From the perspective of the development of high-speed railway engineering, the development of high-speed railways in China was briefly reviewed to demonstrate that China must closely combine engineering technology and engineering science, so as to take a lead in high-speed railway engineering. The rapid rising of high-speed railways in China and their paths to the world-leading position were reviewed in terms of incubation, exploration, maturation, and evolution stages. The Fuxing high-speed train is a successful example of indigenous innovation of high-speed railways in China, and it marks a milestone for high-speed railways in China from lagging behind and catching up with, to overtaking high-speed railways in other countries, which initially occupies a world-leading position. The severe challenges to the world-leading position of high-speed railways in China were analyzed, which came from the transformation to higher speed and digitalization in high-speed railways of Germany, France, and Japan and from the high-speed and super high-speed pipeline magnetic levitation systems of Japan and the United States. Proactive countermeasures to these challenges were proposed centered on the strategy of “the wheel/rail connects the world, and superconducting maglev will shape the future”. The trend of development in the high-speed railway age and post-high-speed railway age and the future development of high-speed maglev were looked forward to striving for the best status that high-speed railway in China will retain world-leading position in engineering.

The levitation frame is a key subsystem that carries EMS (electro-magnetic suspension) medium−low-speed maglev trains, which affects the levitation stability, comfort and safety of the train and needs to be studied in depth. According to domestic and overseas current application cases of EMS medium-low speed maglev trains, the technical solutions, and characteristics of (suspension) end-set levitation frame and (suspension) mid-set levitation frame are concluded, and the key technical indexes are summarized. With the combination of current research and development status of levitation frame technologies, the five major technical research contents which are magnetic-rail interaction relationship, motion decoupling capability, dynamics performance, structural strength and levitation redundant design are discussed. In addition, the existing frontier scientific issues and engineering challenges are summarized by sorting out and summarizing the research contents: first, the track gauge should be unified; second, the dynamic magnetic-rail relationship research is lacking; third, the lateral dynamics of levitation frames needs to be studied; fourth, the fatigue strength analysis and test of the levitation frame is insufficient; fifth, the levitation frame mechanical structure redundant design scheme is less.

The electrodynamic suspension (EDS) train has the advantages of high speed, large suspension gap, and high safety factor. It has a bright application prospect in the field of ultra-high-speed maglev trains. The on-board superconducting magnet is one of the core components of the superconducting EDS train, and its reliability in service is the basis for the safe operation of the train. In this paper, the development history and status of EDS trains in China and abroad were summarized, and the structure and technical solutions of on-board superconducting magnets in global EDS systems were compared and summarized. The high-temperature superconducting (HTS) magnet technology has become an important development direction in the field of superconducting EDS. The thermal and vibration stability of the on-board superconducting magnet system during the running of the train is an important factor affecting its reliable service. The closed-loop operation technology of HTS magnets, the structural design of lightweight and miniaturized cryogenic systems, and that of high-strength and low heat leakage support devices will be the key technical problems that need to be studied and solved for the on-board superconducting magnets in superconducting EDS systems in the future.

In order to reduce the excessive power consumption of vehicle electromagnetic active suspension, a modified linear quadratic regulator (LQR) control strategy considering energy consumption was raised. Firstly, the structure of electromagnetic active suspension was introduced. The thrust model of the linear motor was established by the equivalent magnetic circuit method, and the dynamic model of electromagnetic active suspension was built. Secondly, based on the optimization model of weighting coefficients in the original LQR control strategy, a constraint condition considering energy consumption was put forward, and a modified LQR control strategy was designed. Finally, MATLAB/Simulink was adopted for simulations, and the correctness of the controller was verified by active force values. Energy consumption and dynamic performance in random road were compared. The results show that the active force value of the modified LQR control strategy meets the optimization constraint condition with a probability of 99.89%. Compared with the original LQR control strategy, the modified LQR control strategy reduces the root-mean-square (RMS) of power by 80.29%. In addition, there is no significant difference in the RMS of suspension working space, and the RMS of dynamic tyre deformation is 5% lower than that of the original LQR control strategy. The reduction of body vertical acceleration can still reach more than 50% of the original LQR control strategy.

At present, the decoupling control research on maglev rotor systems is mainly based on rigid rotor systems, but the elastic mode of the rotor cannot be ignored under high speed and high support stiffness. Aiming at the decoupling control problem of maglev flexible rotors, this paper first built a flexible rotor model, simplified the model by modal truncation method, and obtained the decoupled system through state feedback decoupling; then an internal model controller was designed based on the decoupled system, and the state observer was designed according to the characteristic that the state variables were not easily obtained by the sensors; finally, the decoupling effect of the system was simulated. The simulation results show that the displacement response of the uncoupled system contains multiple frequency components related to the natural frequency of the system, while that of the decoupled system only contains the same frequency component of the excitation; the mechanical coupling within the same coordinate plane has decreased from the order of 10⁻⁵ m to ${10^{ - 6}}$ m, and the coupling between the two radial directions caused by the gyroscopic effect has decreased from the order of ${10^{ - 6}}$ m to${10^{ - 19}}$ m, with both mechanical coupling and gyroscopic effect coupling effectively controlled; the standard deviation of the distance from the axis to the reference point during stable levitation has decreased from $6.52 \times {10^{ - 9}}$ m to $6.38 \times {10^{ - 12}}$ m, and the operation fluctuation of the system is smaller after decoupling; when the rotor accelerates and is disturbed by noises, the system response is no longer affected by the natural frequency and always remains stable; the state feedback decoupling is also effective for different control methods.

In order to improve the overall performance of the ultra-high speed permanent magnet electrodynamic suspension system, multi-objective performance optimization was carried out based on three important indexes: lift-to-weight ratio, lift-to-drag ratio, and suspension stiffness. Firstly, the transverse continuation of the permanent magnet electrodynamic suspension system was carried out, and a three-dimensional electromagnetic force model was derived. In addition, the finite element simulation was performed. Then, in view of the multi-objective optimization problem involving lift-to-weight ratio, lift-to-drag ratio, and suspension stiffness, a parallel optimization strategy based on “system + subsystem” architecture was proposed to obtain the optimal system performance in the sense of linear weighting. Finally, the experimental platform of “Halbach permanent magnet array + flanged aluminum turntable” was built, which demonstrated the effectiveness of the above optimization strategy in improving system performance. Research results show that the suspension force error between theoretical analysis and simulation results is less than 8%, and the error of magnetic resistance is little. By optimization design, the lift-to-weight ratio is increased by 75.50% from 11.0 to 18.3; the lift-drag ratio is increased by 7.50% from 3.5 to 3.8; the suspension stiffness of the unit mass permanent magnet array is increased by 235.94% from 6.1 kN/m to 20.6 kN/m.

To study the power generation characteristics of linear harmonic generators for high-speed maglev trains, based on the space harmonic method, the magnetomotive force distribution model of superconducting coils is proposed, and the magnetic induction intensity distribution formula of superconducting coils in three-dimensional space is deduced. Secondly, the induced magnetic field of the suspension coil current is calculated based on the electromagnetic coupling relationship between the suspension coil and the superconducting coil, and the fifth harmonic magnetic field of the suspension coil is analyzed that to be used for collecting the inductive current. Further, the fifth harmonic magnetic field of the suspension coil is used as the excitation of the collector coil, and the analytical expression of the induced electromotive force of the collector coil is deduced. Finally, taking the MLX01 maglev train on the Yamanashi line in Japan as the engineering background, the numerical analysis value, finite element simulation and the measured data of the Yamanashi line in Japan are used for comparison. The research results show that the relative errors between the analytical values of the magnetic induction intensity, the induced electromotive force and collecting power of the superconducting coil, the finite element simulation and the measured data are all within 10%, which verifies the validity of the magnetomotive force distribution model and the analytical model. When the train speed is more than 100 km/h, the current of the suspension coil and its induced magnetic field tend to be saturated; the induced electromotive of the collecting force coil is approximately linear with the running speed of the train, and the collecting power has a quadratic nonlinear relationship with the speed; when the train speed is 500 km/h, the collecting power is 43.3 kW; the train speed reaches the target collecting power of 25.0 kW at 380 km/h, which ensures the reliability of the on-board power supply of the maglev train.

Electromagnet provides suspension force for medium−low-speed maglev train. When the electromagnet moves relatively to a rail, eddy current is generated on the rail. The external magnetic field generated by the track eddy current offsets part of the original magnetic field generated by the electromagnet, causing the decrease of the suspension force provided by the electromagnet. Firstly, the formation of rail eddy current and ​its effects on air gap magnetic field are analyzed at different vehicle speeds. The influence of train speeds on the suspension force is further studied. Secondly, the laminated F-rail is used to suppress eddy current effect. Combined with the mechanism of the laminated F-rail lifting suspension force, the influence of rail eddy current on the suspension force is analyzed with the F-rails of different laminated layers. Finally, the electromagnet structure of Changsha Maglev Fast Line is simulated by using finite element software. The results show that the laminated F-rail can reduce the rail eddy current, and the air gap magnetic field gradually approaches the one under static conditions. When the coil at the end of the electromagnet model moves at the speed of 120 km/h, the suspension force is 5.7 kN without the non-laminated F-rail and 7.5 kN with the laminated F-rail of two layers, increasing by 30% compared with the case of the non-laminated F-rail.

A self-learning model reference adaptive control strategy was proposed to solve the problems of unknown nonlinear force and uncertain transfer function of levitation controllers, which were caused by track irregularity in electromagnetic levitation trains. The tunable parameters in the control algorithm were adjusted according to the system state, error, and time, so as to make the gap stabilize at a constant value. In order to avoid slow adjustment of tunable parameters, the learning rate was dynamically adjusted according to the error of target gaps, so as to guarantee that the gap fluctuation was smaller during stable levitation. The stability of the model reference adaptive control system was confirmed by a Lyapunov framework, and the proposed control strategy was simulated by MATLAB/Simulink. The results show that the root-mean-square error (RMSE) of the gap of the self-learning model reference adaptive control algorithm is 0.12, and setting appropriate initial values of tunable parameters and limiting their amplitude can improve the robustness of the controller. When the algorithm is tested on a single levitation frame, the acceleration signal is obtained by the controller. The rising and adjustment time of the proposed algorithm is 1.21 s and 2.04 s, respectively. It proves that the learning rate of the method can be adjusted dynamically, which improves the adaptive ability of the controller.

In order to investigate the effect of the scale of a tube train on wave systems, wake vortices, and aerodynamic loads, three model scales (1∶1, 1∶5, and 1∶10) were established based on computational fluid dynamics（CFD） software, and two types of suspension gap relationships (constant relative gap between tracks and constant absolute suspension height) were considered. The improved delayed detached eddy simulation (IDDES) turbulence model and the overlapping mesh method were utilized to simulate the train’s dynamic motion in the tube, and wind tunnel test data were used to validate the numerical method and mesh strategy. The study results demonstrate that as the train scale (Reynolds number) increases, the front piston region lengthens, and the wake disturbance region shrinks in extent; Reynolds number has less effect on vortex pair evolution in the near wake region, but in the far wake region, vortex pair pulsation becomes stronger as the train scale decreases, and the difference in vortex pair strength leads to differences in the normal shock wave pattern in the rear of the train; the maximum positive and negative pressure values on the train surface increase as the scale of the train increases; the suspension gap has less influence on the maximum positive pressure value, but it is positively correlated with the maximum negative pressure value. The scale effect affects the aerodynamic drag from both pressure drag and friction drag. The friction drag of the whole train and the pressure drag of the head and middle trains are positively related to the Reynolds number; the pressure drag of the tail train, however, is influenced by the strength of the attached shock wave in an opposite way. Both train scale and suspension height significantly affect the lift. Compared with the full-scale model, the 1∶10 model (suspension height of 20 mm) has a 3.82% reduction in maximum positive pressure, a 3.94% increase in maximum negative pressure, an 8.64% increase in total drag, a 101.56% reduction in the lift of the head train, and a 15.88% increase in the lift of the tail train.

Extracorporeal membrane oxygenation (ECMO) can replace human heart and lung work and create opportunities to save lives. ECMO has made outstanding achievements in defending against the novel coronavirus pneumonia and has thus been called a lifesaving appliance. In view of the power source of ECMO, namely the maglev artificial heart pump, its maglev system and contactless high-efficiency magnetic coupling driver were studied. The maglev artificial heart pump was controlled by a multi-input and multi-output intelligent control system to realize variable speed and stable operation. The experiments of pressure, flow, and speed of the maglev artificial heart pump were carried out. The developed maglev artificial heart pump was used for three days of animal experiments and active withdrawal. The results show that the extracorporeal maglev centrifugal pump shows excellent stable operation characteristics and keeps the speed unchanged; the pressure difference between the inlet and outlet does not change much when the flow rate varies greatly. The pressure difference between the inlet and outlet of the extracorporeal maglev centrifugal pump can reach 750 mmHg at a speed of 5 000 r/min, which has a wide working range. After 15 days of continuous reliability experiments, all test parameters conform to the law of characteristic curves. During the test, the vital signs of the sheep were monitored and were stable after the machine was removed, which verified the effectiveness and safety of the developed maglev artificial heart pump applied in ECMO.

In order to improve the levitation force and enhance the safety of high-temperature superconducting pinned maglev trains, an improved rail-holding suspension frame system was proposed. Firstly, the levitation force between high-temperature superconductor arrays and permanent magnet guideways was calculated based on the equivalent processing method. The levitation forces of high-temperature superconductor arrays and permanent magnet guideways were also measured by the levitation force test device, which validated the equivalent processing method experimentally. Then, the levitation force of the improved suspension frame system was obtained based on the equivalent processing method. According to the relationship between levitation force and levitation gap, the dynamic model of a single improved suspension frame was set up under track irregularity harmonic excitation. The amplitude-frequency equation was derived by linear differential equation theory. Lastly, the influence of running velocity and damping on the steady-state amplitude was investigated. The feasible domain of damping under the maximum running velocity was obtained. The results show that the steady-state amplitude is dependent on the running velocity and damping under a certain mass, stiffness, and track irregularity wave length and amplitude. In addition, the steady-state amplitude increases as the running velocity improves, or as the damping decreases. With the maglev safety index as the constraint, the damping should be more than 6 905 Ns/m under the maximum running velocity of 600 km/h.

In order to solve model uncertainty and susceptibility to external disturbances of the maglev ball system, a global fast terminal sliding mode control (GFTSMC) method based on a terminal sliding mode disturbance observer (TSMDO) was proposed. Firstly, the mathematical model of the maglev ball system was analyzed, and its dynamic equation was established. Then, a TSMDO was designed to observe and estimate system disturbances. It was proven that the estimated disturbance error of the observer converged in finite time. Secondly, in order to overcome the influence of system uncertainty and external disturbance, a global fast terminal sliding-mode controller (GFTSMC) based on a TSMDO was developed to realize the global fast convergence. The designed control law did not include switching terms, which could weaken the chattering and improve the anti-disturbance and robustness of the system. Finally, the effectiveness of the proposed TSMDO-GFTSMC was verified by simulation. The results show that compared with the continuous sliding mode control method based on the extended state observer, the response time of the maglev ball floating is shortened by 0.38 s, and the displacement deviation is reduced by 90%. The tracking error is reduced from 0.420 mm to 0.032 mm. The proposed method improves the observation accuracy against disturbance, optimizes the control effect of the maglev ball system, and enhances the robustness of the system.

To investigate the quasi-static force-relaxation characteristics of a YBCO bulk levitated above a Halbach permanent-magnetic guideway, using the top-seed-melt-texture-growth method, the complete relaxation process is defined and divided into the excitation process (involved initial state, dynamics process, and termination state), relaxation process, and steady state. With the same initial and termination states, the effect of different displacements of the dynamics process on the steady state is experimentally investigated using a specialized apparatus. Then, on the basis of magnetization and the Anderson-Kim model, a relaxation model is established and several laws are formulated. The results indicate that the steady states of the four displacements tend to be the same. However, the maximum levitation force (MLF) is affected by the round-trip times and displacement velocity. The MLF points are distributed around a curve that decays logarithmically with time. Prior to the relaxation process, the levitation force of the terminating state is positively correlated with the velocity; the steady state results after the relaxation process tend to be consistent. Furthermore, after the relaxation process, the influence of the velocity on the MLF is greatly reduced (the MLF difference decreases from 3.7 N to 2.0 N). Relaxation phenomena are in both the excitation and relaxation processes of superconductors, and the effect of the velocity and round-trip times on the MLF is manifested in the relaxation during the excitation process.

A novel permanent magnet electrodynamic suspension system is proposed to improve the guidance ability and reduce the drag force. First, a three-dimensional electromagnetic-force analytical model considering the longitudinal end-edge effect of the magnets is established and solved. Second, a three-dimensional finite element model is built. Compared with simulation results, the accuracy and reliability of the analytical model are verified. On the basis of the finite element model, the time domain characteristics of electromagnetic forces and the coupling process between the magnets and the guideway coils are analyzed. Finally, the levitation performance and levitation-drag characteristics of the system are studied according to the levitation-to-weight ratio and the levitation-to-drag ratio. Compared with those of a flat-type electrodynamic suspension system, the results reveal that the proposed system is feasible, with a simple structure, low energy consumption, and large levitation-to-drag ratio. The system overcomes issues associated with a weak guidance ability and a low levitation-to-drag ratio. In the high-speed range, the levitation-to-drag ratio can reach 65, which is 2.5 times higher than that of planar permanent magnet electrodynamic suspension. The proposed system and the corresponding three-dimensional analytical model can lay a foundation for future maglev transportation.

In order to explore the influence of the electromagnet remanence on the vertical electromagnetic force of EMS medium−low-speed maglev train, firstly, the change rule of the relative permeability of electromagnet is analyzed, and the levitation model of a single electromagnet is established based on the equivalent magnetic circuit method. Secondly, the limit hysteresis loop state of the levitation electromagnet is studied according to the Jiles-Atherton Hysteresis Theory, and the dynamic effect of the electromagnet remanence is analyzed. Finally, the vertical electromagnetic force is verified by the electromagnetic force bench test, and measures to maximize the use of electromagnetic efficiency are proposed. The results show that when the coil current is 0−20 A, the levitation electromagnet remanence is approximately equal to a constant, and the main influence factor of vertical electromagnetic force is the coil current. When the coil current is 20−40 A, the levitation electromagnet reaches the magnetic saturation state, and the levitation electromagnet has the maximum residual magnetism due to the limit hysteresis state, and the maximum difference is about 1 kN. With the further increase of the coil current, the reduction of the relative permeability of levitation electromagnet gradually weakens the remanence effect.

In order to analyze the electromagnetic force characteristics of high-speed maglev electromagnets more accurately and efficiently and achieve good matching with control and dynamics models, a modeling method of electromagnetic force of high-speed maglev electromagnets based on nonlinear materials was proposed. Firstly, when the equivalent magnetic circuit (EMC) model of the electromagnet was built, the nonlinearity of the magnetic material was considered, and its reluctance was calculated based on the internal magnetic flux. The analytical model of the electromagnet was derived, with voltage and gap as input and current and electromagnetic force as output. The characteristics of the electromagnetic force, gap, and current were calculated and compared with traditional EMC models. Secondly, a finite element method (FEM) model of the electromagnet was built to validate the results of the nonlinear EMC model. Finally, the electromagnetic force of the maglev electromagnet was tested on a ground test bench, verifying the accuracy of the EMC and FEM models. The research results indicate that compared with that calculated by the traditional electromagnetic force model, the electromagnetic force calculated by the EMC model in this paper will experience saturation in the high current range, which is closer to the actual situation and has a wider application range. Under the magnetic gap of 12.5 mm and current of 50 A, the electromagnetic force deviation between EMC and FME is only 4.5%, and it is highly consistent with the test results. Therefore, the high-precision nonlinear electromagnetic force model lays the foundation for joint analysis of dynamic characteristics and parameter optimization of levitation systems.

In order to effectively reduce the natural frequency of systems and realize the strong attenuation of external vibrations in multiple frequency bands, a magnetic suspension vibration isolation platform with quasi-zero stiffness was designed, in which the permanent-magnet and electromagnetic hybrid actuator was the negative stiffness structure, and an active vibration control system based on fuzzy PID (proportional integral differential) algorithm was implemented. Firstly, based on the theory of quasi-zero stiffness, the scheme of the magnetic suspension vibration isolation platform with quasi-zero stiffness was designed through characteristic analysis and parameter calculation; secondly, the model of the magnetic suspension vibration isolation system was established, and the active vibration control strategy based on fuzzy PID algorithm was designed to actively adjust the equivalent stiffness and damping of the system; finally, an active vibration control system was developed based on the Speedgoat real-time target machine. A vibration isolation test platform was built, and a series of vibration isolation performance tests were carried out. The results show that the magnetic suspension vibration isolation platform with quasi-zero stiffness can actively adjust PID parameters by adopting a fuzzy PID control strategy and dynamically adjust the equivalent stiffness and damping of the system. When the external vibration frequency is 20–100 Hz, the vibration attenuation rate is greater than 80%; when the external vibration frequency is 100–500 Hz, the vibration attenuation rate is greater than 90%.

Traditional magnetorheological dampers involve sedimentary working media, high sealing requirements, rapidly increasing damper stiffness, and serious energy consumption attenuation under medium- and high-frequency excitation. In order to address these problems, a magnetorheological composite material with excellent settlement stability and low sealing requirements was prepared and tested, and an improved Herschle-Bulkley model was established to characterize the mechanical properties of the composite material. Furthermore, a shear magnetorheological damper was designed and manufactured based on the composite material, and the performance response law of the damper under medium- and high-frequency excitation was tested by designed experiments. The results show that the dynamic stiffness of the damper increases from 4.87 × 10⁵ N/m to 6.29 × 10⁵ N/m when the test frequency is increased from 5 Hz to 20 Hz under the current excitation of 3 A, and the single-cycle energy consumption of the damper under the full-band is about 0.04 J, which verified the energy consumption capacity of the designed magnetorheological damper under medium- and high-frequency vibrations.

In order to detect data-driven anomalies of the suspension system in medium-speed maglev trains, firstly, the paper introduced an anomaly detection method based on parameterized residuals. Secondly, in response to the lack of prior information on anomalies in the current suspension system, the paper established a confidence set for the health data and anomaly data of the suspension system and determined the anomaly detection and evaluation function and threshold for the suspension system. Thirdly, to minimize the missed detection rate of anomalies at a fixed anomaly false alarm rate, the paper designed an optimal parameter vector from a mathematical perspective and constructed an anomaly detection algorithm for the suspension system based on the minimum missed detection rate. Finally, taking the operational data of the suspension system in the Changsha Maglev Express as an example, the paper detected the gap mutation anomaly, rail smashing anomaly, and acceleration sensor anomaly of the suspension system. The experimental results show that the proposed method can detect all three typical anomalies at a false alarm rate of 5%, without any missed detections of the three anomalies or false detections of normal data segments. The maximum anomaly detection delay is 0.2 s.

Based on the newly discovered interaction behavior between a permanent magnet and a superconducting coil, a novel superconducting energy conversion/storage device is proposed with a structure of a permanent magnet and a closed superconducting coil. Several groups of experiments with different trajectories and speeds of the magnet are carried out. When the magnet is at different positions, the interaction force between the magnet and the closed superconducting coil and the current in the superconducting coil are measured and analyzed to validate the principle of the proposed device and clarify the function properties. When the magnet is stationary, the current attenuation in the coil over time is measured to obtain the operating loss characteristics of the device. Results show that the proposed device can realize the conversion from mechanical energy to electromagnetic energy to mechanical energy without additional generator/motor, and the energy conversion efficiency can reach more than 90%. This indicates that the proposed device is promising in applications such as regenerative braking of urban vehicles and electromagnetic aircraft ejection.

This paper aims to improve the torque performance of a flywheel motor and reduce its permanent magnet cost. Firstly, according to the operating mode of the flywheel battery, the design requirements of the flywheel motor were proposed, and the output torque, torque ripple, and consumption of permanent magnets were selected as the design objectives. On this basis, the equivalent magnetic circuit method and finite element method were used to calculate the main size and performance of the motor, and the appropriate number of slots and poles and initial structural parameters were determined. Secondly, the correlation coefficient method was utilized to analyze the correlation between the structural parameters of the motor and the optimization objectives, and the priority of rotor sizes and stator sizes was divided reasonably. Finally, the finite element surrogate model and the multi-objective optimization algorithm, namely the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) were used to optimize the design parameters step by step, and the correctness of optimization results was verified by the field-circuit co-simulation method and prototype experiment. The results show that the proposed method of parameter priority division can reduce the sampling of data points in the optimization process and shorten the time of finite element analysis in the whole process. After optimization, the back electromotive force of the motor is more trapezoidal. The torque ripple is reduced by 40%, and the consumption of permanent magnets is reduced by 8%.

A novel magnetic spring element with high static stiffness and low dynamic stiffness was designed to address the conflict between low natural frequency and high bearing capacity in the field of low-frequency vibration isolation. First, the spring force and stiffness models of the magnetic spring were built based on electromagnetic field theory and molecular current method; secondly, the dynamics model of the system was established, and the influence of coils with different currents on displacement transmissibility was analyzed and compared with the equivalent linear spring; finally, an experimental prototype was developed, and an experimental study was carried out. The simulation and experimental results show that the air-gap stiffness curve of the magnetic spring presents a nonlinear relationship of being initially flat and then sharp, which indicates obvious characteristics of high static stiffness and low dynamic stiffness. The stiffness is approximately linear with the current. The magnetic spring can achieve a wide range of stiffness adjustment by changing the current, and the stiffness response is rapid; when no current is applied, the starting vibration isolation frequency and peak transmissibility are decreased by 26% compared with the equivalent linear spring. When a negative rated current is applied, the starting vibration isolation frequency and peak transmissibility are reduced by 41%.

Magnetic fluid seal of integrated pole shoe has promising prospect. To study the factors affecting its pressure resistance, the structural parameters of the integrated pole shoe are analyzed. First, the pressure resistance formula of the magnetic fluid sealing structure is deduced. Second, the finite element simulation is used to analyze the pressure performance of the magnetic fluid seal structure, in terms of thin-wall presence, thin-wall thickness, axial distance between pole teeth and thin wall, and the distribution ratio of multi-stage pole shoe size. Finally, the magnetic fluid sealing device of integrated pole shoe was made, and an experimental platform was built. The results show that the pressure resistance of the integrated pole shoe is slightly smaller than that of the traditional pole shoe, but the difference is trivial; the thin wall thickness and the axial distance between pole teeth and the thin wall are inversely proportional to the pressure resistance of the sealing structure; for the multi-stage pole shoe structure, the length of the pole shoe between the magnets is longer than the pole shoe length on both sides, which is more conducive to the pressure resistance of the magnetic fluid seal.

To determine the mineral separation process for the non-magnetic material precision sorting problem based on the first-order buoyancy of a magnetic fluid, this study examines the stress of non-magnetic objects immersed in a magnetic fluid by changing the distance between the permanent magnet and the magnetic fluid when the permanent magnet is used as a magnetic source. A structural model of automatic flotation separation is then designed. In the design plan, the lifting stroke of the electric scissor lift platform used for the lifting of the magnetic source was 100 mm; different magnetic field strengths can be provided to the magnetic liquid by lifting the magnetic source. Accordingly, a Cartesian robot and an end effector are designed to separate the non-magnetic materials to salvage and separate non-magnetic objects suspended at different heights. Then, the ANSYS Maxwell software is used to conduct two-dimensional and three-dimensional simulations of the design situation. The approximately calculated first-order buoyancy of the non-magnetic objects provides a certain basis for the design of the lifting platform’s load-bearing capacity. The results show that the suspension height of the specified non-magnetic cylinder in the magnetic liquid is 60–70 mm from the bottom of the container according to the simulation data calculation, which provides a theoretical basis for the design of a flotation separation device. A cylindrical permanent magnet with a height of 30 mm and a radius of 80 mm is used to provide the magnetic field. Converting the first-order buoyancy of the non-permeable magnet into density, the density range of the non-permeable magnet that can be floated using this design is approximately 1.65 × 10³‒ 6.66 × 10³ kg/m³.

In order to suppress the unbalance vibration of the rotor system effectively, the electromagnetic damper considering dynamic stiffness was applied to the rotor system in this paper. Firstly, the motion equations of the rotor system were established and nondimensionalized; secondly, based on the equivalent magnetic circuit method, the electromagnetic damper model considering the eddy-current effect was established, and the influence of the eddy-current effect on the stiffness of the electromagnetic damper was analyzed. The particle swarm optimization (PSO) algorithm with nonlinear dynamic adaptive inertia weight was used to optimize the three control parameters of the proportion integration differentiation (PID) of the electromagnetic damper; finally, the dynamic characteristics of the rotor were analyzed. The results indicate that under the influence of the eddy-current effect, the stiffness of the electromagnetic damper dynamically changes. When the speed is 100 kHz, the displacement stiffness and current stiffness decrease by 10.0% and 6.6% respectively; the PID parameters optimized by the PSO algorithm with nonlinear dynamic adaptive inertia weight have great control effects, such as fast response and small overshoot, and they can quickly adjust the deviation of the disk to 0 within 0.1 seconds; compared with static stiffness, the amplitude of the disk increases slightly after considering dynamic stiffness. When the speed is 4 782 Hz, the amplitude of the disk increases by 5.33%; the increase in eccentricity will lead to an increase in the amplitude of the disk. When the speed exceeds 242 Hz, the amplitude of the disk increases almost proportionally to that of the disk eccentricity.

In order to meet the demand for power supply and signal transmission for maglev vehicle gap sensors, a full-duplex simultaneous wireless power and signal transmission (SWPST) method was proposed. Firstly, the full-duplex SWPST system of the maglev gap sensors was established. The S/LCC compensation structure was adopted in the power circuit to stabilize the voltage, and the LC parallel branch was used in the signal receiving circuit to suppress ipsilateral signal carrier interference. Secondly, the power and signal transmission characteristics of the system were analyzed respectively. Then, the voltage gain of signal transmission, the interference of power transmission on signal transmission, and the crosstalk between bidirectional signal transmission were analyzed. In addition, some laws about the influence of system parameters on the transmission characteristics of the system were obtained. Finally, an experimental platform of 20 W was built. The experimental results show that the LC parallel branch in the signal receiving circuit can effectively eliminate the crosstalk between signals, and power transmission has less impact on signal transmission. It is verified that the proposed topology can realize wireless power supply and full-duplex simultaneous transmission of distributing control commands and uploading gap signals for the sensors.