On torque computation in electric machine simulation by harmonic mortar methods

Herbert Egger,Melina Merkel,Richard Löscher,Mané Harutyunyan,Sebastian Schöps

doi:10.1186/s13362-022-00121-2

Abstract

The use of trigonometric polynomials as Lagrange multipliers in the harmonic mortar method enables an efficient and elegant treatment of relative motion in the stator-rotor coupling of electric machine simulation. Explicit formulas for the torque computation are derived by energetic considerations, and their realization by harmonic mortar finite element and isogeometric analysis discretizations is discussed. Numerical tests are presented to illustrate the theoretical results and demonstrate the potential of harmonic mortar methods for the evaluation of torque ripples.

Highlights

1 Introduction A particular challenge for electric machine simulation is the relative motion of stator and rotor and the computation of quantities of interest depending on the rotation angle, e.g., the torque as a measure for the magneto-mechanic energy conversion
Energy balance and torque computation As a step, we introduce the magnetic energy of the system
It has been shown that the electromagneto-mechanic energy balance holds exactly on the discrete level

Summary

Introduction

A particular challenge for electric machine simulation is the relative motion of stator and rotor and the computation of quantities of interest depending on the rotation angle, e.g., the torque as a measure for the magneto-mechanic energy conversion. We consider harmonic mortar finite element and isogeometric analysis methods proposed in [3, 10], which are based on finite element or isogeometric analysis approximations of the magnetic problems in the stator and rotor subdomains, coupled by a Lagrange multiplier technique using trigonometric functions. Where the first term denotes the electric work required to maintain the electric current je in the stator coils (neglecting Ohmic losses), and the second term is the mechanic work required for an infinitesimal rotation of the system These energy-based considerations immediately give rise to the following definition of the torque. Which may be more convenient depending on the particular setting

Galerkin approximation

KR jM aR where x

Discussion