| The simultaneous relative motion of the electromagnetic exciter above a conducting track create velocity dependent lift and drag forces.Due to advantages such as simplicity and reliability,in particular self-stability of the system,this so-called electrodynamic suspension(EDS)system has a great potential for being widely used in high-speed maglev transportation as well as in electro-magnetic launchers.However,in the current analytical method for the linear permanent magnet(PM)EDS system,the calculation errors and uncertainties may be caused to the engineering design since the end effect was nelected in the derived equations.Thus in this work,an analytical modeling method which was expanded by the conventional equations,has been proposed for studying the characteristics of the end effect generated by a linear PM EDS system.Firstly,based on the assumption that there are no normal eddy currents exists in the conducting track after selecting the reference plane,the induced eddy current within the track can be derived by the magnetic vector potential(MVP)and superposition principle.The Fourier sin/cos coefficients of source flux density is calculated via a two-dimensional Fourier transform,and then the general solution of MVP is solved with a combination of the separation of variables method as well as the continuity boundary condition.After obtaining the eddy current distribution with in conducting region,the Maxwell stress tensor is applied for calculating the distribution of force density on the suspension track.After the verification between the developed analytical equations and numerical method,it is noticed that an inaccuracy may be generated in the calculation of lateral force due to the difference between the eddy current distribution of the MVP model and the real distribution within inducting track.Therefore,a developed method of second order vector potential(SOVP)assisted by the truncated region eigenfunction expansion(TREE)is introduced in this work to improve the versatility and accuracy of analytical equations.In order to investigate the unity and difference between the two proposed methods and the existing three-dimensional(3-D)analytical model which is assumed to ignore the end effect of the EDS device.The numerical as well as analytical experiments have been implemented for evaluating the characteristic of the presented EDS topology,especially the topology with linear PM mover and plate type track.The air-gap flux density,eddy current field distribution and electromagnetic forces are verified with the corresponding numerical models,respectively,and after that the applicability of three kinds of analytical methods were discussed in detail.To illustrate the universality of the proposed methods,the device performance of several extra kinds of EDS topology with both translational and rotational velocities have also been investigeted.Furthermore,experimental setups were constructed to simulate both the translational and rotational motion effects of EDS topology,respectively.The validity and accuracy of the generalized method to take the end effect of the EDS track into account,can be eventually demonstrated both numerically and experimentally.For the existing EDS topologies with engineering application potential,the parametric sweep analyses and performance comparison were carried out to evaluated both the advantages and disadvantages between all the typical topologies.Additional,the potential of different EDS topologies was also disscussed under various application conditions.After the performance comparison between various topologies,a novel asymmetrical double-sided topology of an EDS device was proposed in this work,the weight of lift-drug and lift-weight performances can be selected in a balanced way via adjusting the height ratio of the upper and lower PM Movers.In order to optimally select the configuration of the EDS system,an efficient multi-objective optimization algorithm assisted by a gradient enhanced Kriging metamodel with optimally selected basis functions is proposed in this paper.Moreover,typical analytical test functions were applied for investigating the fitting accuracy,the validity and efficiency of proposed algorithm is furthermore demonstrated via the TEAM Workshop Problem 22.The verified surrogate metamodel can be trained by the appropriate model,and finally,the Pareto-optimal solutions of the presented EDS topology were solved in a balanced way via the hybird optimization algorithm. |
