Analytical study of air-gap surface force – application to electrical machines

Raphaël Pile,Thomas Henneron,Guillaume Parent,Emile Devillers,Yvonnick Le Menach,Jean Le Besnerais,Jean-Philippe Lecointe

doi:10.1515/phys-2020-0147

Abstract

AbstractThe Maxwell stress tensor (MST) method is commonly used to accurately compute the global efforts, such as electromagnetic torque ripple and unbalanced electromagnetic forces in electrical machines. The MST has been extended to the estimation of local magnetic surface force for the vibroacoustic design of electrical machines under electromagnetic excitation. In particular, one common air-gap surface force (AGSF) method based on MST is to compute magnetic surface forces on a cylindrical shell in the air gap. However, the AGSF distribution depends on the radius of the cylindrical shell. The main contribution of this study is to demonstrate an analytic transfer law of the AGSF between the air gap and the stator bore radius. It allows us to quantify the error between the magnetic surface force calculated in the middle of the air gap and the magnetic force computed on the stator teeth. This study shows the strong influence of the transfer law on the computed tangential surface force distribution through numerical applications with induction and synchronous electrical machines. Finally, the surface force density at stator bore radius is more accurately estimated when applying the new transfer law on the AGSF.

Highlights

The Maxwell stress tensor (MST) method based on a closed surface is commonly used to accurately compute the electromagnetic torque and global forces in electrical machines [1,2,3,4,5]
Recent developments in the field of electromagnetic vibrations for electrical machines show a preference for estimating local magnetic forces based on the MST in the air gap [12,13,14,15,16,17]
The air-gap surface force (AGSF) method based on MST consists in computing equivalent magnetic surface forces with a cylindrical shell in the middle of the air gap

Summary

Introduction

The Maxwell stress tensor (MST) method based on a closed surface is commonly used to accurately compute the electromagnetic torque and global forces in electrical machines [1,2,3,4,5]. Recent developments in the field of electromagnetic vibrations for electrical machines show a preference for estimating local magnetic forces based on the MST in the air gap [12,13,14,15,16,17]. Analytical models are able to calculate the magnetic field of the electric machine only in the middle of the air gap. Semi-analytical methods [23,24] are able to calculate the magnetic field in the whole air-gap band. The energy derivation methods are not compatible with analytical and semianalytical methods to compute magnetic local forces as the knowledge of the magnetic field is not available everywhere in the electrical machine. Only the AGSF method is available for analytical methods

Objectives

Discussion

Conclusion