IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4, JULY 2001
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The Application of Linear Halbach Array to Eddy Current Rail Brake System Seok-Myeong Jang, Member, IEEE, Sang-Sub Jeong, and Sang-Do Cha
Abstract—This paper proposes two kinds of eddy current brakes with permanent magnet. One consists of hexahedron shape of a segmented permanent magnet and iron core (et seq iron core–PM array). The other is composed of only a segmented permanent magnet (et seq Halbach array). We use a finite element method to compute the magneto static field. Also, we use the Galerkin-FEM with linear interpolation function may oscillate between the adjacent nodes to calculate the braking and attraction force. The advantages of the Halbach array compared with the iron core–PM array are discussed. Index Terms—Eddy current brake, Halbach array, iron core–PM array. Fig. 1. Eddy current braking system with permanent magnet: (a) eddy current brake system, (b) dc-excite magnet type, and (c) permanent magnet type.
I. INTRODUCTION
E
DDY CURRENT current braking system of high speed railway is developed because of the adhesion limit. Linear eddy current braking systems are used in magnetic levitation applications and in high velocity trains in order to avoid the abrasion of mechanical disc brake. Recently, the brake forces are to take a portion of an adhesion and an eddy current in high-speed vehicle [1], [2]. For example, ICE in Germany is using with main brake regenerative and eddy current brake in the high-speed. It is also using adhesion force in low velocity or emergency situation [3]. The eddy current braking system with dc-excited magnet inherently needs the power supply and has the consequent power losses. If the dc-excited magnetic poles are replaced with permanent magnet the braking system can be obtained a high efficiency due to no power losses and a high power/weight ratio [3]. The permanent magnet array is mounted under the train bogie between the wheels with a fixed air-gap above the rail. To obtain high magnetic flux density, the permanent magnet excited brake systems are produced in two different manners of construction, i.e., the iron core–PM array and the Halbach array. The fundamental field of Halbach array is stronger by 1.4 than with a conventional array [4]. Furthermore, the latter has self-shielding property [5]. An eddy-current braking force is generated proportional the velocity of vehicle, the magnetic flux density of air-gap and the conductivity of rail, etc. The prototype of eddy current brake equipped with iron core–PM array and the linear Halbach array is analyzed and tested. We use a finite element method to compute the flux distribution and density Manuscript received October 13, 2000. This work was supported in part by the Electrical Engineering and Science Research Institute (Korea Electrical Power Corporation) and Korea Energy Management Corporation. The authors are with the Electrical Engineering Department, Chungnam National University, Taejeon, Korea (e-mail:
[email protected]). Publisher Item Identifier S 0018-9464(01)07197-7.
Fig. 2. Iron core–PM array: (a) eddy current brake, (b) flux distribution without iron rail, and (c) flux distribution with iron rail.
in the airgap. Also, we use the Galerkin-FEM with linear interpolation function may oscillate between the adjacent nodes to calculate the braking and attraction force. This paper presents the advantages of the Halbach array compared with the iron core–PM array are discussed II. APPLICATION OF THE HALBACH ARRAY TO EDDY CURRENT BRAKE A. Eddy Current Braking System with Permanent Magnet As shown in Fig. 1, the dc-excited magnetic poles are replaced with permanent magnet. Then, the electrical controller and power systems can be removed. However, the iron core–PM array proposed in [3] has lower flux density than dc-excited magnetic pole. To obtain stronger magnetic field and braking force, we propose the eddy current braking system with Halbach array. Figs. 2(a) and 3(a) show the iron core–PM array and Halbach array with iron rail, respectively. The arrows in each block
0018–9464/01$10.00 © 2001 IEEE
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4, JULY 2001
TABLE I MECHANICAL DIMENSION AND CONDUCTIVITY OF RAIL
Fig. 3. Halbach array: (a) eddy current brake, (b) flux distribution without iron rail, and (c) flux distribution with iron rail.
where
is the conductivity of rail. Therefore, (1) becomes: (6)
indicate the direction of magnetization. As shown in Fig. 3(a), Halbach array type is composed of only permanent magnet. This array uses four blocks per period, with the magnetization axis rotating by 90 degrees in each subsequent block. Following up on a suggestion from Klaus Halbach, we have investigated the utility of such arrays as the permanent magnet structure for eddy current brake. The concept of the Halbach array is that the magnetization vector should rotate as a function of distance along the array so as to maximally aid the desired field distribution [5]–[7]. The magnet to be used the eddy current braking system is NdFeB that is one of rare earth magnetic materials. In Section III, we will describe the static field of permanent magnet arrays, respectively.
and is the vector potential. Assuming the where, motion is only -direction and the eddy current is -component, becomes: (7) . Consequently, the governing equation for the 2-dimension finite element analysis of PM eddy current brake is expressed as: (8)
B. Governing Equation Because the magnetic poles are excited by permanent magnet, dc source is zero. Assuming the geometry to be invariant in the direction of motion the governing equation for electromagnetic field problem with eddy currents due to motion are: (1) (2) is eddy current density induced in the rail, is relawhere tively velocity. The quantities and are related through magas netization (3) It is convenient to represent the intrinsic magnetization by: (4) where is the remnant magnetization in the preferred direction of magnetization, is the remanence, and is the susceptibility. Eddy current due to motion is: (5)
where
is relative permeability. III. MAGNETO-STATIC FIELD
Table I is the mechanical dimension and the conductivity of rail. We use a finite element method to compute the static flux distribution in the models as shown in Figs. 2(b) and 3(b), respectively. The flux distribution of iron core–PM array is symmetrical, while that of Halbach array is nonsymmetrical. In Halbach array, one side is much stronger flux density than the other side of the array. As shown in Figs. 2(c) and 3(c), the flux distribution of each model is similar when the permanent magnet array is close on a rail. When the array lift from the rail the flux of iron core–PM array turns toward a frame. Therefore, it is necessary to shield magnetic flux. Hence, the Halbach array makes up for a defect of the iron core–PM array. Fig. 4(a) and (b) show the -component magnetic flux density of the analysis and measurements data in air-gap with 5 [mm]. The difference results from not considering -component fringing flux in 2D-FE analysis. The flux density of Halbach array is higher 35% than that of iron core–PM array. As a result, the Halbach array will be expected a stronger braking force that is proportional to air gap flux density. Fig. 5 shows the result of 3D FEA, which is similar to the measured results.
JANG et al.: THE APPLICATION OF LINEAR HALBACH ARRAY TO EDDY CURRENT RAIL BRAKE SYSTEM
Fig. 4. Air-gap flux density distribution for each model (a) 2D finite element analysis (b) experiment.
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Fig. 6. Attraction and braking force, (a) iron core–PM array and (b) Halbach array.
V. CONCLUSIONS
Fig. 5.
Air-gap flux density distribution of Halbach array using 3D FEM.
IV. ATTRACTION AND BRAKING FORCE In order to simplify the analysis, the following assumptions are made for the methods. i) The rail is sufficiently thick. ii) The magnetic poles are free of end-effects. iii) The conductivity of rail is constant. In order to calculate the braking and attraction force, the Galerkin-FEM with linear interpolation function is used. We have been analyzed to investigate stability of solutions with Dirichlet, Neumann and periodic boundary condition. Fig. 6 shows that the attraction and braking force with the velocity. As the result of simulations, the braking force of Halbach array rises remarkable in proportion to velocity.
This paper proposed the eddy current brake system with permanent magnet Halbach array. The air-gap flux density, attraction force and braking force have been discussed in the Halbach array and the iron core–PM array, respectively. Especially, the Halbach array has several advantages compared with the iron core–PM array. The Halbach array develops higher braking force because of the strong flux density. Also it has self-shielding property. REFERENCES [1] P. J. Wang, “Analysis of eddy-current brakes for high speed railway,” IEEE Trans. Magn., vol. 34, no. 4, 1998. [2] M. Fujita, “3-dimensional electromagnetic analysis and design of an eddy-current rail brake system,” IEEE Trans. Magn., vol. 34, no. 5, 1998. [3] K. D. Hyun, “Permanent magnet excited eddy current brake,” Korea, Patent 10-1998-044 938, 1998. [4] J. Ofori-Tenkorang, “A comparative analysis of torque production in Halbach and conventional surface-mounted permanent-magnet synchronous motors,” in Proc. IEEE IAS Annual General Meeting, Orlando, 1995, p. 657. [5] D. L. Trumper, “Magnet arrays for synchronous machines,” in Proc. IEEE IAS 28th Annu. Meet., 1993, pp. 9–18. [6] K. Halbach, “Physical and optical properties of rare earth cobalt magnets,” Nuclear Instruments and Methods, vol. 187, pp. 109–117, 1981. [7] M. Marinescu, “New concept of permanent magnet excitation for electrical machines. Analytical and numerical compution,” IEEE Trans. Magn., vol. 28, no. 2, 1992.
