Search Results (71)

The paper presents the development of analytical and finite element models, focusing on both magnetostatics and thermal solutions, of axial classical and hybrid active magnetic bearings (AMBs). An improved hybrid axial AMB design is proposed, combining permanent magnets and an electromagnet, where the bias magnetic flux is provided by the permanent magnets. This configuration significantly reduces the power consumption and heat generation. Numerical modeling is conducted using 2D magnetostatic and both 2D and 3D thermal finite element analysis. The study focuses on the system’s mass reduction, electrical power consumption, and heat flow output while maintaining the bearing’s load capacity. Digital control systems and algorithms have been developed and fabricated for both axial classical and hybrid axial AMBs, using an ESP32 microcontroller. Two experimental setups have been designed, fabricated, and tested. Full article

Displacement self-sensing active magnetic bearings (AMBs) have garnered significant attention from both academia and industry for their potential to reduce cost, enable system integration, and enhance reliability. While numerous self-sensing methodologies have been researched, the field lacks a unified framework for discussing their theoretical foundation and practical applicability. This paper analyzes and summarizes various displacement self-sensing methods, deriving the underlying principles and essence of these techniques, and clarifying the intrinsic interconnections of different schemes. The process of self-sensing is constructed through two steps: online inductance estimation and electromagnetic inductance modeling. A novel framework is then proposed, categorizing online inductance estimation, with dedicated discussion on modeling and handling critical nonlinearity like magnetic saturation and the eddy current effect. Furthermore, this review conducts a systematic comparative analysis, evaluating prevalent schemes against key performance metrics such as robustness, stability, signal-to-noise ratio (SNR), and system complexity. Finally, persistent challenges and future research trends are discussed. This review provides a valuable reference for both researchers and engineers when selecting and implementing self-sensing technologies for AMB systems. Full article

With the development of active magnetic bearings (AMBs) toward higher speeds, understanding high-speed rotor dynamics has become a crucial focus in AMB research. Traditional finite element modeling (FEM) methods, however, are unable to rapidly and comprehensively uncover the complex interplay between controller parameters and dynamic behavior. To address this limitation, a surrogate modeling approach based on a hybrid gated recurrent unit–Kolmogorov–Arnold network (GRU-KAN) is introduced to mathematically capture the effects of coupled control gains on rotor dynamics. To enhance model generalization, a genetic algorithm-driven uniform design sampling strategy is also implemented. Comparative studies against support vector regression and Kriging surrogates indicate a higher coefficient of determination ($R^2=0.9887$) and lower residuals for the proposed approach. Experimental validation across multiple controller parameter combinations shows that the resulting machine learning surrogate predicts the critical speed with a mean absolute error of only 38.51 rpm and a mean absolute percentage error of $1.56\times {10}^{-1}\%$, while requiring merely $1.14\times {10}^{-4}$ s per evaluation—compared to 201 s for traditional FEM. These findings demonstrate the surrogate’s efficiency, accuracy, and comprehensive predictive capabilities, offering an effective method for rapid critical speed estimation in AMB–rotor systems. Full article

The authors have designed a gyro-system for orientation (guidance) and stabilization, with two gimbals and a rotor in magnetic suspension (AMB—Active Magnetic Bearing) usable for self-guided rockets. The gyro-system (DGMSGG—double gimbal magnetic suspension gyro-system for guidance) orients and stabilizes the target coordinator’s axis (CT) and, at the same time, the AMB–rotor’s axis so that they overlap the guidance line (the target line). DGMSGG consists of two decoupled systems: one for canceling the AMB–rotor translations along the precession axes (induced by external disturbing forces), the other for canceling the AMB–rotor rotations relative to the CT-axis (induced by external disturbing moments) and, at the same time, for controlling the gimbals’ rotations, so that the AMB–rotor’s axis overlaps the guidance line. The nonlinear DGMSGG model is decomposed into two sub-models: one for the AMB–rotor’s translation, the other for the AMB–rotor’s and gimbals’ rotation. The second sub-model is described first by nonlinear state equations. This model is reduced to a second order nonlinear matrix—vector form with respect to the output vector. The output vector consists of the rotation angles of the AMB–rotor and the rotation angles of the gimbals. For this purpose, a differential geometry method, based on the use of the output vector’s gradient with respect to the nonlinear state functions, i.e., based on Lie derivatives, is used. This equation highlights the relative degree (equal to 2) with respect to the variables of the output vector and allows for the use of the dynamic inversion method in the design of stabilization and guidance controllers (of P.I.D.- and PD-types), as well as in the design of the related linear state observers. The controller of the subsystem intended for AMB–rotor’s translations control is chosen as P.I.D.-type, which leads to the cancellation of both its translations and its translation speeds. The theoretical results are validated through numerical simulations, using Simulink/Matlab models. Full article

Active magnetic bearings (AMBs), pivotal in high-speed rotating machinery for their frictionless operation and precise control, demand power amplifiers with exceptional dynamic performance and minimal current ripple. However, conventional amplifier designs often overlook eddy current effects, a critical oversight given the high-frequency switching inherent to pulse-width modulation (PWM). These induced eddy currents distort output waveforms, amplify ripple, and degrade system bandwidth. This paper bridges this critical gap by proposing a comprehensive methodology to model, quantify, and mitigate eddy current impacts on three-level half-bridge power amplifiers. A novel mutual inductance-embedded circuit model was developed, integrating winding–eddy current interactions under PWM operations, while a discretized transfer function framework dissects frequency-dependent ripple amplification and phase hysteresis. A voltage selection criterion was analytically derived to suppress nonlinear distortions, ensuring stable operation in high-precision applications. A Simulink simulation model was established to verify the accuracy of the theoretical model. Experimental validation demonstrated a 212% surge in steady-state ripple (48 mA to 150 mA at 4 A DC bias) under a 20 kHz PWM operation, aligning with theoretical predictions. Dynamic load tests (400 Hz) showed a 6.28% current amplitude reduction at 80 V DC bus voltage compared to 40 V, highlighting bandwidth degradation. This research provides a paradigm for optimizing AMB power electronics, enhancing precision in next-generation high-speed systems. Full article

Active magnetic bearings (AMBs) are a class of electromechanical equipment that effectively integrate Magnetic Bearing technology with PMSM technology, particularly for applications involving high-power and high-speed permanent magnet motors. However, as the rotor operates in a suspended state, the motor’s trajectory changes continuously. The installation of a speed sensor poses a risk of collisions with the shaft, which inevitably leads to rotor damage due to imbalance, shaft wear, or other mechanical effects. Consequently, for the rotor control system of PMSM, it is crucial to adopt a sensorless speed estimation method to achieve high-performance speed and position closed-loop control. This study uses the rotor system of a 75 kW AMB high-speed motor as a case study to provide a detailed analysis of the principles of high-frequency square wave signal injection (HFSWSII) and current signal injection for speed estimation. The high-frequency current response signal is derived, and a speed observer is designed based on signal extraction and processing methods. Subsequently, a speed estimation model for PMSM is constructed based on HFSWSII, and the issue of “filter bandwidth limitations and lagging effects in signal processing” within the observer is analyzed. A scheme based on the high-frequency pulse array current injection method is then proposed to enhance the observer’s performance. Finally, to assess the system’s anti-interference capability as well as the motor’s static and dynamic tracking performance, its dynamic behavior is tested under conditions of increasing and decreasing speed and load. Simulation and experimental results demonstrate that the PMSM control system based on HFSWSII achieves accurate speed estimation and shows excellent static and dynamic performance. Full article

In an active magnetic bearing (AMB) rotor system, the mass imbalance of the rotor is inevitable due to uneven materials, machining errors, assembly errors and other factors. When the rotor rotates, the unbalanced mass generates centrifugal force at the same frequency as the rotational speed, which causes vibration and affects the smooth operation of the rotor. Aiming at the mass imbalance of AMB rotor, a new method based on an adaptive notch filter (ANF) and the influence coefficient method (ICM) is proposed. Firstly, the improved ANF is used to track the rotor displacement signal, and the amplitude and phase information of the displacement signal are calculated. Then, according to the amplitude and phase information calculated by ANF, the ICM is used to calculate the counterweight information of the rotor dynamic balance, which includes the counterweight mass and counterweight position. Finally, the dynamic balance correction of the AMB rotor is realized by adding the calculated counterweight mass to both sides of the rotor. This paper validates the feasibility of the proposed method for the dynamic balance correction of the AMB rotor through simulation and experiment. The four radial displacement unbalances of the rotor were reduced by 56.6%, 62.8%, 49.2% and 63.7%, respectively. Full article

This paper proposes an adaptive fuzzy controller based on a switching notch filter to address the rotor unbalance vibration control problem of an active magnetic bearing (AMB) high-speed motor system in the full rotational speed range. Aiming at the complex nonlinear and time-varying characteristics of the AMB rigid rotor system, this study designs an adaptive fuzzy controller (AFC) that obtains fuzzy quantities by blurring the rotor vibration information and vibration rate of change as the input signals and then obtains the fuzzy set through fuzzy reasoning and modifies the parameters of the initial fuzzy controller. The initial fuzzy controller parameters are modified through fuzzy reasoning to improve the control effect and ensure the stable suspension of the rotor during high-speed rotation. At the same time, in order to effectively suppress the vibration of the rotor in high-speed operation due to unbalance and other factors, this paper introduces an adapting notch filter (ANF) as a vibration control strategy on the basis of AFC, and the notch filter is able to monitor the rotor vibration signals and adaptively adjust the center frequency and bandwidth. Finally, the correctness and effectiveness of the adaptive fuzzy controller based on a switching notch filter (AFC-ANF) are verified via simulations and experiments. The simulation results demonstrate that compared to traditional PID control, the AFC reduces the response time by 0.11 s. Under constant-speed operating conditions, the AFC-ANF strategy decreases rotor vibration by 60%, while under variable-speed conditions, it reduces rotor vibration displacement by 40%, showcasing significant vibration suppression effectiveness. This research provides a novel solution for vibration control in magnetic bearing systems, offering both important theoretical significance and practical application value. Full article

The installation distance between the speed sensor of the traditional rolling or sliding bearing permanent magnet synchronous motor and the rotor was very close, and the rotor of the magnetic levitation motor supported by Active Magnetic Bearings (AMBs) was in suspension. When the motor was running at high speed, the radial trajectory of the rotor changed all the time. The same frequency vibration caused by the unbalanced mass of the rotor made it easy to cause mechanical collision between the sensor and the rotor, resulting in direct damage of the sensor. Therefore, the sensorless speed estimation method was needed for the rotor control system of the magnetic levitation motor (MLM) to achieve high performance closed-loop control of speed and position. More importantly, in order to control or compensate the unbalanced force of the electromagnetic bearing rotor system, the rotor rotation speed signal should be obtained as accurately as possible. Therefore, the principle of adaptive sliding mode observer (SMO) was analyzed in detail by taking the rotor system of MLM as an example. Then, the sliding mode surface was designed, the speed estimation algorithm based on adaptive SMO was derived, and the stability analysis was completed. Finally, in order to verify the anti-disturbance performance of the system and the static and dynamic tracking performance of the motor, the dynamic performance was verified by increasing and decreasing the speed and load. The results showed that the speed estimation method based on adaptive SMO could achieve accurate speed estimation and had good static and dynamic performance. Full article

Chatter commonly emerges during milling procedures, resulting in an array of problems such as defective workpiece surface and diminished machining efficiency. To control chatter, an active electromagnetic tool holder system is proposed, including the active structure with an electromagnetic actuator installed at the tool holder position and a time-delay output feedback chatter control method for low immersion milling. More specifically, a noncontact two-degree-of-freedom active magnetic bearing (AMB) actuator is developed and integrated with displacement sensors at the tool holder position, making the actuator and sensors closer to the cutting point. Under low immersion milling conditions, both the thin-walled workpieces and tool flexibility are considered in the controller design, as well as practical physical limitations including the bandwidth of the power amplifier and the output current constraints of the actuator. Numerical simulation and experiments under low immersion milling conditions are carried out. The results demonstrate that the proposed active electromagnetic tool holder system exhibits good control consequences on the chatter of thin-walled workpieces and tools under low immersion milling. Full article

The authors have designed a structure for a gyro system (used for the guidance of self-guided missiles) with two gimbals and a rotor in magnetic suspension (AMBs—active magnetic bearings). The system (double-gimbal magnetic suspension gyro system for guidance—DGMSGG) orients the common axis rotor AMB (the sight line) in the direction of the target line (the guide line) by means of some control system of the gyro rotor’s rotations and translations, as well as by means of some servo systems for the gimbals’ rotation angle control. The DGMSGG provides specific signals for the missile’s autopilot, to guide it toward the target, so that the guidance line translates parallel to itself to the point of interception of the target (according to the self-guidance method by parallel approach). Based on the DGMSGG’s established mathematical model, the authors propose and design adaptive control systems for the decoupled dynamics of the gyro rotor’s translations and rotations and of the gimbals’ rotations; the concept of dynamic inversion is used, as well as linear dynamic compensators (P.D.- and P.I.D.-type), state observers, reference models, and neural networks. The theoretical results are validated through numerical simulations, using Simulink/Matlab models’ stabilization and orientation operating regimes. Full article

Featured with optimal power consumption, active magnetic bearings (AMBs) have been extensively integrated into turbomachinery applications. For turbomachinery components, including the rotor and impeller, their connection is generally based on bolted joints, which would easily induce excessive interface contact. As a result, the pre-tightening torque can induce modal vibrations in the rotor upon levitation. Although a notch filter can be adopted to suppress the vibrations, it should be noted that the current reported notch filters are based on fixed center frequency, making it challenging to enable high effectiveness over a broad range of rotor speeds, particularly in cases where the gyroscopic effect is significant. Herein, a modal vibration suppression based on a varying-frequency notch filter is proposed, considering gyroscopic effect and interface contact. First, the rotor–AMB system was developed, taking into consideration the bolted-joint interface contact. This modeled the effect of the interface contact as a time-varying force in the positive feedback. Secondly, the relationship between vibration frequency and rotational speed was obtained, based on simulations. Lastly, a test rig was configured to validate the performance of the frequency-varying notch filter. The experimental data confirm that the filter is capable of attenuating the modal vibrations resulting from interface contact across all operational speeds. Full article

The 5-degree-of-freedom active magnetic bearings (5-DOF AMB) and high-speed permanent magnet synchronous motor (HPMSM) were combined and applied to energy-recovery-type air compressors for fuel cells, which gives full play to the advantages of both and meets the design requirements for air compressors in fuel cells. Based on the energy recovery air compressor for fuel cells with a power of 30 kW and a rated speed of 100,000 rpm, this paper combined 5-DOF AMB with HPMSM and used it as its support and drive system. Multi-physics field and multi-objective optimization were carried out by integrating the multi-physics field with the Multi-objective Grey Wolf Algorithm (MOGWO), and the feasibility of the design of the system and its reliability were verified using finite element software. Full article

The flywheel energy storage system (FESS) of a mechanical bearing is utilized in electric vehicles, railways, power grid frequency modulation, due to its high instantaneous power and fast response. However, the lifetime of FESS is limited because of significant frictional losses in mechanical bearings and challenges associated with passing the critical speed. To suppress the unbalanced response of FESS at critical speed, a damping ring (DR) device is designed for a hybrid supported FESS with mechanical bearing and axial active magnetic bearing (AMB). Initially, the dynamic model of the FESS with DR is established using Lagrange’s equation. Moreover, the dynamic parameters of the DR are obtained by experimental measurements using the method of free vibration attenuation. Finally, the influence of the DR device on the critical speed and unbalanced response of FESS is analyzed. The results show that the designed DR device can effectively reduce the critical speed of FESS, and increase the first and second mode damping ratio. The critical speed is reduced from 13,860 rpm to 5280 rpm. Compared with FESS of the mechanical bearing, the unbalanced response amplitude of the FESS with DR is reduced by more than 87.8%, offering promising technical support for the design of active and passive control systems in FESS. Full article

This paper conducts an in-depth study on the dynamic stability and complex vibration behavior of a 12-pole active magnetic bearing (AMB) system considering gravitational effects under a PD controller. Firstly, based on electromagnetic theory and Newton’s second law, a two-degree-of-freedom control equation of the system, including PD control terms and gravitational effects, is constructed. This equation involves not only parametric excitation, quadratic nonlinearity, and cubic nonlinearity but also a more pronounced coupling effect between the magnetic poles due to the presence of gravity. Secondly, using the multi-scale method, a four-dimensional averaged equation of the system in Cartesian and polar coordinates is derived. Finally, through numerical analysis, the system’s amplitude–frequency response, motion trajectory, the relationship between energy and amplitude, and global dynamic behaviors such as bifurcation and chaos are discussed in detail. The results show that the PD controller significantly affects the system’s spring hardening/softening characteristics, excitation, amplitude, energy, and stability. Specifically, increasing the proportional gain can quickly suppress the rotor’s motion, but it also increases the system’s instability. Adjusting the differential gain can transition the system from a chaotic state to a stable periodic motion. Full article