A new method for the analytical determination of the complex relative permeance function in linear electric machines with slotted air gap

The complex relative permeance function is a useful mathematical tool to study the magnetic field of electric machines with slotted air gap. In the literature, the complex permeance function is usually identified by means of numerical techniques based on conformal mapping. In this paper an alternative analytical approach is proposed. The method is based on solving the magnetostatic differential field equation over a portion of the slotted air gap by imposing suitable boundary conditions in the slot opening region. Such boundary conditions exploit the mathematical law which governs the divergence of the magnetic field in the neighborhood of corner-shaped ferromagnetic regions. Furthermore, the results of Carter theory on slot fringing effects on the air gap field are used. A simple easy-to-compute formula is obtained for the complex permeance function. Its accuracy is assessed by comparison with Finite Element Analysis (FEA).