Studies Of The Static And Dynamic Characteristics Of High-temperature Superconducting Levitation Body Based On The Finite Element Method

High-temperature superconducting(HTS)Maglev realizes stable levitation of vehicle body through magnetic field interaction between HTS bulk and permanent magnet guideway(PMG).HTS,as one of the most revolutionary frontiers in the field of rail transit,offers the advantages of suspension/guidance integration,no inherent magnetic resistance,reliable structure and so on.This thesis was under the support from NSFC,studying the static and dynamic characteristics of HTS Maglev.(a)A two-dimension translational symmetry maglev electromagnetic force model is derived by using vector potential method and magnetic field intensity method respectively.The finite element method(FEM)and the finite difference method(FDM)are used to discrete the partial differential equation in space and time respectively,and the improved conjugate gradient method is used to solve the equation.(b)Two numerical models of HTS Maglev are compared.The results indicate that the vector potential method has relatively weak dependence on the finite element grid.Under the same condition,meanwhile,the number of grids to be divided by the magnetic field intensity method is about 4 times of that by the vector potential method with a lower calculation speed.When the levitation force is calculated,the results can be more accurate by employing vector potential method;as for the guiding force,the accuracy of its calculation and simulation of the hysteresis effect can be well improved by adopting the magnetic field intensity method.(c)At present,the loading capacity of HTS Maglev is insufficient.In this thesis,the size of PMG is globally optimized.The maximum levitation force is obtained under the condition of fixed amount of permanent magnet to improve the load capacity of magnetic levitation system.And the levitation force of the optimized system is increased by about5%.(d)In recent years,the analytical vibration model of HTS Maglev generally tends to use the method of fitting the levitation force/guide force with the ignorance of the nonlinear high-order components,so it can only qualitatively analyze the vibration characteristics with limited guidance value for actual design.In this thesis,on the basis of the numerical model,combined with the electromagnetic constitutive relationship of superconductors and Newton’s second law to establish the vertical and lateral vibration models of the HTS Maglev.(e)Based on this model,this thesis studied the free vibration characteristics of HTS Maglev,the nonlinear stiffness and damping in free vibration process,the drift characteristics and chaos characteristics of HTS Maglev in vertical and lateral direction under pulse excitation and harmonic excitation are studied respectively.The results attest that: First,in the vertical direction,the levitation drift will occur under the harmonic excitation.And the larger the excitation frequency is,the smaller the levitation drift of the system is;the larger the excitation amplitude is,the larger the levitation drift is.Second,in the lateral direction,when the magnetic levitation system is excited by the pulse less than the maximum guiding force,it can return to the stable position.Thirdly,when the harmonic excitation is applied,a small drift will occur and exhibit good stability.Lyapunov exponent is used to study the chaotic characteristics of the system.The results manifest that: when the excitation frequency is small,the system presents periodic motion;when the excitation frequency increases to a certain extent,the system presents chaotic motion;when the excitation amplitude increases,the maglev system will first change from periodic motion to chaotic motion,and then from chaotic motion to periodic motion.(f)This thesis studied the dynamic reponse of of HTS Maglev under the excitation of track irregularity and magnetic field irregularity.In the simulation,magnetization is proposed to simulate the magnetic field irregularity,and the combination of irregularity excitation and the high-temperature superconducting magnetic levitation finite element model is firstly introduced to calculate the irregularity excitation response more accurately.In addition,Sperling stability index is adopted to evaluate the stability of the high-temperature superconducting magnetic levitation system.It is found that the magnetic levitation system has good stability performance under the excitation of uneven magnetic track under different working conditions,which well defines the potential of the maglev system for high-speed operation.(g)The influence factors of restraining levitation drift of HTS Maglev in operation are studied.The results show that the increase of the critical current density can improve the levitation performance as well as the stability of the system,and better restrain the drift.Secondly,external damping can be introduced to improve the dynamic stability of the system.At the same time,some relevant measures in the field cooling process are given to suppress the floating drift.