Mohamed Wael Zouaghi

MEC-Based Modeling and Sizing of a Tubular Linear PM Synchronous Machine

Linear machines are currently considered as viable candidates for direct-drive wave and free-piston energy converters. This paper is devoted to an approach based on a magnetic equivalent circuit (MEC), which is also called lumped circuit, dedicated to the modeling and sizing of a tubular linear permanent-magnet synchronous machine (T-LPMSM). The proposed approach considers, in a first step, the cancelation of the end-effect phenomenon. To do so, a dedicated design procedure, consisting in achieving a

Prediction of the air gap flux density distribution of a T-LSM with quasi-Halbach magnetized PMs: Application to the cogging force minimization

2\pi/3

A design approach to reduce the end effect in linear tubular PM machines

-shift between the armature phase flux linkages by selecting a fractional ratio of the stator pole pitch to the mover one and balancing the amplitudes of the phase flux linkages by extending the stator magnetic circuit with teeth of appropriate dimensions, is firmly applied on two basic T-LPMSM topologies using a dedicated MEC. Then, an investigation of the influent sizing parameters on the force production capability of the initial concept is carried out. The MEC-based prediction of the force requires the incorporation of the mover displacement, yielding the so-called “position varying MEC” on one hand and the armature magnetic reaction on the other hand. The finite-element analysis of the armature phase flux linkages and the developed force enable the validation of the results yielded by the established MECs.

No-load Features of T-LSMs With Quasi-Halbach Magnets: Application to Free Piston Engines

The paper is aimed at a dual sizing-based approach to minimize the cogging force of a tubular linear synchronous machine (T-LSM) with quasi-Halbach magnetized PMs in the mover. The study is initiated by the prediction of the spatial repartition of the no-load air gap flux density. Then, a formulation of the cogging force, based on the predicted spatial repartition of the no-load air gap flux density, is developed, considering (i) the case of an “infinite” length machine and (ii) the case of a finite length one. A case study, corresponding to an initial concept, is treated with a focus on the prediction of its spatial repartition of the no-load air gap flux density and its cogging force. With this done, the study is extended to a first cogging force reduction procedure considering the case of an “infinite” length machine. It consists in the investigation of the effects of two influent sizing parameters on the cogging force, that enables the identification of a pre-optimized concept. The cogging force of this latter is then predicted in the case of a finite length machine. The study is achieved by a second cogging force reduction procedure, consisting in a quasi-cancellation of the end effect. The prediction of the cogging force of the optimized T-LSM with quasi-Halbach magnetized PMs has clearly demonstrated the effectiveness of the proposed dual sizing-based approach.

On the analytical prediction of the force production capability of a quasi-Halbach PM excited T-LSM

The paper is aimed at a design approach dedicated to the reduction of the longitudinal end effect in a linear tubular permanent magnet machine. The proposed approach consists in a two-step procedure, such that: (i) achieving a 2π/3-shift between the armature winding flux linkages by arranging the ratio of the stator pole pitch to the mover one, and (ii) balancing the amplitudes of these flux linkages by extending the stator magnetic circuit with teeth of appropriate dimensions. A magnetic equivalent circuit (MEC) of the linear PM machine is established taking into account the proposed approach. A FEA-based investigation of the flux linkage validates the MEC results.

Characterization of the no-load operation of quasi-Halbach PM excited T-LSMs

The paper is devoted to the prediction followed by the enhancement of the no-load features of tubular linear synchronous machines (T-LSMs) with quasi-Halbach magnetized PMs in the mover. The study is initiated by the prediction of the spatial repartition of the no-load air gap flux density. Then, a formulation of the back-EMF and the cogging force, based on the predicted spatial repartition of the no-load air gap flux density, is developed, considering 1) the case of an infinite length machine and 2) the case of a finite length one. A case study, corresponding to an initial concept, is treated with the prediction of its no-load features. The study is extended to the enhancement of these features with emphasis on the effects of two influent sizing parameters, assuming an infinite length machine. This enables the identification of a preoptimized concept. The back-EMF and the cogging force of this latter are then predicted in the case of a finite length machine. A further enhancement of these features is gained, thanks to a quasicancellation of the end effect. The prediction of the back-EMF and the cogging force of the optimized T-LSM with quasi-Halbach magnetized PMs has clearly demonstrated the effectiveness of the proposed approach.

Investigation of the eccentricity effect on the quasi-Halbach magnetized PM T-LSM features

The paper is devoted to an analytical prediction of the force production capability of a quasi-Halbach PM excited tubular-linear synchronous machine (T-LSM). To start with, the air gap flux density is derived considering both PMs excitation and armature magnetic reaction. The no-load operation is then characterized with the prediction of the back-EMFs and the cogging force. The obtained results are validated by 2D finite element analysis (FEA). Accounting for the armature magnetic reaction, the analytical model makes it possible the prediction of the developed force with emphasis on its synchronizing and reluctant components. The study is extended to an investigation of the effects of two major design ratios: (i) the radially-magnetized PM width to the pole pitch ratio, and (ii) the stator slot opening to the stator tooth shoes opening ratio, on the developed force mean value and ripple. This enables the selection of an optimized T-LSM design for which an investigation of the force-displacement characteristics is carried out for different values of the maximum current density. The analyticallypredicted characteristics are validated by 2D FEA.

3D FEA-based design of an iron-assisted quasi-Halbach segmented PM T-LSM

The paper is aimed at a dual analytical characterization of the no-load operation of tabular-linear synchronous machines (T-LSMs) equipped by quasi-Halbach magnetized PMs in the mover. To start with, an approach to establish a 2D model based on the air gap flux density formulation is developed. Then, a second approach based on the magnetic equivalent circuit (MEC) modelling of T-LSMs is proposed with the derivation of a numerical procedure dedicated to its resolution. Both analytical models are applied to the prediction of the no-load features: the phase flux linkages, the back-EMFs, and the cogging force. A comparison of the obtained results with those computed by 2D finite element analysis (FEA) highlights the validity of the proposed analytical models.

Position varying MEC-based investigation of the no-load operation of T-LPMSMs

The paper is devoted to the investigation of the effect of the mover eccentricity on the features of tubular-linear synchronous machines (T-LSMs) with quasi-Halbach magnetized PMs. The investigation is initiated by the analytical prediction of air gap flux density distribution considering the two cases (i) coaxial mover with respect to the stator and (ii) the presence of an eccentricity of the mover with respect to the stator. Then, the radial magnetic forces applied to the mover are formulated and their variation with respect to the eccentricity is investigated. The study is achieved by the formulation of the synchronising component of the electromagnetic force in terms of eccentricity. 3D finite element analysis is carried out and enables the validation of the analytically-predicted results.

Dynamic MEC modeling of a linear tubular PM machine

The paper is devoted to a 3D finite element analysis (FEA)-based design and feature investigation of tubular-linear synchronous machines (T-LSMs) equipped with iron-assisted mover with segmented quasi-Halbach magnetized permanent magnets (PMs). The mover design-sizing procedure is initiated by an investigation of the influences of the width and the height of the iron rings, on the maximum value of the phase flux linkages and the peak-to-peak cogging force. This enables the selection of a set of parameters achieving a high phase flux linkage with reduced cogging force. In order to highlight the effectiveness of the proposed concept, its comparison with the case of an ironless mover its carried out, with emphasis on the no-load features. A 50% increase of the amplitude of the fundamental back-EMF is gained thanks to the included iron rings in the mover.