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.

Analytic Magnetic Fields and Semi-Analytic Forces and Torques Due to General Polyhedral Permanent Magnets

“…The field due to magnet A is found using a similar method to Rubeck et al [16], but the equations are more efficient. Unlike the field equations presented by Janssen et al [15], all expressions and sub-expressions here are purely real. The magnetic field is found by first taking a polyhedral permanent magnet, such as that shown in Figure 1a, and decomposing it into its polygonal facets.…”

“…Other authors, however, have been more successful in solving for the exact magnetic field. Janssen et al [15] and Rubeck et al [16] were able to find analytic expressions for the magnetic field of a polyhedral magnet by decomposing it into a collection of simple two-dimensional planar surfaces. Meessen et al [14] and Lee & Gweon [17] studied trapezoidal magnets in a Halbach array using discretised magnets and magnets of infinite thickness respectively and found improvement in the maximum magnetic field strength over more traditional cuboidal Halbach arrays.…”

Semi-analytical calculation of the force between two magnets with rhombus-shaped cross-sections

“…The semi-analytical method in this paper is based on the assumption that µ r = 1, which means J is always equal to J r according to (43). But the relative permeability µ r of a real Nd-Fe-B magnet is slightly greater than 1 (approximately 1.03-1.07 [22]), which leads to a decrease in J from J r . Therefore, measurement results are slightly smaller than analytical/semi-analytical results, as shown in figure 9.…”

“…In addition to inclined cuboidal magnets (shown in figure 3(a)), other prismatic magnets (e.g. magnets shown in figures 3(b) and (c)) may also improve the performance for magnetic springs or bearings and should therefore be subject of investigation [22]. However, force calculations for these prismatic magnets are beyond the scope of aforementioned analytical expressions as well.…”

Analytical Calculation of Magnet Systems: Magnetic Field Created by Charged Triangles and Polyhedra

“…In 2010, J. L. G. Janssen has presented a method for the calculation of the field of prismatic magnets [9]. The work is based on a similar decomposition, but the field expressions are slightly different because the origin has been taken in the middle of the triangle hypotenuse, when the origin is at a triangle corner in our work [10].…”