Rotor drop and following thermal growth simulations using detailed auxiliary bearing and damper models

Catcher bearings (CBs) or auxiliary bearings provide mechanical backup protection in the events of magnetic bearing failure. This paper presents numerical analysis for a rotor drop on CBs and following thermal growths due to their mechanical rub using detailed CB and damper models. The detailed CB model is determined based on its material, geometry, speed and preload using the nonlinear Hertzian load–deflection formula, and the thermal growths of bearing components during the rotor drop are estimated using a 1D thermal model. A finite-element squeeze film damper provides the pressure profile of an annular oil film and the resulting viscous damping force. Numerical simulations of an energy storage flywheel with magnetic suspensions failed reveal that an optimal CB design using the detailed simulation models stabilizes the rotor drop dynamics and lowers the thermal growths while preventing the high-speed backward whirl. Furthermore, CB design guides based on the simulation results are presented.     

Vibration analysis of a rotating system due to the effect of ball bearing waviness

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modelled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian contact theory is applied to calculate the elastic deflection and non-linear contact force, while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the non-linear governing equations of the rotor, which are solved by using the Runge–Kutta–Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e., the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing, but also between those of two or more ball bearings constrained by the rotor.     

Detailed ball bearing model for magnetic suspension auxiliary service

Catcher bearings (CBs) provide backup protection for rotating machines with active magnetic bearings (AMBs). The CBs are required in the event of an AMB failure or high transient loads. Numerical simulations of a rotor drop on CBs in flywheel energy storage system are conducted with a detailed CB model which includes a Hertzian load–deflection relationship between mechanical contacts, speed-and-preload-dependent bearing stiffness due to centrifugal force, and a Palmgren's drag friction torque. The transient simulation results show the rotor shaft response variations with the design parameters: shaft/bearing friction coefficients, axial preload, support damping of damper liner, and side loads from magnetic bearings. The results reveal that friction coefficients, support damping, and side loads are critical parameters to satisfy CB design objectives and prevent backward (super) whirl.     

Design and analysis of a novel inset permanent magnet synchronous motor

This paper presents the design of a permanent magnet (PM) synchronous motor with the magnets laid flush in slots let into the rotor surface, called inset magnet rotor. The finite element field analysis coupled with the drive circuit equations are briefly discussed for obtaining the motor performance. Experimental results obtained are in good agreement with the finite element analysis.     

Design and construction of shaft-driving type piezoceramic ultrasonic motor

A new approach in design of shaft-driving type piezoceramic ultrasonic motor is proposed. The stator of motor consisted of a commercial available buzzer disk in which a piezoceramic membrane is adhered to a metal sheet. The wave propagation on the metal sheet was generated by extended-shrunk force from piezoceramic oscillation. Driving energy came from the vibration modes by mechanical-electrical oscillation of the metal sheet in corresponding to converse piezoelectric effect using a single-phase AC voltage power. Where the relative elliptic motion was occurred between the bearing seat and rotor in order to kinematical delivery, the rotor being driven was connected directly on the bearing seat to transmit the dynamic power with frictional contact force. In analysis of dynamic features, the system transfer function of admittance and equivalent circuit was obtained. The rotating speed of the prototype motor could be reached as high as 2000 rpm on the driving condition of 72 kHz, +/-10 V(pp), and 0.2 A. The maximum torque was less than 0.003 Nm. It could be utilized in the driver of CD, or the cooling fan in the computer CPU.     

Dynamics and stability of rigid rotors levitated by passive cylinder-magnet bearings and driven/supported axially by pointwise contact clutch

A stable rotor—supported laterally by passive magnetic bearings and longitudinally by magnetic forces and a clutch—loses suddenly its contact to the clutch and executes abruptly longitudinal movements away from its original equilibrium position as a result of small increases in angular velocity. Such an abrupt unstable behaviour and its reasons are thoroughly theoretically as well as experimentally investigated in this work. In this context, this paper gives theoretical as well as experimental contributions to the problem of two dimensional passive magnetic levitation and one dimensional pointwise contact stability dictated by mechanical–magnetic interaction. Load capacity and stiffness of passive multicylinder magnetic bearings (MCMB) are thoroughly investigated using two theoretical approaches followed by experimental validation. The contact dynamics between the clutch and the rotor supported by MCMB using several configurations of magnet distribution are described based on an accurate nonlinear model able to reliably reproduce the rotor-bearing dynamic behaviour. Such investigations lead to: (a) clear physical explanation about the reasons for the rotor's unstable behaviour, losing its contact to the clutch and (b) an accurate prediction of the threshold of stability based on the nonlinear rotor-bearing model, i.e. maximum angular velocity before the rotor misses its contact to the clutch as a function of rotor, bearing and clutch design parameters.     

永磁体结构对高温超导推力轴承静态特性的影响

基于商用电磁场有限元软件以及M e issner效应假设,提出了对由块状高温超导体和永磁体组成的高温超导推力轴承静态特性进行分析的方法,分析了永磁体的结构对高温超导推力轴承悬浮力的影响。结果发现:永磁体的结构及磁极排列方式对高温超导推力轴承悬浮力的影响很大,适当地选择永磁体的结构和磁极排列方式可以显著地提高高温超导推力轴承的悬浮力。     

Nonlinear dynamic analysis of a rotor-bearing-seal system under two loading conditions

The operating speed of the rotating machinery often exceeds the second or even higher order critical speeds to pursue higher efficiency. Thus, how to restrain the higher order mode instability caused by the nonlinear oil-film force and seal force at high speed as far as possible has become more and more important. In this study, a lumped mass model of a rotor-bearing-seal system considering the gyroscopic effect is established. The graphite self-lubricating bearing and the sliding bearing are simulated by a spring-damping model and a nonlinear oil-film force model based on the assumption of short bearings, respectively. The seal is simulated by Muszynska nonlinear seal force model. Effects of the seal force and oil-film force on the first and second mode instabilities are investigated under two loading conditions which are determined by API Standard 617 (Axial and Centrifugal Compressors and Expander-compressors for Petroleum, Chemical and Gas Industry Services, Seventh Edition). The research focuses on the effects of exciting force forms and their magnitudes on the first and second mode whips in a rotor-bearing-seal system by using the spectrum cascades, vibration waveforms, orbits and Poincaré maps. The first and second mode instability laws are compared by including and excluding the seal effect in a rotor system with single-diameter shaft and two same discs. Meanwhile, the instability laws are also verified in a rotor system with multi-diameter shaft and two different discs. The results show that the second loading condition (out-of-phase unbalances of two discs) and the nonlinear seal force can mainly restrain the first mode instability and have slight effects on the second mode instability. This study may contribute to a further understanding about the higher order mode instability of such a rotor system with fluid-induced forces from the oil-film bearings and seals.     

DYNAMIC BEHAVIOR OF THE FULL ROTORSTOP RUBBING: NUMERICAL SIMULATION AND EXPERIMENTAL VERIFICATION

The dynamic behavior of a rotor rubbing, especially rubbing fully with a motion-limiting stop is investigated by numerical and experimental methods. In the dynamic simulation, the sinuous excitation force with low frequency excites the large whirl of the unbalanced rotor and thus causes the rubbing between the rotor and the stop. The simple Coulomb friction model and the multiple segments linear spring model are used to reveal the nature of the rubbing forces. The torque equation of the rotor is built to extract the rotating speed during partial and full rubbing. The stable partial rubbing motion demonstrates that the stop limits the violent vibration amplitude of the rotor effectively. The rubbing experiments confirm the idea of using the inner type of stop to suppress the violent backward whirl with low frequency. When the amplitude of the excitation force exceeds a certain value, the full rubbing occurs with serious continuous friction. During full rubbing, the center of the rotor moves counter-clockwise and whips in the amplitude exceeding the rotor/stop gap dramatically. Moreover, the whip frequency is much higher than the frequencies of the excitation and the unbalance force. And then the rotor rotation is broken quickly by the stop. The predicted dynamical behavior is verified by the rubbing experiments. The relation between the stop/bearing stiffness ratio and such dynamical behavior as the initiation of the rubbing, the over-limit ratio and the contact-ratio is discussed.     

Design and construction of shaft-driving type piezoceramic ultrasonic motor

A new approach in design of shaft-driving type piezoceramic ultrasonic motor is proposed. The stator of motor consisted of a commercial available buzzer disk in which a piezoceramic membrane is adhered to a metal sheet. The wave propagation on the metal sheet was generated by extended-shrunk force from piezoceramic oscillation. Driving energy came from the vibration modes by mechanical–electrical oscillation of the metal sheet in corresponding to converse piezoelectric effect using a single-phase AC voltage power. Where the relative elliptic motion was occurred between the bearing seat and rotor in order to kinematical delivery, the rotor being driven was connected directly on the bearing seat to transmit the dynamic power with frictional contact force. In analysis of dynamic features, the system transfer function of admittance and equivalent circuit was obtained. The rotating speed of the prototype motor could be reached as high as 2000 rpm on the driving condition of 72 kHz, ±10 V_pp, and 0.2 A. The maximum torque was less than 0.003 N m. It could be utilized in the driver of CD, or the cooling fan in the computer CPU.     

Identification of magnet and superconductor contributions to the ac loss in a magnet-superconductor levitation system

By measuring the quality factor of the mechanical oscillator with an attached magnet we investigated the amplitude dependence of the energy loss in a permanent magnet-YBCO superconductor system. When a non-conducting ferrite magnet is used the energy loss is proportional to the amplitude to the 2.79 power. This value is close to the value of 3 expected for the hysteretic motion of flux lines from the Bean model. When a conducting magnet is used the exponent decreased to the value of 2.5. This reflects the contribution of eddy current dissipation in a conducting magnet to the overall loss. We identified a novel mechanism of ac loss in the magnet-superconductor system. According to this mechanism the eddy current in a magnet is induced by the ac field generated by the ac supercurrent in response to the motion of a magnet. This mechanism would take place in a rotary bearing if circumferential inhomogeneity of the rotor magnetization occurred.     

超导磁悬浮支承系统干扰力矩及漂移误差分析

在超导磁悬浮支承系统中, 如果被悬浮的超导球形转子是一个理想的球体, 并且是表现出完全的迈斯纳态, 那么由于球体的对称性, 就不会产生干扰力矩. 但实际的情况并非如此, 一般情况下, 超导球形转子总是存在加工制造误差, 且在高速旋转时总是存在离心变形, 因此转子的表面并不是理想的球面, 当超导转子悬浮在磁场中时, 沿转子表面法线方向的磁悬浮力, 不是完全通过转子质心, 将会产生磁支承干扰力矩, 从而引起转子的漂移误差. 本文从超导转子磁支承干扰力矩的物理机理出发, 对干扰力矩及其引起的漂移误差进行了分析, 包括转子非球形产生的一次干扰力矩、转子非球形与失中度和装配误差产生的二次干扰力矩, 并推导出了磁支承干扰力矩引起的漂移率计算公式, 代入转子参数计算出各种干扰力矩引起的漂移率大小, 为转子漂移测试和系统误差补偿提供了参考, 对于转子的结构优化设计具有指导意义.     

Mechanics of a magnet and a Meissner superconducting ring at arbitrary position and orientation

The force and torque exerted by a magnetic dipole on a superconducting ring (or hollow cylinder) in the Meissner state at arbitrary position and orientation are calculated using a Maxwell-London model previously proposed by the authors. The center of the ring is an unstable equilibrium point for the magnet. At this point the ring tends to align the magnet but tends to expel it for any small axial deviation from the center. There is also a non-monotonic and oscillatory dependence of the forces and torques on the position caused by the finiteness of the ring and a torque arises when the magnet is displaced both radially and axially from the center of the cylinder which corresponds to the experimental data. Therefore, the use of a magnet in a Meissner superconducting ring as a self aligning bearing requires a centered position and that the axial unstability to be compensated by additional mechanical means.     

Direct transition of potential of water droplets to electric energy using aligned single-walled carbon nanotubes

In this paper, we report that an electromotive force (EMF) can be induced in a rope of aligned single-walled carbon nanotubes (SWNTs) when water droplets fall on this rope. The magnitude of this EMF depends sensitively on the slant angle of the SWNTs. Most interestingly, both the magnitude and the direction of the induced EFM can be modulated by applying a current to the SWNTs. The concepts of electrical slip and no-slip are proposed and can be quantitatively described by ``electrical slip resistance'. This kind of generator does not need any magnet, rotor, {etc} and shows quite a different operating mechanism and design compared with a conventional large scale hydroelectric power generator.     

Optimizing magnetization orientation of permanent magnets for maximal gradient force

The force exercised on a permanent magnet (PM) in a nonuniform field (gradient force) is dependent on the magnetization orientation of the magnet. In this paper, it is shown theoretically that the gradient force is greatest when the magnetization through the magnet, or at least at its surface, is collinear with the external field. The formulae for calculating the force between an axis-symmetric optimal magnet and a coaxial axis-symmetric coil are presented. Using the finite element method (FEM), calculations of the magnetic field distribution of an optimal cylindrical magnet and some its approximations are performed. The forces between these magnets and a pancake coil are computed and compared. For a system consisting of a magnet with a height of 1 unit and a diameter of 2 units and magnetization invariant in field and an annular pancake coil with a diameter of 2.4 units, a thickness of 0.2 units, an inner diameter of 0.4 units and a distance from the magnet of 0.2 units, the force on the optimal magnet was 1.44 times greater than the force on an axially magnetized magnet of the same size and magnetization magnitude. The optimal magnetization may be approximated by magnetization inclined at a constant angle to the axis and by a combination of axially and radially magnetized sections. With magnetization at a constant angle to the axis in the axis plane, the force was greatest when the angle was about 45°, being 1.38-fold compared to the force on an axially magnetized magnet. When the magnet was composed of an axially magnetized cylindrical core and a radially magnetized outer ring, the force was greatest when the volume of the core was approximately equal to the volume of the ring, being 1.26-fold compared to the force on an axially magnetized magnet. The optimal magnet and its approximations also provided a reduced stray field. A short review of methods of the fabrication of permanent magnets (PMs) with a continuous variation of the magnetization orientation and with radial magnetization orientation is given.The results of this study can be used to design linear electromagnetic (micro)actuators.     

Rotor–stator contact dynamics using a non-ideal drive—Theoretical and experimental aspects

The possible contact between rotor and stator is considered a serious malfunction that may lead to catastrophic failure. Rotor rub is seen as a secondary phenomenon caused by a primary source, i.e. sudden mass unbalance, instabilities generated by aerodynamic and hydrodynamic forces in seals and bearings among others. The contact event gives rise to normal and friction forces exerted on the rotor at impact events. The friction force plays a significant role by transferring some rotational energy of the rotor to lateral motion. A mathematical model has been developed to capture this for a conventional backup annular guide setup. It is reasonable to superpose an impact condition to the rub, where the rotor spin energy can be fully transformed into rotor lateral movements. Using a nonideal drive, i.e. an electric motor without any kind of velocity feedback control, it is even possible to stop the rotor spin under rubbing conditions. All the rotational energy will be transformed in a kind of “self-excited” rotor lateral vibration with repeated impacts against the housing. This paper studies the impact motion of a rotor impacting a conventional backup annular guide for the case of dry and lubricated inner surface of the guide. For the dry surface case, the experimental and numerical analysis shows that the rotational energy is fully transformed into lateral motion and the rotor spin is stopped. Based on this study this paper proposes a new unconventional backup bearing design in order to reduce the rub related severity in friction and center the rotor at impact events. The analysis shows that the rotor at impacts is forced to the center of the backup bearing and the lateral motion is mitigated. As a result of this, the rotor spin is kept constant.     

辅助永磁体的引入方式对单畴GdBCO超导块材磁场分布及其磁悬浮力的影响

通过对永磁体辅助下单畴GdBCO超导体和方形永磁体在液氮温度、 零场冷、 轴对称情况下磁悬浮力的测量, 研究了三种不同组态中辅助永磁体的引入方式对单畴GdBCO超导块材磁场分布及其磁悬浮力的影响. 实验结果表明, 如果处在超导体上方的测量用方形永磁体N极向下, 则在轴对称情况下, 当方形辅助永磁体N极向上与超导体下表面贴在一起时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N增加到31.8 N, 提高到222%; 当方形辅助永磁体放置在超导体上表面、 N极垂直向上且场冷后去掉辅助永磁体时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N增加到21.6 N, 增加到151%; 当方形辅助永磁体放置在超导体上表面、 N极垂直向下且场冷后去掉方形辅助永磁体时, 超导体的最大磁悬浮力从没有引入辅助永磁体磁化的14.3 N减小到8.6 N, 减小为无辅助永磁体时的60%.这些结果说明, 只有通过科学合理地设计超导体和永磁体的组合方式, 才能获得较高的磁场强度, 有效地提高超导体的磁悬浮力特性, 该结果对促进超导体的应用具有重要的指导意义.     

高温超导磁悬浮飞轮储能系统样机

在日益严峻的能源问题背景下,为展示无源高温超导磁悬浮技术在能量储存领域的应用前景,我们设计制作了一台全高温超导磁悬浮形式的飞轮储能样机.样机主要由高温超导磁悬浮轴承、飞轮转子、永磁电机和电路控制及负载部分组成.上下两个轴向型高温超导磁悬浮轴承用于悬浮和稳定飞轮转轴,直径200mm重量1.4kg的飞轮转子作为储能载体,最高可实现13000r/min的转速.在演示运行中,采用灯泡作为负载,该样机完成了从电能→机械能→电能的相互转换.     

基于ANSYS的高温超导混合磁轴承悬浮力分析

基于商用电磁场有限元软件ANSYS以及Bean临界态模型,对由圆柱形高温超导块材、永磁体和超导线圈组成的新型高温超导混合磁轴承的电磁场分布及悬浮力进行了仿真分析,研究了超导线圈对高温超导混合磁轴承悬浮力的影响,同时还通过实验测试了悬浮力。结果表明:仿真与实验具有较好的一致性,使用软件仿真方便可行,其结果较为准确可靠,可为高温超导混合磁轴承的设计和优化提供理论依据。     

永磁体辅助下单畴GdBCO超导体和永磁体之间的磁悬浮力研究

通过对永磁体辅助下单畴GdBCO超导体和圆柱形永磁体在液氮温度、零场冷、轴对称情况下磁悬浮力的测量,研究了两种不同组态下辅助永磁体对超导体磁悬浮力特性的影响.实验结果表明,当长方体辅助永磁体水平磁化、且磁极N指向超导体时,超导体的最大磁悬浮力从没有引入辅助永磁体的29.8 N增加到61.5 N,增加为没有引入辅助永磁体时的206%.当长方体辅助永磁体的N极与圆柱形永磁体的N极反平行时,超导体的最大磁悬浮力从没有引入辅助永磁体的29.8 N减小到19.6 N,减小为无辅助永磁体时的65.8%.这些研究结果说明,通过科学合理地设计超导体和永磁体的组合方式,能有效地提高超导体的磁悬浮力.该研究结果对促进超导体的应用具有重要的指导意义. 关键词： 单畴GdBCO 永磁体 磁悬浮力