A low-speed direct drive PMSG for sports equipment has been designed as a multi-slot and multi-pole type in order to improve the output power [1]. Generally an open slot structure should be applied in a multi-slot-type machine to overcome winding difficulties, but this design has the drawback of a large cogging torque.

The stator skew slot is often adopted to reduce torque ripple; however, it declines the output torque at same time. Besides, the difference between positive rotation performance and negative rotation performance, which caused by the skew slot are often ignored. In all machines, the angle of skew should be selected among values of mechanical angles between 0 and 2pi /Q, where Q stands for the least number of slots on either stator or rotor side.

Major task of skew is to get rid of the cogging torque. In all machines, the angle of skew should be selected among values of mechanical angles between 0 and 2π/Q, where Q stands for the least number of slots on either stator or rotor side. A basic role of skew should be the cancellation of the most inﬂuential slot harmonic of the magnetic. Developed for surface mounted permanent magnet machines with skewed slots via the subdomain technique and the multislice method. In another study, the authors study a step skewed rotor which is applied to the design to reduce electro-magnetic exciting force so that both reduction of.

Therefore, a slot wedge with high permeability is used to reduce the cogging torque. Ferrite is typically used in slot wedges, as it has a slightly higher permeability than air. Ferrite slot wedges can decrease the cogging torque due to the reduction in the imbalance of the magnetic resistance between the slots and the stator teeth. However, these wedges do have drawbacks in terms of the vibration and frangibility [2]. Recently, soft magnetic composite (SMC) slot wedges have been studied. SMCs can be easily produced in various shapes. However, their applications are limited because of their higher costs and lower efficiency, which is a result of their low permeability in low frequency regions compared to cast steel [3]. Therefore, iron material, which can be formed into a greater variety of shapes than ferrite and can be used to produce slot wedges more cheaply than SMC, has been utilized [4]. With the use of iron slot wedges in an open-slot-type PMSG, the cogging torque is lower than with ferrite or SMC. However, the output power also rapidly decreases because the high permeability of the iron material results in high flux leakage in the slot wedge.

Moreover, skewed stator teeth have also been used to reduce the cogging torque of permanent magnet synchronous machines [5]. However, when the stator teeth of a PMSG with multiple slots and multiple poles are skewed, the winding work becomes more difficult [6]. To facilitate the winding work and reduce the cogging torque, the stator core of the PMSG can be laminated. Laminations are rotated with slot pitch intervals [7]. However, this approach cannot increase the output power due to the same effective flux linkage path cross sectional area.

This paper proposes a novel skewed-type iron slot wedge that improves the output power and reduces the cogging torque, as it can increase the effective cross-sectional area of the flux linkage. Moreover, to maximize the output power, an optimal design using a Kriging model based on the Halton sequence method and a genetic algorithm is performed.

2.1 Open and closed slot type

2.1.1 Configuration and specification

Figs. 1 (a) and (b) show an open slot type PMSG, and (c) shows a closed slot type with an iron slot wedge. The outer rotor consists of surface-mounted type permanent magnets with 50 poles, whereas the inner stator consists of 45 slots. Table 1 gives the specifications of an open-slot-type PMSG.

Fig. 1.Structures of PMSGs: (a) An open slot type PMSG; (b) Open slot; (c) Closed slot

Table 1.Basic specifications of an open-slot-type PMSG

Ferrite and SMC have been widely used for conventional slot wedges [2]. However, ferrite is vulnerable to vibrations and is limited in terms of the possible shape designs. On the other hand, although SMC can facilitate flexible shapes, its high cost is disadvantageous. However, iron material allows for flexible shape design and is cheaper than SMC, so the iron composite ss400 is utilized for the slot wedges in the proposed machine. The characteristics of ss400 are shown in Table 2.

Table 2.Characteristics of ss400 composite

2.1.2 Characteristics of the two type PMSGs

Cogging torque is generated due to energy changes in electric devices with rotor rotation. Most of this energy change occurs in the airgap. The cogging torque is determined by (1) [8].

where n=ks, k=1,2, … , s is the lowest common multiple of the numbers of slots and poles, D is the outer diameter of the rotor, Lstk is the stack length, sin(nσLstk ) /nσLstk is the effect of the skew, σ is the skew angle, Λn is the n-th harmonic of the permeance coefficient, fn is the n-th space harmonic of the flux distribution, and ξ is the rotational angle of the rotor.

As shown in (1), since the frequency of the cogging torque is determined from the lowest common multiple of the numbers of slots and poles, the period of the cogging torque (mechanical angle) can be calculated from (2) [9].

where s is the number of slots, p is the number of poles, and LCM(s, p) is the lowest common denominator of the numbers of slots and poles. Using (2), the period of the cogging torque for 45 slots and 50 poles is 0.8°. The 3DFEA results for an open-slot-type PMSG are shown in Table 3. The cogging torque of a closed-type PMSG with an iron slot wedge is decreased to less than that of an open slot type, because the closed-type PMSG reduces the imbalance of the magnetic resistance compared to the open slot type. However, the output power is almost zero.

Table 3.Analysis results of open-slot-type and closed-type PMSGs

Fig. 2 shows the flux lines of open-slot-type and closedtype PMSGs. The rotation of magnet causes the flux linkage of windings to alternate and so generate an EMF.

Fig. 2.Flux lines of PMSGs: (a) Flux lines of an open-slottype PMSG; (b) Flux lines of a closed-type PMSG

where ω is the angular velocity, θ is the rotor position, and ψ is the flux linkage of the winding. The first expression is faraday's law which is described correlation of flux linkage, velocity and EMF. As shown in (3), The EMF is proportional to rotational velocity and increasing flux linkage on the rotor position change. It means the imbalance in the magnetic resistance between slot area and teeth increase the EMF.

The imbalance in the magnetic resistance of the closed type was reduced more than that of the open slot type because the iron slot wedge has a higher permeability than air. Thus, the flux linkage of the closed type was also reduced. In addition, the flux leakage in the slot wedge of the closed type was increased. Therefore, the output power of the closed type was almost zero.

2.2 Proposed skewed-type iron slot wedge

2.2.1 Configuration

To improve the output power as well as reduce the cogging torque, a skewed type iron slot wedge is proposed. Fig. 3 (a) shows a stator with the conventional skew method, which can be applied to stator teeth or permanent magnets. Although the conventional skew method cannot decrease the open slot area, the proposed skewed slot wedge can decrease the open slot area in proportion to the skew angle. Therefore, the cogging torque of a skewed type PMSG can be less than that of the open slot type, and the output power is increased. The skew angle of the analysis model was determined to be 2º. Fig. 3 (b) shows the slot structure of the skewed-type PMSG with the proposed slot wedge, which has a 2º skew angle.

Fig. 3.Structure of skewed type PMSG: (a) skewed stator; (b) skewed slot wedge

2.2.2 Characteristics of the three type PMSGs

Figs. 4 and 5 show the results of the finite element analysis. The output power is from dynamic analysis of 3DFEM and used average value on the stable section of the output power. The rotor of PMSG rotates 70 rpm, and is connected to converter for saving DC voltage from AC. And the output power vary with the load of circuit. The three slot type PMSGs are compared with same load condition. As seen in Fig. 4, the flux linkage of the skewed-type PMSG inc

Skewed Slots In Synchronous Machines