Active Magnetic Bearing Rotor System Research Articles

Finite element simulation of iron losses for an Active Magnetic Bearing–Rotor system constructed of Hiperco laminations

Iron losses appear in Active Magnetic Bearings (AMBs) mostly because of the rotor's movement, but also because of the fluctuation of the control current in the stator's coils. They can be divided into three categories: the hysteresis losses, the eddy current losses and the excess losses and while they depend significantly on the rotating speed and the magnetic flux density applied on the poles, the most contributing factor is the magnetic material used for the core. In this paper, a 2-D Finite Element Method transient model is used to simulate the rotational motion of the shaft inside the AMB and calculate the iron losses that occur due to the alternating magnetic flux inside the rotor, as well as the mechanical load capacity on the vertical direction of the AMB for each case. A simulation is carried out, at first, for a constant control current value and a speed range of 0–30,000 rpm, followed by a second one, for constant rotational speed and control current values 0–0.5 A. Geometry remains the same for all simulations. When it comes to the materials selected for the stator and the rotor, the cases of Hiperco 27, Hiperco 50 and Hiperco 50 HS laminations are tested. The iron losses of the three alloys are compared to the losses of 3 % silicon-iron. The results show that the three iron cobalt alloys have significantly lower losses than the silicon iron for the same AMB size and rotor's speeds. Hiperco 50 has the lowest loss among the three Hiperco alloys, while Hiperco 50 HS provides slightly higher mechanical load capacity under the same operating conditions.

Sliding model control of active magnetic bearing rotor system based on state observer

Sliding model control of active magnetic bearing rotor system based on state observer

Self-Calibration Method of Displacement Sensor in AMB-Rotor System Based on Magnetic Bearing Current Control

Displacement sensors are the key components of the active magnetic bearing rotor (AMB-rotor) system to realize the closed-loop control of the rotor displacement. The aging and failure of the displacement sensor components will lead to the changes of sensor sensitivity and zero point, which can directly affect the suspension performance of the rotor and even cause the instability of the AMB-rotor system. Therefore, it is significant to calibrate the sensor regularly. This paper proposes a self calibration method based on the detection and control of the magnetic bearing current without additional calibration equipment and hardware circuits. In addition, a new control structure of the AMB-rotor system is proposed to achieve efficient calibration, which can control the rotor displacement based on current following control method. Finally, experimental results verify the effectiveness of the proposed method on the displacement sensor calibration.

Study on the Mechanism and Suppression of Harmonic Vibration of AMB-Rotor System

The AMB-rotor system is complex and has strong coupling characteristics, which allows multi-harmonic disturbances to enter the system through different ways to produce vibrations with rich spectrum components, which has a great influence on the improvement of micro-vibration accuracy of the rotor system. To further achieve active control of the micro-vibration in the AMB-rotor system, firstly, the mechanism of multi-source disturbance is analyzed according to the working principle of the AMB-rotor system, and the mathematical and physical relationship between the mechanism of disturbance generation and the inducement is deeply studied. Then, the structure of a novel adaptive notch filter, the method of adaptive frequency estimation and analysis of harmonic current suppression in the AMB system are presented. Finally, simulation and experimental research using an MSCMG system demonstrate the feasibility of the proposed method regarding the elimination of harmonic control current.

Synchronous Vibration Force Suppression of Magnetically Suspended CMG Based on Modified Double SOGI-FLL

The mass imbalance of the rotor will produce the synchronous vibration force that is transmitted to the magnetically suspended control moment gyroscope (MSCMG) through the magnetic levitation stator, which affects the imaging performance of the satellite. The suppression of the synchronous vibration force needs the speed signal. In order to solve the synchronous vibration force of the MSCMG when the speed measurement sensor fails, this paper proposed an modified double second-order generalized integral frequency-locked loop (SOGI-FLL) method, which uses the frequency of the disturbance signal generated through the mass imbalance of the rotor to adaptively estimate the rotor speed and suppress the synchronous vibration force generated by the active magnetic bearing system. The phase compensation is introduced to ensure the stability of the system in full frequency band. The electromagnetic force is directly used as the input signal of the control algorithm to achieve zero magnetic force control. Simulation and experimental are carried out, and the results are given to prove that the algorithm proposed in this paper can accurately estimate the rotation speed and achieve the vibration force suppression in the full rotation speed range. It is of great significance for the high-precision control of the active magnetic bearing rotor system.

Synchronous disturbance suppression of active magnetic bearing rotor systems using variable period adaptive control algorithm

This paper aims to investigate the issue of suppressing synchronous vibration in active magnetic bearing (AMB) systems. The rotor mass imbalance is a challenging problem for the AMB system, which will cause synchronous vibration and severely affect the system stability and safety. However, existing algorithms based on the iterative feed-forward control strategy find it difficult to simultaneously ensure system’s stability and competent convergence performance. They struggle to maintain tolerable robustness within the system operating bandwidth. This paper proposes a variable period adaptive control algorithm to address these challenges. The overall control scheme can achieve current and displacement elimination separately by switching control structures and is applicable to variable speed conditions. This algorithm can adaptively adjust the iteration period based on rotational speed to ensure both splendid convergence performance and system dynamic performance. Furthermore, this work employs the Lyapunov method to analyze the algorithm’s asymptotic stability and provides a lookup table for algorithm parameters. This could significantly enhance the robustness and stability of the algorithm within the system operating bandwidth. Finally, this methodology has proven to be effective and superior in simulations and experiments.

Division Linearization Zero-Bias Current Control for AMBs–Rotor System With Uncertainties and Saturation

Traditional constant current sum (CCS) distribution strategy is always employed in the nonlinear active magnetic bearing (AMB) system control for linearization, but the bias current in CCS causes extra power consumption and limits the AMBs' capacity. In this paper, a division linearization zero-bias current (DLZBC) distribution strategy is proposed as a substitution for CCS strategy. Under this strategy, a linear active disturbance rejection controller (LADRC) with a static anti-windup compensator (SAWC) is applied to deal with model uncertainties and current saturation. For different types of AMB-supported machines, a partial normalized nonlinear model is established. Subsequently, the performance of the CCS strategy is analyzed, and a DLZBC strategy is presented to reduce the power consumption and transform the system into a linear plant with a lumped uncertain parameter. Afterward, a LADRC is designed to enhance robustness, whose parameters are chosen according to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu -$</tex-math></inline-formula> synthesis framework and are convenient for adjustment practically. For anti-saturation, a SAWC is developed to help the system escape quickly from current saturation and enlarge the stability domain of the saturated system. Comparative simulations and experiments results show that the proposed control method can significantly reduce power consumption and achieve good response in AMB-rotor system.

Stiffness Compensation Control for Centrifugal Compressors Based on Online Parameter Identification of Magnetic Bearings

Significant temperature rise will degrade the stability of the active magnetic bearing (AMB) rotor system, which is an obstacle to the industrial implementation of magnetically suspended centrifugal compressors (MSCCs) with high power density. Aiming to ensure stable operation of the suspended rotor at high temperatures, this paper presents a stiffness compensation method based on online parameter identification. First, the linearized model at the operating point is derived through the establishment of a magnetic circuit model. The analysis of the temperature factor of bearing stiffness parameters is conducted. Then, the forgetting factor recursive least squares online identification algorithm is employed to obtain the coil resistance affected by bearing temperature in real time. Finally, a stiffness compensation control scheme is designed based on the identification results and current rotor displacement, in combination with series and feedback compensation to apply the same electromagnetic force to the rotor during temperature rise. Simulation and experimental results validate that the proposed method can effectively suppress the low-frequency fluctuation and guarantee the stability of the AMB rotor system.

Nonlinear dynamics of two dimensional rotor-active magnetic bearing system with generalized-pole legs: stability state diagram and control strategy

Nonlinear dynamics of two dimensional rotor-active magnetic bearing system with generalized-pole legs: stability state diagram and control strategy

Feedback Linearization and Robust Control for Whirl Mode With Operating Point Deviation in Active Magnetic Bearings-Rotor System

The whirl mode, seriously affecting the stability of active magnetic bearings (AMBs), is a hot issue in the AMBs-rotor system. This article stresses a whirl mode problem accompanied by the operating point deviation when the magnetically suspended control moment gyro outputs torque. A feedback linearization controller is proposed to decouple the whirl mode effects from the system state-space representation. A robust controller for uncertain systems is also used to solve the operating point deviation problem. First, the AMBs-rotor system's state-space representation containing the whirl mode terms is described. Next, a system uncertainty caused by the operating point deviation is discussed. Then, a feedback linearization controller combined with a robust controller for uncertain systems is designed. Finally, simulations and experiments for validity verification are presented, and comparative experiments with a PID controller and a robust controller are shown and compared in this article.

Dynamic analysis and vibration control of a rotor-Active magnetic bearings system with base motion

High-speed and high-precision rotating machinery is widely applied in industry, which promotes the rapid development of non-contact bearings represented by active magnetic bearings (AMBs). The rotor-AMBs system is usually installed on the base. Due to the base motion, it affects the dynamic characteristics of the rotor-AMBs system. In this paper, the dynamic analysis of the rotor-AMBs system with base motion is carried out. The dynamic model of the system with base motion is first derived, and the control model is then established. The influence of the inherent property of the base, the excitation mode of the base motion, and the control method for the rotor-AMBs system are analyzed with numerical simulation. In addition, the combination of feedforward control and PID control is employed to eliminate the vibration disturbance caused by the base motion and improve the suspension accuracy of the rotor. The experimental results show that the proposed hybrid control can effectively reduce the vibration of the rotor-AMBs system with base motion.

A General Double-Input Synchronous Signal Processor for Imbalanced Vibration Mitigation in AMB-Rotor Systems

Imbalanced vibration is an urgent yet challenging problem in active magnetic bearings (AMBs) rotor manufacturing due to the rotor mass imbalance effect. The virtue of active control in AMB systems lies in enabling substantial online mitigation of imbalanced vibrations. However, in practice, due to the lack of speed sensors in most of the existing AMB-rotor systems, efficient rotational speed feedback is still on the way. As a remedy, this article proposes a rotational speed sensor-free synchronous signal processor (SSP) with the double inputs: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$</tex-math> </inline-formula> -and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$</tex-math> </inline-formula> -axes direction displacement measurements of radial AMBs. The proposed SSP is capable of estimating the rotational speed and accordingly generating synchronous signals of the imbalanced vibrations by filtering noise in both directions. Such signals are afterward implemented as a feedforward compensator for eliminating the periodical imbalance effects. With the assistance of the Lyapunov theory, the conditions of the proposed SSP method together with the feedforward imbalance compensator are derived to guarantee the stability of the closed-loop AMB-rotor system. Extensive experimental results substantiate the effectiveness and superiority of the proposed SSP method in terms of imbalanced vibration suppression.

Influence of displacement sensor runout on active magnetic bearing-rotor system and control analysis

In the active magnetic bearing (AMB)-rotor system, a displacement sensor is one of the indispensable components. It detects the displacement of the rotor in real time and feeds back to the control system to realize the stable suspension of the rotor. However, due to electromagnetic interference, unstable power supply, poor grounding, and uneven rotor surface, the signal runout of the displacement sensor can often occur, resulting in rotor vibration. Given the above problems, this paper establishes the control model of the AMB-rotor system, lists three typical sensor runout signals, then analyzes the influence of different types of sensor runout on the system, and discusses the control methods under different sensor runout conditions. The research results have a specific guiding significance for vibration control of the maglev rotor under sensor runout influence.

Unbalanced Magnetic Pull Disturbance Compensation of Magnetic Bearing Systems in MSCCs

Unbalanced magnetic pull (UMP) disturbance seriously affects the stable operation of the magnetically suspended rotor (MSR) system. This article proposes an UMP disturbance suppression method based on a linear extended state observer (LESO) and adaptive peak filter (APF). The cascade structure of LESO and APF can accurately estimate the UMP disturbance in the whole speed range. First, the dynamic model of the active magnetic bearing rotor systems is established and the UMP caused by the dynamic eccentricity in the MSR system is analyzed. Second, a third-order LESO and an APF are designed. The performance evaluation of the LESO indicates that estimation error of disturbance decreases with the increase of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega _{o}$</tex-math></inline-formula> , and the addition of APF can make UMP disturbance estimation unaffected by the high-frequency noise. After adding this method, the closed-loop system remains stable within the working rotation speed range. Finally, simulation results show that the UMP disturbance can be estimated and compensated. Experimental results validate the proposed method can well suppress the large vibration of the UMP on the rotor.

Dynamic Characteristics Analysis of Magnetic Levitation Rotor Considering Unbalanced Magnetic Pull

The working principle of the motor can cause unbalanced magnetic pull (UMP) between stator and rotor unavoidably. Previous research about nonlinear vibration excited by UMP was focused on the rotor supported by traditional mechanical bearings or gas bearings. However, the magnetic levitation rotor is particular due to the low rigidity provided by the active magnetic bearing (AMB). UMP amplifies rotor vibration in the resonant zone and further excites the nonlinear electromagnetic force, thus producing different vibration phenomena. The paper calculates rotor orbit, spectra analysis, and time-history plot with numerical methods and studies the influence of the rotation speed, eccentricity, key control parameters, and UMP on rotor dynamics in detail. Results illustrate displacement response spectra of the magnetic levitation rotor are quite different from previous research results. The appearing frequency components are inducted by universal formulas in this paper. Furthermore, research shows a slight adjustment of the control parameters affect significantly harmonic components and vibration characteristics. The research results have practical reference significance for fault diagnosis, feature recognition, and controller optimization of the AMB-rotor system.

Control System Design for Low Power Magnetic Bearings in a Flywheel Energy Storage System

This paper presents a theoretical and experimental study on controller design for the AMBs in a small-scale flywheel energy storage system, where the main goals are to achieve low energy consumption and improved rotordynamic stability. A H-infinity optimal control synthesis procedure is defined for the permanent-magnet-biased AMB-rotor system with 4 degrees of freedom. Through the choice of design weighting functions, notch filter characteristics are incorporated within the controller to reduce AMB current components caused by rotor vibration at the synchronous frequency and higher harmonics. Experimental tests are used to validate the controller design methodology and provide comparative results on performance and efficiency. The results show that the H-infinity controller is able to achieve stable rotor levitation and reduce AMB power consumption by more than 40% (from 4.80 to 2.64 Watts) compared with the conventional PD control method. Additionally, the H-infinity controller can prevent vibrational instability of the rotor nutation mode, which is prone to occur when operating with high rotational speeds.

Study of active magnetic bearings (AMB) on non–synchronous rotors

A rotor is never free from vibration owing to constant centrifugal force acting on it while rotating. A practical rotor has inherent mass unevenness flaw, or bearing misalignment flaw, or self-weight bow flaw, or presence of discontinuity or cracks flaw. If the vibrations are not controlled within limits, the rotor’s purpose of existence is lost. These vibrations can be synchronous if the frequency of vibration is equal to, or multiple of, the speed of rotation of the rotor. Or may be non-synchronous if the frequency of vibration of the rotor is not a multiple of its rotational frequency. Active magnetic bearings (AMBs) have been in use for vibration control, vibration suppression, rotor stability and condition monitoring of rotordynamic systems, since many years. A lot of authors have performed various numerical and experimental works in an AMB–rotor configuration and reported their findings. The goal of this paper is to report and present the effect of AMB solely on non–synchronous rotors for the benefit of the scientific community. Firstly, this paper briefly introduces the constructional features on AMB–rotor system. Then, the gist of every paper is written, as well as specification of the work provided in tabular form. Finally, some comments on limitations and future applications are made. The paper is separately sectioned into numerical investigations, and experimental investigations.

Design and Optimization of a Radial Magnetic Bearing Considering Unbalanced Magnetic Pull Effects for Magnetically Suspended Compressor

In magnetic suspended centrifugal compressors, the unbalanced magnetic pull (UMP) may cause saturation on power amplifier currents driving the coils of the active magnetic bearing (AMB), eventually affecting the stability of the rotor. This article addresses the issue on the stable operation of the AMB-rotor system subject to the UMP. A mathematical model of the UMP with uneven magnetization of permanent magnet (PM) and eccentricity is proposed for a surface-mounted PM synchronous motor supported by magnetic bearings. Based on this model, an improved radial magnetic bearing (RMB) with control and bias separated coil structure is designed and optimized to decrease the compensation current used to balance the UMP. First, a mathematical model containing the unevenness of the magnetization and eccentricity is established to estimate the UMP. Next, the compensation current for the UMP is analyzed based on the UMP model. Then, with the aim of minimizing the compensation current, the proposed RMB is optimized under the constraints of the starting current, the magnetic bearing volume, and the coil current density. The compensation current of the optimized RMB is reduced by 25%, compared with that of the original RMB. Finally, the experimental results on a 132-kW magnetic suspended centrifugal compressor, equipped with the optimized RMB, show the effectiveness of the modeling and optimization design.

Analysis of Nonlinear Characteristics and the Factors Affecting the Operation of the Active Magnetic Bearings Rotor System Considering Alford Force

Based on a test rig supported by active magnetic bearings (AMBs), this paper focuses on the study of the nonlinear dynamic characteristics and the factors affecting the operation of a rotor system under the coupling of magnetic bearing force and Alford force. In order to solve the nonlinear dynamic response of rotor system, a dynamic equation of the rotor which introduces Alford force and the electromagnetic force of the AMBs controlled by PID is established. By changing the control parameters (kPP and kDD), operation parameters (rotational speed), and structural parameters (clearance between impeller and volute), the equation is solved by using Runge−-Kutta method. The results show that the rotor system exhibits complex nonlinear dynamic characteristics under the coupling action of Alford force and magnetic bearing force. The rotor system appears different dynamic behaviors such as single period, multi multi-period, and quasi quasi-period when changing the control parameters. Among all the control parameters, adjusting kDD is more effective to ensure system stability. The amplitude of rotor increases from 8.2 μμm to 11.9 μμm with the increase of speed from 6000 rpm to 10,000 rpm, while that decreases from 9.6 μμm to 8.2 μμm with the increase of clearance between impeller and volute from 1mm to 4 mm. Therefore, under the influence of Alford force, apart from the control parameters, the operation parameters and structural parameters of magnetic bearings also affect the operation of the rotor system supported by the AMBs.

Surge Disturbance Suppression of AMB-Rotor Systems in Magnetically Suspension Centrifugal Compressors

Surge is one of the main factors affecting the stability of the centrifugal compressor. This article investigates surge disturbance suppression of active magnetic bearing (AMB)-rotor systems in magnetically suspension centrifugal compressors. An active disturbance control method is adopted to make the rotor stably levitate under surge disturbance. First, the dynamic model of the magnetic bearing rotor is established and simplified into a single-channel model. Second, a third-order linear extended state observer (LESO) and a linear active disturbance rejection controller are designed. The performance analysis of the controller shows that the estimation error accumulation of the observer is bounded and the estimation errors decrease with the increase of the observer bandwidth. Furthermore, the variable differential parameter added in the differential link of the controller can flexibly adjust the system damping. A method of tuning parameters for linear active disturbance rejection control (LADRC) is proposed to suppress surge disturbance while satisfying the stability of the system. Finally, the results of the experiment demonstrate that the proposed scheme is effective in suppressing the large-scale vibration effect of the surge disturbance on the rotor, and the magnetically suspended centrifugal compressor (MSCC) can run stably with low amplitude under the modified surge and mild surge.