D. Hawkins

An Improved Subdomain Model for Predicting Magnetic Field of Surface-Mounted Permanent Magnet Machines Accounting for Tooth-Tips

The paper developed an improved analytical subdomain model for predicting the open-circuit magnetic field in surface-mounted permanent magnet machines accounting for the tooth-tips in the slots. The whole field domain is divided into four types of simple subdomains, viz. magnets, air-gap, slot openings, and slots. The analytical expression of each subdomain is derived and the field solution is obtained by applying the boundary conditions and interface conditions between subdomains. Compared with the conventional subdomain models, the subdomain model accounting for tooth-tips can accurately predict the flux density inside the slots. Based on the developed field model, the cogging torque is computed by the Maxwell stress tensor. The finite element analysis is carried out to validate the analytical model. It shows that the developed subdomain model accounting for tooth-tips is more accurate, especially for the machines having larger slot opening width compared with tooth-tip height.

Comparison of Analytical Models of Cogging Torque in Surface-Mounted PM Machines

This paper compares four analytical models for predicting the cogging torque in surface-mounted permanent-magnet machines, viz., lateral force (LF), complex permeance (CP), and exact subdomain (SD) models, together with an SD model based on a single slot/pole. The models are evaluated for the air-gap flux density, cogging torque, back electromotive force (EMF), electromagnetic torque, saturation effect, and computational complexity, with particular focus on the influence of design parameters, such as the slot-depth-to-slot-opening ratio and the optimal pole-arc-to-pole-pitch and slot-opening-to-slot-pitch ratios, on the cogging torque. It shows that all studied analytical models have similar high accuracy for the fundamental back EMF and average torque. However, their predictions are quite different for the ripples in the back EMF, cogging torque, and electromagnetic torque waveforms. Overall, the SD models have high accuracy, while the exact SD model is the most accurate among the studied models by accounting for mutual influence between slots, albeit with high computational complexity. The computation of the SD models is slower than that of the LF model but can be quicker than that of the CP model. The comparison is validated by the finite-element and experimental results.

Analytical Model of Eddy Current Loss in Windings of Permanent-Magnet Machines Accounting for Load

This paper presents an analytical model for predicting open-circuit, armature reaction and on-load resistance limited eddy current losses in the conductors of surface-mounted permanent-magnet machines, based on the subdomain field model accounting for tooth-tips. The analytical model can be applied to machines having single-layer, two-radial-layer, or two-circumferential-layer windings. The interaction between spatial harmonics is accurately accounted for in the calculation of the AC copper loss. The investigation shows that neglecting the interaction in the analytical model has negligible influence on the prediction of total AC copper loss but results in significant error in the predicted loss distribution among conductors. The influence of tooth-tip dimension, conductor segmentation, and current on the AC copper loss is also investigated by the analytical model. The finite element analysis has verified the validity of the developed analytical model.

Analytical Model for Predicting Magnet Loss of Surface-Mounted Permanent Magnet Machines Accounting for Slotting Effect and Load

Based on the subdomain field model accounting for tooth-tips, the eddy current losses in magnets are calculated for surface-mounted permanent magnet machines. The contributions of both self action of each harmonic and mutual interaction between field harmonics of different orders to magnet loss are accounted for in the developed model. It allows for predicting magnet losses due to the open-circuit, armature reaction and load fields. By using the model, the influence of the slots, tooth-tips, tooth body shape, and current angle on the magnet loss is studied and the mutual interaction between field harmonics of different order are analysed. Extensive finite element analysis demonstrates excellent accuracy of the developed analytical model.

Subdomain Model for Predicting Armature Reaction Field of Surface-Mounted Permanent-Magnet Machines Accounting for Tooth-Tips

A subdomain model considering the influence of tooth-tips is developed for predicting the armature reaction field in surface-mounted permanent-magnet machines having either non-overlapping or overlapping windings. In the developed model, the field domain is divided into three types of subdomains, viz. air gap including magnet, slot openings, and slots. The expression of the vector potential distribution in each subdomain is obtained by the variable separation method, and the field solution is obtained by applying the boundary and interface conditions. Compared with the conventional subdomain model, the subdomain model considering the tooth-tips predicts similar flux density in the air gap and magnets, but exhibits much higher accuracy for the flux density in the slot openings and slots. The finite-element results validate the analytical prediction.

Comparison of analytical models for predicting cogging torque in surface-mounted PM machines

The paper compares five analytical models for predicting the cogging torque in surface-mounted permanent magnet machines, viz. lateral force (LF), complex permeance (CP), and combined CP models, together with subdomain (SD) models based on single slot/pole and exact SD model. The models are evaluated for the cogging torque waveforms and the prediction of optimal pole-arc to pole-pitch and slot-opening to slot-pitch ratios for cogging torque reduction. It shows that all analytical models predict similar waveforms but different magnitudes. The performance of the LF model is very stable and it is very accurate for slot-opening to slot-pitch ratio less than 0.2, but tends to underestimate above this. Both CP models have similar and relatively lower accuracy and usually overestimate the cogging torque due to neglecting the deformations of magnets and the path to predict the airgap flux density in the conformal mapping. The SD models have high accuracy while the exact SD model is most accurate by accounting for mutual influence between slots.

Study of the thermal aspects in brushless permanent magnet machines performance

This paper addresses the analysis of the main thermal phenomena in brushless permanent magnet machines, such as demagnetization of the magnets due to the heat created by losses. Several methods are investigated to mitigate complex loss components; i.e., magnet losses and AC copper losses. The efficiency of the cooling system, with natural or forced convection, is also presented.

Modern heat extraction systems for electrical machines - A review

This paper presents a review of modern cooling system employed for the thermal management of electrical machines. Various solutions for heat extractions are described: high thermal conductivity insulation materials, spray cooling, high thermal conductivity fluids, combined liquid and air forced convection, loss mitigation techniques.

Thermal Analysis of Duplex Three-Phase Induction Motor Under Fault Operating Conditions

The paper describes a thermal model for a duplex three-phase induction machine for fault tolerant applications. Three-phase and six-phase variations of duplex three-phase machine operation under fault conditions are considered. Different winding configurations are investigated. Thermal analysis is performed using analytical and finite-element models. Experimental validation is presented for load operating conditions.

Influence of different end region cooling arrangements on end-winding heat transfer coefficients in electrical machines

In this paper the influence of the end-winding heat transfer on the thermal analysis of induction motors is presented. Experimental tests on two induction motor configurations - Open Drip Proof (ODP) and Total Enclosed Fan Cooled (TEFC) frames - are performed and the heat transfer coefficients are determined and validated in a lumped thermal analysis network. The cooling effect of the wafters present in the induction motor cage end-rings is also discussed.