Magnetically Suspended Flywheel Research Articles

An Integrated 5-DoF Displacement Sensor System of Magnetically Suspended Flywheel

The displacement measurement of the magnetically suspended flywheel (MSFW) on five degrees of freedom (DoFs) is critical to the accurate position control of the flywheel rotor. Therefore, an integrated 5-DoF displacement sensor is designed to measure the dynamic displacements of the MSFW. Firstly, the detection surfaces of the MSFW on five DoFs are introduced, and the displacement coordinates are established. Moreover, the detection principle and the dynamic responses of the integrated 5-DoF displacement sensor are analyzed. The single-winding probe is used as the radial displacement sensor, and the series-connection dual-winding probe is applied in the axial displacement sensor to measure the large displacement variation. Furthermore, the magnetic intensity and the quality factor of the integrated 5-DoF displacement sensor are simulated and tested. Finally, the measurements of the translational displacements and the deflection angles are conducted. The results show that the linear ranges of the radial single-winding probe and the axial series-connection dual-winding probe are 1.3 mm and 2.4 mm, respectively. The frequency bandwidth could be 10 kHz, and the maximum temperature drift is only 3.87%.

Force analysis and measurement of permanent magnet biased AMB and PMB in hybrid magnetically suspended flywheel

For the hybrid magnetically suspended flywheel (MSFW), the magnetic forces generated by the permanent magnet (PM) biased AMB could make the flywheel rotor suspends at the radial equilibrium position, and the magnetic forces of the permanent magnetic bearing (PMB) could suspend the flywheel rotor at the axial equilibrium position. Firstly, the force model of the PM-biased AMB is developed, the weak coupling of magnetic forces among the x axis and y axis is quantitatively analyzed, and then the active suspension control of the flywheel rotor is realized by the PM-biased AMB. Furthermore, the force and torque models of the PMB are established, and the force characteristic of PMB with a negative stiffness could push the flywheel rotor back to the balanced status. Finally, the measurement experiments are conducted to verify the force characteristics of the PM-biased AMB and the PMB, the active control performance and weak coupling of the hybrid MSFW are verified by measuring displacement deflections.

Vibration analysis, measurement and balancing of flywheel rotor suspended by active magnetic bearing

For the hybrid magnetically suspended flywheel (MSFW) with radial two degrees of freedom (DOFs) active magnetic bearing (AMB) and axial three DOFs AMB, the vibration analysis, measurement and balancing are conducted to mitigate the influences caused by unbalance terms in this article. Firstly, the force models of MSFW rotor are developed, and the vibration phenomenon caused by the residual unbalance mass of flywheel rotor is analyzed. Furthermore, the vibration testing platform for measuring the vibration of MSFW on five DOFs is introduced, and then the vibration balancing method is investigated. Finally, the vibration magnitude of MSFW rotor induced by the residual unbalance mass is analyzed by measuring dynamic displacements, and the effectiveness of vibration balancing method is verified by comparing vibration magnitudes and power spectrum densities of the MSFW system with different situations, the static unbalance term is reduced by 90.5%, and the dynamic unbalance term is reduced by 82.4%.

Gimbal effect of magnetically suspended flywheel with active deflection of Lorentz-force magnetic bearing

The magnetically suspended flywheel (MSFW) could output gyroscopic moment for attitude control. The conical magnetic bearing (MB) with cone-shape airgap is designed to stably suspend the rotor on three translational degrees of freedom (DOFs), and the Lorentz-force MB with long torque-arm could actively deflect the rotor around radial axes on two DOFs. Firstly, the force models of the conical MB are developed on the basis of the equivalent magnetic circuit, and then the force characteristics of the Lorentz-force MB are analyzed. With the stable position control of rotor, the gimbal effect of the Lorentz-force MB is investigated, and then the gimbal moment generated by rapid deflection via the Lorentz-force MB is quantitatively analyzed. Finally, the experimental results prove that the maximum deflection angle approaches to 1.7°, and the outputted gyroscopic moment reaches to 10Nm with 3.14°/s deflection velocity. Therefore, the gimbal effect of MSFW with the conical MB and the Lorentz-force MB is demonstrated by actively deflecting the rotor.

Stiffness identification of magnetic suspension system based on zero-displacement and zero-current models

Based on the dynamic displacement and the control current of the magnetically suspended flywheel (MSFW) system with great self-weight, an identification method of the displacement and current stiffnesses of MSFW rotor is proposed in this article. The structure of MSFW rotor is introduced, and the dynamic displacement models of MSFW rotor in radial directions are established. Furthermore, to obtain the current stiffness and the displacement stiffness, control models including the zero-displacement model and the zero-current model are designed for MSFW rotor, and then the frequency characteristics of the zero-displacement model and the zero-current model are analyzed. Finally, experiments are conducted to measure the synchronous components of dynamic displacements and control currents so that the displacement and current stiffnesses of the MSFW system can be estimated.

Parallel Automatic Balance Control Method for the Magnetically Suspended Flywheel

In order to attenuate the vibration caused by the radial imbalance in the Magnetically Suspended Flywheel (MSF), a parallel automatic balance control method is proposed. First, after the conduction of comparison between the parallel and series notch filter, a conclusion is drawn that the MSF achieves a better dynamic performance with greater attenuation on current vibration using the parallel notch filter. Then, experiments are performed under three conditions: without using the unbalance control, using radial unbalance control, and using axial unbalance control. The experimental results indicates that the stable automatic balance control and faster converging speed are achieved with the adoption of the proposed method. Furthermore, the vibration on the base is reduced significantly when the proposed method is introduced for all channels.

Force Analysis and Measurement of Permanent Magnet Biased Amb and Pmb in Hybrid Magnetically Suspended Flywheel

Force Analysis and Measurement of Permanent Magnet Biased Amb and Pmb in Hybrid Magnetically Suspended Flywheel

Detailed design and life prediction methodology of novel SMA actuated repeatable launch locking protective device (RLLPD) for magnetically suspended flywheel (MSFW)

This paper proposes a detailed design of a novel bias shape memory alloy (SMA) actuated repeatable launch locking protective device (RLLPD) for the magnetically suspended flywheel (MSFW) during the launching state. The proposed SMA actuated RLLPD consists of two bias SMA-spring actuators. One is designed to realize locking/unlocking and the other is intended for triggering. Besides, self-locking blocks are employed to ensure that the MSFW can be safely locked under the vibration of the launching process. Considering the locking method by compressing the flywheel against the mechanical bearing, there are at least three or four locking points to maintain the balance and enhance the locking reliability of the flywheel. Additionally, a force amplifying linkage mechanism is employed using one bias SMA-spring actuator to actuate the movement of two clamps, further reducing the total weight of the RLLPD and amplifying the locking strength. Furthermore, the recovery envelope curve which represents the recovery ability of SMA wire under various spring rate is proposed and computed using thermodynamics constitutive model. Simulation results indicate that the recovery envelope curve coincides with the austenite unloading curve. The thermodynamics constitutive model of SMA considering functional fatigue is utilized to calculate the evolution rate of functional fatigue of SMA wire in the RLLPD. The functional fatigue evolution rate computation algorithm and results are presented. After the design and simulation, a prototype of the locking device is fabricated and tested. According to the performance results, the SMA-actuated locking device can release a preload up to 1000 N. The simulation and experimental results indicate that the life cycle of the locking device is more than 50 times.

Dynamic Correction Model Considering Influence of Foundation Motions for a Centripetal Force Type-Magnetic Bearing

Conventional suspension forces modeling methods are usually only focused on the computation of the internal magnetic field of the magnetic bearing itself. However, the modeling accuracy is also affected by its actual application, especially for the magnetic bearing in moving situation, such as magnetic suspended flywheel battery system for electric vehicles. In this article, taking the centripetal force type-magnetic bearing as an example, a dynamic correction model considering influence of foundation motions is proposed, which has several submodels to cover as many driving conditions as possible. First, a universal static model based on spherical coordinate system is established. Then, the dynamic model is derived, which includes the control current, offset, and variables of foundation. Given the complexity and diversity of real-time operating conditions of vehicles will affect the calculation accuracy of variables of foundation, resulting in the increase of the error in single dynamic model. Therefore, the idea of foundational weight factor is brought up and fitted by analyzing the dynamic response laws of rotor under different foundation motions. Finally, the dynamic stiffness experiments and performance tests are carried out. The good experiment results show that the proposed model is more practical and has higher precision than traditional model.

Optimal control for hybrid magnetically suspended flywheel rotor based on state feedback exact linearization model.

For a hybrid magnetically suspended flywheel (MSFW) rotor suspended by permanent magnet biased active magnetic bearing (AMB) and passive magnetic bearing (PMB), the dynamic functions are nonlinear and coupling among different degrees of freedom (DOFs). In this article, the nonlinear dynamic functions in two controllable DOFs of the hybrid MSFW rotor are developed based on the equivalent magnetic circuit, and then the nonlinear dynamic function is linearized by using the state feedback exact linearization (SFEL) in order to minimize the coupling in two controllable DOFs. Furthermore, an optimal control based on the SFEL model is designed to reduce displacement runout and coupling among two controllable DOFs of the hybrid MSFW rotor at the rated speed. Finally, the simulation and experimental results validate the effectiveness of the optimal control based on SFEL model, and the stability of the hybrid MSFW rotor with an impulse-type disturbance is improved.

Parallel mode notch filters for vibration control of magnetically suspended flywheel in the full speed range

Undesired vibration force caused by harmonic currents is a common problem in a magnetically suspended flywheel (MSFW) rotor system. It poses a potential threat to system stability and performance degradation. In this work, multiple different phase-shift notch filters are connected in parallel mode to suppress the vibration harmonics. First, the multi-frequency vibrations in the MSFW is modelled and analysed. Then multiple different notch filters in parallel mode are proposed to plug into the baseline magnetically suspension system. The performance comparison with the conventional multiple notch filters is investigated. The parameters design and calculation for the proposed method are analysed in details. Moreover, the closed-loop stability of the overall system is given in the full speed range. Finally, simulation and experimental results for the MSFW demonstrate the superiority of the proposed method on both harmonics suppression and stability preservation.

Vibration Torque Suppression for Magnetically Suspended Flywheel Using Improved Synchronous Rotating Frame Transformation

Synchronous vibration, a common issue in active magnetic bearing (AMB) system, is mainly caused by mass imbalance of the rotor. It comes with high-power consumption and serious impact on the housing base, dramatically degrading the performance of AMB. Magnetically suspended flywheel (MSFW), which owns a flat rotor and consequently shows strong gyroscopic effects even at low operating speed, requires additional attention not only for suppressing the synchronous vibration but also for maintaining the overall stability faced with the coupled dynamics. In this work, in order to suppress the vibration torques in MSFW with significant gyroscopic effects, an improved synchronous rotating frame- (SRF-) based control method is proposed. The proposed method introduces the compensation phase for stability adjustment and aims at simultaneously suppressing the synchronous components in the coupled axes. Firstly, the vibration torque model of MSFW is established, and the baseline control strategy for suspension and gyroscopic effects restrain is derived. Then, the principle and implementation of the improved SRF-based vibration torque method are analyzed, which aims at suppressing the synchronous vibration torques through attenuating synchronous components in coil currents. Moreover, the stability of the overall closed-loop system is analyzed. Finally, the effectiveness of the proposed method is verified through simulation and experimental results.

High precision synchronous vibration suppression for a MSFW subject to phase lag influence

Abstract A magnetically suspended flywheel (MSFW) always suffers from rotor mass imbalance disturbances, which result in synchronous vibration forces and affect the high precision control. The synchronous vibration forces in MSFW are mainly comprised of current stiffness forces and displacement stiffness forces. In this paper, a lead feedforward compensation method is proposed to simultaneously suppress the two stiffness forces. First, the dynamical model of the synchronous vibration forces and the phase lag influence of the power amplifier on the displacement stiffness forces are given. Then, the principle and implementation of the proposed method used for synchronous vibration forces complete suppression are analyzed. The performance comparison between the conventional scale compensation method and the proposed lead feedforward method is investigated. Simulation and experimental results on a MSFW demonstrate the effectiveness and superiority of the proposed synchronous vibration forces suppression method.

Optimization design of launch locking protective device (LLPD) based on carbon fiber bracket for magnetically suspended flywheel (MSFW)

Because of the launch vibration and shock, magnetically suspended flywheels (MSFWs) are equipped with an additional launch locking protective device (LLPD), and the LLPD performance has great influence on the attitude control precision of the flywheel system. In this paper, a LLPD that takes the carbon fiber bracket as the key clamped and releasable mechanism was presented. And the configuration, operating principle and functional performance requirements were introduced. The locking/unlocking force, maximum stress and contact force of the carbon fiber bracket were analyzed. The dynamic analysis of the single carbon fiber bracket equivalent to the cantilever beam model was carried out. Subsequently, the sensitivity of the constraint variables vs the structural parameters was calculated. The lower and upper parts of the carbon fiber bracket were separately optimized. The result shows that the mass of the carbon fiber bracket can reach to the minimum of 60.5 g when the number of the upper carbon fiber bracket slices is 12. Finally, the LLPD prototype was manufactured and its locking protection for the flywheel system was verified by the swept-sine vibration and the random vibration.

Suppression of high-frequency disturbance to satellite by Vernier-gimballing magnetically suspended flywheel

The high-frequency disturbance acting on a satellite decreases the satellite’s stability and pointing precision. The common flywheel is generally used to suppress it, but the number of the required flywheels is usually five or more and that will make the satellite overweight. The magnetically suspended flywheel (MSFW) with Vernier-gimballing capability (Vernier-gimballing MSFW) is proposed in this paper to suppress the high-frequency disturbance. In addition, a comparative simulation research has been done for a satellite controlled by Vernier-gimballing MSFW or reaction FW. It is worth noting that the Vernier-gimbaling MSFW can not only make the actual angle of the satellite track its reference angle better, but also make the accumulative errors of outer and inner virtual gimbal angle be very small, then the satellite’s stability and pointing precision will be improved accordingly. The Vernier-gimballing MSFW is verified to be able to suppress the high-frequency disturbance effectively when their frequencies are within the frequency bandwidth of MSFW.

Harmonic vibration suppression for magnetically suspended flywheel with rotor unbalance and sensor runout

Rotor unbalance and sensor runout are the two major interference sources in magnetically suspended flywheel (MSF), which can induce undesirable harmonic vibration and reduce the attitude control precision of spacecraft. To further suppress the harmonic vibration caused by multiple interference sources, a compound control method is proposed in this paper. Firstly, the mechanism of harmonic vibration is analyzed. The rotor unbalance mainly generates the single harmonic vibration and the sensor runout generates multiple harmonic vibration. Secondly, on the basis of the characteristics of the two kinds of interference, the generalized notch filter and the repetitive control method are adopted to suppress the harmonic vibration caused by sensor runout and rotor unbalance, respectively. Thirdly, in order to reduce the difficulty of controller design, a plug-in structure is adopted to the repetitive controller. And then the two control methods can be designed independently. The stability and the interference suppression capability of the proposed method were analyzed. Lastly, the effectiveness of the proposed method has been experimentally verified.

Complete Synchronous Vibration Suppression for a Variable-Speed Magnetically Suspended Flywheel Using Phase Lead Compensation

The synchronous vibration rising from the magnetically suspended flywheel (MSFW) will drastically reduce the pointing precision of the satellites. In this paper, the high precision suppression for the frequency-varying synchronous vibration forces in the permanent-magnet-biased hybrid MSFW is investigated. First, the synchronous vibration forces generated in the permanent-magnet-biased hybrid magnetic bearing are modeled and analyzed. Then, a practical and effective synchronous vibration suppression method is proposed to plug into the baseline magnetic suspension system. The proposed method ascertains the overall system stability over the entire speed range by an adjustable phase angle. Moreover, it eliminates the residual synchronous vibration forces in the negative displacement stiffness by considering phase-lag influence of the power amplifier. The direct testing for the synchronous vibration forces proves the feasibility of the proposed suppression method.

Control of Rotor's Vernier-Gimballing for a Magnetically Suspended Flywheel

For a magnetically suspended flywheel (MSFW) with two degree of freedom radial magnetic bearings (2-DOF RMBs), both the Vernier-gimballing control method and the Vernier-gimballing characteristics are researched to make the spinning rotor tilt around the radial axes by a pair of 2-DOF RMBs to generate a large torque. The process of Vernier-gimballing is analyzed and the model of rotor's Vernier-gimballing is established based on the presented 2-DOF RMBs, and the gyroscopic coupling is pointed out originally as the main problem in rotor's Vernier-gimballing control. To solve this problem, the reasons of Vernier-gimballing control precision's degradation are researched and the compensation torques generated by a novel feedforward matrix (FFM) are presented considering the negative displacement–force stiffness of 2-DOF RMB. Simulations and series of experiments done on an MSFW with 50 N · m · s angular momentum indicated that this presented control method with an FFM and compensation of negative displacement–force stiffness can effectively improve the precision of rotor's Vernier-gimballing control.

Self-adaptive phase compensation characteristics and safeguard-phase-margin design of an unsymmetrical current-sensing resistor for magnetically suspended flywheels

This paper presents the self-adaptive phase compensation characteristics and quantitative design of an unsymmetrical current-sensing resistor for magnetically suspended flywheel (MSFW) system with strong gyroscopic effects. Aimed at the nutation stability of the MSFW control system, the self-adaptive phase compensation characteristics of PWM H-bridge unipolar switching power amplifiers with unsymmetrical current-sensing resistor with inductance variations is analyzed firstly, including the initial compensation frequency and compensation phase in the compensation working regions. Secondly, the quantitative safeguard-phase margin design method for the asymmetrical factor in H-bridge unipolar switching power amplifiers is proposed based on the nutation stability criterion. Finally, the influence of the unsymmetrical current-sensing resistance network on the nutation stability is further analyzed. Simulation and experimental results demonstrate the correctness and effectiveness of the proposed method.

Improving Operational Performance of Magnetically Suspended Flywheel With PM-Biased Magnetic Bearings Using Adaptive Resonant Controller and Nonlinear Compensation Method

Permanent magnet-biased magnetic bearings (PBMBs) are widely used in flywheel energy storage systems because of their comprehensive advantage in power loss and controllability. However, there is a nonlinear relationship between magnetic force, control current, and eccentric displacement of the PBMB. When the system is required to be high performance, the nonlinear dynamics of the PBMB must be considered in a control design. Therefore, this paper proposes a novel nonlinear compensator based on the nonlinear model of the PBMB and it is applied to a magnetically suspended flywheel (MSF) with PBMBs. To implement the perfect nonlinear compensation, an adaptive resonant controller is also presented to compensate the dynamics of the current-mode amplifier. Finally, the proposed method is verified by experiments on the test rig of the MSF and can be used to improve the performance of the system.