| It is an important strategic decision to accelerate building a strong transportation network in China,raising significant needs for developing the high-speed magnetic levitation(Maglev)technology.The superconducting electrodynamic suspension(EDS)is the only Maglev technology that has achieved a manned speed of 603 km/h up to date,becoming one of the primary development technology for ultrahigh speed rail transit.The onboard superconducting magnet provides the suspension,guidance,propulsion and braking forces for EDS train,being the key component of the train.Compared to the low-temperature superconducting magnet,the high-temperature superconducting(HTS)magnet possesses higher operating temperature and avoids the use of liquid helium,making the liquid-helium-free superconducting EDS train available.In recent years,several countries including Japan,Korea and China have begun the researches on the HTS EDS technique.Japan had fabricated a real-scale HTS EDS magnet.The research in China started relatively late.To promote the development of HTS EDS technique,this paper carried out the following researches.For the racetrack structure of HTS EDS magnet,based on the assumption of uniform current density and Biot–Savart’s law,through discretization of both the cross-section and centerline of the magnet,three analytical models,i.e.line current model,surface current model and volume current model,were established to calculate the magnetic fields of racetrack HTS magnet.These analytical models were validated against finite element method(FEM)model.It was proven that these analytical models improve the computing efficiency at least three times than the FEM model in terms of calculating the magnetic field at any point in space.A comprehensive comparison was conducted on the computational accuracy and efficiency for these analytical models.In terms of the racetrack magnet with elliptical segment,the linear current analytical model has the highest calculation efficiency,and the surface current analytical model has the highest calculation accuracy.The volume current analytical model has the advantages of high computational efficiency and accuracy for the racetrack magnet with circular segment,and is more suitable for calculating the magnetic fields of HTS EDS magnet.Furthermore,the magnetic field distribution of racetrack HTS magnet was investigated.It is found that the maximum magnetic field(Bmax)firstly decreases and then increases as the elliptical coefficient of the elliptical segment of the magnet enlarges.Besides,when the elliptical coefficient is less than 1,the position of Bmax will change,which provides a significant reference for the estimate of the critical current(I_c)of racetrack HTS magnet.An improved self-consistent model was established for estimating the I_c of racetrack HTS magnet.The modeling efficiency and computing accuracy are improved by using the homogenized modeling technique and Dirichlet boundary condition.The effect of both the size of Dirichlet boundary and the number of homogenized bulk on the estimate result of I_c was analyzed.It is found that a smaller size of Dirichlet boundary corresponds to a higher computing accuracy,and the calculation efficiency is inversely proportional to the number of homogenized bulk,while the calculation error is less dependent on the number of homogenized bulk.With the Japanese MLX01 EDS train as a practice,compared with the original self-consistent model,the I_c calculation error of the improved self-consistent model is less than 0.5%,while the calculation efficiency is improved by an order of magnitude.Based on the improved self-consistent model,it is found that the adjacent magnets and ground coils have a week impact on the I_c of HTS EDS magnet.That is to say,the I_c of HTS EDS magnet that is composed of multiple magnets connected in series is approximately equal to the I_c of an individual magnet under the self-field.For calculating the electromagnetic forces between the superconducting magnets and nullflux suspension coils,a 3-D FEM model and a semi-analytical model were established.In the 3-D FEM model,the Dirichlet boundary condition is used to simulate the magnet movement,which avoids the use of moving mesh and simplifies the modeling.In the semi-analytical model,the calculation accuracy of inductance and electromagnetic forces is improved though discretizing the cross-section of magnets and suspension coils.Correctness of the two models was verified by comparing the measured data from the Japanese Yamanashi test line.Based on the established models,the induced current in suspension coils and the electromagnetic force density distribution in the superconducting magnets were studied,followed by the analyses on the mean electromagnetic forces acting on the magnets under different operating conditions of the EDS train.It is found that when the train occurs a lateral displacement,the induced current flowing in the four loops of cross-connected suspension coil presents varied peak values and both the maximum and minimum peaks appear in the lower loops.The drag force and suspension force density are respectively located on the semi-circular segment and straight segment of the EDS magnet,while the guidance force density is located in the whole magnet.In order to improve the computational efficiency of the model without compromising the computational accuracy,at least two magnetic poles are needed to simulate.In consideration of the application conditions of EDS train,a conduction-cooled HTS EDS magnet was designed and fabricated.At first,the geometric structure and parameters of HTS coils were optimized,and the coil skeleton was designed from two aspects of improving the cooling effect and mechanical strength.Afterwards,two HTS coils were wound and their critical currents were measured under 77 K,followed by the determination of the operating temperature of the HTS magnet.Then,from the aspects of material selection,structure design and strength check,a conduction-cooled cryogenic vessel was designed.Finally,the cryogenic system was fabricated and the HTS magnet was assembled.Calculation shows that the thermal contraction on cooling is a primary factor leading to the stress and deformation of the HTS magnet.Besides,the total AC loss produced by HTS coils during the magnet excitation has a week effect on the magnet temperature.An experimental platform was built in order to evaluate the multiple performances of the HTS magnet.The coil voltages and losses versus the exciting current were measured,and the temperature coupling relationship among these key metal components in the magnet was revealed,as well as the magnetic field distribution and electromagnetic force properties of the magnet were analyzed.It is proved that the HTS magnet can be cooled to 14.3 K and the exciting current has reached to 240 A.When the train runs at a speed of 110 km/h,the suspension force of the magnet can reach 5 kN,and its saturation value is around 5.5 kN.In summary,the primary parameters of the magnet have reached the overall design goal,validating the reliability of the optimization design method.A FEM model was established utilizing the vector magnetic potential method to calculate the eddy current losses of the HTS magnet when subjected to the travelling magnetic fields generated by ground propulsion coils.Numerical investigations were conducted on the spatial distribution of traveling magnetic fields and the ensuing eddy current density in the magnet,and the impact of the frequency and amplitude of traveling magnetic fields on the eddy current losses.An experimental rig was set up for testing the losses and temperature rise of the HTS magnet under the travelling magnetic fields.Based on the experimental rig,the temperature distribution of the magnet was measured and the thermal coupling relationship among key components in the magnet was elucidated.Through combining the simulation and experiment,the variation tendency of the temperature of the magnet as the frequency and amplitude of travelling magnetic fields was predicted.It is found that under the excitation of travelling magnetic fields,the temperature of the magnet shows an overall upward trend.The temperature rise of the radiation shield is the most significant with the same temperature rise in its each plate,but the temperature rise of the coil case is very small and negligible.As the increase of the frequency and peak of travelling magnetic fields,the temperature rise of the radiation shield,the first-stage cold head of the refrigerator and the HTS current leads all increase monotonously.Besides,the temperature rise of the radiation shield will make the temperature of the first-stage cold head rise,which brings the temperature rise of HTS current leads.To reduce the temperature rise of key components in the magnet,it is suggested that the radiation shield and cryogenic vessel are made of high conductivity material. |
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