Force Calculation in 3-D Magnetic Equivalent Circuit Networks With a Maxwell Stress Tensor

Abstract

Magnetic equivalent circuit (MEC) models are increasingly valuable for analysis and design of electromechanical devices, particularly electrical machines, because of their moderate computational effort and reasonable accuracy. Force and torque calculations in prior MEC implementations are almost exclusively based on the virtual work method (VWM) adapted to the specific device model. But VWM does not easily extend to a general MEC modeling approach. In this paper, the more direct Maxwell stress tensor (MST) method is applied to a general 3-D MEC modeling framework. MST theory and implementation are presented. Its application is discussed with the example of an electromagnet. Results are compared to both measurements and analytical and finite-element models. Index Terms-3-D magnetic equivalent circuits (MECs), electromagnet, force calculation, Maxwell stress tensor (MST), modeling of electromechanical devices, virtual work method (VWM).

2D–3D Magnetic equivalent circuit of the flux focusing permanent magnets synchronous machine

“…Furthermore, as all inductions components are estimated by 978-1-4799-7300-2/14/$31.00 ©2014 IEEE this method, the Maxwell stress tensor can be used to estimate torque [15]. This method was applied in 3D structure and used for many machines topologies by [16]- [17].…”

Geometric formulation of edge and nodal finite element equations in electromagnetics

“…It is well known that the ratio of the volume of the ith hexahedron to the element volume V e is related to the ith interpolating function of the nodal element, but it is rarely appreciated that the facets and edges of the volume v i inside the element represent interpolating functions of the associated edge or facet elements. For example, the interpolating function w e4,8 of the edge element for the edge P 4 P 8 expresses the ratio of the facet vector s 4,8 to the volume V e (Fig.1a), while the ratio r i /V e describes the interpolating function w fi of the facet element for the facet S i . In a similar manner the interpolating functions for triangular prisms and pentahedron elements may be expressed.…”

“…As an example, for the pentahedron of Fig. 1b, the expressions for the interpolating functions of the edge element for the edges P 4 P 5 and P 2 P 5 take the form w e4,5 =s 4,5 /(2V e ) and w e2,5 = s 2,5 /V e , respectively, while the interpolating functions of the facet element for the facets S 3 and S 4 are given by w f3 =r 3 /(2V e ) and w f4 =r 4 /V e , respectively. By analysing the relevant integrals, where the geometrical forms provided are integrands, it may be easily inferred that the volume integral in V e of the product of w ei,j and the current density vector, or flux density vector, represents current, or flux, associated with the region next to P i P j .…”

Measurement of Levitation Forces in High Temperature Superconductors

“…Some of these methods are Lorentz force equation (Chun &Lee, 2002), Maxwell's stress tensor (Amrhein & Krein, 2009) and virtual work methods (Vandevelde& Melkebeek, 2001). The Lorentz force equation method is important to know the exact distribution of the critical current density and the magnetic field.…”