Research On The Characteristic And Stability Control Of Permanent Magent And Electromagnetic Hybrid Halbach Array Electrodynamic Suspension

The permanent magnet electrodynamic suspension(EDS)system uses the vehicle-mounted Halbach permanent magnet array motion to cut the non-magnetic conductor plate track,and produces eddy current in the track,which interacts with gap magnetic field to generate the required levitation force.This system uses the permanent magnet as the magnetic field source and the non-magnetic conductor plate as the track.It has the advantages of simple structure,low construction cost,high reliability and self-stability suspension.However,when the system is disturbed,it is easy to produce vibration,has poor suspension stability,and even can not be self-stability in serious cases because of its own under-damped characteristic.This dynamic characteristic greatly limits its development and application.This paper proposed a permanent magnet and electromagnetic hybrid Halbach array electrodynamic suspension system,and studied its electromagnetic characteristics and suspension stability by the analytical method and simulation analysis.First of all,the suspension stability of the permanent magnet EDS system was studied.We derived the 2D electromagnetic forces analytical expression,analyzed the system suspension stability by using the derived levitation force,and obtained its under-damped characteristic and poor suspension stability.In order to increase the system damping,the suspension stability of permanent magnet EDS system with a passive damping plate was studied.We derived the 2D electromagnetic forces analytical expression of the permanent magnet EDS system with a passive damping plate,analyzed the system suspension stability,and found that the system was still under-damped and the suspension stability was still poor due to the long duration of vibration under the external disturbance.Next,the external magnetic field of the proposed permanent magnet and electromagnetic hybrid Halbach array was studied.Basing on the surface current method and Biot-Savart law,the 2D and 3D magnetic field analytical expressions outside the array were derived.The analytical results were in good agreement with the finite element numerical calculation method.The effects of coil current and width on the external magnetic field were analyzed.Then,the 2D electromagnetic force analytical expression of the permanent magnet and electromagnetic hybrid Halbach array EDS system was derived.The external magnetic field with longitudinal end effect and air gap harmonic of the permanent magnet and electromagnetic hybrid Halbach array was decomposed into the superposition of sinusoidal magnetic fields by the Fourier transform.The vector magnetic potential equations were established and the boundary conditions were used to solve the vector magnetic potentials produced by each sinusoidal magnetic field cutting the conductor plate track.And then the analytical solutions of system magnetic field and electromagnetic forces were obtained.The corresponding 2D finite element numerical calculation model has been established to verify the correctness of the analytical solution.The effects of coil current and width on the levitation force were analyzed.Once more,considering the influence of the system transverse width,the 3D electromagnetic force analytical expression of the permanent magnet and electromagnetic hybrid Halbach array EDS system was derived.The second-order vector magnetic potential equations were established.Using array source magnetic field and the magnetic field boundary conditions,the second-order vector magnetic potentials of each region were obtained.And then the analytical expressions of system magnetic field and electromagnetic forces were derived.The corresponding 3D finite element numerical calculation model has been established to verify the correctness of the analytical solution.The effects of coil current and width on the levitation force were analyzed.Finally,the acceleration feedback suspension controller of the permanent magnet and electromagnetic hybrid Halbach array EDS system was designed,and the suspension stability of the system under the track and load disturbance was simulated and analyzed.The simulation results showed that the acceleration feedback suspension controller based on the3 D and 2D levitation force analytical expression could make the system have good suspension stability under the external disturbance.So it proved that the proposed permanent magnet and electromagnetic hybrid Halbach array EDS system could overcome the under-damped problem of the permanent magnet EDS system.