Active Magnetic Bearing Rotor Research Articles

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.

Nonlinear dynamics and static bifurcations control of the 12-pole magnetic bearings system utilizing the integral resonant control strategy

In this study, the Integral Resonant Controller (IRC) is presented along with the Proportional-Derivative (PD) controller as a novel control technique to control the dynamical behaviors of the 12-pole rotor active magnetic bearing system. According to the proposed control strategy, the system model has been derived as a two-degree-of-freedom nonlinear dynamical system coupled with two first-order filters. The obtained mathematical model has been analyzed utilizing the asymptotic analysis. The nonlinear algebraic system that governs the steady-state vibration amplitudes and corresponding phase angles of the considered system has been extracted. The influence of the IRC control parameters on the rotor dynamics has been explored by plotting the different bifurcation diagrams. The analytical investigations demonstrated that the vibration suppression efficiency of the combined controller (i.e., PD and IRC) is proportional to the product of control and feedback gains of the IRC as well as the derivative gain of the PD-controller. In addition, it is found that the controller efficiency is inversely proportional to both the square of the internal loop feedback gain of the IRC and the position gain of the PD-controller. Accordingly, an objective function has been derived to design the best control gains of the proposed controller strategy. The analytical and numerical simulations confirmed that the suggested control method can suppress the system vibration and eliminate the catastrophic bifurcation behaviors if the control gains are selected according to the proposed objective function. Finally, the effect of failing one of the coupled integral resonant controllers on the rotor dynamics has been explored as a precautionary procedure. It is found that the failure of one of the coupled integral resonant controllers may breakdown the bifurcation symmetry of the rotor system, but the system does not lose its stability.

Nonlinear oscillation of active magnetic bearing–rotor systems with a time-delayed proportional–derivative controller

Nonlinear oscillation of active magnetic bearing–rotor systems with a time-delayed proportional–derivative controller

Simultaneous Identification of Free and Supported Frequency Response Functions of a Rotor in Active Magnetic Bearings

Frequency response functions (FRFs) of rotor systems can be used as indicator functions for condition monitoring. Component-wise FRFs are of high interest to locate errors in the case of defects. To enable continuous monitoring, measurements should be taken during operation. This contribution shows methods of using active magnetic bearings (AMBs) for simultaneously determining different FRFs of a rotor system. The AMBs, in addition to supporting the rotor, are used simultaneously as sensors and actuators. Two different types of FRFs, namely, the one associated with the free rotor and with the supported rotor can be determined from a single experiment. This procedure does not need any change in the assembly because the AMBs are simultaneously used as bearing and excitation device. Considering as excitation the total bearing force of the AMBs results in the FRF of the free rotor. The FRF of the supported system is determined by considering a perturbation force only, which is applied on top of the controlled AMB force. As a showcase, an academic rotor test rig is used with and without rotation to verify the applicability of the method. To evaluate and interpret the results of the experiments, a numerical model of the rotor using finite-element formulations is used.

An Improved Resonant Controller for AMB-Rotor System Subject to Displacement Harmonic Disturbance

The controller contains harmonic components due to the detection error of the displacement sensor. The harmonic component acts on the magnetic bearing coil in the form of harmonic current, resulting in undesirable harmonic vibration force, which is not conducive to the microvibration control of active magnetic bearing (AMB) rotor system. In order to solve the problems of slow response speed and limited harmonic frequency range in series mode, an improved resonant controller in parallel mode is proposed in this article, which greatly improves the response speed of the system and the suppression effect at harmonic frequency. In addition, the gain and phase angle at each harmonic frequency can be adjusted, so the robustness of each harmonic frequency can be independently controlled, and the system stability can be guaranteed in a wide range of operating speeds. Finally, the effectiveness of the proposed algorithm is verified by simulation and experiment, which has important significance and application value for harmonic current suppression of AMB-rotor system.

Vibration Control of a Time-Delayed Rotor-Active Magnetic Bearing System by Time-Varying Stiffness

Active magnetic bearing (AMB) can actively control the vibration of the rotor, and its control law plays a key role. In this study, the vibration control of a rotor-AMB system with time delay is studied. The nonlinear vibration equation is derived based on the Newton law considering the time-varying stiffness (TVS) control. The method of multiple scales is applied to obtain the approximate solutions in the case of the primary parametric resonance and 1:1 internal resonance. The results show that the vibration amplitude and stable region are both periodic with respect to time delay. Their period is exactly equal to the rotating period of rotor. Additionally, the eccentricity-response curves are constructed to illustrate the vibration control of the time-varying stiffness. The results show that the time-varying stiffness control suppresses the vibration effectively. At the same time, it is also found that the time-varying stiffness control may cause an increase in vibration amplitude or even instability in small range of unbalance eccentricity. The influence of time delay on the time-varying stiffness control is investigated. It is found that the time-varying stiffness controller exhibits different performance depending on the time delay.

Experimental and theoretical investigations of unbalance flexible rotor in active magnetic bearings considering backup bearings contacts

This paper describes the experimental verification of an unbalance flexible rotor model in active magnetic bearings. The dynamic modeling takes into account the gyroscopic moments of the disk, geometric coupling of the magnetic actuators, and contact forces of the backup bearings. The Rung–Kutta method is used to integrate the equations of motion. The nonlinear dynamic response is analyzed using bifurcation plots, disc center trajectories, Fast Fourier Transforms, Poincaré maps, and maximum Lyapunov exponent. The analysis is carried out for different values of rotating speed and unbalance eccentricity. In the unbalance test, a concentrated mass of 5 gr is attached in three radial position of the disk. The numerical simulations and experiments prove that a variety of nonlinear dynamical phenomena such as period -3, -4, -8, periodic, quasi-periodic, and chaotic motions occur in the system. The results indicate that the response of the rotor returns back to a regular motion by increasing the rotational speed. Also, by increasing the unbalance eccentricity, the first irregular motion initiates at much higher rotational speeds. Therefore, sufficient attention should be paid to these factors in design of a flexible rotor system equipped with both active magnetic bearings and backup bearings in order to ensure system reliability.

Adaptive odd repetitive control for magnetically suspended rotor harmonic currents suppression

Magnetic levitation rotating machinery has been widely used in industrial applications. Odd harmonic currents in the active magnetic bearing coils, which are caused by rotor mass unbalance and sensor runout, increase the power consumption and the base vibration. Repetitive control has recently been used to suppress harmonic currents in magnetic bearing systems. However, repetitive control needs the rotor rotational speed information and has some limitations without a speed sensor. In this paper, an adaptive odd repetitive control which does not need the speed sensors is proposed to suppress the active magnetic bearing odd harmonic currents. Compared to the conventional repetitive control, the second-order generalized integral frequency-locked loop is applied in adaptive odd repetitive control to estimate the rotor speed in real time without additional speed sensors. The magnetically suspended rotor with harmonic disturbances is modeled. The work principle, structure, and design of the adaptive odd repetitive control are addressed. The simulation and experiments are carried out on a rotor active magnetic bearing test rig to validate the effectiveness of the proposed adaptive odd repetitive control, and the results show that the active magnetic bearing odd harmonic currents are well suppressed.

Integral Resonant Controller to Suppress the Nonlinear Oscillations of a Two-Degree-of-Freedom Rotor Active Magnetic Bearing System

Within this article, the nonlinear vibration control of the rotor active magnetic bearings system is tackled utilizing the integral resonant controller for the first time. Two integral resonant controllers are proposed to mitigate the system lateral oscillations in the horizontal and vertical directions. Based on the suggested control technique, the whole system dynamical model is derived as a two-degree-of-freedom nonlinear system (i.e., rotor system) coupled linearly to two first-order filters (i.e., the integral resonant controllers). The nonlinear autonomous system that governs the oscillation amplitudes of the controlled system as a function of the control parameters is extracted by applying perturbation analysis. The obtained autonomous system showed that the linear damping coefficients of the rotor system are functions of the control gains, feedback gains, and internal loop feedback gains of the coupled controller. Accordingly, the sensitivity of the rotor oscillation amplitudes to the different control parameters is explored. The stability margins and the optimal control gains are reported via plotting the different stability charts in two-dimensional space. The main acquired results demonstrated that the vibration suppression efficiency of the proposed controller is proportional to the product of both the control and feedback signal gains, and inversely proportional to the square of the internal loop feedback gains. In addition, the analytical investigations confirmed that the proposed integral resonant control method can force the rotor system to respond as a linear one with a single periodic attractor when the control parameters are designed properly. Finally, numerical simulations are performed that have illustrated the excellent correspondence with the obtained analytical results.

Design and Modeling of 2 MW AMB Rotor With Three Radial Bearing-Sensor Planes

Active magnetic bearings (AMBs) provide reliable solution for high-speed rotors, where oil-free and reliable operation are crucial. In high-power applications benefits of AMBs, compared to traditional rolling element bearings or fluid film bearings, are highly valued. Typical AMB rotors comprise two radial AMBs, which are designed with compressor or generator wheels integrated on the rotor. AMB dimensions and locations are carefully selected for each new application. The system design is being iterated such that the nodes of the lowest frequency rotor bending modes are sufficiently far away from the AMB and sensor nodes to ensure robust AMB control. The design is very challenging and cost sensitive. This work focuses on electromagnetic design, modeling, and control of fully levitated AMB-rotor with three radial AMBs. The additional bearing ensures that the same design can be reused with different applications and regardless of the changes in locations of nodes of the first bending mode. The control plant is modeled based on flexible rotor dynamics; while bearing inductances and forces are modeled with 2-D and 3-D finite element method (FEM) electromagnetic simulations. The presented multi-input multi-output (MIMO) model-based control is coupled and centralized with three actuator-sensor pairs for radial suspension. The control design is verified in simulations using nonlinear engineering models. Additionally, experimental identification results are included.

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.

Nonlinear Dynamics and Motion Bifurcations of the Rotor Active Magnetic Bearings System with a New Control Scheme and Rub-Impact Force

This article is dedicated to investigating the nonlinear dynamical behaviors of the 8-pole rotor active magnetic bearing system. The rub and impact forces between the rotating disc and the pole-legs are included in the studied model for the first time. A new control scheme based on modifying the 8-pole positions has been introduced. The proposed control methodology is designed such that four poles only are located in the horizontal and vertical directions (i.e., in +X,+Y,−X,−Y directions), while the other four poles are inserted in a way such that each pole makes 45° with two of the axes +X,+Y,−X,−Y. The control currents in the horizontal and vertical poles are suggested to be proportional to both the velocity and displacement of the rotor in the horizontal and vertical directions, respectively, while the control currents in the inclined poles are proposed to be dependent on the combination of both the displacement and velocity of the rotor in the horizontal and vertical directions. Accordingly, the whole-system mathematical model is derived. The derived discontinuous dynamical system is analyzed employing perturbation methods, Poincare maps, bifurcation diagrams, whirling orbits, and frequency spectrum. The obtained results demonstrated that the controller proportional control gain can play a significant role in changing the vibratory behaviors of the system, where the proposed control method can behave either as a cartesian control strategy or as a radial control one depending on the magnitude of the proportional gain. In addition, it is found that the rotor system can vibrate with periodic, periodic-n, quasiperiodic, or chaotic motion when the rub and/or impact forces occur. Moreover, it is reported for the first time that the rotor-AMB can oscillate symmetrically in X and Y directions either in full annular rub mode or quasiperiodic partial rub mode depending on the impact stiffness coefficient and the dynamic friction coefficient.

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.

Transverse Vibration of Geared-Rotor Integrated With Active Magnetic Bearings in Identification of Multiple Faults

Abstract This paper presents a novel concept of the modeling, active control of transverse vibration responses, and identification of fault parameters in a geared-rotor system integrated with active magnetic bearings (AMBs). The sources of error in gears while in the operation are the gear mesh deformation, transmission error, and runout, resulting in dynamic forces, excessive vibration, and noise. To avoid any undesirable effect on the gear-pair and other supporting structures, it is essential to investigate these forced vibrations in time and frequency domain. Hence, an approach to monitor and control the transverse vibration of mating gears is presented with the help of AMBs. The AMBs are capable of suppressing the vibration of the system (transients as well as steady-state) by controlled electromagnetic forces considering the rotor vibrational displacement with a closed-loop feedback system. A mathematical model has been developed with geared rotor faults, like the mesh deformation, gear run-out, and asymmetric transmission error. The transmission error has been modeled as the sum of mean and varying components of error in two orthogonal transverse directions. Based on the mathematical model, an identification algorithm has been developed. Considering full spectrum analysis of the rotor vibration and AMB current information, estimation of system parameters, i.e., the equivalent mesh stiffness, mesh damping, gear runouts, the mean and varying transmission error magnitude and phase angles, and the current and displacement constants of AMBs has been performed. Gaussian noise in responses and modeling errors in mathematical models have been added to test the robustness of the proposed algorithm to comply with the experimental settings.

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.

Dynamic Analysis of Active Magnetic Bearing Rotor System Considering Alford Force

Dynamic Analysis of Active Magnetic Bearing Rotor System Considering Alford Force