Magnetic Force Calculation Using Lorentz Force and Energy Conservation in Electrical Machines

In many engineering textbooks, very simple algebraic relations are used for magnetic forces. The simplicity of the relations lies in the well-known magnetic circuit model from which they have been derived. However, some applications require more accuracy. One niche application is the calculation of magnetic forces in electrical machines due to slotting effect. The application is twofold: ۱) vibration analysis which requires calculation of the net torque ripple (leading to cogging torque) and the oscillation of resultant normal force (attractions/repulsions). ۲) deformation analysis which requires calculating the surface and volume force density distribution. Given the magnetic field distribution, the analyses can be furnished by leveraging advanced formulae of magnetic force. Thus in order to increase the accuracy, engineers would have to resort to ۱) more advanced magnetic models that yield a precise two-dimensional magnetic field distribution and ۲) a reliable method of magnetic force calculation. The latter is the subject of this paper. To be a reference for engineering community, this paper follows these objectives: ۱) since not all engineers are accustomed with advanced physics topics; this paper aims to bring a handful of formulae from the outset. Additionally, two novel formulae are derived: surface force density and Maxwell couple stress tensor. ۲) Revisiting the underlying theory and derivation of the related formulae for three purposes: ۲-۱) providing subjective foresight, ۲-۲) elucidating the limitation of the usage of the formulae and ۲-۳) to point out common mistaken interpretations. Two case-studies are investigated to verify the identity of all formulae.

کلیدواژه ها:

Analytical model ، Maxwell stress tensor ، vibration ، deformation ، virtual work