Active Magnetic Bearing Rotor Research Articles

Preliminary Study on Recontrol Evaluation of a Magnetic Bearing Rotor Falling on Touch-Down Bearings

The dynamic control of an active magnetic bearing (AMB) rotor after the rotor falls to its touch-down bearings has always been a difficult problem for applications such as flywheel energy storage. The rotor drop process has obvious nonlinear dynamic characteristics. This paper first discusses the structure of AMBs and the basic principles of their control. Starting from the electromagnetic forces that electromagnets can provide, the problem is simplified to the influence of an electromagnetic force with constant damping characteristics on the dynamic characteristics of a dropped rotor. A dynamic model of an AMB rotor with touch-down bearings was built and the contact force model between the rotor and the touch-down bearings was determined. A constant damping electromagnetic force was applied in two ways to verify the dynamic control feasibility of a dropped rotor through magnetic bearings. The simulation results show that the dropped rotor recovery control is feasible by applying a reasonable electromagnetic force.

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.

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.

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

This paper addresses a novel sliding mode control based on state observer for active magnetic bearing rotor system. Firstly, the state-space model of a radial AMB rotor system is established with considering unbalance disturbance and gyro effect for a vertical flywheel energy storage system. Then a sliding mode function and switching surface are constructed based on an observer. Meanwhile, a separation and decoupling strategy based on Finsler’s lemma is proposed. Through this method, the constraint relationship between the controller gain, active magnetic bearing matrices and the Lyapunov variables is eliminated. After that a method for chattering reduction in the sliding-mode controller is raised. Relied on these techniques, new sufficient conditions for the stability of AMB rotor system are given in the framework of linear matrix inequalities. Finally, the effectiveness of the proposed sliding mode controller is validated on the experimental platform of the flywheel energy storage system.

Configuration angle effect on the control process of an oscillatory rotor in 8-pole active magnetic bearings

<abstract> <p>In an active magnetic bearings (AMBs) model, every pair of opposite poles is aligned at an angle with the horizontal axis. In some configurations, there is a pair of poles which is in line with the horizontal axis. In other configurations, the same pair of poles might make a nonzero angle with the horizontal axis. This paper focused on the effect of changing such a configuration angle on the control process of an oscillatory rotor in an 8-pole active magnetic bearings model. Adopting the proportional-derivative (PD) control algorithm, the radial or Cartesian control techniques were applied. It was found that the rotor's oscillation amplitudes were not affected by the change in the configuration angle, even if its rotation speed and eccentricity were varied in the radial control scheme. However, the amplitudes were severely affected by the change in the configuration angle except at a specific angle in the Cartesian control scheme. The approximate modulating amplitudes and phases of the rotor's oscillations were extracted by the method of multiple-scales and a stability condition was tested based on the eigenvalues of the corresponding Jacobian matrix.</p> </abstract>

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

Position Decoupling Control of Rigid Rotor of Active Magnetic Bearing

The magnetic bearing rotor system has the problem of positional coupling in the direction of the radial degrees of freedom. This paper proposes a linear output feedback method which decouples the multi-variable coupling system into four single-degree-of-freedom second-order integral subsystems. Firstly, a five-degree-of-freedom(5-DOF) mathematical model of active magnetic bearing rotor is derived. Then, a sliding mode variable structure controller is designed for the decoupled subsystems and the stability of system is guaranteed by the Lyapunov stability theory. The results of computer simulation show that the design controller of sliding mode variable structure controller can more effectively enhance the magnetic bearing rotor performance stability compared with the conventional PD controller, fuzzy PD controller, no matter in the position respond control and anti-disturbance control. Moreover, the sliding mode variable structure controller make the system have better tracking performance.

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.

Optimal phase compensation for a rotor-AMB system considering interface contact

Rotor-Active magnetic bearing (rotor-AMB) systems offer significant advantages in power consumption and are increasingly being applied in fluid machinery. However, in such machinery, the impeller and the rotor are commonly connected by bolt fastening. Once a certain pre-tightening force is applied to the bolted connection and the interface contact between the rotor and the impeller is formed, the flexible modal vibration will be excited when the rotor is levitated. The conventional Proportional-Integral-Derivative (PID) controller is limited in this vibration suppression and it is essential to increase the damping at bending mode to inhibit vibration. However, the calculation of the optimal phase compensated is based on the rotor-AMB model considering interface contact. In this work, the effect of the interface contact is equivalent to massless spring units, and the disturbance generated by spring units is acted upon the mechatronic system in the way of positive feedback. The detailed description of the transfer function from the disturbance to rotor deformation at fourth bending mode is obtained by theoretical model and system identification. The optimal phase of the system needed to inhibit the disturbance is determined by minimizing the gain of the transfer function at fourth bending mode. A combination of PID control and phase compensation is implemented in the experiment. The results show that the optimal phase is 50° as the calculation and the optimal phase compensation control can sufficiently inhibit the modal vibration.

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.

The annulling of the sudden appearance of an unbalance in rotary machines by using active magnetic bearings

The application of magnetic bearings has become more frequent during the last 20 years and represents a significant aspect of improvements in the construction of machines with rotary motion. With the advancement of technology, the number of applications in which magnetic bearings have found their application is increasing. In this paper, it is shown how the effect of magnetic forces can annul the negative influence of unbalance, which suddenly appeared in a rotor supported in active magnetic bearings. Such cases may occur in operation due to breakage and rotor parts falling off (e.g., fan blades), which will lead to a sudden change in the mass balance of the rotor system and dislocation of the centre of mass in relation to the geometric centre of the rotor. In the paper, a mathematical model of the dynamic behaviour of a rigid rotor in active magnetic bearings was developed. The model is nonlinear and has five degrees of freedom and can only be solved numerically. The Newmark beta method and the Newton-Raphson method were used to solve the system of nonlinear differential equations. The results of the simulation showed the advantages of using active magnetic bearings for annulling sudden occurrences of unbalance in rotary machines.

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.

Dynamic and Thermal Investigations of the Forward Dry-Friction Whirl/Whip of a Vertical Rotor-AMB System during Touchdowns

When an active magnetic bearing (AMB) rotor drops, it impacts the touchdown bearing (TDB) and produces friction on its surface. The vertical AMB rotor has no stable support in the radial direction, and the rotor exhibits a violent whirl motion in the gap of the TDB. In this study, a complete dynamic and thermal model of the AMB-rotor-TDB system was established, and the complete drop process was simulated. When the rotor dropped, it obtained stable support after several bounces on the thrust surface of the TDB inner ring in the axial direction. In the radial direction, the rotor entered whirl motion after the initial collisions. There is a natural whirl frequency so that the drop forward whirl is divided into the dry-friction whirl and whip states. The contact force and heat generation of the TDB were monitored in the simulation and had different performancs in the two states. Both the initial collisions and the stabilized whirl motions were studied to evaluate the reliability of the TDB. Finally, a series of drop tests were performed, and the experimental results were in good agreement with the simulation.

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.

Robust Dynamic Balancing of Dual Rotor-Active Magnetic Bearing System Through Virtual Trial Unbalances as Low and High Frequency Magnetic Excitation

Abstract This work focuses on in situ residual unbalance estimation of the dual rotor system with the implementation of active magnetic bearing (AMB) as a controller and exciter. The excessive vibration generated due to the presence of residual unbalances limits the operating speed of the system. The compact structure of the dual rotor system provides constraints to the conventional balancing procedure that requires manual addition of the trial unbalances for balancing. In order to overcome the difficulty in balancing of the dual rotor system, an identification algorithm based on the modified influence coefficient method (MICM) is developed for the simultaneous estimation of residual unbalances in both inner and outer rotors with the generation of virtual trial unbalances as magnetic excitation through AMB. The controlling action of AMB attenuates the vibrational response of the system within the required limit and allows the safe operation of the system in the presence of rotor faults and additional excitations. The vibrational responses of the system at the limited locations and the magnitude and phase of the virtual trial unbalances are only required in the MICM for the estimation of unbalances. To numerically illustrate the present methodology, the displacement response is obtained from the developed finite element model of the dual rotor system with discrete disk unbalances and randomly distributed shaft. The robustness of the algorithm in the estimation of residual unbalances is verified with the addition of a different percentage of measurement noises. After balancing, the dual rotor system is found to traverse its critical speed with a less vibrational response.