3-D Analytical Model of Helical Winding PM Machines Including Rotor Eddy Currents

Helical windings (or zigzag windings) are used in a number of applications, however, in electrical machines, mainly employed in low-power, high-speed permanent magnet (PM) brushless dc machines due to the cost effectiveness of the winding type while maintaining reasonable performance. Typically, helical windings are used for low-voltage applications due to their spiral form, which makes them most suitable for a small number of turns. In high-speed electrical machines, such a low number of turns are applicable. It is apparent that high-speed PM machines suffer from rotor eddy-current losses, which in some cases may lead to PM demagnetization due to overheating. The performance of the machine is compromised by these losses; hence, they have to be considered during the design procedure. There are many papers analyzing the magnetic field of these machines employing helical windings; however, none of them present a simple and precise electromagnetic model of a machine with the helical winding. This paper presents an analytical approach to model the resulting 3-D magnetic field of the helical winding, considering eddy currents in the conducting media of the rotor. The model is verified with the 3-D finite-element method by means of comparing magnetic field and rotor eddy-current losses.