# Magnetics Business & Technology - Spring 2014 - (Page 8)

FEATURE ARTICLE Magnetic Design and Applications Using Halbach Theory By Heeju Choi and Jinfang Liu * Electron Energy Corp. Permanent magnets (PMs) are used in many applications including hybrid electric vehicles, motors, generators and most consumer electronic devices. With growing demands for rare earth elements, which are essential to rare earth magnets, combined with ongoing environmental concerns and China's control on rare earth exports in recent years, fears of a global rare earth shortage have emerged. This concern has prompted engineers to come up with designs that do not use rare earth magnets. In April 2012, Hitachi developed an 11 kW PM motor without rare earth materials[1]. It is essential to understand the critical factors and application environment when designing magnetic circuits for satisfactory performance of the device. This is an important step in the design process, which determines the appropriate magnetic parameters used for analytical and/or numerical analysis. In this article, Halbach theory and its applications are introduced. PM Halbach arrays are very useful for a variety of applications including high field magnet sources, magnetizing and de-magnetizing systems, and high power/efficient motors and generators.[2][3] A Halbach progressive magnetization design can maximize the coupling torque, while a double Halbach cylinder provides an adjustable magnetic field. Principle of Klaus Halbach Theory Klaus Halbach (1924-2000), a staff physicist with the Lawrence Berkeley National Laboratory, investigated novel designs for PM arrays, using advanced analytical and innovative approaches. In 1979, he published a paper entitled Design of Permanent Multipole Magnets with Oriented Rare Earth Cobalt Material.[4] In this paper, he introduced a novel method of generating multipole magnetic fields using innovative geometrical arrangements of PMs. Figure 1 shows an example of linear and circular Halbach arrays. /H/ is independent of dipolar orientation. The field orientation angle a with respect to the axis is twice q. A Halbach ring assembly with progressive magnetization can be realized by discrete magnet segments. The direction of magnetization in each individual magnet segment can be expressed by the following relation: qm = (1±p)qi (4) where qi is the angle between q = 0 and the center of the ith magnet segment, p is the number of pole-pairs, "+" is for an internal field cylinder, and "-" is for an external field cylinder. Single Halbach Cylinder The design of a Halbach cylinder is relatively simple. According to Equation 3, all segments have contributions to a uniform field across the airgap in the vertical direction. The flux density in the airgap of a Halbach cylinder is: B = Br ln(r2/r1) (5) where r1 and r2 are the inner and outer radii. Halbach theory enables PMs to be fully competitive with electromagnets for fields up to 2T, and fields as high as 5T can be produced[5]. Equation 5 suggests there is no upper limit for the field of Halbach cylinders, but practically it is limited by the physical dimensions and the demagnetizing effect for permanent magnets. Single Halbach principle has been used extensively in a variety of applications, especially for PM brushless machines because of sinusoidal air-gap field distribution, electromotive force waveform, and negligible cogging torque[6]. Due to the self-shielding of the Halbach progressive magnetization, back iron is not essential; therefore the mass and the inertia can be reduced. This will improve the dynamic performance. In addition, magnets can have a significantly high working point compared to conventional designs. This improves the effective utilization of the magnet material and increases the Figure 1. Linear (left) and Circular (right) Halbach Array According to the Halbach theory, if the magnetization of an infinite line source oriented perpendicular to its axis is rotated about that axis, the field it produces remains everywhere constant in magnitude and is everywhere rotated by the same angle in the opposite sense. For an infinite dipole, the tangential and radial field components are: Hq = l sinq / 2pr2 Hr = l cosq / 2pr2 (1) (2) where l is the moment per unit length, and q is the angle measured from the dipolar axis in polar coordinates. Therefore the magnitude of H is: /H/ = (Hq2 + Hr2)1/2 = l/2pr2 8 (3) Magnetics Business & Technology * Spring 2014 Figure 2. Single Halbach Cylinder Configuration, Prototype and Test Data www.MagneticsMagazine.com http://www.MagneticsMagazine.com

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# Magnetics Business & Technology - Spring 2014

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