As a typical representative of the new rail transit technology, magnetic levitation (maglev) transport has the advantages of no mechanical contact wear, high running speed, being safe and reliable, environment-friendly and so on. After 60 years of development, maglev transport is gradually becoming mature. Firstly, the developments of maglev trains at home and abroad were reviewed. Subsequently, permanent magnet suspension (PMS), electromagnetic suspension (EMS), electrodynamic suspension (EDS), and high-temperature superconducting pinning levitation (HTSPL) were presented from the structural principles, core technologies, and application fields. Then, the suspension characteristics, suspension gap, electromagnetic force calculation, and technology maturity of these four magnetic levitation modes were described. After that, eight key problems for the development of the 600 km/h high-speed maglev train were proposed which include construction of test platform, motor control strategy, emergency braking, line maintenance, wireless energy transmission, wireless communication, aerodynamic noise, and maglev turnout. Finally, the research progress and the research topics of ultra-high-speed evacuated tube transportation system were discussed and prospected.

In order to investigate the small curve negotiation performance of high-speed maglev trains, the flexible vibration of the levitation chassis is explored, and the finite element model of levitation chassis is established to calculate its elastic modes; then the dynamics model of the high-speed maglev vehicle is built. According to the track conditions, speed curve and fitted track irregularities from Tongji University’s maglev test line, the influence of flexible vibration of levitation chassis is analyzed on the gap and electromagnetic force of guidance and levitation electromagnet. Meanwhile, a dynamics model of a rigid levitation chassis is built for comparison purpose. The results show that the dynamic performance of electromagnet is greatly affected by flexible vibration of the levitation chassis when the negotiating curve has a smaller radius of 400 m. The difference of the guidance force between the two models is about 12.5 kN, while the difference of the levitation force is 6.0 kN or so. The comparison with the simulation demonstrates that the results from the model of the levitation chassis flexibility is more close to the test results. The main frequencies of the vertical and lateral levitation chassis vibration are 10.4 Hz and 13.2 Hz respectively, which are similar to modal frequencies of relative pitching and anti-phase yawing between the front and rear levitation frame. The flexibility of levitation chassis should be taken into account in the key issues of high-speed maglev trains, such as control parameter optimization, suspension parameter optimization, and running stability.

In order to study the influence of key parameters of the main beam of a low-medium speed maglev turnout on the coupled vibration of the vehicle-turnout system, modal tests of the main beam of maglev turnout are carried out in various conditions, and a vehicle-turnout coupling dynamic model considering the elastic vibration of the main beam of turnout is established for numerical simulation analysis of the levitating stability. First, the modal characteristics of the turnout main beam are modified through comparisons between simulation and experiment. Based on the modified vehicle-turnout coupling dynamic model, the influence of different design parameters of the maglev turnout main beam on levitating stability is then studied. The results obtained are as follows: The intermediate bogie can be equivalent to a 50 MN/m elastic constraint to meet the ideal error requirements, and the two-bogie support scheme is easier to avoid the resonance frequency between vehicle and turnout than the three-bogie support scheme. With the increasing of the first-order vertical bending frequency of the main beam, the stability range of the levitating control parameters becomes smaller; when the first-order vertical bending frequency of the main beam of turnout is greater than 12 Hz, the phenomenon of vehicle-turnout coupled vibration is more likely to occur. As the stiffness of the turnout main beam increases, the stability range of the levitating control parameters becomes smaller. Besides, increasing the structural damping ratio of the turnout active beam can only reduce the vibration amplitude but cannot solve the coupling resonance problem between vehicle and turnout. It is also found that the higher the linear density of the turnout main beam, the less likely the vehicle-turnout resonance is to occur; when the linear density is lower than 1500 kg/m, the levitating stability range drops sharply. In addition, a greater equivalent support stiffness of the intermediate bogie leads to a smaller stability range of the control parameters, but the influence range is small.

In order to study the effect of bridge flexibility on the dynamic response of medium-low-speed maglev vehicles running on a horizontal curve with a curve radius of 70.0 m, a comparative analysis of the vehicle dynamic response through a flexible bridge and a rigid track is carried out. Firstly, a spatial dynamics vehicle model with 122 degrees of freedom is established, and the two-dimensional magnet/rail relationship with active levitation and passive guidance characteristics is considered in the model. Secondly, a horizontal curve finite element model consisting of flexible bridges is developed by using a parametric modeling method of three-dimensional Timosheko beam. Finally, the rigid-flexible coupled dynamic model of the vehicle-curve bridge system is constructed with the connection of levitation forces. The results show that, the self-oscillation characteristics and dynamic displacement response of the 17.0 m span circular-curve bridge meet the requirements of relevant standards. Compared with the case of a vehicle passing the rigid track, the dynamic response of the vehicle system under the influence of the flexible bridge is more drastic, and evident in the lateral dynamic response of the vehicle system, while the difference in the response of the levitation gap and the vertical acceleration of the car body is smaller, and the curve passing ability of the vehicle will be overestimated in the case of the rigid track. The maximum lateral displacement of the electromagnet calculated with the flexible bridge and rigid track models does not exceed 6.0 mm, and the levitation gap fluctuates within ±4.0 mm of the rated value, indicating that the vehicle has a good curve passing performance in the comparison analysis.

Maglev trains are subjected to great aerodynamic lift force when running at high speeds, especially the tail car, which may deteriorate the suspension performance and even cause the suspension control system to fail. All these will affect the ride comfort and operation safety of high-speed maglev trains. Therefore, it is urgent to study and improve the lift force characteristics of the tail car of high-speed maglev trains. To this end, a numerical simulation of the high-speed maglev train is carried out in comparison with a wind tunnel test, and the surface pressure coefficient of the train obtained through numerical simulation is in good agreement with the wind tunnel test results. Then, aerodynamic wings (aero-wings) are installed to improve the aerodynamic lift force performance of the tail car, and the influence of the angle and number of the aero-wings on the aerodynamic characteristics of the tail car is studied. The results show that the aerodynamic lift force of the wing decreases with the increase of angle when only one is installed, but the aerodynamic lift force of the tail car decreases first and then increases. Moreover, the lift force of the tail car is the smallest when the aero-wing angle is 12.5°. Compared with the original maglev train, the aerodynamic lift force coefficient of the winged train is reduced by 3.9%, while the resistance of the aero-wing and the tail car is slightly increased. On the basis that the tangent angle between the aero-wing and the car body remains unchanged, multiple 12.5° aero-wings are installed on the tail car. The aerodynamic resistance of the aero-wings at different positions is basically the same, and the aerodynamic resistance of the tail car increase as the number of aero-wings increases. However, the aerodynamic lift force of the aero-wing at different positions is different, which decreases toward the tip of the nose. The aerodynamic lift force of the tail car first decreases with the increase of the aero-wing number and then stabilizes. Finally, the aerodynamic performance of the maglev train with two aero-wings is found relatively better. Compared with the original maglev train, the aerodynamic lift force of the tail car is reduced by 4.6%, and the resistance of the whole vehicle is only increased by 1.4%.

In order to solve the controller parameter tuning problem caused by the complex nonlinearity of the maglev train levitation system model, a data-driven fast parameter tuning method for the maglev train levitation system is proposed, which is based on only the input and output data of a single levitation tuning of the levitation system. First, the open-loop instability and complex nonlinearity of the levitation system are analyzed by modeling of the maglev train levitation system. Aiming at the problem of determining the reference model in the virtual reference feedback tuning method, estimation of the closed-loop response is then used to realize the data-driven controller parameter tuning. Considering that the interference noise in the data will affect the tuning of controller parameters, a data noise suppression method of maglev system based on signal projection is proposed. Finally, taking a single-rail levitation system for example, the effectiveness of this data-driven parameter tuning method for maglev train levitation system was verified through the single-rail levitation experiment. The results show that the open-loop instability and complex nonlinearity of the suspension system will bring great difficulties to the rapid adjustment of parameters; the noise suppression method based on signal projection can reduce the variance of noise data by 54.1%; and the parameter tuning method based on data driven technique can quickly set the controller parameters of the suspension system. Compared with the PID feedback control system with only coarse tuning under the initial conditions, the step response overshoot of the system after parameter tuning is reduced by 72.0%, the square error integral (ISE) is reduced by 79.8%, and the absolute error integral (IAE) is reduced by 54.5%.

In order to scientifically and accurately analyze and evaluate the ability of electromagnetic high-speed maglev train passing through the plane curve line, a novel quantifiable evaluation index system is proposed based on fuzzy comprehensive evaluation method by using the state information of guide gap, current and acceleration in maglev train operation. The evaluation index is proposed to analyze and evaluate the active guidance ability of the train under different curve radiuses, running speeds and payloads. The effectiveness of evaluation results is verified by the actual line test. The results indicate that the active guidance ability of the electromagnetic high-speed maglev train is closely related not only to the ability of the guidance system itself, but also to the line radius, running speed and other factors. The proposed method is able to evaluate the active guidance ability, and provide a reference basis for verifying the actual utility and application boundary of the guidance system.

Aiming at the on-board power supply requirements of high-speed maglev trains in economy and reliability in narrow spaces, utilizing the coupling magnetic circuit, electrical performance simulation, and design optimization, a new type of transmitter, a non-contact power supply system (inductive power supply, IPS), is proposed, which features a multi-turn coil at the transmitting end, no magnetic core, and pickup ends similar to a double U-shaped coupled magnetic. First, according to the power supply requirements of high-speed maglev trains, the main parameters of each device are determined through theoretical calculations, and the IPS system design plan is completed. Then design and simulation analysis of the coupling magnetic circuit is conducted, including the use of Maxwell software to perform 3D simulation analysis on various coupling magnetic circuits, determining the optimal design scheme of the coupling magnetic circuit, and three-dimensional electromagnetic simulation to obtain the mutual inductance between the pickup device and the ground transmitting coil. Next, electrical performance simulation analysis is conducted with the use of Matlab software to establish an electrical simulation model of the IPS system, simulate the transmission power and efficiency of the IPS system, and determine the compensation device, ground inverter power supply and DC/DC parameters according to the power supply requirements. Finally, the 150 kW magnetic-field coupling contactless power supply system was developed and deployed on the maglev prototype test line. The on-site EMC (electromagnetic magnetic compatibility) performance and electrical performance test verification was completed. The transmission power exceeds 150 kW and the efficiency is 92%, achieving the expected objectives of the project

Application of the magnetic levitation technology in ultra-clean transmission can effectively reduce dust pollution. The permanent magnetic levitation platform with a variable flux path has the characteristics of low-power consumption and anti-adsorption, which can avoid the large temperature rise in electromagnetic levitation systems and poor safety of hybrid electromagnetic levitation systems. To avoid the instability in the floating, three floating control methods are presented and validated, which are decentralized control, centralized control and integral separation. At first, the magnetic-force control mechanism of the platform is analyzed to build its dynamic model, and the decentralized control strategy is adopted to realize the floating. Furthermore, a 3-DOF centralized control strategy is proposed to prevent platform tilt, in which the vertical controller is PD (proportional differential) and the rolling and pitching are controlled by PID (proportional integral differential). Finally, the integral separation method is used for subsection control to realize the accurate vertical positioning. The results indicate that the centralized control method realizes the self-correction of the platform tilt angle with the adjustment time of 0.5 s, which solves the platform tilt caused by the magnetic characteristics difference of each pole in the decentralized control. Moreover, when using the integral separation method, the vertical steady-state error of the platform can be reduced from 0.23 mm to 0 with the adjustment time of 3.0 s.

In order to study the multi-degree-of-freedom coupling problem in the magnetic levitation platform system, a design idea of using passive force between permanent magnets to reduce the active control in the vertical direction is proposed, and the structure design of a repulsion maglev platform is given. The stator of the magnetic suspension structure studied is composed of permanent magnet and electromagnetic coils. Its characteristic is that the permanent magnet provides the main suspension force, and the electromagnetic coils provide the horizontal driving force, so as to reduce the number of coils responsible for active suspension, and reduce coil power consumption and heat generation. Firstly, the Laplace equation satisfied by the scalar potential was derived based on the magnetic charge model, the analytical expression of the scalar potential was obtained by using the separation variable method. And the force of the float in the whole magnetic field was accurately calculated. Next, the stable region of passive suspension force between stator and mover permanent magnet was fully studied and discussed, the decoupling of the force in the vertical direction was simplified and ignored, and the mathematical model of the controlled object was established. The digital integrated controller centered on the micro-control unit was developed. The levitation performance of the platform was studied by experiments. The research results show that the hybrid repulsion maglev platform proposed in this paper can realize the stable motion control of the above float within the horizontal range of ± 4 mm of the suspension height of 23 mm, and can realize the stable horizontal motion, and the displacement change of the float in the vertical direction does not exceed 0.2 mm.

Aiming at the problem of nonlinear and difficult to establish accurate mathematical model of a single-degree-of-freedom magnetically levitated system, the model-free adaptive control method based on full-format dynamic linearization (FFDL-MFAC) was applied to a single-degree-of-freedom magnetically levitated system. Firstly, model-free adaptive control algorithm, pseudo gradient estimation algorithm, pseudo gradient reset algorithm and dynamic data model of single degree of freedom magnetic levitation system were used to design the controller of single degree of freedom magnetic levitation system. Then the influence of MFAC control parameters on the control effect of the single-degree-of-freedom magnetically levitated system and the response characteristics of step response signal, interference signal and noise signal are analyzed by simulation, and the experimental verification was carried out on the magnetic levitation ball experimental device. Finally, the experimental verification was carried out on the magnetic levitation ball experimental device. The results show that the FFDL-MFAC method only needs to collect the I/O data of the single-degree-of-freedom magnetically levitated system under the working state, and does not need to establish an accurate mathematical model of the single-degree-of-freedom magnetically levitated system. The high precision and stable suspension control can be realized by setting the parameters of the model free adaptive controller, and the controller has good adaptability and robustness. Compared with PID, FFDL-MFAC reduces the overshoot of the system by 0.005, and the root mean square error of stable suspension displacement is reduced by 0.2607.

As to the problem that traditional signal point suspension control method of maglev train lacks consideration of coordination and synchronization of multiple electromagnets, a novel coordination control method is developed through tracking error cross-coupling. The novel method can reduce tracking error and synchronization error of multiple points suspension system and enhance anti-disturbance ability at the same time. Firstly, through dynamic analysis, the dynamic equations of four electro magnets (two control modules) suspension system considering unknown disturbance are established. Secondly, in order to estimate and compensate the unknown disturbance of the system, a disturbance observer is introduced. Next, considering the coupling dynamic characteristics of adjacent electromagnet control modules, a sliding mode coordinated controller of error cross coupling is designed. Finally, the asymptotic stability of the closed-loop system is proved without linearization. The experiments show that the presented control method can compensate the coordination relationship of electromagnet modules, suppress the effect of disturbance, reduce the synchronization error by 40%, and inhibit the coupling disturbance between electro magnets significantly.

Aiming at the problems of slow response speed and poor anti-interference ability of the traditional linear sliding mode control (LSMC) for electromagnetic levitation systems, a levitation control method based on adaptive non-singular terminal sliding mode control (ANTSMC) is proposed. The proposed method introduces an adaptive controller into the terminal sliding mode control (TSMC) to take its advantage of insensitivity to disturbance in sliding mode control. The convergence law coefficients in the sliding mode control are adjusted on line by adaptive control to improve the dynamic performance of the levitation system. First, a mathematical model of the electromagnetic levitation system is established. Then the stability of the designed controller is proved by Lyapunov stability theory. Finally, simulation and experimental verification are carried out. Experimental results show that the system with ANTSMC has a faster response speed and a smaller steady-state error in signal tracking. For sinusoidal or sawtooth interference with peak to peak value of 2 N, air gap fluctuations can be limited to 0.2 mm. The air gap fluctuates 0.6 mm during the 0.1 kg loading and unloading experiments. Generally the proposed levitation controller based on ANTSMC has better performance than those based on TSMC and LSMC.

In order to study the suspension stability of the electrodynamic suspension (EDS) with permanent magnet (PM) and electromagnet hybrid halbach array under different control methods, Firstly, the 2D levitation force analytical expression was derived by using the electromagnetic field theory and the corresponding finite element model (FEM) was built to verify the suspension force analytical expression. Secondly, the vertical dynamic model of the system was established, and the fixed air gap PID controller and variable air gap PID controller based on the air gap feedback were designed respectively. Finally, the system suspension air gap and current density waveforms under external disturbances were simulated and analyzed. The simulation results indicate that both controllers can make the system suspend stably at the rated state and have the same dynamic process under the 1 mm track settlement disturbance. When the system is disturbed by the ± 1000 N disturbing force, the fixed air gap PID controller can make the system suspend stably at the 30 mm rated air gap, and apply the steady state coil current of 2.12 A/mm² and −2.17 A/mm² respectively. The variable air gap PID controller makes the system suspend stably at 28.5 mm and 31.6 mm respectively, and applies the steady-state coil current of 0.

In order to study broadband vibration isolation and make a system have better vibration isolation performance, a compound vibration isolation system combining electromagnetic suspension isolation and mechanical spring isolation is proposed. First, a dynamic model of the designed vibration isolation system is established, and the control characteristics of the linearized model are analyzed. Aiming at the problem of system vibration control, a controller design scheme based on active disturbance rejection technology is then presented, and the active disturbance rejection control of system is realized by simulation. Finally, the feasibility of the control scheme is verified on a compound vibration isolation platform. The experimental results show that the control system in 0−10 Hz frequency band can achieve good performance of low-frequency tracking, the amplitude attenuation increases gradually in 10−100 Hz, and the vibration isolation effect in 100−300 Hz frequency band exceeds −14.9 dB. The control scheme proposed in this paper provides a new idea for the control of the compound vibration isolation system.

Electromagnetic suspension (EMS) type maglev trains adjust currents of suspension electromagnets through maglev choppers and then control the suspension force to keep the car body stable suspension. The suspension electromagnet current ringing generated by the maglev chopper will increase the switching loss, cause electromagnetic interference (EMI), and even affect the suspension control. Studying the suspension electromagnet current ringing’s generation mechanism is helpful to find its suppression measures. An equivalent circuit model of suspension electromagnet is proposed in view of the current ringing characteristics. Firstly, the general form of the suspension electromagnet’s impedance function is derived by the driving-point function method. Then, based on the suspension electromagnet current’s unit-step response characteristics, the simplest expression of the impedance function and the corresponding equivalent circuit model are determined. Next, the influences of different circuit parameters on current ringing characteristics are analyzed by discriminant and simulation methods. Finally, with the same suspension electromagnet, the simulation and experimental waveforms of the current ringing are compared. The results show that for the specified parameters, the current ripple amplitude, ringing peak value, and ringing frequency of the suspension electromagnet obtained from the experiment are 9.7%, 20%, and 11% lower than the simulation results, respectively. In addition, the simulated current ringing attenuation time is about 1 μs, which is close to the experimental results. The simulation and experimental results of the suspension electromagnet current ringing are in good agreement in terms of the amplitude, frequency, and attenuation characteristics, validating the proposed circuit model.

To reduce the mechanical contact of scroll compressor during operation, a novel permanent magnetic compliance mechanism is proposed according to the structural characteristics of oil-free scroll compressor, and its mechanical properties are analyzed. Firstly, the working principle of the permanent magnetic compliance mechanism is analyzed, the magnetic force model is established by the virtual displacement method, and the magnetic induction intensity at the working air gap of permanent magnetic compliance mechanism is analyzed by using theoretical formula, finite element simulation and experimental measurements. Secondly, the relationship between structural parameters and mechanical characteristics of permanent magnetic compliance mechanism is analyzed by theoretical formula calculation and finite element simulation. Finally, the mechanical properties of the permanent magnetic compliance mechanism are verified by the performance parameters of the magnetic scroll compressor and the magnetic force test. The results show that within a certain range, the radial magnetic force of the permanent magnetic compliance mechanism is proportional to the radial displacement and inversely proportional to the axial displacement. Radial displacement has approximately linear relationship with stiffness coefficient when permanent magnetic compliance mechanism works. Within the working distance, the minimum axial magnetic force of the single group magnetic ring with permanent magnetic compliance mechanism is 8.73 N, and the radial force on working trajectory is 4.8 N, which meets the working requirements of the magnetic scroll compressor.

The suspension magnetic force of electro-permanent magnets features strong nonlinearity, which is closely related to the magnet structure. The existing analytical calculation formula for magnetic force of the hybrid magnet ignores the influence of magnetic circuit leakage and some other factors, consequently resulting in big errors in actual calculations. To solve this problem, two common hybrid magnetic circuit models are established to analyze the influence of edge magnetic flux distribution and magnetic circuit leakage on the working magnetic circuit of the magnet. On this basis, the magnetic circuit equations and related reluctance of the two hybrid magnets are deduced, and a corrected calculation method of the hybrid ferromagnetic force is put forward. Finally, the corrected magnetic force of the hybrid magnets with the two structures is verified by finite element analysis. The results show that due to the large suspension air gap, the influence of magnetic flux leakage of an electro-permanent magnet cannot be ignored in the calculation of electromagnetic force. Using the magnetic force correction formula proposed in this paper, the electromagnetic force errors of magnets with the above two hybrid structures are reduced to 3.8% and 8.3%, respectively.

For timely controlling the gap between poles in electrical discharge machining (EDM), a single-degree-of-freedom magnetic actuator is designed with merits of high precision, fast response, wide frequency band and long stroke. As the local actuator in EDM, it is optimized by a fuzzy PID control method that modify the control parameters online and in real time. Firstly, the dynamic model of the magnetic actuator device is analyzed, and the transformation relationship is built between the coil current and the mover displacement in the magnetic actuator. Secondly, a conventional PID controller is designed according to the characteristics of the magnetic actuator device, and fuzzy control is introduced to optimize the performance of micro-positioning control. Finally, the controller performance is verified by the micro-positioning simulation and experiment on the magnetic actuator. Simulation and experimental results show that the magnetic actuator has a micron-level positioning resolution, a wide frequency band greater than 50 Hz, and a positioning stroke of 2 mm, which fully meets the fine-tuning requirements of EDM.

Aiming at tilt caused by the difference of magnetic characteristics of each MLU (magnetic levitation unit), a permanent magnetic levitation platform is designed for contactless transportation; and an independent cascade control method is presented, which allows integral feedback of air gap deviation. Firstly, the dynamic model and equilibrium conditions of the levitation are analyzed to establish the transformation relationship between the air gap of each suspension unit and three degrees of freedom of the platform. Secondly, given each MLU features, the cascade control system with a double closed-loop is designed, in which the outer loop plays a major regulating role for the air gap, the inner loop works as a follow-up control for the rotation angle, and air gap error among each MLU runs as the integral feedback. Finally, the levitation experiment is conducted to verify the proposed controller. The results show that, when introducing the integral feedback, the air gap of each MLU is the same after levitating, and the air gap increases 0.12 mm synchronously when 0.1 kg of weight is applied to different positions. The platform adjusts the rotational angle to control the difference of magnetic characteristics and fulfill the horizontal levitation under eccentric load. However, the adjusting time of the system is about 1.4 times that of the independent cascade control system without integrated feedback.

Magnetic suspension support-flywheel system is the core component of a flywheel battery system (flywheel energy storage system), its stable operation directly affects the operation quality of the whole flywheel battery device. In order to promote the development of new energy technology in China and accelerate the realization of “dual carbon” goal, based on a large number of cutting-edge research, the complex vibration behavior which affects the operation quality of system is systematically analyzed and summarized. And it is concluded that modal self-excited vibration and forced response vibration are the two main factors leading to the instability of flywheel rotor system. Then based on the two types of unstable factors, the research status of topological structure, dynamic modeling, control strategy, auxiliary protection and other key technologies related to the stable operation of the system are introduced. Moreover, research prospects were proposed for high integration of topological shafting, reasonable ratio of system materials, fault tolerance of auxiliary control, and high reliability of spare bearings. The study provides solutions for the high stability of magnetic suspension support-flywheel system．

In order to reduce the eddy current loss and increase the axial magnetic force for three degrees of freedom axial-radial hybrid magnetic bearings (ARHMB), a thrust bearing made of soft magnetic composite materials (SMCs) in the axial direction was proposed. The Halbach array was introduced at the air gap between the thrust plate and the rotor to enhance the magnetic density of the axial air gap. In the radial direction, the laminated structure was used for the radial bearing. Firstly, based on the dynamic magnetic flux distribution and the equivalent magnetic circuit method, the equivalent reluctance model considering eddy current, magnetic leakage and cross-coupling effects was established. Then, the influence of material types and cross-coupling effect on the equivalent reluctance frequency response and dynamic stiffness was analyzed. Finally, ARHMB was studied by incomplete derivative PID control considering the effect of eddy current, magnetic leakage and cross-coupling. The results show that ARHMB prepared by SMCs can provide greater and more stable magnetic force and larger bandwidth than that made of carbon steel, and has better dynamic characteristics under high-frequency conditions. When considering the cross-coupling effect, the dynamic characteristics of ARHMB made of SMCs have a large change rate at high frequency and cannot be ignored. For low-bandwidth carbon steel bearings, the cross-coupling effect is not obvious. The system of magnetic bearing has a fast response speed, small overshoot, and approximately zero steady-state error, which has good control characteristics.

The magnetic suspension rotor needs to meet the requirements of anti-interference and resonance isolation at the same time, in order to lay the design foundation from the perspective of magnetic bearing structure, the design method of high stiffness magnetic bearing is studied based on the influence of magnetic bearing structural parameters on support stiffness. Firstly, through the derivation of the analytical formula of the stiffness of the magnetic bearing, the influencing factors of the structural parameters on the support stiffness are analyzed, and the optimization direction of the support stiffness is determined; Secondly, the design method of high stiffness magnetic bearing is proposed, and the optimization effect of support stiffness is analyzed; Finally, the feasibility of the proposed method is verified by rotor natural frequency test and compressor frequency rise experiment. The results show that in the compressor prototype, when the magnetic bearing adopts the structure of unequal magnetic circuit area with the tooth yoke width ratio 1.2, the support stiffness of the magnetic bearing under the worst working condition, that is, the maximum control current, can improve by 25% compared with the equal magnetic circuit area, and the compressor can effectively avoid resonance in the operating range, which provides a reference for the optimization design of the support stiffness of magnetic bearing in engineering application.

Aiming at the problems of low efficiency, high cost and large volume of the traditional waste heat power generation equipment, a waste heat generator equipped with the 5-DOF (5-degree of freedom) active magnetic bearing for Organic Rankine waste heat generation system was designed. Firstly, based on the rotor diameter limit and maximum bearing capacity requirements, the structural forms of radial and axial magnetic bearings were determined. Furthermore, the dimensions and performance parameters of magnetic bearings were calculated and checked by one-dimensional magnetic circuit model and two-dimensional finite element analysis. Secondly, in order to ensure the stability margin of the magnetic bearing, a three-level PWM (pulse-width modulation) power amplifier was used to reduce the output current ripple, and an incomplete differential PID controller incorporated with unbalance compensation were used to realize the 5-DOF stable suspension. Finally, the waste heat generator equipped with magnetic bearing was applied to the actual customer site. The reliability of the waste heat generator was verified from three dimensions of stability margin, bearing capacity and shaft peak-to-peak value. The field test results show that the waste heat generator system has operated stably and reliably in all operation conditions, and can achieve full-power generation and long-term operation. The sensitivity function of the magnetic bearing system is less than 12 dB, and the peak-to-peak vibration value of the rotor of the waste heat generator is less than 53 μm, which meet the long-term stable operation requirements of ISO14839. The maximum axial bearing capacity reaches 3 600 N, which meets the requirements of actual working conditions.

Aiming at misalignment vibration detection of magnetic suspension multi-span rotors, the dynamic model of magnetic suspension rotor system and coupling misalignment model are firstly established. Secondly, the rotor misalignment vibration state is simulated based on the multi-span rotors mechanics model, and the speed of vibration signal is identified by second order generalized integrator-frequency locked loop (SOGI-FLL). Furthermore, the speed identification information is input to SOGI for co-frequency notch filtering, and then misalignment vibration detection of magnetic multi-span rotors is performed on the notch signal by SOGI-FLL with prefilter (SOGI-FLL-WPF). Finally, the feasibility of the proposed detection method is verified by the simulation of magnetic suspension multi-span rotors at constant and ascending speeds. The experimental results show that the amplitude and frequency of the vibration signal at double speed frequency caused by rotor misalignment can be quickly identified, which lays a foundation for the application of magnetic suspension multi-span equipment.

To reduce the core loss of six-pole RAHMB (radial-axial hybrid magnetic bearing) at high rotation speeds, a novel partially laminated rotor is proposed. Firstly, the suspension force model of six-pole RAHMB is built by using equivalent magnetic circuit method. The structure parameters of six-pole RAHMB are designed according to the mathematical model of suspension force. The core loss and suspension force under different depths of lamination part are analyzed to select the optimal depth value. Then, in the finite element analysis, the rotation speed of rotor is set to be 50000 r/min, and the maximum radial and axial control currents are injected to six-pole RAHMB respectively to analyze the core losses of the solid rotor and partially laminated rotor when the magnetic bearing generates maximum suspension force. Finally, the eddy current loss and hysteresis loss of laminated rotors are simulated and calculated under sinusoidal disturbance current. The results show that the partially laminated rotor can reduce the core loss by 69.7% while producing the maximum bearing capacity; although the axial bearing capacity is reduced by 14.7%, it still meets the design requirement; besides, the core loss is reduced by 55.4% under sinusoidal disturbance current.

In active magnetic bearing (AMB)-rotor system, the unbalance vibration of system is caused by the uneven mass distribution with respect to the axis. In order to improve the system stability and reduce the unbalance vibration of the rotor at first-order bending critical speed, the mechatronic model of AMB-flexible rotor system considering unbalanced force and unbalanced magnetic pull is established, and combined with the radial basis function (RBF) neural network algorithm, an approximation model of rotor vibration amplitude related to the structure parameters of AMB is obtained. Combined with parametric sensitivity analysis and multi-island genetic algorithm (MIGA), the structural parameters are optimizied with the goal of minimizing the amplitude of rotor vibration. Numerical simulation results show that increasing bias current, area of magnetic poles, number of turns and decreasing air gap within a certain range can increase the system damping, and can reduce unbalanced amplitude at the first-order bending critical speed. The unbalance amplitude is reduced by nearly 50% than before.