Abstract

This paper presents a new method to find available slot–pole combination of a permanent magnet (PM) vernier motor with fractional-slot concentrated winding (FSCW) configurations instead of the conventional design rule. To this aim, for a common structure of PM vernier machines with FSCW, the air gap flux densities including modulation flux due to vernier effects are investigated from the magnetic view points and then a general condition to effectively use the modulation flux is derived. Under the obtained condition, the specific design condition for slot–pole combinations are established for the most popular FSCW configurations with the coil spans of ±2π/3. Using the established condition, all available vernier structures including those which could not be found by the previous rule are obtained, and the back-electromotive force (EMF) of each structure is analytically estimated to check the vernier effects. During these procedures, it is also revealed that some of general FSCW-PM motors possess vernier effects and thus can be classified into vernier motors. To verify the proposed ideas, the characteristics of back EMF are analyzed through finite element (FE)-simulations for various models, and compared with their analytical calculation results. Finally, the characteristics of torque regarding to slot–pole combinations of the vernier motors are discussed.

Highlights

  • The vernier permanent magnet (PM) motor is being recently considered a strong candidate able to meet the needs for higher power density, especially in low-speed electro-mechanical systems such as electric vehicles and wind power generators

  • = 11 and and 22 of of n which are chosen to confirm the vernier effects of the one with p since they have been aux m naux = 1 which are chosen to confirm the vernier effects of the one with pm = 2 since they have been commonly

  • To improve the theoretical uncertainty andwindings, restrictions case that the previous design rule is applied to the machines with slot-concentrated the in necessary condition for design rule is applied to the machines with slot-concentrated windings, the necessary condition effective utilization of vernier effects, Qfmp > pm, is firstly obtained, and under the condition, thefor effective utilization of vernier effects, Qwere pm, is firstly and case thenofunder the of condition, fmp >

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Summary

Introduction

The vernier PM motor is being recently considered a strong candidate able to meet the needs for higher power density, especially in low-speed electro-mechanical systems such as electric vehicles and wind power generators. To avoid this ambiguity associated with winding pole pairs and to find every available vernier structure with FSCW configurations, firstly, both the useful air gap fluxes are available vernier structure with FSCW configurations, firstly, both the useful air gap fluxes are expressed for a generalized PM vernier structure, and the induced voltage of a single conductor expressed for a generalized PM vernier structure, and the induced voltage of a single conductor due to the both fluxes are investigated from an electro-magnetic view point. By coupling the condition with a given slot angle for three phase FSCWs, the criterion for slot–pole combination of the vernier machines can be specified.

General Structure of a SPM Vernier Machine with FSCWs
Air Gap Flux Density Equation
Br gm π μrec μ0
Necessary Condition for Vernier Effects Utilization
Derivation of Design Criteria for Various Auxiliary Poles
Analytical Calculations of Back EMF using a Single Conductor Voltage
Results
Conclusions
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