack depths is rather small. The instability speeds of the rotor-bearing system increase due to the presence of the crack fault. The results obtained using the new finite element model, presented for computation and analysis of dynamic responses of the rotor-bearing systems with coupled faults, are in accordance with measurements in experiment. The formulations given can be used for diagnosis of faults, vibration control, and safe and stable operations of real rotor-bearing systems.     

基于频域整形的电磁轴承最优控制

针对电磁轴承刚性转子的不平衡振动，提出基于频域整形最优控制，该控制器的设计，包括保证系统稳定的最优调节器设计，以及频域整形的权函数设计，通过权值函数，改变轴承动特性，从而实现电磁轴承系统不平衡振动的力补偿或位移补偿。实验结果表明，电磁轴承频域整形最优控制可有效抑制主轴不平衡振动。     

消除柔性系统残留振荡有限冲击控制研究

将时滞滤波器用于具有刚性模态的柔性系统中，可以抑制残留振荡，但容易产生冲击运动。为了降低运动冲击，对控制信号的时间变化率加以限制，设计有限冲击指令，同时将最小最大优化思想引入时滞滤波器的设计中，提出一种新型控制器——有限冲击时滞控制器。计算机仿真和试验结果表明，这一控制器能降低振荡的最大幅值．在一个振荡周期内有效抑制残留振荡;在系统参数变化范围内，控制器的复数零点能有效抵消系统的极点，因此有更强的鲁棒性；与常用的时滞滤波器相比，能抑制控制信号的高频成分，降低未建模动态激励和运动冲击。     

磁悬浮高速电机转子低频振动机理及补偿方法

在实际工业应用中,磁悬浮电机转子时常出现与转速无关的低频振动。针对该问题,从数学模型及外部激励两个层面对该低频振动进行了分析,结果表明磁悬浮电机转子的低频振动由闭环控制系统的固有频率决定,且该振动会在噪声的激励下被激发。研究了基于扩展状态观测器的振动补偿策略,并提出了引入扩展状态观测器后控制系统稳定性的判据方法。通过仿真与试验对提出的振动补偿策略进行了验证。结果表明：在同样白噪声激励下,加入补偿器后转子最大振动量较单独使用PID控制时下降约21%;在30 000 r/min转速下,补偿器的作用更为明显,转子最大振动量减少了26.6%。     

Robust-optimal active vibration controllers design for the uncertain flexible mechanical systems possessing integrity via genetic algorithm

In this paper, a robust-optimal control approach is proposed to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under mode truncation, linear time-varying parameter uncertainties in both the controlled and residual parts, feedback gain perturbations, estimator gain perturbations and partial actuator failures. A sufficient condition is proposed to ensure that the flexible mechanical systems with time-varying structured parameter uncertainties are asymptotically stable against partial actuator failures. Systems which have such a property of keeping stable under partial actuator failures are said to possess integrity, and this is an inherent property of MIMO systems. Based on the robust stability constraint and the minimization of a defined H₂ performance, a hybrid Taguchi-genetic algorithm (HTGA) is applied to solve the optimal state feedback controller and observer design problem of uncertain flexible mechanical systems. A design example of a flexible rotor system is given to demonstrate the applicability of the proposed approach. It is shown that the proposed approach can obtain satisfactory results.     

柔性转子加速过临界瞬态响应特征分析

对于工作一阶或多阶临界转速以上的转子系统,转子如何安全平稳越过临界转速已成为研究热点。本文中建立了考虑变速转子运动微分方程以及越过临界转速时瞬态动挠度随速度变化的新模型,通过Newmark-β积分法得到越过临界转速的动挠度、进动角速度随加速度和阻尼系数变化的曲线,得出加速度和阻尼系数会影响进动角速度及动挠度波动频率和幅度。小阻尼系数会加剧转子过临界的波动并产生反进动以及反进动与动挠度变化的对应关系,阻尼系数大到一定数值能使转子平稳越过临界转速等一系列规律。     

磁力轴承支承刚性转子的临界转速计算

针对磁力轴承支承转子的结构特点提出了一种用于分析该类转子的简化处理方法,并使用Samcef Rotor有限元软件建立了某刚性转子的轴对称模型,计算得到了转子的临界转速及振型。研究了该转子的临界转速与磁力轴承支承刚度的关系。计算结果及相关结论将为磁力轴承和传感器的布置以及控制系统的设计提供重要依据。     

电磁轴承转子表面圆度误差对系统的影响

通过对转子表面圆度误差的机理分析,建立了圆度误差的数学模型,并实验验证了数学模型的正确性。分析讨论了圆度误差对采用PID控制策略的电磁轴承系统的控制精度的影响。研究结果表明:圆度误差会使转子作周期振动,当圆度误差信号的频率等于系统固有频率时,振动幅值较大,在这个频率后随频率的增加振动幅值减小。