3-D Analytical Model of Axial-Flux Permanent Magnet Machine With Segmented Multipole-Halbach Array

Abstract

This paper presents a 3-D analytical model of an axial-flux permanent magnet (AFPM) machine with a segmented multipole-Halbach PM array. Closed-form solutions are self-consistently derived in terms of modified Bessel functions of the first-and the second-kind by solving analytically Laplace and Poisson equations by the method of magnetic scalar potential subject to the appropriate boundary conditions. In the preceding studies, their formulations are based on 2-D or quasi 3-D geometry, and their discussions are often limited to the magnetic fields with the low-poles of the regular PM. The proposed model successfully provides more rigorous and widely applicable expressions for magnetic fields, back-electromotive force, Lorentz torque and torque constant without limitations on the number of poles and the arrangement of the PMs. Behavior of the torque constant is then shown against the number of poles ranging widely from low-poles to high-poles of the regular PM, the standard-Halbach PM and the multipole-Halbach PM for changeable geometrical parameters. The obtained results are of much use in understanding intrinsically the performance characteristics of the AFPM.

Two-Level Scheme for Identification of the Relaxation Time Spectrum Using Stress Relaxation Test Data with the Optimal Choice of the Time-Scale Factor

“…The modified Bessel functions of the second kind, and especially K 0 (x) [47], have many applications in science and engineering, for example, in physics to describe the flow of magneto-hydrodynamic (MHD) viscous fluid in a Darcy-type porous medium [48], in engineering to derive a closed analytical form of the model of a axial-flux permanent magnet machine with segmented multipole-Halbach PM array [49] and to describe the perunit-length internal impedance of two-layer cylindrical conductors [50]. The applications of the Bessel functions in the description of the dynamic response of a mono-pile foundation in homogeneous soil and varied layered soil-rock conditions under horizontal dynamic loads [51], to obtain a fully coupled poroelastic solution for spherical indentation into a half space with an impermeable surface when the indenter is subjected to step displacement loading [52] and to express a distribution of the traveling distance in heterogeneous populations [53] come from material science and ecology.…”

“…tr z N z T N z N z T N = z T N z N tr z N z T N = z T N zand by the diagonal structure of Λ λ (α)(49), we havetr Λ T λ (α)Λ λ (α)Λ T λ (α)Λ λ (α) = ∑ r(α) i=1…”

A Novel Analytical Formulation of the Magnetic Field Generated by Halbach Permanent Magnet Arrays

“…Consequently, the use of this technology is limited to special applications, where performance cannot be degraded in favour of costs. In order to overcome these issues, the most common and cheap solution applied in industry is segmented magnetization, which consists of dividing the magnet into several segments, which are magnetized to reproduce a normal flux density component as close as possible to a sine wave [3][4][5]. However, a closed-form analytical model of the air-gap field resulting from this configuration is not available in the literature.…”