A new stress tensor approach for application to the conductor surface

Abstract

Purpose

The purpose of this paper is to derive a new stress tensor for calculating the Lorentz force acting on an arbitrarily shaped nonmagnetic conductive specimen moving in the field of a permanent magnet. The stress tensor allows for a transition from a volume to a surface integral for force calculation.

Design/methodology/approach

This paper derives a new stress tensor which consists of two parts: the first part corresponds to the scaled Poynting vector and the second part corresponds to the velocity term. This paper converts the triple integral over the volume of the conductor to a double integral over its surface, where the subintegral functions are continuous through the different compartments of the model. Numerical results and comparison to the standard volume discretization using the finite element method are given.

Findings

This paper evaluated the performance of the new stress tensor computation on a thick and thin cuboid, a thin disk, a sphere and a thin cuboid containing a surface defect. The integrals are valid for any geometry of the specimen and the position and orientation of the magnet. The normalized root mean square errors are below 0.26% with respect to a reference finite element solution applying volume integration.

Originality/value

Tensor elements are continuous throughout the model, allowing integration directly over the conductor surface.

Citation

Petkovć, B., Ziolkowski, M., Toepfer, H. and Haueisen, J. (2024), "A new stress tensor approach for application to the conductor surface", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/COMPEL-10-2023-0543