3D analytical field calculation using triangular magnet segments applied to a skewed linear permanent magnet actuator

Abstract

Purpose

The purpose of this paper is to present novel analytical expressions which describe the 3D magnetic field of arbitrarily magnetized triangular‐shaped charged surfaces. These versatile expressions model that the field of triangular‐shaped permanent magnets (PMs) are very suitable to model skewed slotless machines.

Design/methodology/approach

The analytical 3D surface charge method is normally used to provide field expressions for PMs in free space. In this paper, the analytical surface charge integrals are analytically solved for charged right‐triangular surfaces. The resulting field is compared with that obtained by finite element modeling (FEM) and subsequently applied in two examples.

Findings

The comparison with FEM shows that the 3D analytical expressions are very accurate and exhibit very low‐numerical noise. These fast‐solving versatile expressions are therefore considered suitable to model triangular‐shaped or polyhedral‐shaped PMs.

Research limitations/implications

The surface charge method assumes that the relative permeability is equal to 1 and therefore soft‐magnetic materials need to be modeled using the method of images. The PMs are assumed to be ideal in terms of homogeneity, magnetization vector, permeability, demagnetization, and geometrical tolerances.

Practical implications

Many applications, such as the subclass of slotless synchronous linear actuators with a skewed PM structure and planar magnetic bearings, are very suitable to incorporate this modeling technique, since it enables the analysis of a variety of performance data.

Originality/value

As an addition to the common 3D analytical field expressions for cuboidal or cylindrical PMs, this paper presents novel expressions for magnets having triangular surfaces.

Citation

Janssen, J.L.G., Paulides, J.J.H. and Lomonova, E.A. (2010), "3D analytical field calculation using triangular magnet segments applied to a skewed linear permanent magnet actuator", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 29 No. 4, pp. 984-993. https://doi.org/10.1108/03321641011044406