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。     

Dynamic characteristics of the rotor in a magnetically suspended control moment gyroscope with active magnetic bearing and passive magnetic bearing

For a magnetically suspended control moment gyroscope, stiffness and damping of magnetic bearing will influence modal frequency of a rotor. In this paper the relationship between modal frequency and stiffness and damping has been investigated. The mathematic calculation model of axial passive magnetic bearing (PMB) stiffness is developed. And PID control based on internal model control is introduced into control of radial active magnetic bearing (AMB), considering the radial coupling of axial PMB, a mathematic calculation model of stiffness and damping of radial AMB is established. According to modal analysis, the relationship between modal frequency and modal shapes is achieved. Radial vibration frequency is mainly influenced by stiffness of radial AMB; however, when stiffness increases, radial vibration will disappear and a high frequency bending modal will appear. Stiffness of axial PMB mainly affects the axial vibration mode, which will turn into high-order bending modal. Axial PMB causes bigger influence on torsion modal of the rotor.     

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%。     

Identification of the dynamic parameters of active magnetic bearings based on the transfer matrix model updating method

The stiffness and damping coefficients of Active magnetic bearings (AMBs) have a great impact on the dynamics of a high-speed rotor AMB system, from its bending critical speed to the modes of its vibration and stability. To accurately obtain the stiffness and damping coefficients of AMBs, this study proposes a new identification approach based on the transfer matrix model updating method. By minimizing the error between the unbalance response calculated through the transfer matrix approach and the experimental measurements, the stiffness and damping coefficients are obtained using the simplex optimization algorithm based on the updating method of the model. According to the experimental data, we identify the parameters from 20 Hz to 260 Hz (1200 rpm to 15600 rpm). To verify the identified results, a finite element rotor AMBs model is created, and the theoretical unbalance response is predicted using the identified parameters. The theoretical unbalance responses closely coincide with the experimental measurements, indicating the effectiveness of the proposed method.     

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.     

Model validation and controller design for vibration suppression of flexible rotor using AMB

This paper discusses the model validation and vibration suppression of an AMB flexible rotor via additional LQG controller. The main difficulty in the vibration suppression of the flexible rotor using AMB is to realize a controller that can minimize resonance without injuring the stabilized rigid modes. In order to solve this problem, simple scheme for system modeling and controller design are developed. Firstly, the AMB flexible rotor is stabilized with a PID controller, which leads to a new stable rotor-bearing system. Then, authors propose the model validation procedure using measured open-loop frequency responses to obtain an accurate model of the AMB flexible rotor system. After that, LQG controller with modal weighting is designed to suppress resonances of the stable rotor-bearing system. Due to the poor controllability and observability of flexible modes compared to rigid ones, balancing of two Gramians is prerequisite for the fair LQG controller design. Simulation with step disturbance and experimental results of unbalance response up to 10,000 rpm verified the effectiveness of the proposed scheme.     

差动变压器式位移传感器及其在磁悬浮轴承中的应用

针对差动变压器式位移传感器的性能及其在磁悬浮轴承中的应用,理论分析传感器与磁悬浮轴承转子之间加入不同隔层时对传感器输出的影响;对传感器进行静态和动态标定,并将其应用于2自由度和5自由度磁悬浮轴承试验台进行静态和动态悬浮。研究结果表明：该传感器测试范围在–0.5～＋0.5 mm时,线性度可达±1.38%,灵敏度为20.18 mV/μm,截止频率在800 Hz左右;理论分析加入非导磁隔层不影响传感器性能,但实际中涡流、漏磁等多方面原因将影响传感器的静动态性能;在2自由度试验台上实现磁悬浮转子2自由度的静态悬浮,不加入隔层时转子的静态位移振动峰峰值小于5 μm,加入隔层时转子的静态位移振动峰峰值小于10 μm;在5自由度试验台上实现了磁悬浮转子的高速旋转,转速为30 kr/min,不加隔层时转子两端的径向振动峰峰值为25 μm,加入隔层时转子两端的径向振动峰峰值为25 μm,但波形没有不加隔层时规则。研究结果为差动变压器式位移传感器的设计,并将其应用于磁悬浮轴承系统中提供一定的理论和试验基础。     

Modeling and performance evaluation of machining spindle with active magnetic bearings

Active magnetic bearings (AMBs) are increasingly employed in the machine tool industry to exploit their advantages over classical bearings such as high speed capability, rotation accuracy, high stiffness, and accurate displacement tracking capability. Furthermore, the possibility of on-line monitoring of the machining process (e.g., cutting force measurement, tool wear) makes AMB spindles very appealing to the High-Speed Machining (HSM) industry. Despite significant progress already reached in HSM technology, there remain numerous open challenges in modeling and control of magnetic bearings as applied to machining spindles. These include optimum control given AMB magnetic saturation levels, management of nonlinear effects, reduction of chatter, and rotor properties. This paper describes a five-degree-of-freedom, high-speed machining spindle supported on AMBs. The rotordynamic modeling and experimentally extracted transfer functions are presented and analyzed. The experimentally measured tool tip compliance is used to compare PID and mu-synthesis control schemes. The primary finding is that the achieved tool tip stiffness is substantially higher with the μ-synthesized controllers than with the best PID we were able to design.     

一种可控滑动轴承-转子系统性能计算方法*

针对可控滑动轴承油膜性能计算困难问题,提出一种考虑基础参振的滑动轴承性能计算的动网格模型,阐述网格更新原理,给出可控滑动轴承所支撑转子系统轴心轨迹的计算方法。在滑动轴承-转子-基础系统的性能计算时,该方法保证油膜径向网格线和轴颈表面垂直,能减小轴承油膜性能计算的累计误差。通过不平衡载荷条件下的转子轴心静平衡位置计算结果与油膜力数据库方法、经典数据进行对比,验证了该模型的正确性,并利用该方法分析受正弦位移激励的滑动轴承-刚性转子系统的工频振动情况。结果表明：选择合适相位和幅值的正弦位移激励来控制轴承座,可减小转子系统的不平衡振动。这为基于超磁致伸缩材料的轴承、基于压电陶瓷材料的轴承、柔性铰链可倾瓦轴承等可控轴承-转子系统的性能计算提供了一种新方法。     

转子在线自动平衡研究

研究了转子在工作转速下实现在线自动平衡的方法。以电磁执行器作为施力装置,运用傅里叶分析和线性系统的叠加原理,对不停车的情况下转子不平衡振动的识别和抑制的算法进行了推导,并在一滚珠轴承支承的转子系统上进行了试验研究。结果证明该方法和装置能够使旋转工作频率下转子的不平衡振动大大减小。     

径向电涡流阻尼器对柔性转子系统振动的控制

为了抑制转子系统的振动和研发高性能的转子系统振动主动控制执行元件,基于电涡流原理提出了一种新型的转子系统径向电涡流阻尼器,在一个带有双盘的柔性转子系统上详细地测量了不同磁场强度条件下径向电涡流阻尼器支撑的转子系统在非旋转状态下的传递函数、在恒定转速下的运动轨道以及在慢加速运行过程中的不平衡响应曲线,并进行了利用径向电涡流阻尼器对转子系统的振动进行分段和比例控制的有效性试验。结果表明了这种新型的径向电涡流阻尼器不仅具有结构简单、无需流体介质、无机械接触等特点,而且其动力特性还容易控制,在设计合理的条件下能够显著地减小转子系统的振动,是一种被动和主动兼备具有良好发展和应用前景的转子系统阻尼结构。     

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。     

车载飞轮电池的振动控制策略研究

针对车载飞轮电池在不同工况下振动及磁悬浮轴承非线性和本质不稳定性的特点,开发了基于单神经元的PID控制软件,利用单神经元的自学习能力并通过加权系数自适应地对PID各控制参数进行调整,使得控制器的输出为PID各控制参数的非线性组合,克服了单一PID控制参数无法满足系统动态性能需要及控制参数整定困难的缺点。通过仿真分析和飞轮转子系统的高速运行试验,对比研究了不完全微分PID策略和单神经元自适应PID策略的控制效果。研究结果表明,与不完全微分PID策略相比,单神经元自适应PID策略具有无超调、鲁棒性好、调节时间短等优点,飞轮转子系统具有更好的动态性能。     

磁悬浮轴承-转子系统的机电耦合动力学模型

对磁悬浮轴承 -刚性转子系统建立了完整的机电耦合动力学模型 ,其中除了人们通常所考虑的陀螺效应外 ,着重考虑和增加了推力磁轴承对转子横向振动的耦合效应和由于轴颈倾斜所引起的径向磁轴承之间的耦合效应 ,以及控制系统的电学微分方程和传感器与磁轴承非共点安装对系统性能所带来的耦合影响。该模型可用于五自由度磁悬浮轴承 -刚性转子系统的机电耦合动力学性能研究     

主被动磁悬浮转子的不平衡振动自适应控制

针对主被动磁悬浮控制力矩陀螺转子高速旋转时产生的不平衡振动,提出了基于滑模观测器和陷波器的主被动磁悬浮转子不平衡振动自适应控制方法。该方法采用滑模观测器使同频振动的控制不受磁轴承的刚度参数摄动和磁力耦合的影响,将滑模观测器与陷波器结合,无需区分电流刚度力和位移刚度力,无需设计算法补偿功率放大器的影响,可自适应消除不平衡振动。对该方法进行了仿真和实验验证。仿真结果显示该方法可使同频轴承力大幅减小;实验结果显示,虽然主被动磁悬浮转子的被动轴承不可控,同频振动仍由0.053g减小为0.012g,减小了77%。得到的结果表明,该方法不仅适用于主被动磁悬浮转子,也适用于全主动磁悬浮转子。     

一种磁悬浮离心式心脏泵刚度与阻尼特性分析

针对一种磁悬浮离心式心脏泵系统的动态特性,需要分析其刚度与阻尼。为此,分析了径向永磁轴承和开关磁阻电机的径向力学特性,得到磁悬浮转子径向运动方程和控制系统框图; 并结合PD控制器,推导出系统径向刚度与阻尼数学表达式,最后通过实例仿真,得到径向刚度与阻尼特性曲线。研究表明,比例和滤波环节对系统动刚度、阻尼比和固有频率均有显著影响,且在低频段,微分系数与阻尼比近似成正比关系。上述研究为磁悬浮离心式心脏泵控制系统的设计和磁悬浮转子径向位移控制提供理论指导。     

主被动磁悬浮高速转子系统的自动平衡控制

针对主被动磁悬浮转子高速旋转时质量不平衡和被动磁轴承磁中心的偏移导致的同频振动力问题,提出了一种基于位移陷波加前馈补偿的自动平衡控制方法。首先,在转子为零位移控制状态下提取控制电流的同频成分,计算获得与被动磁轴承磁中心偏移相关的参变量;然后,在额定转速下设计通用陷波器以消除同频电流,前馈补偿主动磁轴承、被动磁轴承位移负刚度力和被动磁轴承磁中心偏移力,使主被动磁轴承的同频输出力为零,实现了转子绕惯性中心旋转。对提出的方法进行了仿真和实验验证并与仅补偿质量不平衡的算法进行了对比。仿真结果显示:提出的方法的同频磁轴承力减小到了只进行质量不平衡补偿算法的6%;实验结果显示:同频振动加速度减小到只进行质量不平衡补偿算法的23.3%。仿真和实验验证了该方法的有效性,表明该方法对同频振动抑制效果显著,实现了转子的自动平衡控制。     

永磁型电主轴多频率振动的主动控制

为了有效抑制由砂轮质量不平衡及外部干扰引起的永磁型电主轴转子系统砂轮端的多频率成分振动,在无轴承永磁电机径向磁悬浮力产生原理的基础上,提出了一种基于最小方差快捷分块(FBLMS)的自适应滤波的永磁型双绕组电主轴柔性转子系统砂轮端多频率成分振动的主动控制方案。首先研究了双绕组永磁型电主轴结构及工作原理和径向控制力的模型,借助有限元法建立了永磁型电主轴柔性转子系统的动力学模型,分析了控制电流的不同成分对永磁体涡流损耗及电机定子铁损的影响,设计了永磁型电主轴柔性转子系统砂轮端多频率成分振动的主动控制系统,结果表明,提出的永磁型电主轴柔性转子系统砂轮端多频率成分振动控制方案具有明显的控制效果。     

Effects of unbalance location on dynamic characteristics of high-speed gasoline engine turbocharger with floating ring bearings

For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings(FRBs), the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.     

转子系统径向电涡流阻尼器

基于电涡流原理提出了一种新型的转子系统径向电涡流阻尼器，分析了这种阻尼器的结构和动力模型，并在不同磁场强度条件下测量、研究了径向电涡流阻尼器所支撑的柔性转子系统在非旋转状态下的传递函数、在恒定转速下的运动轨道,以及在慢加速运行过程中的不平衡响应。结果表明：这种新型的径向电涡流阻尼器不仅具有结构简单、无需工作介质、无机械接触等特点，而且还可以对其动力特性进行控制，能够显著地减小转子系统的振动。