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In contrast to the directly integrated magnetically geared machines, the class of the ux modulated magnetically geared (FMMG) machines were derived from the development of an existing electrical machine concept. But, with the advent of the high energy density rare earth PM materials, which has replaced the DC coil excitations previously used in the primitive models, these machines can also be linked to the newly emerged ux modulated CMGs due to the observed similarities in their basic operation principles. That is, they work on the same concept of magnetic gearing through the modulation of the air-gap elds as in CMGs, hence they are logically regarded as ux modulated magnetically geared machines. Unlike in CMGs, it is not necessary to maintain two mechanical clearances

CHAPTER 1. INTRODUCTION 10 and/or two rotating components since the ux modulating ring can be combined with either the stator or the rotor core. There are three main types of machines in the class of FMMG machines, being:

ˆ Permanent magnet vernier (PMV) machines ˆ Stator permanent magnet machines

ˆ Transverse ux permanent magnet (TFPM) machines

The stator PM machines have evolved from the principle of DC eld excited variable ux reluctance machines (VFRM), and they can be traced back to the early inventions such as the stator PM alternator by Rauch and Johnson proposed in the mid 1990s (Fig. 1.9) [12]. As their collective name suggests, the PMs are placed on the stator while the ux- modulating pieces become one component with the rotor yoke, creating a simple salient rotor structure. The location of the PMs on the stator leads to three dierent types of stator PM machines named as the ux-switching PM (FSPM), ux-reversal PM (FRPM) and the doubly-salient PM (DSPM) machines depicted in Fig. 1.10 [13; 15;16].

(a) (b)

Figure 1.9: Variable ux reluctance PM (VFRPM) machine [12] (a) 2-salient pole rotor and (b) 6-salient pole rotor.

(a) (b) (c)

Figure 1.10: Stator PM ux-modulated magnetically geared machines [1316]: (a) ux- reversal (FRPM), (b) ux-switching (FSPM) and (c) doubly-salient (DSPM).

In the FSPM, one PM pole is sandwiched in between each stator tooth, the FRPM has a pair of PM poles on the stator-teeth surface adjacent to the air-gap while the DSPM has the PM poles alternately inserted in the stator yoke. The non-overlapping concentrated winding is commonly employed in these machines even though it is possible to apply con- ventional distributed winding [115;116]. Comparison between these stator PM machines reveals that FSPM machine has better performance characteristics than the other two [14; 15; 117]. One of the main drawbacks of the FRPM is a signicant PM ux leakage

CHAPTER 1. INTRODUCTION 11 that negatively impacts its performance, while the DSPM is hampered by the low PM material utilization ratio leading to a poor torque per PM mass ratio.

The second group of FMMG machines is the PMV machines, which, unlike the stator PM machines, has the PMs mounted on the rotor. The modulating pieces are combined with the stator to be one component so as to add more compactness to their structure. PMV machine concepts were derived from the decades old principle of electrically excited vernier machines by incorporating a PM rotor. The early vernier machine designs, such as those proposed by Chubb [19], Dicke [20] and Lee [118], had obvious drawbacks of manu- facturing diculties and low eciencies due to complex electrical excitation arrangement [119]. Although this idea remained dormant for several years after its earliest inventions, more interest and substantial studies on it resurfaced with the electromagnets being re- placed by the PMs, leading to the the emergence of the PMV machine [46; 100; 120]. Their success to being torque dense competitive machines was further enhanced by the advancement in high energy product PM materials. The three basic structures of the PMV machines are shown by Fig. 1.11. The conventional PMV is usually designed with distributed overlapping windings, whereas the other two congurations employ the tooth concentrated non-overlapping winding.

(a) (b) (c)

Figure 1.11: Basic permanent magnet vernier machines' structures: (a) conventional PMV, (b) with separate modulator and (c) split-teeth stator PMV.

Transverse ux PM machines consists of three identical single phase rings enclosed in a housing. Each ring is made up of the stator segments, the coils and the PM rotor assembly. Figure 1.12 illustrates the simplest conguration of the TFPM machines. The adjacent single phase stator cores are stacked at 120 electrical degrees shifts relative to each other in order to form a symmetrical 3-phase distribution [17; 18]. The fundamental design convention is that the rotor magnetic poles be more than those of the stator (usually by a factor of two), which implies they engage through the magnetic gearing [121]. However, one main distinction of the TFPM to conventional electrical machines is that its stator ux distributions are perpendicular to the rotor movement. In addition to having a simple structure conguration, the TFPM machines are more compact and have good power densities.

It is clear from their description that the topologies of the machines under the class of the FMMG can be derived from either the ux modulated CMG or from their basic primitive concepts by adding the PMs and applying some minimum structural changes. One of the common characteristic property that make them belong to one family is that they share the same torque production principle. That is, since the number of stator and rotor magnetic poles are always dierent, the torque in these machines is produced from the modulation of the air-gap eld harmonics by stationary or rotating salient pole-pieces.

CHAPTER 1. INTRODUCTION 12

Figure 1.12: Transverse-ux PM (TFPM) machine structure [17;18].

This inherent magnetic gearing eect closely relates them to the ux modulated CMGs. In comparison to the traditional PMSM machines, the torque density capability in the FMMG machines comes as a result of their pole-ratio acting as a scaling factor to the basic torque equation parameters. In other words, the rotor-to-stator pole-ratio appears to be an indirect additional coecient that boosts their torque performance even at relatively low electromagnetic loading, as shown below [14; 122]:

PMV machines: Tair-gap ∝ m₂ p_pr s

ABgVg

TFPM machines: Tair-gap ∝ m₂ pr ABgVg

Stator PM machines: Tair-gap ∝ m

2 Ns

ps ABgVg

⇒ A = Electric loading

Bg =Air-gap magnetic loading

Vg =Air-gap volume

(1.4)

The implications of the above equation (Eqn. 1.4) is that the higher pole-ratio will theoretically give a machine design with a higher torque density. Therefore, in order to utilize the magnetic gearing eect for torque improvement, the FMMG machines are normally designed with a large margin between the stator and rotor magnetic pole-pairs whenever possible.

With regard to their performance, both the TFPM and the stator-PM FMMG ma- chines have a characteristically high cogging torque and ux leakage [123;124]. In TFPM machines, these problems are addressed by gluing the laminated magnetic steel shunts be- tween the stator poles to block the eld leakage from the rotor PMs [125;126]. Although it does help in leakage reduction, it is not a complete x, since even in the presence of the magnetic shunts, the cogging and ripple torques remain signicantly higher compared to other conventional PM machine types. The shunts also add more to the manufactur- ing complexity and costs. Moreover, the cost of the TFPM rapidly increases with an increase in power density, while the cogging torque also gets worsened, as reported by Dobzhanskyi [18]. On the other side, the fringing leakage ux in stator PM machines also deteriorates their torque density, which leads to them having low PM material utilization factor. That means, in addition to higher torque ripple, these machines have small torque output per-kilogram of PM material, and this may result in the increase for their cost.

CHAPTER 1. INTRODUCTION 13 They also seem to be performing better at medium to high speeds, hence they may not be favorable for low speed applications like wind turbine generators.

The PMV machine appears to be the best performers out of the three FMMG machines because it has higher torque density than any of them. Although they do have some leakage elds problem, their cogging and ripple torques are much smaller and they are even less than those of traditional PMSM machines if proper pole-slot combination is selected.