Semi-analytical determination of inductances in windings with axial and azimuthal wires

Abstract

Purpose – Optimizing an electromechanical device often requires a significant number of evaluations of the winding inductance. In order to reduce drastically the computing costs associated with the calculation of inductances, the purpose of this paper is to propose a semi-analytical toolbox to calculate inductances in any winding made of axial and azimuthal wires and lying in the air. Design/methodology/approach – First, this paper presents a typical rectangular, spiral winding and the way its geometry is approximated for inductance calculations. Second, the basic formulas to calculate inductances of various windings arrangements are provided. The analytical model of the inductances is exposed, and the formulas for the inductances are derived. Finally, a validation is proposed by comparing analytical predictions to 3D FE simulations results and experimental measurements. Findings – The semi-analytical predictions agree with the finite element methods (FEM) and experimental data. Furthermore, the calculation of the inductances was done using much fewer resources with the semi-analytical model than with FEM. Research limitations/implications – The analytical formula for the mutual inductance between coaxial circular arcs is a series with an infinite number of terms which should be truncated appropriately. This is necessary because the term are found using a recurrence formula which may be unstable for a high number of terms. Practical implications – The paper includes implications for the optimization of electromechanical devices comprising windings made of axial and azimuthal pieces of wires. Originality/value – The main original result resides in the analytical expression of Neumann’s integral for the inductance between two coaxial circular arcs.