Characteristic Analysis Of Electromagnetic Forces Created By Low-Speed PM Electrodynamic Suspension

Permanent magnet electrodynamic suspension, characterized by simple structure, stable system and high reliability, is one of the most important maglev model. However, this system will create large drag force, and that is why it is not been widely used in transportation. In order to find a good electrodynamic suspension (EDS) method which can be used in urban railway system, general 2D and 3D analytic models were proposed in this paper, and based on these it studied the suspension characteristics of every EDS maglevs, after all, double EDS was considered to be the best urban EDS maglev. So this paper calculated the forces and other characters of this model, which is never studied by other researcher before. And a set of parameters was given to make the system meet the engineering demands.Firstly, based on two different hypothesis, analytic calculation of the outer magnetic field, created by any permanent magnet arrays, has been studied, respectively. The first way, on the basis of Ampere molecular hypothesis, equivalent the permanent magnet by current sheets, and the field can be get, because of Biot-Savart law and superposition principle. On the hand, in line accordance with magnetic charge theory, the magnetic field regard as the effect of magnetic charge, something like the electric charge. So the equations, which are used in electric field, can be used in magnetic calculation similarly, due to the duality principle. Based on these two methods, this paper perfect the 2D analytic solution of linear Halbach field, made it much more accurate at end of the array and in the condition of small air gap. In addition, this paper gave the 3D analytic solution of this array, which is never studied before, and it is highly accurate, proved by FEM.Secondly, a general 2D analytic model, suitable for any permanent magnet electrodynamic suspension, was proposed. Solving the time harmonic magnetic vector potential, we can get the analytic solution of eddy current, consisting of sine wave and conductive plate. According to Fourier series, any magnetic field can be treat as summation of sine waves, so the formulation of magnetic forces and field can be get, at any field.Thirdly, on the basis of 2D solution, a 3D solution model was proposed. We established the equations of second order vector potential (SOVP), and reduced variables when choose the right coordinate system. Separation of variables was employed to solve those equations, yields, the formulations of fields, eddy currents and forces can be get. Proved by FEM, the analytic solutions, proposed in this paper, no matter 2D or 3D, are general, which means it is suitable for any permanent magnet electrodynamic suspensions. Furthermore, the moving can be random direction, even it is rotating.Then, using the analytic method, proposed in this paper, we calculated the forces created by every permanent magnet EDS systems, and compared with FEM, the average error percentage is only 1.2% in 2D model. Especially for the linear Halbach model, the error percentage reduced to 0.6%, and it was 17.4% when we used the equations given by other researchers. What more important is we calculated the force in 3D model, for the first time, and it was verified that the error percentage is less than 1%. Thanks for the 2D and 3D solutions, we compared all the existed EDS systems, and affirmed that double Halbach EDS system is the best one, for the urban transportation.After that, we studied and calculated the double Halbach model for the first time, and analyzed the effect of permanent magnet geometric parameters, thickness of plate, air gap and some other parameters on the suspension characters. So we gave a set of parameters to make the system meet the engineering demands. According to the calculation, at velocity 150km/h, the levitation/drag ratio is improved to 19.2 in optimized system, compared to 3.8 in single Halbach system.Finally, we built an experimental platform, to test the forces at different air gap conditions, and this is the only full size double Halbach rotating platform in the word, since now. Taking temperature into account, the test results are highly consistent with analytic calculation, so it proved the analytic model again and also proved that the platform was designed well. This platform is significant for further EDS studies.