High-speed slotless permanent magnet machines: modeling and design frameworks

Abstract

The number of applications driven by high-speed electrical machines has drasti-cally increased during the recent decades. Some applications require high speedsto operate effectively, e.g. turbocompressors, spindles and turbomolecular pumps.In other applications, for instance in space or transport, these machines are vitaldue to their high power density. Among these machines, high-speed slotless per-manent magnet (PM) machines are attractive at very high speeds (>100 000 rpm)and low-power applications because of the absence of cogging torque and lossescaused by slotting.

Slotless winding configurations with skewed conductors require 3D field modeling.In this case, traditionally, the finite element method (FEM) modeling is applied.However, often it requires a significant calculation time, which is unsatisfactory inoptimization of machine designs. On the other hand, (semi-) analytical approachesare much faster alternatives compared with FEM. Nevertheless, no (semi-) analyt-ical electromagnetic modeling approaches that are able to model various complexslotless winding configurations can be found in the literature.

In this thesis, the semi-analytical harmonic modeling technique is extended to beable to model 3D electromagnetic fields in cylindrical coordinates. This extendedharmonic modeling technique is obtained by incorporating the 2D harmonic mod-eling, formulated by the magnetic vector potential, and the 3D harmonic modeling,formulated by the second order magnetic vector potential. The spatial distributionof the magnetic field source, given by a linear current density, is described by 2DFourier series, which includes current density components with single or doublecoordinate dependencies. This electromagnetic modeling technique can be appliedto model high-speed slotless PM machines with a wide range of slotless windingconfigurations. Moreover, it is able to model eddy currents induced in conducting regions, such as permanent magnet material and rotor retaining sleeve. Predic-tion of the rotor eddy currents is essential for high-speed machines, because itfacilitates assessing the rotor eddy-current losses.

Based on the armature and PM magnetic field distributions, obtained by the har-monic modeling, expressions to calculate the machine electromagnetic quantities,such as electromagnetic torque, electromotive force (emf) induced by the PM field, and synchronous inductance, are derived. A generalized expression to calculatethe electromagnetic torque is obtained using the armature and PM field solutionsin the air gap for 2D and 3D electromagnetic problems using Maxwell’s stresstensor. The torque expression can be employed to calculate the time and positiondependent torque profiles. The emf induced by the PM field is calculated by inte-grating the magnetic field over the winding’s spatial distribution. The calculationof the synchronous inductance using the field obtained by the harmonic modelingtakes into account the reaction field of the rotor eddy currents.

Following, using the electromagnetic field distribution, a research on calculationof the electromagnetic losses occurring in high-speed slotless PM machines is con-ducted. Precise assessment of losses in electrical machines is of primary impor-tance, as it facilitates an accurate prediction of the machine efficiency, thermalstresses on vulnerable machine parts, and accounting for the material propertychange caused by the temperature variation. Rotor eddy-current losses producedby the armature reaction field are calculated using the Poynting vector. Expres-sions for the calculation of skin and proximity losses in winding conductors causedby the changing PM field are introduced for straight and skewed conductors. Cal-culation of other electromagnetic losses, such as DC Joule and iron, is also con-sidered in the thesis.

Since all high-speed machines are supplied by power converters, the investigationof the influence of the current ripple produced by the PWM on rotor eddy-currentlosses is performed. An analytical approach to predict the current ripple causedby the PWM is presented. This approach is based on the solution of the electricalcircuit of the slotless PM machines with frequency-dependent circuit parameters,where the PWM is defined as a Fourier series over the frequency domain.

Further, a design framework for high-speed slotless PM machines is developedbased on the described electromagnetic modeling framework. This framework isapplied to design a slotless high-speed PM machine for a benchmark application, which is a mobile medical ventilation system. In this application the high-speedslotless PM machine drives a miniature centrifugal blower in highly dynamic mo-tion profile within wide speed and torque ranges. Therefore, the optimizationof the machine is performed considering a highly dynamic operation for the ex-treme neonatal and adult ventilation cases. The mechanical stability of the rotoris ensured by limiting the mechanical stresses in the rotor parts originated fromcentrifugal forces as well as considering the rotor-dynamic stability. The thermalbehavior of the machines is predicted by using the thermal equivalent circuit model, and temperature conditions of the wire insulation and PMs are kept below theirfatigue points. During the design procedure three different machines with variousslotless windings, namely toroidal, concentrated, and Faulhaber, have been ana-lyzed. The optimization is done towards minimization of the power consumptionof the machine. A prototype of the high-speed PM machine with Faulhaber wind-ing has been manufactured, and measurements have been conducted to validatethe developed electromagnetic modeling and design frameworks.