Magnetic Bearing Rotor Research Articles

Adaptive control of DGMSCMG using dynamic inversion and neural networks

The paper presents a nonlinear dynamic model for DGMSCMGs, sometimes used as actuators to control the attitude of large satellites. The developed models describe the translation dynamics, the rotation dynamics of the Active Magnetic Bearing Rotor, as well as the rotation dynamics of the two mobile gimbals. Two control architectures are initially designed by using the dynamic inversion concept, proportional-integrator-derivative/proportional-derivative dynamic compensators, linear observers, and a neural network to compensate the effect of the dynamic inversion error. One also develops a similar adaptive control architecture consisting of a proportional-integrator dynamic compensator, a feed-forward neural network, and a linear observer. The latter system models two interconnected nonlinear servo-systems and controls the angular rates of the two mobile gimbals actuated by the attitude controller of the satellite. The validation of the novel control architectures is achieved in Matlab/Simulink, the obtained results proving a very good angular rate precision and the robustness of the control systems in relation to the external disturbances.

Dynamic Modeling and Parametric Analysis of the Magnetic Stiffness on a Radial Heteropolar Rotor Magnetic Bearing (RMB)

This paper presents both the dynamic modelling and the study of the variation of certain physical parameters (pole area, gap and base current) that change the magnetic stiffness of a radial heteropolar Rotor Magnetic Bearing (RMB) aiming at the analysis of the magnitude of its control current for three different equilibrium points. The RMB is modelled as a fully uncoupled symmetric active 8-pole magnetic bearing. The analysis is performed using spectral cubes for a better visualisation of the posed problem. The saturation analysis of the RMB is also performed. At last, it is shown that a control current with the same magnitude as the base current is reached with minimum pole area and air gap s0 = 528 um.

Unbalance Vibration Control for MSCMG Based on High-Precision Synchronous Signal Detection Method

The active magnetic bearing rotor in magnetically suspended control moment gyro (MSCMG) will produce unbalance vibration due to the mass unbalance, and the frequency equal to the rotation speed. In order to suppress the unbalance vibration of MSCMG, the working principle of the active magnetic bearing (AMB) is introduced and the unbalance vibration model is established. And then, a high-precision closed-loop detection method of the synchronous signal based on synchronous rotating frame transformation (SRFT) is proposed. This method can detected synchronous signals in two directions at the same time, with less calculations. The synchronous current is suppressed by detecting and compensating the synchronous component in the output signal of the displacement sensor, which can reduce most of unbalance vibration. The phase modulation angle is introduced to make the algorithm have a wider stable range. In order to simplify the analysis method, the orthogonal characteristic of the output signal of the displacement sensor is used to equalize the dual output system to a complex-coefficients single-input system, and the dual frequency Bode diagram is used to analyze and evaluate the stability of the system. Finally, experimental results are given to verify that this method can effectively suppress synchronous current.

Suppression of Harmonic Vibration in AMB-Rotor Systems Using Double-Input Adaptive Frequency Estimator

The suppression of harmonic vibration of active magnetic bearing (AMB) rotor system depends on the speed signal. Aiming at the problem of harmonic vibration suppression when the speed measurement sensor fails, a dynamic model of the AMB-rotor system, including mass unbalance and sensor runout, is established. This article analyzes the main sources of harmonic vibration force, and proposes a double-input filter based on adaptive frequency estimation. The characteristic that the displacement output signals of the radial X- channel and Y-channel of the rotor are orthogonal to each other can be used to quickly and accurately estimate the actual speed of the rotor adaptively. At the same time, the harmonic components of the control current are also compensated. Finally, the effectiveness of the proposed harmonic vibration suppression method with adaptive frequency estimator is verified by the simulation and experiments.

Performance for rotor system of hybrid electromagnetic bearing and elastic foil gas bearing with dynamic characteristics analysis under deep learning.

The bearing-rotor system is prone to faults during operation, so it is necessary to analyze the dynamic characteristics of the bearing-rotor system to discuss the optimal structure of the convolutional neural network (CNN) in system fault detection and classification. The turbo expander is undertaken as the research object. Firstly, the hybrid magnetic bearing-rotor system is modeled into the form of four stiffness coefficients and four damping coefficients, so as to analyze and explain the dynamic characteristics of the system. Secondly, the ambient pressure is introduced to analyze the dynamic characteristics of the elastic foil gas bearing-rotor system based on the changes in the dynamic stiffness and dynamic damping of the gas bearing. Finally, the CNN is introduced to be applied in the detection of faults of bearing-rotor system through determining the parameters of the constructed CNN. The results show that the displacement of the rotor increases and the stiffness decreases with the acceleration of the speed of the electromagnetic bearing. The maximum displacement of the rotor can reach 135μm, and the maximum stiffness can be reduced to 35×105N/m. Increase of ambient pressure causes enhancement of main stiffness of the gas bearing, and the main damping decreases accordingly. Analysis of the classification accuracy and loss function based on the CNN model shows that the convolution kernel size of 7*1 and the batch size of 128 can realize the best performance of CNN in fault classification. This provides a data support and reference for studying the dynamic characteristics of the bearing-rotor system and for the optimization of CNN structure in fault classification and detection.

Dynamic Analysis of Active Magnetic Bearing Rotor System Considering Alford Force

Dynamic Analysis of Active Magnetic Bearing Rotor System Considering Alford Force

Analysis of supercritical pitchfork bifurcation in active magnetic bearing-rotor system with current saturation

The bifurcation characteristics of the active magnetic bearing-rotor system subjected to the external excitation were investigated analytically when it was operating at a speed far away from its natural frequencies. During operation of the system, some nonlinear factors may be prominent, for example, the nonlinearity of bearing force and current saturation. Nonlinear factors can lead to some complicated behaviors, which have negative effects on the operating performance and stability. To analyze the bifurcations happening at the speed far away from harmonic resonances, an approximate analytical method that can be applicable to the bifurcation analysis of the forced vibration system was proposed. By applying it to the active magnetic bearing-rotor system, multiple static equilibriums and periodic solutions were obtained, and then, the stability analysis was conducted based on Floquet theory. The validity and accuracy of the approximate analytical method were verified by the numerical integration method and generalized cell mapping digraph method. It was found that there was supercritical pitchfork bifurcation of static equilibrium in the active magnetic bearing-rotor system. The influences of external excitation and controller parameters on dynamical characteristics were discussed. Based on analysis results, controller parameters were also improved to prevent nonlinear behaviors and improve system performance.

Stability Control for a Centripetal Force Type-Magnetic Bearing-Rotor System Based on Golden Frequency Section Point

Synchronous vibration and gyroscopic effect are the key factors affecting the global stability of flywheel batteries in the full speed region. The existing control methods generally treat them as two separate problems; however, they have something in common that can be exploited. In this article, a novel stability control method based on golden frequency section point is proposed for gyroscopic effect and synchronous vibration. The golden frequency section point is the bifurcation point of the nutation and precession of gyroscopic effect, and it is also the switching point of the control method with synchronous vibration at low and high speed. A case study of the centripetal force magnetic bearing-rotor (CFT-MB-R) system is taken as an example to verify it. First, the dynamic model of magnetic bearing rotor system is established. Then, the golden frequency section point is designed, and on this basis, the stability in the low-speed region and the high speed region are analyzed, respectively. Finally, simulations show that the vibration amplitude is reduced by nearly 50% at low speed and 66.6% at high speed. Moreover, the vehicle condition simulation results show the robustness of the system can also be improved. The experimental results further indicate that the method is an effective in suppressing the synchronous vibration and gyroscopic effect of the rotor system, and the stability and even robustness of the system can be greatly improved.

Multi-branch convolutional neural network with generalized shaft orbit for fault diagnosis of active magnetic bearing-rotor system

Fault diagnosis based on vibration signals in active magnetic bearing-rotor systems is an important research topic. However, it is difficult to obtain discriminative features to represent faults due to the nonlinear and non-stationary characteristics of the vibration signals and diverse sources of failures. Hence, this paper proposes a novel end-to-end learning mechanism of multi-sensor data fusion to learn fault representation based on the structural characteristics of active magnetic bearings. Taking the five displacement sensors of active magnetic bearing as signal sources, generalized shaft orbits are constructed and converted into discrete 2D images. Based these 2D images, a multi-branch convolutional neural network is designed to achieve high discriminative features and fault types. The experiments are performed on the rig supported by active magnetic bearings, and the effectiveness of the proposed algorithm is verified, proving it suitability in cases with changing rotating speeds and sample lengths.

Vibration Feedforward Compensation for Magnetically Suspended Control and Sensitive Gyroscope with Spherical Rotor

Magnetically suspended control and sensitive gyroscope (MSCSG) with two capabilities including attitude control and attitude measurement is promising in meeting the requirements of novel spacecraft. When the momentum vector of a high-speed rotor suspended in five directions is tilted by Lorentz force-type magnetic bearing, the instantaneous large control moment is obtained. The spacecraft attitude can be sensed by a high-speed rotor without deflection interference torque. In this paper, a novel MSCSG with sphere rotor is presented, and its spherical structure and working principle are introduced. The magnetic bearing-rotor dynamic model is established based on Newton’s second law and the gyrokinetic equations. The generating mechanism of three interferences, including bearing dynamic reaction force, deflection torque, and centrifugal force, is analyzed. The feedforward compensation control against three interferences for MSCSG is adopted, and the loading sequence of three interferences is simulated. The optimal sequence of bearing dynamic reaction force, deflection torque, and centrifugal force is used. The radial and axial vibration displacement amplitudes are reduced from 20.8 μm and 31.7 μm to 9.4 μm and 14.9 μm, respectively. The experimental results are in good agreement with the simulation, which indicates the MSCSG rotor unbalance vibration is suppressed effectively by the feedforward compensation method.

Stable Control of Nutation and Precession for the Radial Four-Degree-of-Freedom AMB-Rotor System Considering Strong Gyroscopic Effects

The stable control of the active magnetic bearing rotor (AMB-rotor) system is the key technology for a magnetically suspended control moment gyroscope, which is used in the spacecraft attitude control system. The nutation and precession instability caused by strong gyroscopic effects is the principal issue of the AMB-rotor system. In order to solve the gyroscopic effects problem, in this article, a state-space model of the radial four-degree-of-freedom AMB-rotor system is established, and the strong gyroscopic effects term varying with the rotor speed is regarded as a bounded perturbation. The regional pole assignment method of an uncertain system is used to design a robust controller to maintain the system stability over the full rotor speed range. However, the controller designed by the regional pole assignment method does not consider the influence of closed-loop stiffness of the magnetic bearing, which will lead to the start-up oscillation and structural mode self-excited oscillation problems. Therefore, on the basis of the regional pole assignment, the system stiffness is further constrained and a robust controller is solved. Experiments show that the designed controller can not only deal with the start-up oscillation and the structural modal vibration problems, but also can achieve the stable control of the nutation and precession.

Experimental Study of Macro Fiber Composite-Magnet Energy Harvester for Self-Powered Active Magnetic Bearing Rotor Vibration Sensor

The paper presents the design, fabrication, and characterization of an energy harvester for an active magnetic bearing (AMB) rotor vibration using a macro fiber composite (MFC) with magnetic coupling. The MFC cantilevers configuration, together with neodymium magnets, is used for the contact-free rotor radial vibration self-powered sensor. The permanent magnets attached to the rotor and to the four MFC element beams ensure the mechanical energy transfer and the MFC cantilever vibration excitation. In the proposed prototype, the MFC transducer output voltage depends on the air-gap between two magnets. This paper investigates the optimum conditions to harvest as much as possible electric energy at different clearances and rotational speeds. Furthermore, to assess the rotor vibration sensitivity, the experimental results of the MFC-magnet self-powered sensor are compared with measurements obtained using a fiber optic sensor. The maximal obtained harvesting power equals 673.47 µW for the rotor speed of 3150 rpm. Moreover, the MFC cantilever was proposed as the rotor vibration sensor. The MFC-magnet self-powered vibration sensor output was compared with the fiber optic laser sensor. The mismatched vibration amplitude for both sensors does not exceed 1 µm.

Research on the Dynamic Characteristics of Magnetic Bearing-rotor System with Auxiliary Bearing

Non-linear factors such as magnetic force and rub-impact force are comprehensively considered on the basis of the classic Jeffcott rotor system model, and the dynamic model of the magnetic bearing-rotor system is established. The dimensionless motion equation is obtained by introducing dimensionless parameters. The pattern types and distribution regions of adjacent fundamental periodic motions of the system are obtained based on multi-objective and multi-parameter co-simulation analysis, and the dynamic behaviour is analysed through three-dimensional bifurcation diagram, two-parameter bifurcation diagram, single-parameter bifurcation diagram and axis locus diagram. The reasonable matching range of parameters of system and speed ratio is obtained in this paper, which optimizes the structural parameter design of the rotor system and determines its reasonable and stable working interval.

Design of a combined self-stabilizing electrodynamic passive magnetic bearing support for the automotive turbocharger rotor

The purpose of this study is to create a concept for what would be a structurally simple and operationally robust support for the automotive turbocharger rotor in electrodynamic passive magnetic bearings. Because this kind of magnetic suspension—in its fundamental version—is dynamically unstable, to avoid the disadvantages contained therein, what is being proposed is the addition of external damping through the employment of the newly designed combined self-stabilizing electrodynamic passive magnetic bearing. The electromagnetic stiffness and damping characteristics of combined electrodynamic passive magnetic bearings have been determined for various shaft rotational speeds by means of the advanced 3D finite element method. In this study, a dynamic interaction between the turbocharger rotor shaft and the passive magnetic suspension is proposed as a support for both the fundamental electrodynamic passive magnetic bearings and the suggested combined self-stabilizing passive magnetic bearings. Here, the main attention is focused on the asymptotic stability of both the rotor shaft suspension variants. The additional damping magnitudes required to stabilize the most sensitive lateral eigenmodes of the object under consideration have been determined by means of the Routh–Hurwitz stability criterion.

Application of Spherical Magnetic Bearing in Magnetically Suspended Control and Sensitive Gyro

This paper presents a spherical magnetic bearing and analyzes its application in magnetically suspended control and sensitive gyro (MSCSG). The main advantage of the spherical magnetic bearing is that it can eliminate the interference torque in the process of rotor tilt and improve the suspension accuracy of the rotor. By comparing the finite element analysis results of spherical magnetic bearing and traditional cylindrical magnetic bearing, the interference torque to the rotor of cylindrical magnetic bearing increases gradually with the increase of the rotor tilt angle. The interference torque to the rotor of spherical magnetic bearing does not change with the rotor tilt, and the interference torque is basically 0 Nm. Then, dynamic and static experiments were carried out to verify the interference torque generated in the process of spherical magnetic suspended rotor tilting. The experimental results show that the runout value of the rotor’s translation and tilt signals in both static and dynamic states is basically consistent with the value of the equilibrium state of the rotor (tilt angle = 0). Therefore, spherical magnetic bearing will not produce interference torque, which is of great significance for realizing the high-precision control of magnetic suspension inertia mechanism.

Modeling and experimental validation of transient response of magnetic suspension rotor contacting with auto-reducing clearance auxiliary bearing

The major purpose of this study is to indicate the transient responses of an active magnetic bearing (AMB) rotor contacting with auto-reducing clearance auxiliary bearing (ACAB). Considering the radial vibration of the single support, the real-time clearances between the outer ring (OR) and each support, and the swing of the supports, the dynamic models of the rotor and the ACAB are formulated. The dynamic behavior of the rotor-ACAB system is investigated by the dynamic trajectories of the rotor and the OR, the movement of each support, and the dynamic forces generated in the ball bearing and between the OR and supports. Furthermore, the AMB-rotor dropping tests, in which a strain gauge based measurement system and a high speed camera equipment are adopted to separately survey the interaction force between the support and the OR and record the movements of the OR and the supports, are performed. The results show that, after the rotor drops on ACAB, the swing supports rapidly reduce the protective clearance and then stably maintain the rotor to operate around the center of ACAB. Finally, the ball bearing only suffers the centrifugal force of the rotor without impact forces, while big interaction forces always exist between the OR and each support.

Non dimensional analysis of axially polarized passive magnetic bearings

Ranges of investigation on passive magnetic bearing exist where radial and axial forces and variations of a few coefficients of radial and axial stiffnesses are shown for a particular set of chosen parameters and dimensions. The paper presents a non-dimensional approach for the same with additional parameters like all coefficients of stiffnesses and natural frequency. The model is considered for static analysis of axially polarised ring shaped magnets for both stator and rotor part in three degrees of freedom with three linear translations in 3D Cartesian coordinate system. The significance of this non-dimensional method is more generalised to the designer where boundary parameters like maximum force on the rotor of passive magnetic bearing, natural frequency, etc. can be easily estimated by simple conversion without doing separate numerical simulation for different parameters every time. The analysis of additional parameters like non-dimensional natural frequency can be the input for non-dimensional dynamic analysis. This paper also provides a way for maximization of radial force with the optimized solution of physical dimensions of passive magnetic bearing as inner radius of stator and outer radius of rotor magnet while keeping others as input parameters. The proposed model is validated with data available for radial and axial forces as well as for radial and axial stiffnesses that found in existing literature for similar kind of problem.

Whirl Mode Suppression for AMB-Rotor Systems in Control Moment Gyros Considering Significant Gyroscopic Effects

For a magnetically suspended control moment gyroscope with strong gyroscopic effects, the whirl mode (nutation and precession) stability control of the active magnetic bearing (AMB) rotor system has always been a challenging problem. This article proposes a robust control method combined with regional pole assignment to achieve the stability control of the whirl mode in the AMB-rotor system. First, the physical model of multi-degree-of-freedom magnetic bearing system is analyzed in detail, and the state-space model of the system is established. Then, the gyroscopic effects varying with the rotor speed are considered as a bounded parameter perturbation of the system, and the constraints on the controller to achieve the system stability are obtained. Furthermore, in order to increase the system stability margin and the whirl mode damping, the additional constraints on the controller are derived through the regional pole assignment method. Finally, all constraints are converted into the form of linear matrix inequalities (LMIs), and a controller satisfying all the constraints can be obtained by solving the LMIs. Experimental results demonstrate that the designed robust controller can achieve the stability control of nutation and precession as well as keeping a satisfactory system performance.

Design of Interval Type-2 Fuzzy Controllers for Active Magnetic Bearing Systems

This article proposes an active levitation control system composed of an active magnetic bearing (AMB) rotor and an interval type-2 (IT2) model-based fuzzy logic controller (FLC). The controller aims to achieve fast and stable levitation by compensating for system uncertainties via proper design of IT2 membership functions. In particular, the complex nonlinear dynamics of the AMB are modeled as a set of local linear systems around multiple operating points, which can be stabilized by a parallel distributed compensation scheme. Sufficient conditions are derived to guarantee the asymptotical stability of the closed-loop system based on the linear matrix inequality approach and the Lyapunov stability theory. Moreover, input constraints are applied in an enhanced version of the controller. Experiments on a real AMB platform were conducted to demonstrate the effectiveness and superiority of the proposed IT2 FLC.

A novel iterative learning control method and control system design for active magnetic bearing rotor imbalance of primary helium circulator in high-temperature gas-cooled reactor

As one of the key technologies of high-temperature gas-cooled reactor, primary helium circulator–equipped active magnetic bearing provides driving force for primary helium cooling system. However, repetitive periodic vibration produced by rotor imbalance may introduce risks to primary helium circulator (even for high-temperature gas-cooled reactors). First, this article analyzes a periodic component extraction algorithm which is widely used in active magnetic bearing rotor unbalance control methods and points out the problem that the periodic component extraction algorithm occupies numerous computing resources which cannot satisfy the real-time request of active magnetic bearing control system. Then, a novel iterative learning control algorithm based on the iteration before last iteration of system information (iterative learning control-2) and a plug-in parallel control mechanism based on the existing control system are put forward, meanwhile, an integrated independent distributed active magnetic bearing control system is designed to solve the problem. Finally, both the simulation and experiment are carried out, respectively. The corresponding results show that the control method and control system proposed in this article have significant suppression effect on the repetitive periodic vibration of the active magnetic bearing system without degrading the real-time requirement and can provide important technical support for the safe and stable operation of the primary helium circulator in high-temperature gas-cooled reactor.