3-D sub-domain analytical model to calculate magnetic flux density in induction machines with semi-closed slots under no-load condition

In this paper, a novel 3-D sub-domain analytical model is developed to determine magnetic flux distribution in a squirrel-cage induction machine with skewed rotor bars under no-load condition. The analytical method is based on the resolution of 3-D Laplace and Poisson's equations in cylindrical coordinates using separation of variables method to calculate the magnetic vector potential for corresponding sub-domain. The proposed model is sufficiently general to be used for any slot/ pole combination including slotting and tooth-tips for both stator and rotor, which were usually neglected in previous 2-D solutions due to complexity of the differential equations. To evaluate the performance of the proposed 3-D analytical model, calculated magnetic field distribution is compared with those obtained from the 3-D finite element analysis (FEA) and experimental results.