Most control strategies for magnetic bearings are typically formulated upon the linearized suspension force model, and the nonlinear characteristics are neglected or regarded as the disturbance and variation in parameters of the control system. The controllers based on linearized suspension force model struggle to achieve fast response under disturbance. Therefore, a nonlinear mathematic model that simultaneously represents the main nonlinearity of suspension force and facilitates the design of high-performance controller is necessary to establish. In this study, a new mathematical model of suspension force with varying current stiffness is developed, and a specific controller was designed based on this model. Firstly, the nonlinear mathematical model of six-pole radial–axial hybrid magnetic bearing (RAHMB) is established. Secondly, the characteristics of the current stiffness varying with rotor displacement are analyzed and the expression between current stiffness and rotor displacement is fitted. Then, the linearized model is built via Taylor expansion of the nonlinear model. Subsequently, the varying current stiffness model is constructed by substituting the fitted expression of varying current stiffness into linearized model. Finally, an adaptive nonsingular terminal sliding mode controller (ANTSMC) is designed based on the proposed varying current stiffness model. The simulation and experiment results have shown that the ANTSMC based on varying current stiffness model reduces chattering more than 64% and reduces convergence time more than 70% to the NTSMC based on the linearized model.

Performance analysis of active magnetic bearing supported rotor system on moving platform

Enhancement of YBCO superconductor magnetic bearing capability by using multiple bulks

Temperature-induced vibration instability in a non-spinning vertical rotor supported by active magnetic bearings—Theory and experiment

Superconducting magnetic bearings are friction-free devices and therefore in principle suitable for long-term operation, as no wear is observed. However, other degradation mechanisms can influence the operation. Up to now, it has not been clear to what extent degradation of either the bulk superconductors or the permanent magnets impacts the overall bearing performance on long timescales. Therefore, we studied the bearing properties of a 20-year-old rotational superconducting magnetic bearing, which was cooled down occasionally in an open liquid nitrogen bath for presentation. Otherwise, the bearing was stored under ambient conditions. To characterize the current status, we measured the bearing’s static and dynamic stiffness in radial and axial directions. Comparing our results to the values measured after the setup of the bearing revealed a stiffness degradation of up to 77%. This decrease is mainly attributed to the degradation of the bearing’s superconducting bulks and the permanent magnets. Analysis of both components showed clear signs of degradation. The permanent magnetic rotor’s magnetic field is around 19% smaller compared to the original state. The superconducting bulks now only inhomogeneously trap magnetic flux. Critical current calculation based on this data revealed a significant reduction compared to the original measurements. Nonetheless, the bearing allows for a stable levitation.

The green transition to reduce reliance on fossil fuels and minimize global warming is driving an increasing demand for NdFeB permanent magnets. These magnets play a crucial role in electric motors, which power vehicle propulsion, as well as in magnetic brakes, bearings, and other components. Sintered NdFeB magnets bring significant benefits to electric vehicles. Their superior magnetic properties enable electric motors to achieve a high torque-to-weight ratio, enhancing vehicle performance and acceleration. Moreover, their compact design facilitates the creation of smaller, lighter motors, contributing to more streamlined and efficient vehicle designs. These magnets also excel in heat resistance, making them ideal for the challenging conditions within electric vehicle motors. Their ability to operate effectively at relatively high temperatures ensures consistent motor efficiency and reduces the likelihood of component failures. Relatively rapid transformation from internal combustion engine vehicles to electric vehicles also requires a steep change in the demand for and supply of the raw materials used in the production process. Overall, NdFeB magnets are inevitable in modern technology and are found in numerous products and systems we encounter daily.However, NdFeB magnets are prone to degradation in harsh environments due to the low corrosion resistance of both iron and neodymium. Consequently, magnets require corrosion protection since their magnetic properties would be jeopardized due to the degradation caused by the corrosion process. Commonly used commercial coatings are Ni-Cu-Ni-based.The present study investigated the effect of temperature of automotive transmission fluid (ATF) on the corrosion of Ni-Cu-Ni coated neodymium-iron-boron permanent magnets. ATFs are complex mixtures containing various additives designed for the automatic transmissions performance. The compounds react with each other to form a stable lubricant surface. Hydrocarbons in mineral oil themselves do not cause corrosion, but the presence of water content, sulphur molecules and acid compounds can cause a chemical attack on the surface of sintered NdFeB magnets and their coatings. Therefore, additives can be chemically aggressive, potentially exacerbating the corrosion of NdFeB magnets. In particular, sulphur compounds, which are inherently contained in the purified mineral oil and originate from the ATF compositions, are highly corrosive to the metal of electric circuits and NdFeB magnets. After exposing materials to higher temperatures (ranging from 80 to 140 degrees Celsius) for extended periods, the changes in the composition of ATF were analyzed using different methods of organic analysis (nuclear magnetic resonance and liquid chromatography with mass spectrometry). On the other hand, the changes in microstructure, morphology and chemical composition of the Ni-Cu-Ni coatings were investigated using scanning electron microscopy with energy-dispersive X-ray spectroscopy. As reference materials, copper and nickel metals were studied.The results show that the temperature of automatic transmission fluid has a decisive effect on the protective ability of Ni-Cu-Ni coating deposited on NdFeB magnets.Acknowledgements: This study was part of the project financed by the Gremo i-Motion programme (No. 12816). The financial support by the Slovenian Research and Innovation Agency (ARIS) is also acknowledged (core programme funding P2-0393).

Decoupling control of neural network inverse system based on improved online learning Levenberg–Marquardt for 3-DOF hybrid magnetic bearing

Comparison of the Characteristics of φ140 mm Superconducting Magnetic Bearings with Ring-shaped Permanent Magnets and Laminated Superconductors with Different Magnetization Directions for Application in Submersible Pumps

Nonlinear dynamics of a geared rotor system supported by active magnetic bearings

In the field of rotating machinery, such as marine propulsion shafting, magnetic bearing-supported propulsion systems have garnered significant attention due to their non-mechanical contact advantages. To address the problem that the design of magnetic bearing controllers, based on theoretical models, neglects the dynamic characteristics of practical components like power amplifiers and displacement sensors, making it difficult to achieve ideal performance in practical applications, this paper proposes a control method for Hybrid Magnetic Bearings (HMBs) that combines a time-domain identification model with robust control. The method first models the power amplifier, HMB, and displacement sensor as an equivalent single system and obtains its high-precision transfer function model by performing system identification on its time-domain data using the least squares method. Based on this foundation, a PID controller is designed using the loop-shaping method to enhance the system’s robustness and control performance. Both simulations and experiments on an HMB test rig confirmed the controller’s effectiveness. The system showed excellent levitation, dynamic stability, and disturbance rejection, with experimental results closely matching simulations. The experimental results are consistent with the simulation results. This method provides a practical and feasible technical approach for enhancing the control performance of magnetic bearing-supported propulsion shafting.

Abstract Superconducting magnetic bearings (SMBs) provide contactless operation for rotating applications like ring spinning. However, their lateral stiffness might be insufficient to reduce the amplitude of coupled vibrations during operation. This study systematically investigates small-scale permanent magnet (PM) arrangements to enhance the lateral bearing stiffness. Therefore, three exemplary designs were experimentally and numerically analyzed: a single PM, an antiparallel PM pair, and a Halbach arrangement, focusing on their impact on lateral restoring forces. The characterization combined magnetic field profile measurements and restoring force measurements under field-cooling conditions. For the numerical analysis, a 3D hybrid H-φ formulation model was applied, incorporating the anisotropic properties of bulk superconductors and tape stacks. The 3D simulation model was successfully validated against the experimental data, enabling the accurate calculation of acting forces between the PM arrangements and the superconductors. Additionally, a derived 2D model is used to optimize the PM geometries within a defined 15 mm × 6 mm design space. As a result, a optimized Halbach array was found showing an about four times higher restoring force in comparison to the standard single PM reference magnet. Alternatively, an antiparallel PM pair can be used showing a lateral stiffness, which is more than twice as high as the reference.

Inverstigation on the lateral force of superconducting magnetic bearing with multi-surface levitation by H-φ formulation

To effectively suppress vibrations in an active magnetic bearing flexible rotor system, we propose an optimal control strategy based on virtual co-location and state feedback decoupling. First, we develop the mathematical model of the system using the finite element method and employ modal truncation to simplify the system order. This reduces the number of state variables and facilitates controller design. Next, a Luenberger full-dimensional state observer is employed to correlate the displacement at the sensor position with that required at the active magnetic bearing position, achieving virtual co-location of the system. Subsequently, employing the state feedback decoupling method, the active magnetic bearing flexible rotor system with complex multivariable coupling is resolved into four independent single-input, single-output subsystems. Based on this framework, the system’s stability and bearing air gap are imposed as constraints, while the overshoot, settling time, and vibration amplitude of control system are taken as the optimization objectives. An evaluation function is then constructed based on the specific importance assigned to each optimization criterion. The multidimensional visualization method is applied to optimize the controller parameters of the decoupled subsystem, identifying the optimal feasible region for the control parameters P and D . Subsequently, a system simulation model validates the control performance of the proposed strategy. The findings demonstrate that the control algorithm effectively mitigates vibrations in the active magnetic bearing flexible rotor system, exhibiting traits of robust stability, minimal overshoot, rapid adjustment, and high resilience to interference. Compared with the traditional decentralized PID control, the maximum amplitude of the active magnetic bearing flexible rotor system with the control strategy proposed in this paper can be reduced from 20 µm to 5.4 µm in the full speed range.

Traditional active magnetic bearing power amplifiers usually adopt hard-switching circuit topologies with simple structures and strong practicability. However, such topologies suffer from high switching losses and easy generation of current noise. To address these issues, this paper proposes a soft-switching power amplifier topology for active magnetic bearings. By employing soft-switching technology, zero-voltage notches are generated through an auxiliary resonant circuit, enabling the switching transistor s to turn on and off at the zero-voltage notch moment, thereby reducing switching losses and improving system efficiency. The working principle of the soft-switching power amplifier topology is analyzed in detail, and the proposed scheme is verified through system simulation and experiments. Results show that the soft-switching power amplifier can effectively reduce switching losses and current noise, while its dynamic performance and operating bandwidth are comparable to those of traditional hard-switching power amplifiers. With an output current of 3 A, the efficiency of the soft-switching power amplifier can be enhanced by 10%.

Abstract Ring-spinning is one of the most commonly used processes to produce yarn but faces limitations due to friction in the ring/traveler system; innovations such as superconducting magnetic bearings have significantly increased spindle speeds to 50,000 rpm, leading to the necessity of continuing yarn dynamics research. Traditional models for yarn balloon dynamics involve complex formulations, but a spring-mass chain approach simplifies the analysis while maintaining essential behaviors. In this work, different effects were added to the spring-mass approach, such as air drag, contact with the control ring, and the flow of fibers through the yarn. The addition of the drag force leads to a three-dimensional yarn balloon in steady state. The contact between the control ring and the yarn balloon is modeled as a rigid body contact using a spring. Moreover, the distribution of the yarn tension was analyzed for different cases. The final steady-state solution worked as a point of equilibrium for linearizing the system and analyzing the natural oscillations. Additionally, the influence of fibers flowing through the yarn path was tested using the impulse-momentum equation, showing that the flowing material effect can be neglected.

Active Magnetic Bearings (AMBs) are inherently nonlinear because of the complex interaction between magnetic forces and the position of the suspended rotor or load. To achieve stable bearing operation, AMBs require the integration of controllers, sensors, and power electronic drives within a closed-loop configuration. Since a closed-loop AMB system consists of multiple components with varying parameters, careful design and coordination are essential to ensure reliable performance. Therefore, a small variation in those variables affects its performance. The input voltage, the inductance of the electromagnetic coil, the mass of the rotor, the air gap between the actuator and rotor, and controller settings are some of the most important factors. This paper suggests a closed loop active magnetic bearing system, as well as the necessary components. A hardware model of an active magnetic bearing system is created, and a linearized transfer function is calculated using the physical parameters’ values. Using this transfer function in conjunction with a lead controller, the influence on the closed-loop functionality of the proposed AMB system is examined by modifying the key variables. As a result, sensitivity and performance analysis of the system is performed in this manuscript. Further, an experimental step-up is formed to verify the simulation results.

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 () 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 , while requiring merely 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.

Theoretical Contribution to multiphysical modeling of flywheel energy storage systems with a focus on thermal effects in magnetic bearings

Control Strategy for Hybrid Magnetic Bearing Based on Improved Cascaded Reduced-Order Active Disturbance Rejection Controller

In this paper, the multi-objective optimization of the 12-pole radial active magnetic bearing (RAMB) is investigated. In the optimization of the RAMB, the decision-maker is more interested in the Pareto-optimal solutions in a certain region. This paper proposes a decomposition-based and preference-based multi-objective evolutionary algorithm (MOEA/D-Pref). The proposed MOEA/D-Pref not only allows the number of Pareto-optimal solutions to be more concentrated in the region of interest but also preserves solutions in other regions. These preserved solutions enable decision-makers to observe a more complete Pareto front, thus gaining more comprehensive insights. In this paper, a mathematical model of the 12-pole RAMB is established, and, with the help of this model and the proposed algorithm, the optimal design of the 12-pole RAMB is completed. The difference between the current stiffness coefficients of the optimized RAMB, calculated by the proposed algorithm and by the finite element method, is 2.3%. The difference between the displacement stiffness coefficient of the optimized RAMB as calculated by the proposed algorithm and by the finite element method is 3.9%. These differences, being less than 4%, are relatively low and verify the reliability of the mathematical model established.