Very-High-Speed Miniaturized Permanent Magnet Motors: Modeling and Experimental Validation

Abstract

The purpose of this paper is to present an experimental method to separate losses components due to the rotation of the rotor in very-high-speed permanent magnet machines with ball bearings. In addition, it presents and validates an analytical model for the computation of induced eddy current losses in rectangular section conductors due to a rotating magnetic field. It also validates an empirical windage losses model. The measurements are performed on a very-high-speed miniaturized permanent magnet motor up to 400 krpm. To the authors' knowledge it is one of the smallest and fastest electrical motor ever operated.

Very-High-Speed Miniaturized Permanent Magnet Motors: Design and Optimization

“…where ρ is the density of the fluid in the airgap, Ω the rotational speed, L δ the axial length of the airgap and c f the friction coefficient. The friction coefficient given by Mack's model [19] has been experimentally validated in [3], [20], [21] and is used during the optimization process.…”

“…where ρ w is the resistivity of the wire, h w and w w are respectively the height and the width of a wire and the α n are the end-winding opening angles of each turn. An analytical model for the computation of induced eddy current losses in the winding due to the PM field is developed in [3]. The model considers a single rectangular section wire, computes the induced current density all over its surface S w and then integrates this current density over a time period T .…”

“…The rotor losses can be computed analytically [25] or by FEM [26]. However, as demonstrated experimentally in [3], rotor losses are negligible in miniaturized slotless machines and hence are not modeled here.…”

“…The values of the constants for the model of ball bearing losses (7) and the model of iron losses due to the PM field (8) are given in TABLE I. They have been established experimentally in [3].…”

“…A slotless structure has been chosen mainly because this reduces the induced rotor losses, as there are no slotting harmonics. All the models used in this paper have been validated and/or obtained by regression thanks to measurements on this motor [3]. Subsequently, an optimization can be carried out to minimize the total losses and give the optimal dimensions of the motor under some constraints.…”