Electromagnetic Bearings Research Articles

Nonlinear dynamics and motion bifurcations of 12-pole variable stiffness rotor active magnetic bearings system under complex resonance

In this study, we analyze the nonlinear dynamic characteristics of a 12-pole variable stiffness rotor active magnetic bearings (rotor-AMBs) under intricate resonance conditions. Using the principles of electromagnetic bearings, a model for the 12-pole variable stiffness rotor-AMBs system is developed. Next, the dynamic equations for a two-degree-of-freedom 12-pole variable stiffness rotor-AMBs system are derived, incorporating both quadratic and cubic nonlinearities, through Newton's second law. Considering the primary parametric resonance, 1:1 internal resonance, and 1/2 subharmonic resonance, the multiple time scale perturbation method is applied to derive the average equation of the system. Based on these averaged equations, the characteristics and complex dynamics of the system are analyzed. Finally, MATLAB software is employed for numerical simulations of the 12-pole variable stiffness rotor-AMBs system. The simulation results indicate that the nonlinear control parameters can modify the system's softening and hardening spring behaviors. Varying the parametric excitation amplitude leads to diverse dynamic behaviors, including single-periodic motion, double-periodic motion, and chaotic vibrations.

Determination of the rational shift value the center of the magnetic system electromagnetic bearing

The article sets the task of determining the rational value of the displacement of the center of the magnetic system of an electromagnetic bearing relative to the axis of rotation, at which, with equal currents in opposite electromagnets, the weight force falling on one axis of the bearing will be completely compensated. To achieve the set, the equations of motion of the rotor in the field of electromagnets are considered. It is shown that the rational value of the displacement of the center of the magnetic system is determined from a fourth-order algebraic equation. The analytical solution of Descartes-Euler of this equation is applied. Analytical expressions are found that allow to determine the rational value of the displacement of the center of the magnetic system relative to the axis of rotation according to the known parameters of the electromagnetic bearing. A study was made of the stability of a three-circuit control system of an electromagnetic bearing when the center of the magnetic system is shifted by a rational value relative to the axis of rotation. It is proved that the displacement of the center of the magnetic system by the calculated value does not affect the stability of the control system of the electromagnetic bearing with the settings of the regulators selected for the central position of the rotor.

Optimization Design of Electromagnetic Bearing for Long-life Centrifugal Pump

Aiming at the problems of traditional centrifugal pump mechanical bearing, short life, low speed, and difficulty solving of motion sealing, it is carried out to adapt to the design of electromagnetic bearing design that is suitable for liquid work quality and high pressure, and the rationality of the structural design is verified through electromagnetic field simulation and experimental testing. The results show that: (1) Through electromagnetic field simulation analysis of electromagnetic bearings, under a working gap of 0.3 mm and a working current of 2 A, the electromagnetic force is 129.7 N, meeting the bearing capacity requirement of 124 N; (2) Through simulation analysis of the magnetic field of electromagnetic bearings under different pole arrangements, to reduce the mutual coupling between magnetic circuits, the radial electromagnetic bearings should adopt a circumferential NSSN pole arrangement; (3) Through the analysis of the impact of working current on the performance of electromagnetic bearings, when the current is below 1.8 A, the electromagnetic force is proportional to the square of the current; when the current increases from 1.8 A to 3 A, the electromagnetic force is not obvious with the increase of current, showing nonlinear characteristics. Therefore, when designing the electromagnetic bearing, the maximum magnetic induction intensity selected is generally the critical point of the linear interval, so that the electromagnetic bearing works in the linear interval.

Analysis of the operation of electromagnetic bearings in the difference of the center of the magnetic system relative to the axis of rotation and variations of the supply voltage

The article sets the task of reducing the consumption of electrical energy by electromagnetic bearings. To achieve this goal, it is proposed to shift the center of the magnetic system of bearings that compensate for the weight of the rotor relative to the axis of rotation. The displacement value is assumed to be equal to half the clearance value in the safety bearings of the unit under consideration. A mathematical model of a radial electromagnetic bearing, its design scheme, taking into account the displacement of the center of the magnetic system relative to the axis of rotation, a block diagram of a three-loop control system and formulas for calculating the parameters of regulators are presented. Regulator settings for a specific type of electromagnetic bearings are determined. A calculation model has been developed that makes it possible to study the operation of an electromagnetic bearing when the center of the magnetic system is displaced relative to the axis of rotation and the supply voltage is varied. The results of simulation in the Matlab Simulink software environment of the process of rotor ascent from safety bearings and rotor levitation in a displaced state at different values of the supply voltage are given. It is shown that the voltage reduction by 16.7% ensures stable operation of the electromagnetic suspension of the rotor in all possible modes. Therefore, shifting the center of the magnetic system can reduce the power consumption of electromagnetic bearings by 30%.

Research on magneto-hydraulic proportional control strategy for single degree of freedom supporting system of magnetic-liquid double suspension bearing.

Compared with the traditional active electromagnetic bearing, the additional hydrostatic supporting concept is imported to form magnetic-liquid double suspension bearing (MLDSB) without affecting the support performance. Therefore, the bearing carrying capacity and stiffness are greatly increased and the operational stability and reliability of MLDSB are also improved. The controlling strategy and the regulating mode have the major impact on the safe and stable operation of MLDSB, which directly determines the performance quality. MLDSB adopts the magnetic-liquid coupling supporting mode with electromagnetic suspension as the main and hydrostatic supporting as the supplement, which greatly increases the complexity and difficulty of MLDSB. Therefore, the proportional control strategy and the magneto-hydraulic coupled nonlinear controller of MLDSB are explored in this paper. First, the regulation mechanism of the single degree of freedom (DOF) supporting system is revealed, and the proportional-integral-differential controller of the electromagnetic and hydrostatic closed-loop is designed. Then, the fuzzy control idea is introduced into the single DOF supporting system to design a magnetic-liquid variable proportional fuzzy controller, and the difference between the proportional/variable proportional control modes is compared. Finally, the rotor displacement following characteristics and anti-interference characteristics in the proportional/variable proportional control mode are compared on a magnetic-liquid double suspension test bench. The results show that compared with the proportional control method, the variable proportional control method combines the advantages of fast regulation speed of the electromagnetic system and the stable and reliable advantages of the hydrostatic system. In the same step signal, the rotor can achieve unbiased following under two control modes of proportional/variable proportion, and the adjustment time of the variable proportional control mode is shorter. In two control modes, the rotor can be restored to the original equilibrium position. The maximum offset under the variable proportional control mode is smaller, and with the continuous increase of the displacement, the performance of the variable proportional control method is more obvious. The stability control of MLDSB is provided on the theoretical basis in this article.

Effect of Conical Spiral Flow Channel and Impeller Parameters on Flow Field and Hemolysis Performance of an Axial Magnetic Blood Pump

For a blood pump, the blood flow channel and impeller parameters directly affect the performance of the pump and the resulting blood circulation. The flow channel in particular has a great impact on the hydraulic performance of the pump (e.g., flow and pressure), which directly determines the overall performance of the blood pump. Traditional bearing-supported blood pumps can cause mechanical damage to blood cells, leading to hemolysis and thrombosis. In this study, therefore, we designed a conical spiral axial blood pump with magnetic levitation. The blood pump was supported by electrodynamic bearings in the radial direction and electromagnetic bearings in the axial direction. The impeller and the front and rear hubs were integrated to minimize blood stagnation and reduce the formation of thrombosis. The hub had a conical spiral flow channel design, which not only reduced the size of the impeller but also increased blood flow and pressure while meeting the design requirements. Computational fluid dynamics (CFD) analysis was used to analyze the flow field of the axial blood pump, a power function model was used to establish a hemolysis prediction model, and the particle tracking method was used to obtain the flow trajectories of individual blood cells, thereby predicting hemolysis-related performance of the blood pump. The simulation results showed that the main high shear stress area in the blood pump was located in the impeller inlet and the clearance between the top of the impeller and the inner chamber of the blood pump. When the hub taper angle of the blood pump was 0.72° and the clearance was 0.3 mm, the average hemolysis prediction value was 0.00216. This prediction value was smaller than that of traditional axial blood pumps. These findings can provide an important reference for the structural design of axial blood pumps and for reducing the hemolysis prediction value.

Dynamics and adaptive backstepping control of multibody spacecraft connected with active magnetic bearing

In this paper, to realize the high-resolution observation mission, a new type of multibody optical spacecraft connected with active magnetic bearing (AMB) is introduced. Then, to address the attitude control problem facing high-precision observation for multibody spacecraft, the dynamic model of the multibody system is developed and an adaptive backstepping controller (ABC) is subsequently proposed. First, a high-precision electromagnetic force model of AMB is developed. Different from traditional models that only consider rotor position and current, the relative attitude between rotor and platform is considered. Then, based on the AMB model, the dynamic and kinematic model of multibody spacecraft is derived. Additionally, considering the electromagnetic bearing is unstable statically, an ABC method is proposed. The stability of the closed-loop system is guaranteed by the Lyapunov theorem. Finally, to indicate the effectiveness of the proposed method, some numerical simulations of comparison with the iterative learning control (ILC) method are performed. As indicated by the simulation results, the ABC is capable of eliminating periodic deviation, and it is more effective than the ILC in solving the control problem caused by periodic disturbance.

Research on Fractional-Order Modeling of Nonlaminated Electromagnetic Bearings Considering Eddy Current Effects

Research on Fractional-Order Modeling of Nonlaminated Electromagnetic Bearings Considering Eddy Current Effects

Analysis and testing of a superconducting maglev submersible cryogenic liquid pump

This paper studies a superconducting maglev submersible cryogenic liquid pump (CLP) using superconducting magnetic bearing (SMB). A new structure is proposed for the self-stability of high-temperature superconducting magnetic levitation, and the compact structure of disk motor-pump. The rotor of the axial-flux disk motor is connected with a centrifugal impeller to form an impeller-rotor of the proposed superconducting CLP. Supported by a SMB system, the impeller-rotor rotates frictionlessly with self-stabilisation as a suspension rotor. The SMB system includes a radial-type SMB, an auxiliary permanent magnet bearing, and an electromagnetic bearing composed of the stator and the rotor of disk motor. Theoretical calculations and experimental measurements are performed to examine the axial and radial levitation force behaviours of the SMB system. Then, a kinetic model of the suspension rotor is established and analysed to assure force balance and stable levitation. Finally, a prototype pump is fabricated and an experimental setup for liquid nitrogen transmission is constructed for validation purposes. The experimental tests on the pump head and the flow rate are carried out, which demonstrate the effectiveness of the proposed superconducting maglev submersible CLP.

Comparison of static and dynamic characteristics of electromagnetic bearing using machine learning algorithm

Comparison of static and dynamic characteristics of electromagnetic bearing using machine learning algorithm

Comparison of static and dynamic characteristics of electromagnetic bearing using machine learning algorithm

Comparison of static and dynamic characteristics of electromagnetic bearing using machine learning algorithm

Study on Electromagnetic Structure Design of Electromagnetic Bearing Body for Control Rod Drive Mechanism

The electromagnetic structure design is the core of the design of electromagnetic bearing body for control rod drive mechanism (CRDM). In order to obtain a reasonable electromagnetic structure, a certain electromagnetic structure is selected according to different shapes of magnetic flux distribution, and used to build the analytical model and finite element model for electromagnetic analysis. Then, the working point of the electromagnetic bearing is determined by finite element simulation and analysis, and the key performance parameters, such as current stiffness and displacement stiffness, of the electromagnetic bearing are further analyzed and studied. Finally, cross verification is performed by comparison between the finite element simulation and analysis results and the analytical calculation results. The verification results show that the electromagnetic structure design of the CRDM electromagnetic bearing body is appropriate, and all performance indexes can meet the design requirements.

Electromagnetic Bearings With Power Electronic Control for High-Speed Rotating Machines: Review, Analysis, and Design Example

This article reviews electromagnetic bearings with power electronic control for high-speed machinery, which are termed active magnetic bearings (AMBs). AMB is a contactless-type bearing, which uses magnetic force to support the rotor. This is suitable for high-speed applications, harsh operating conditions, and also clean environments. However, the AMB has nonlinear characteristics and is inherently unstable. Due to recent advancements in fast-switching power devices, high-switching-frequency power converters, high-bandwidth current control, nonlinear control strategies, advanced digital controllers, and sensors, AMBs have become promising for high-speed aerospace, industrial, and energy applications. This article contains a brief tutorial on the AMB, covering its operating principle, system-level block diagram, magnetic-circuit-based analysis, dynamic load due to rotor mass unbalance, load capacity, force slew rate, and response to large force disturbance. Furthermore, a design example of an eight-pole AMB with four excitation coils is presented to achieve a load capacity of 180 N. A preliminary design, based on magnetic circuit analysis, is seen to fall short in terms of load capacity. Iterative changes to the AMB dimensions achieve the required load capacity, but the characteristics are still nonlinear. Finite-element analyses bring out the effects of magnetic saturation on load capacity, linearity between force and current, force slew rate, and relationships between maximum force generated and AMB dimensions. An improved design procedure is presented to achieve both desired load capacity and linear characteristics, while balancing the compactness requirement. The improved design also achieves the desired slew rate besides faster response and improved stability.

Impact-Rubbing Dynamic Behavior of Magnetic-Liquid Double Suspension Bearing under Different Protective Bearing Forms

The magnetic-liquid double suspension bearing (MLDSB) is a new type of suspension bearing, with electromagnetic suspension as the main part and hydrostatic supports as the auxiliary part. It can greatly improve the bearing capacity and stiffness of rotor-bearing systems and is suitable for a medium speed, heavy load, and frequent starting occasions. Compared with the active electromagnetic bearing system, the traditional protective bearing device is replaced by the hydrostatic system in MLDSB, and the impact-rubbing phenomenon can be restrained and buffered. Thus, the probability and degree of friction and wear between the rotor and the magnetic pole are reduced drastically when the electromagnetic system fails. In order to explore the difference in the dynamic behavior law of the impact-rubbing phenomenon between the traditional protection device and hydrostatic system, the dynamic equations of the rotor impact-rubbing in three kinds of protection devices (fixed ring/deep groove ball bearing/hydrostatic system) under electromagnetic failure mode are established, and the axial trajectory and motion law of the rotor are numerically simulated. Finally, the dynamic behavior characteristics of the rotor are compared and analyzed. The results show that: Among the three kinds of protection devices (fixed ring/deep groove ball bearing/hydrostatic system), the hydrostatic system has the least influence on bouncing time, impact-rubbing force, and impact-rubbing degree, and the maximum impact-rubbing force of MLDSB is greatly reduced. Therefore, the protective bear is not required to be installed in the MLDSB. This study provides the basis for the theory of the “gap impact-rubbing” of MLDSB under electromagnetic failure, and helps to identify electromagnetic faults.

Optimum design of an eight pole electromagnetic bearing

The paper aims to give the step by step design procedure of an electromagnetic bearing having eight pole for machine tool applications having the shaft diameter of 20 mm and rotate with the speed of 750 rpm. The mathematical procedure consists of the geometrical as well as constraints due to losses occur in the electromagnetic bearing which makes the designing more accurate. Finally, optimization has been done to get the optimum values of the dimension of the electromagnetic bearing. By interior trust method numerical optimization has carried out to find out the optimum values of the dimensions of an electromagnetic bearing to maximize the electromagnetic force exerted by it. This has supported by a CAD model using Solid Works showing the dimensions of the model. The mathematical model compared with the available literature on electromagnetics bearing and found to be an effective with consideration of all iron and copper losses. The results show the designed bearing can produce a magnetic force of 166 N from each electromagnet on the shaft. For the application an electric hand drill machine has to be taken and an electromagnetic bearing consists of 8 electromagnets has been designed which is capable of generating 29 N of electromagnetic force onto the shaft of the electric hand drill machine.

Performance for rotor system of hybrid electromagnetic bearing and elastic foil gas bearing with dynamic characteristics analysis under deep learning.

The bearing-rotor system is prone to faults during operation, so it is necessary to analyze the dynamic characteristics of the bearing-rotor system to discuss the optimal structure of the convolutional neural network (CNN) in system fault detection and classification. The turbo expander is undertaken as the research object. Firstly, the hybrid magnetic bearing-rotor system is modeled into the form of four stiffness coefficients and four damping coefficients, so as to analyze and explain the dynamic characteristics of the system. Secondly, the ambient pressure is introduced to analyze the dynamic characteristics of the elastic foil gas bearing-rotor system based on the changes in the dynamic stiffness and dynamic damping of the gas bearing. Finally, the CNN is introduced to be applied in the detection of faults of bearing-rotor system through determining the parameters of the constructed CNN. The results show that the displacement of the rotor increases and the stiffness decreases with the acceleration of the speed of the electromagnetic bearing. The maximum displacement of the rotor can reach 135μm, and the maximum stiffness can be reduced to 35×105N/m. Increase of ambient pressure causes enhancement of main stiffness of the gas bearing, and the main damping decreases accordingly. Analysis of the classification accuracy and loss function based on the CNN model shows that the convolution kernel size of 7*1 and the batch size of 128 can realize the best performance of CNN in fault classification. This provides a data support and reference for studying the dynamic characteristics of the bearing-rotor system and for the optimization of CNN structure in fault classification and detection.

The Design of Magnetic Suspended Spiral Sludge Dewatering Machine

The bearings used by the stacked screw sludge dewatering machine are traditional bearings. The use of traditional bearings pollutes the environment. The noise is relatively large, and the energy utilization rate is also low. In the long-term continuous heavy-load operation, the bearings need frequent maintenance, while the maintenance cost is high, and the life of the bearings is generally short. The electromagnetic bearings have advantages of no contact, no need for lubrication, and no friction. They can be used to replace the traditional bearing to solve the key problem of the support of the stacked screw machine. In this paper, the design and development of the electromagnetic bearing structure are carried out based on the performance and technical indicators of a stacked screw sludge dewatering test prototype, combined with its supporting layout and shafting structure. The mathematical model of a rotor with single degree of freedom is established, and the control system is simulated in Simulink of MATLAB. In the simulation of Simulink, through the constant adjustment of PID controller, when the proportional coefficient, integral coefficient and differential coefficient are 20,000, 100 and 1, the rotor can quickly return to the origin (about 0.02s).

Research on vibration compensation control of electromagnetic bearings rotor

Research on vibration compensation control of electromagnetic bearings rotor

Research on vibration compensation control of electromagnetic bearings rotor

Research on vibration compensation control of electromagnetic bearings rotor

Control of hybrid electromagnetic bearing and elastic foil gas bearing under deep learning.

The hybrid electromagnetic and elastic foil gas bearing is explored based on the radial basis function (RBF) neural network in this study so as to improve its stabilization in work. The related principles and structure of hybrid electromagnetic and elastic foil gas bearings is introduced firstly. Then, the proportional, integral, and derivative (PID) bearing controller is introduced and improved into two controllers: IPD and CPID. The controllers and hybrid bearing system are controlled based on the RBF neural network based on deep learning. The characteristics of the hybrid bearing system are explored at the end of this study, and the control simulation research is developed based on the Simulink simulation platform. The effects of the PID, IPD, and CIPD controllers based on the RBF neural network are compared, and they are also compared based on the traditional particle swarm optimization (PSO). The results show that the thickness, spread angle, and rotation speed of the elastic foil have great impacts on the bearing system. The proposed CIPD bearing control method based on RBF neural network has the shortest response time and the best control effect. The controller parameter tuning optimization starts to converge after one generation, which is the fastest iteration. It proves that RBF neural network control based on deep learning has high feasibility in hybrid bearing system. Therefore, the results provide an important reference for the application of deep learning in rotating machinery.