A Novel Modular-Stator Outer-Rotor Flux-Switching Permanent ... - MDPI

energies Article

A Novel Modular-Stator Outer-Rotor Flux-Switching Permanent-Magnet Motor Jing Zhao 1,2 , Yun Zheng 1,2 , Congcong Zhu 1,2 , Xiangdong Liu 1,2, * and Bin Li 1,2 1 2

*

School of Automation, Beijing Institute of Technology, Beijing 100081, China; [email protected] (J.Z.); [email protected] (Y.Z.); [email protected] (C.Z.); [email protected] (B.L.) Key Laboratory for Intelligent Control & Decision of Complex Systems, Beijing Institute of Technology, Beijing 100081, China Correspondence: [email protected]; Tel./Fax: +86-10-6891-2460

Received: 12 April 2017; Accepted: 2 July 2017; Published: 6 July 2017

Abstract: A novel modular-stator outer-rotor flux-switching permanent-magnet (MSOR-FSPM) motor is proposed and studied in this paper. Structure, operation and design principles of the MSOR-FSPM motor are introduced and analyzed. Considering that the combination of different pole number and slot number has a great influence on the motor performance, the optimum rotor pole number for the 12-stator-slot MSOR-FSPM motor is researched to obtain good performance and make full use of the space in the MSOR-FSPM motor. The influences of rotor pole number on cogging torque, torque ripple and electromagnetic torque are analyzed and a 12-slot/10-pole MSOR-FSPM motor was chosen for further study. Then, several main parameters of the 12-slot/10-pole MSOR-FSPM motor were optimized to reduce the torque ripple. Finally, the utilization of permanent magnet (PM) in the MSOR-FSPM motor and a conventional outer-rotor flux-switching permanent-magnet (COR-FSPM) motor are compared and analyzed from the point of view of magnetic flux path, and verified by the finite element method (FEM). The FEM results show that the PM volume of MSOR-FSPM motor is only 54.04% of that in a COR-FSPM motor, but its average electromagnetic torque can reach more than 75% of the torque of COR-FSPM motor. Keywords: outer-rotor; flux-switching permanent-magnet (FSPM) motor; modular-stator; rotor pole number; torque ripple; utilization; permanent magnet volume

1. Introduction Due to the serious air pollution and energy shortages all over the world, governments have put forward plans for energy conservation and emission reduction requirements for vehicles. Electric vehicles (EVs) with clean and low energy consumption are widely proposed to effectively alleviate this problem [1]. As the key component, the drive motor is expected to have high torque density, high power density, strong overload capacity, great fault tolerance capability, wide constant power speed range and low cost [2]. Different drive motors have been tried in EVs’ electromechanical energy conversion systems, such as permanent magnet synchronous motors (PMSMs), induction motors, DC motors, and brushless DC permanent magnet motors [3,4]. PMSMs are more favorable candidates in the EVs field due to their high power density, high efficiency and compact structure. Moreover, their structure can be changed conveniently according to different applications [5]. PMSMs can be divided into rotor PM motors and stator PM motors according to whether the PMs are placed on the rotor or the stator. In rotor PM motors, the maximum load is limited by the temperature rise of the PMs and the PMs have the risk of irreversible demagnetization. Stator PM motors, such as flux-reverse permanent-magnet (FRPM) motors, doubly-salient permanent-magnet (DSPM) motors and flux-switching permanent-magnet (FSPM) motors, have been widely investigated in recent years due to their simple and robust rotor Energies 2017, 10, 937; doi:10.3390/en10070937

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structure [6–8]. Compared with rotor PM motors, the armature windings and PMs of stator PM motors are both placed on the stator, which could improve the cooling condition of PMs and prevent the PMs from sliding off due to the centrifugal force. Compared with DSPM motors and FRPM motors, FSPM motors have more sinusoidal back electromotive force (EMF) which is appropriate for brushless AC drive systems [9]. They have better torque and power density performance under starting and climbing conditions [10]. In addition, like for FSPM motors, the magnetic field excited by PMs is in parallel with that excited by armature currents, which is suitable for a wide speed range [11]. Therefore, a large number of researchers have paid more attention to FSPM motors. In [12], the concept and working principles of a FSPM motor were first proposed, and its design principles were established based on the design theory of conventional PMSMs. In [13], a multi-tooth FSPM motor was proposed, whose stator tooth extends a number of virtual teeth; it is verified that this topology has lower torque ripple, and higher torque density at low load. In [14], a topology with step skewing rotor was researched and the finite element method (FEM) results showed that a rotor with reasonable skewing angle has a significant weakening effect on the cogging torque and torque ripple. In order to reduce the rotor core volume and motor losses, a novel FSPM motor with segmental rotor was researched in [15]; its rotor consists of a plurality of separate sector-shaped salient poles and the total motor losses can be reduced by 13% under the same output power. In order to make FSPM motor have larger torque at low speed and a wider constant power speed range, various hybrid excitation FSPM motors were proposed [16]. Moreover, the fault tolerance capability of FSPM motors is also a hot topic, as FSPM motors with fault tolerance capability can continue to work under fault conditions to improve the reliability of the EVs [17–19]. In general, because FSPM motors have simple structure, good controllability, high power density and fault-tolerant performance, they are a good selection for EV drive systems [20], but most of the researched FSPM motors have inner-rotor structures. Nowadays, outer-rotor motors, which can be used as in-wheel motors in the EV industry, have become a key technology, because they can omit the clutch, the reduction gear and the differential gear to provide extra passenger space and independent direct control to make EVs more secure [21]. In addition, tire maintenance is convenient and low cost due to the simple rotor structure of FSPM motors. Therefore, outer-rotor FSPM motors, which combine the advantages of FSPM motors and outer-rotor motors, are generating more and more interest. In [22], an outer-rotor FSPM motor was first proposed and designed using FEM. The loss and efficiency of this motor were researched, and the flux-weakening capability analyzed and further improved by segmental PMs with iron bridges in [23]. Furthermore, its torque ripple was reduced by a systematic multi-level design and control scheme in [24]. In [25], an outer-rotor FSPM motor with specific wedge-shaped magnets that exhibits better torque capability than its counterparts was researched. Based on the principles of an inner-rotor FSPM motor with hybrid excitation, preliminary studies on the design parameters of outer-rotor FSPM motor with hybrid excitation were discussed and presented in [26]. In [27], a new outer-rotor V-shaped FSPM (V-FSPM) motor was proposed to improve the PM utilization and the output torque. In the V-FSPM motor, the stator pole number is reduced by half and two rectangular PM pieces are purposely placed in one stator pole in a V shape, which can realize flux focusing effects to increase the flux density in the air gap. Experimental tests of the above studies verify that outer-rotor FSPM motors are suitable for in-wheel traction. To sum up, outer-rotor FSPM motors are viable for further research and have great potential to be used in EVs traction drives. However, the amount of PMs is excessive and the coupling between three phases is obvious in the outer-rotor FSPM topologies mentioned above. Therefore, this paper proposes a novel modular-stator outer-rotor flux-switching permanent-magnet (MSOR-FSPM) motor whose modular stator can be easily replaced. Compared with conventional outer-rotor flux-switching permanent-magnet (COR-FSPM) motors, the amount PM of the MSOR-FSPM motor is reduced and PM utilization is improved. In this paper, the structure, operation and design principles of the MSOR-FSPM motor are introduced and analyzed. Secondly, the rotor pole number for the 12-stator-slot MSOR-FSPM

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motor is researched, its influences on cogging torque, torque ripple and electromagnetic torque are analyzed suitable topology is chosen for further study. Thirdly, several main dimensions Energiesand 2017,a10, 937 3 of 19of the chosen MSOR-FSPM motor are optimized to reduce the torque ripple. Finally, the utilization of PMs in torque are analyzed anda aCOR-FSPM suitable topology for further study. a MSOR-FSPM motor and motor is is chosen compared from the pointThirdly, of viewseveral of themain magnetic dimensions of the chosen motor are optimized to reduce the torque ripple. Finally, the flux path and verified by theMSOR-FSPM FEM. utilization of PMs in a MSOR-FSPM motor and a COR-FSPM motor is compared from the point of view of the flux Principle path and verified the FEM. 2. Structure andmagnetic Operation of the by MSOR-FSPM Motor 2. Structure andMSOR-FSPM Operation Principle 2.1. Structure of the Motor of the MSOR-FSPM Motor

A 3D structure a cross-sectional view of the MSOR-FSPM motor are shown in Figure 1. 2.1. Structure of theand MSOR-FSPM Motor The rotor consists of a simple laminated iron core with salient poles. The stator consists of three modules A 3D structure and a cross-sectional view of the MSOR-FSPM motor are shown in Figure 1. The MA , rotor MB , and MCof . The structure, sizeiron andcore material of three modules areconsists all theof same. module consists a simple laminated with salient poles. The stator three Each modules represents one phase and consists of one “W”-shaped laminated segment, two “V”-shaped laminated MA, MB, and MC. The structure, size and material of three modules are all the same. Each module segments and one twophase PMs.and “W”-shaped laminated segment is placed in the of thelaminated module, two represents consists of one “W”-shaped laminated segment, twomiddle “V”-shaped “V”-shaped segments are placed at the bothisends of in the two two PMs are segmentslaminated and two PMs. “W”-shaped laminated segment placed themodule, middle ofand the the module, “V”-shaped laminated between segments are at the both ends ofsegment the module, the two PMs are respectively sandwiched the placed “V”-shaped laminated andand “W”-shaped laminated respectively sandwiched between the “V”-shaped laminated segment and “W”-shaped laminated segment. The magnetization direction of each PM is along circumference and it is opposite between segment.PMs. The magnetization of each PMconcentrated is along circumference it is opposite between the adjacent Furthermore,direction non-overlapping armatureand windings are placed in each the adjacent PMs. Furthermore, non-overlapping concentrated armature windings are placed in each stator slot and each phase windings are connected in series. In order to obtain balanced three-phase stator slot and each phase windings are connected in series. In order to obtain balanced three-phase back-EMF and reduce the coupling between three phases, non-magnetic blocks are placed between the back-EMF and reduce the coupling between three phases, non-magnetic blocks are placed between adjacent modules.modules. After theAfter windings are placed the stator slot, the slot, whole will be strengthened the adjacent the windings are in placed in the stator thestator whole stator will be by epoxy resin to ensure the mechanical strength of modular stator. strengthened by epoxy resin to ensure the mechanical strength of modular stator. Phase A w st

hry w rp hrt l g

τp

+

Rotor C

M

τc

C1

-

+

B2

+

-

"V"-shaped laminated segments +

τm -

(a)

MB

Phase C

Phase B

+

C2

B1

PM "W"-shaped laminated segments

ws

+ MAhsy - w pm A2 τd A1

Non-magnetic block

(b)

Figure 1. Structure of the MSOR-FSPM motor: (a) 3D structure of the MSOR-FSPM motor;

Figure 1. Structure of the MSOR-FSPM motor: (a) 3D structure of the MSOR-FSPM motor; (b) Cross-sectional view of the MSOR-FSPM motor. (b) Cross-sectional view of the MSOR-FSPM motor.

2.2. Operation Principle of the MSOR-FSPM Motor

2.2. Operation Principle of the MSOR-FSPM Motor

For simplicity, the module MA is taken as an example to explain how the electromagnetic torque is produced. When rotor rotates the different positionstoθ1explain , θ2, θ3 and θ4,the the electromagnetic distributions of the For simplicity, thethe module MA isto taken as an example how torque main magnetic flux lines in module M A are shown in Figure 2. The rotor poles align with the stator is produced. When the rotor rotates to the different positions θ 1 , θ 2 , θ 3 and θ 4 , the distributions of the when the rotor is at position θ1, and all magnetic flux lines go through winding A from stator mainteeth magnetic flux lines in module MA are shown in Figure 2. The rotor poles align with the stator to rotor and the PM flux linkage of winding A reaches its negative extreme value. Then, the rotor teeth when the rotor is at position θ 1 , and all magnetic flux lines go through winding A from stator to pole aligns with one PM and the rotor slot aligns with the other PM when the rotor rotates to the rotorposition and theθPM flux linkage of winding A reaches its negative extreme value. Then, the rotor pole 2, no magnetic flux lines go through winding A if flux leakage is neglected. Next, the rotor aligns with one align PM and aligns the other when the rotates the position poles again withthe therotor statorslot teeth whenwith the rotor rotatesPM to position θ3.rotor However, theto magnetic θ 2 , no magnetic flux lines go through winding A if flux leakage is neglected. Next, the rotor poles flux lines go through winding A from rotor to stator and its direction is opposite to that of position againθ1align with stator when the rotor rotatesextreme to position . However, thepole magnetic , the PM fluxthe linkage of teeth winding A reaches the positive value.θ 3Finally, the rotor aligns flux one PM and rotor slot aligns rotor with the when the rotor rotates to the position 4, and no θ 1 , lineswith go through winding A from to other statorPM and its direction is opposite to that θof position magnetic flux lines through again.extreme If the rotor continues thepole samealigns the PM flux linkage of go winding A winding reaches A theonce positive value. Finally,rotating, the rotor will be repeated periodically. It can be found from the PM − θr curve in Figure 3 that the withprocesses one PM and rotor slot aligns with the other PM when theΨrotor rotates to the position θ 4 , and flux linkage of winding A is bipolar and it realizes “switching” flux at the position of θ2 and θ4. no magnetic flux lines go through winding A once again. If the rotor continues rotating, the same Analyzed from the “generator-oriented” perspective, back-EMF can be induced based on the

processes will be repeated periodically. It can be found from the Ψ PM − θ r curve in Figure 3 that

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the flux linkage of winding A is bipolar and it realizes “switching” flux at the position of θ 2 and θ 4 . Energies 2017, 10, 937 4 of 19 Analyzed from “generator-oriented” perspective, back-EMF can be induced based on the Faraday’s Energies 2017, the 10, 937 4 of 19 law ofFaraday’s electromagnetic induction. If appropriate is fedcurrent into the electromagnetic law of electromagnetic induction. Ifcurrent appropriate is windings, fed into the windings, Faraday’s law of electromagnetic induction. appropriate current is fed into the windings, torque will be produced to will drive rotor rotating. electromagnetic torque be the produced to driveIf the rotor rotating. electromagnetic torque will be produced to drive the rotor rotating.

-

A2

0 0 A2

A1

A1 + -A2 +θ Position 1

+ +

Position θ1

A2

0 0 A1 A1 + + Position θ2 Position θ2

-A2 -

0 0

+ +

0 0

A2

A1

A1 A1 + + Position θ4 Position θ4

-A2 A1 + + Position θ

-A2 -

3

Position θ3

Figure 2. Distributions themain mainmagnetic magnetic flux MAM . . Figure 2. Distributions ofofthe fluxlines linesininmodule module A Figure 2. Distributions of the main magnetic flux lines in module MA.

e e ψPM ψPM

θ1 θ2 θ3 θ4 θ1 θ2 θ3 θ4

θ1 θ2 θ3 θ4 θ1 θ2 θ3 θ4

θr θr

θ1 θ2 θ3 θ4 θ1 θ2 θ3 θ4

θr θr

θr θr i i

Figure 3. Waveforms of PM flux linkage, no-load back-EMF, and phase current. Figure 3. Waveforms PMflux fluxlinkage, linkage, no-load no-load back-EMF, phase current. Figure 3. Waveforms ofofPM back-EMF,and and phase current. 2.3. Basic Design Principles of the MSOR-FSPM Motor 2.3. Basic Design Principles of the MSOR-FSPM Motor 2.3. Basic Design Principles of the MSOR-FSPM Motor Based on the traditional power equation of FSPM motors, the design equation of the MSORBased oncan thebetraditional power FSPM motor deduced as [28]: equation of FSPM motors, the design equation of the MSORBased on thecan traditional power equation of FSPM motors, the design equation of the MSOR-FSPM FSPM motor be deduced as [28]:

motor can be deduced as [28]:

Pout Dso2 lef  Pout Dso2 lef  2 33 N r 2 k2sio As Bg max ncs 2 N r kd kPs out 2 Dso le f = √120 N k k k 3 N s d s2 sio As Bg max ncs 2π Nr 120 120 Ns ks d k s k sio As Bgmax ncs η

(1) (1)

where Dso is stator outer diameter, lef is the effective length of the motor, Pout is the output power, Nr

(1)

Dstator so is stator outer diameter, lef is the effective length of the motor, Pout is the output power, Nr isDthe number of rotordiameter, poles, Ns lis number of stator poles, kd ismotor, magnetic leakage coefficient, wherewhere outer is the effective length of the Poutflux is the output power, Nr is so is ef the is the number of rotor kpoles, Ns ratio is theofnumber of stator poles, kd is magnetic flux leakage coefficient, k s is chute coefficient, sio is the inside diameter and outside diameter of the stator, A s is the the number of rotor poles, Ns is the number of stator poles, kd is magnetic flux leakage coefficient, kline s is chute coefficient, ksio is the ratio of inside diameter and outside diameter of the stator, As is the load, B gmax is the peak air gap flux density at no-load, n is the rotation speed, cs is the pole arc ks is chute coefficient, ksio is the ratio of inside diameter and outside diameter of the stator, As is the line load, Bof gmax is the peak air gap flux density at no-load, n is the rotation speed, cs is the pole arc coefficient stator tooth, and η is the motor efficiency. line load, Bgmaxofisstator the peak air density at no-load, n is the rotation speed, cs is the pole arc coefficient tooth, andgap η isflux theMSOR-FSPM motor efficiency. The main design parameters of motor are shown in Figure 1b. The air gap length coefficientThe of stator tooth,parameters and η is the motor efficiency. main design of MSOR-FSPM motor are motor shownthat in Figure The air gap lg is chosen as 0.5 mm. It is the same with inner-rotor FSPM stator 1b. tooth width wst,length stator The main design parameters of MSOR-FSPM motor are shown in Figure 1b. The air length lyoke g is chosen as 0.5 mm. It is the same with inner-rotor FSPM motor that stator tooth width wst,gap stator height hsy and permanent magnet width wpm are equal to each other, but the stator slot width ws yoke height andstator permanent magnet wpm are equal tomotor each other, the tooth stator slot width s lg is chosen as 0.5hsymm. It is tooth the same with inner-rotor FSPM that stator width wst ,wstator is three times the width wstwidth to obtain a larger stator slot area.but When the stator diameter three times the stator tooth width w st to obtain a larger stator slot area. When the stator diameter yoke is height h and permanent magnet width w are equal to each other, but the stator slot width ws sy pm Dso is obtained, wst, hsy, wpm and ws are calculated according the following relationship [22]: Dsotimes is obtained, wst, htooth sy, wpm and ws are calculated according the following relationship [22]: is three the stator width wst to obtain a larger stator slot area. When the stator diameter Dso is obtained, wst , hsy , wpm and ws are calculated according the following relationship [22]:

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wst = hsy = w pm = ws /3 = πDso /6Ns

(2)

In order to prevent the magnetic saturation of the rotor pole and rotor yoke, the rotor pole height hrt and rotor yoke height hry are preselected as 1.4 wst . Moreover, the rotor pole arc coefficient is pre-selected as 0.5. After the main parameters, such as the dimensions of the stator and the rotor pole, are calculated by using the relationships above, the rotor outer radius Rro can be obtained as: Rro =

Dso 1.4πDso + lg + 2 3Ns

(3)

This MSOR-FSPM motor is used for a four-wheel drive vehicle. Its output power Pout is pre-chosen as 1.5 kW, which is appropriately reduced to obtain a small prototype motor to verify the theoretical analysis. The effective length lef of the motor is chosen as 100 mm, which is close to the length of in-wheel motor that used in EVs. When the theoretical sizes are obtained based on the above relationships, they are adjusted slightly considering the processing technology. For example, the main parameters of the initial designed 12-slot/10-pole MSOR-FSPM motor are shown in Table 1. Table 1. Main parameters of the initial designed 12-slot/10-pole MSOR-FSPM motor. Symbol

Machine Parameter

MSOR-FSPM

Unit

m Ns Nr α Ncoil PM n Pout Dro Dsi Dso wst lef hrp hry wrp lg Br Ismax

Phase number Number of stator poles Number of rotor poles Rotor pole arc coefficient Number of turns per coil Magnet material Base speed Based output power Rotor outer diameter Stator inner diameter Stator outer diameter Stator tooth width Motor active length Rotor pole height Rotor yoke height Rotor pole width Air gap length Magnet remanence (20 ◦ C) Rated current amplitude

3 12 10 0.5 70 NTP40UH 800 1.5 155 70 125 5.5 100 7.5 7 19.8 0.5 1.26 15.4

r/min kW mm mm mm mm mm mm mm mm mm T A

Based on the operation principle of MSOR-FSPM motor, the period of back-EMF and magnetic field is one rotor pole pitch. Hence, one rotor pole pitch of the MSOR-FSPM motor is equal to 360◦ (electrical angle), which is expressed as mechanical angle meeting the following Equation (4), and the electrical period of the back-EMF can be determined by the following Equation (5) [29]: τp =

360◦ Nr

(4)

τp 6n

(5)

t EMF =

where τ p is the mechanical angle between two adjacent rotor poles and its unit is degree (◦ ); Nr is the number of rotor poles; n is rotation speed of rotor and its unit is revolutions per minute (r/min); tEMF is electrical period and its unit is second (s). In order to obtain balanced three-phase back-EMF, some key parameters of the stator modules should be carefully designed using the following equations:

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 c  h p

(6)

τc = hτ1p

   k  p 1 2   τm = i + k τp

(6) (7) (7)

 2ll τdd =  jj + 2 m m 

(8) (8)

m  i 

2

  τpp 

!

where represent phase A, phase phase B B where the the value value of of kk and and ll is is 00 or or 1, 1, the the three three stator stator modules modules respectively respectively represent phase A, and phase phase C C in in the the counter-clockwise counter-clockwise direction direction when when ll is is equal equal to to 0, 0, and and respectively respectively represent represent phase phase and A, phase B and phase C in the clockwise direction when l is equal to 1; i, j, and h are all non-negative A, phase B and phase C in the clockwise direction when l is equal to 1; i, j, and h are all non-negative integer, ττcc is is the the mechanical mechanical angle angle between between two two adjacent adjacent slot slot conductors conductors that that belong belong to to the the same same coil, coil, integer, is the the mechanical mechanical angle angle between between two two adjacent adjacent PMs PMs in in each is the the mechanical ττmm is each module, module, ττdd is mechanical angle angle between two adjacent modules. between two adjacent modules. The single-coil vector sum of two adjacent slot conductors. Equation (6) can The single-coilback-EMF back-EMFisisthe the vector sum of two adjacent slot conductors. Equation (6)make can the phase angle of back-EMF in two adjacent slot conductors that belong to the same coil approximately make the phase angle of back-EMF in two adjacent slot conductors that belong to the same coil antiphase, which lets the coil pitch be pitch approximately equal to 1. Equation (7)1.can make the approximately antiphase, which letsfactor the coil factor be approximately equal to Equation (7) phase angle back-EMF in back-EMF different coils that belong thebelong same to phase winding be winding cophase be or can make theofphase angle of in different coils to that the same phase antiphase, which lets the distribution factor of the winding be close to 1. Equation (8) can make the cophase or antiphase, which lets the distribution factor of the winding be close to 1. Equation (8) can phase the difference of no-loadofback-EMF between different be 120◦ (electrical angle). angle). make phase difference no-load back-EMF between windings different windings be 120° (electrical It is is worth worth noting noting that that the the value value of of kk has hasaasignificant significanteffect effecton onthe theno-load no-loadback-EMF back-EMFwaveforms. waveforms. It For example, a 12-slot/20-pole MSOR-FSPM motor is shown in Figure 4, in which the value of1.k For example, a 12-slot/20-pole MSOR-FSPM motor is shown in Figure 4, in which the value of k is is 1. winding The winding connection is shown as Figure be found from Figure that the no-load The connection is shown as Figure 4a. It 4a. canItbecan found from Figure 4b that4bthe no-load backback-EMF waveforms of coil A1 and coil A2 are almost the same, but the positive and negative back-EMF EMF waveforms of coil A1 and coil A2 are almost the same, but the positive and negative back-EMF waveforms induced in in coils of waveforms induced coils are are asymmetrical, asymmetrical, which which makes makes the the no-load no-load back-EMF back-EMF waveforms waveforms of windings 12-solt/10-pole MSOR-FSPM motor is shown in Figure 5, in which windings seriously seriouslyasymmetrical. asymmetrical.A A 12-solt/10-pole MSOR-FSPM motor is shown in Figure 5, in the value of k is 0. The winding connection is shown as Figure 5a. It can be found from Figure 5b that which the value of k is 0. The winding connection is shown as Figure 5a. It can be found from Figurethe 5b no-load waveforms of coil A1of and arecoil different. But the positive waveform that the back-EMF no-load back-EMF waveforms coilcoil A1A2 and A2 are different. But theback-EMF positive back-EMF of coil A1 isof symmetrical the negative waveform of coilwaveform A2, and theofnegative waveform coil A1 is with symmetrical withback-EMF the negative back-EMF coil A2,back-EMF and the waveform of coil A1 is symmetrical with the positive back-EMF waveform of coil A2, which makes the negative back-EMF waveform of coil A1 is symmetrical with the positive back-EMF waveform of coil no-load back-EMF waveforms of windings symmetrical. In order to prevent theIn asymmetrical winding A2, which makes the no-load back-EMF waveforms of windings symmetrical. order to prevent the back-EMF causing poor motor performances, the value of k is chosen as 1. asymmetrical winding back-EMF causing poor motor performances, the value of k is chosen as 1. 150

+

+

A2

+

+

A1 C2 C1

B2

-

+

-

-

-

B1

No-load back EMF (V)

Coil A1

-

-

Winding A

50 0 -50 -100 -150

+

0

(a)

Coil A2

100

40

80

120 160 200 240 280 320 360

Rotor position (elec.deg)

(b)

Figure 4. 12-slot/20-pole MSOR-FSPM motor: (a) Cross-sectional view of the 12-slot/20-pole Figure 4. 12-slot/20-pole MSOR-FSPM motor: (a) Cross-sectional view of the 12-slot/20-pole MSOR-FSPM motor; (b) No-load back-EMF waveforms of coil A1, coil A2, and winding A. MSOR-FSPM motor; (b) No-load back-EMF waveforms of coil A1, coil A2, and winding A.

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+

-

A2

A1

+

-

C2

B1

-

Coil A2

Winding A

50 0 -50 -100

+

+

-

+

C1

B2

Coil A1

100

-

No-load back EMF (V)

+

-

0

40

80

120 160 200 240 280 320 360

Rotor position (elec.deg)

(a)

(b)

Figure 5. 12-slot/10-pole MSOR-FSPM motor: (a) Cross-sectional view of the 12-slot/10-pole Figure 5. 12-slot/10-pole MSOR-FSPM motor: (a) Cross-sectional view of the 12-slot/10-pole MSOR-FSPM MSOR-FSPMmotor; motor; (b) (b) No-load No-load back-EMF back-EMF waveforms waveforms of of coil coil A1, A1, coil coil A2, A2, and and winding winding A. A.

3. Influences of Rotor Pole Number 3. Influences of Rotor Pole Number The electromagnetic torque can be derived by differentiating the co-energy with respect to the The electromagnetic torque can be derived by differentiating the co-energy with respect to the mechanical angle, the co-energy Wc and electromagnetic torque Tem with constant current can be given mechanical angle, the co-energy Wc and electromagnetic torque Tem with constant current can be given as the following Equations [30]: as the following Equations [30]:

1 1 Wc  1Li 22  1  R  Rm  Φ2m2  N coil iΦm Wc =2 Li − 2 ( R + Rm )Φm + Ncoil iΦm 2

2

(9) (9)

c =W∂W c∂θ em   TTem dΦm 1 2 dL 2 dR + N (10) = 2 i dθ − 12 Φm coil i dθ dθ = T + T + T dΦ 1 dL 1cog dRPM rm (10)  i2  Φm2  Ncoil i m 2 d R and Rdm are the reluctances seen by the where i is the coil current; L is the2coildinductance; Trm  Tcog  TPM respectively; Ncoil is the number of turns per coil; magnetomotive force source and themagnetic field,

Φm is the magnetic flux of the PM; θ is the rotor position; Trm is the reluctance torque generated by where i isinductance the coil current; L is therotor coil position; inductance; Rm are the reluctances seen by the winding variations with TcogRisand the cogging torque produced by the PM magnetomotive force source and the magnetic field, respectively; N coil is the number of turns per coil; field energy variations with rotor position; TPM is the PM torque produced by the interaction of the Φ m is the magnetic flux of the PM; θ is the rotor position; Trm is the reluctance torque generated by magnetic field generated by PMs and the coil current. winding inductance variations withT rotor position; Tcog is the cogging torque produced by the PM However, the cogging torque cog will not produce an effective average torque but only cause field energy with rotor position; the PM producedtorque by theT interaction of the torque ripplevariations Trip . The torque ripple Trip canTPM be is defined bytorque the maximum max , the minimum magnetic field generated by PMs and the coil current. torque Tmin and average torque Tavg given by the following Equation (11): However, the cogging torque Tcog will not produce an effective average torque but only cause torque ripple Trip. The torque ripple Trip can be defined Tmax − Tminby the maximum torque Tmax, the minimum · 100% (11) Trip = torque Tmin and average torque Tavg given by the following Equation (11): Tavg

T influences  Tmin Therefore, cogging torque Tcog has on Tripgreat  max  100 %electromagnetic torque Tem and torque (11) Tavgis ignored, the co-energy Wc can be replaced by air ripple Trip . If the energy variation in the iron core gap energy, the cogging torque expression in FSPM motor can be obtained by [30]: Therefore, cogging torque Tcog has great influences on electromagnetic torque Tem and torque core is ignored, ∞ ripple Trip. If the energy variation inπN ther Liron the co-energy Wc can be replaced by air stk 2 2 Tcog (θ )expression = rFSPM nGcan sin(nNr θby (12) ) [30]: n BrnN ∑ 2 − r1 motor gap energy, the cogging torque in beLobtained 4µ0 n =1

 N L where Lstk is the axial stackTcog length; of nthe r2 is rotor; r22  radius r12   nG BrnNstator; sin  nN   r1 is rthestkouter  inner radius of the (12)  r the  4  n 1 0 G and B are the corresponding Fourier coefficients of the relative air gap permeance function and L

n

rnNL

flux density function; NL =length; Nr /(LCM(N Nr )), and LCM(N Nr ) is the common multiple of the s , outer s , stator; where Lstk is the axial stack r1 is the radius of the r2 isleast the inner radius of the rotor; number of stator poles and number of rotor poles. Gn and BrnNL are the corresponding Fourier coefficients of the relative air gap permeance function and flux density function; NL = Nr/(LCM(Ns, Nr)), and LCM(Ns, Nr) is the least common multiple of the number of stator poles and number of rotor poles.

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Equation (12) shows that cogging torque can be weakened by choosing an appropriate number of rotor poles, which will further enhance the torque stability. Therefore, the number of rotor poles Equation (12) shows that cogging torque can be weakened by choosing an appropriate number of in MSOR-FSPM motor should be carefully designed and meet the following principles: rotor poles, which will further enhance the torque stability. Therefore, the number of rotor poles in motor be carefully andto meet the following principles: MSOR-FSPM The number of should rotor poles cannot designed be too large ensure appropriate mechanical strength of rotor poles. The number of rotor poles cannot be too large to ensure appropriate mechanical strength of •  The number of rotor poles cannot be a multiple of 3 to obtain three-phase back-EMF. rotor poles.  The outside diameter, air gap length, stack length, PM width, and stator tooth width of different • The number of rotor poles cannot be a multiple of 3 to obtain three-phase back-EMF. topologies keep constant. • The outside diameter, length, stack length, PM width, and stator tooth width of different  Equations (6)–(8) mustair begap satisfied. topologies keep constant.  The stator tooth cannot be supersaturated. • Equations (6)–(8) must be satisfied.  The stator slot area is utilized as fully as possible. • The stator tooth cannot be supersaturated. The appropriate numbers of rotor poles based on the above principles are 10, 11, 22, and 23. For • The stator slot area is utilized as fully as possible. these four motors, the mainly different parameters are shown in Table 2, and the no-load back-EMF The appropriate of rotor poleswaveforms based on the 10, be 11,found 22, and 23. waveforms of windingnumbers A and cogging torque are above shownprinciples in Figure 6.are It can from For these the mainly different parameters are shown in Tablebecause 2, and the no-load back-EMF Figure 6a four that motors, the no-load back-EMF waveforms are almost coincident different numbers of waveforms ofare winding A and cogging torque waveforms shown in Figure 6. should It can be turns per coil adopted to make the amplitude roughlyare equal to each other. It befound notedfrom that Figure 6a that waveforms the no-load of back-EMF waveforms almost coincident numbers the back-EMF these four motors areare seriously distorted. Itbecause can be different found from Figureof 2 turnsthe perpositive coil aremagnetic adopted to make amplitude roughly equal flux to each other. It should noted that that flux paththe and the negative magnetic path of coils are notbecompletely the back-EMFwhich waveforms four motors seriously distorted.the It can be found Figure symmetrical, resultsofinthese distortion of coil are back-EMF. Moreover, magnetic fluxfrom paths of coil2 thatand thecoil positive magnetic flux and the negativeofmagnetic flux path of coils be arecounteracted not completely A1 A2 are the same, thepath inherent harmonics the coil back-EMF cannot by symmetrical, which results in distortion of coil back-EMF. Moreover, the magnetic flux paths of coil each other when phase back-EMF is obtained. Therefore, the distortion of phase no-load back-EMF A1serious. and coilItA2 arebe theseen same, the Figure inherent6bharmonics of the coil back-EMF cannot beand counteracted by is can from that cogging torque is the minimum has the best each other when back-EMF is obtained. of phase no-load back-EMF periodicity whenphase the rotor pole number is 10.Therefore, Therefore,the thedistortion 12-slot/10-pole MSOR-FSPM motor is serious.toIt be canresearched be seen from Figure chosen further in 6b thethat nextcogging section.torque is the minimum and has the best periodicity when the rotor pole number is 10. Therefore, the 12-slot/10-pole MSOR-FSPM motor is chosen to be Tablesection. 2. Different parameters of MSOR-FSPM motors. researched further in the next Main2.Parameter 10P 11P 22P 23P Table Different parameters of MSOR-FSPM motors. τc (°) 36 32.73 32.72 31.30 54 11P 49.09 57.27 Main Parameterτm (°) 10P 22P 54.78 d (°) 120 120 120 120 τ ◦ τc ( ) 36 32.73 32.72 ◦ τ p (°) 36 32.73 16.36 15.65 τm ( ) 54 49.09 57.27 τ d (◦ ) 120 120 1 n 1 2 120 2 τ p (◦ ) 36 i 1 32.731 316.36 3 n 1 1 2 j 3 3 7 7 i 1 1 3 l 0 1 0 1 j 3 3 7 l

0

10-pole 11-pole

22-pole 23-pole

50 0 -50

0

31.30 54.78 120 15.65 2 3 7 1

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4

Cogging torque (N.m)

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100

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80

120 160 200 240 280 320 360

Rotor position (elec.deg)

(a)

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120 160 200 240 280 320 360

Rotor position (elec.deg)

(b)

Figure 6. No-load performances of different MSOR-FSPM motors: (a) No-load back-EMF waveforms Figure 6. No-load performances of different MSOR-FSPM motors: (a) No-load back-EMF waveforms of winding A; (b) Cogging torque waveforms. of winding A; (b) Cogging torque waveforms.

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4. Optimization of the Main Parameters in the 12-Slot/10-Pole MSOR-FSPM Motor The average electromagnetic electromagnetic torque torque and and torque torque ripple ripple of of the the 12-slot/10-pole 12-slot/10-pole MSOR-FSPM MSOR-FSPM motor are 19.97 19.97 N N·m and47.08%, 47.08%,respectively. respectively.It Itis is obvious that torque ripple is too large. of ·m and obvious that thethe torque ripple is too large. TheThe aim aim of this this section is to reduce the torque ripple by optimizing the parameters that mainly influence the section is to reduce the torque ripple by optimizing the parameters that mainly influence the torque torque performance, these parameters are shown in Figure the 7. Considering the motor performance, and theseand parameters are shown in Figure 7. Considering motor manufacture, it is manufacture, it place is notwindings practical to place windings if theopen. statorIn slot is fully open. In order to slipping prevent not practical to if the stator slot is fully order to prevent windings windings slipping the stator slot, it isa appropriate a pole to the stator slotsthe to off the stator slot, itoff is appropriate to add pole shoe to to theadd stator slots shoe to conveniently install conveniently install the However, themagnetic pole shoe change theand magnetic field slot wedge. However, theslot polewedge. shoe can change the fieldcan distributions, the width of distributions, and the of stator slottoopening an important factor to influence ripple stator slot opening is anwidth important factor influenceistorque ripple and average torque. torque Therefore the and average torque. Therefore and size of poledesigned. shoe (hw, hOn h, htthe ) should strictly designed. shape and size of pole shoe (hwthe , hh ,shape ht ) should be strictly other be hand, rotor pole arc On the other rotor pole arc coefficient (wrpperformances /τp) has a significant effect on the performances of coefficient (wrphand, /τ p ) has a significant effect on the of the salient motor, rotor pole width the salient motor, rotor pole width (w rp ) is changed to get an appropriate pole arc coefficient. In (wrp ) is changed to get an appropriate pole arc coefficient. In addition, it can be seen from Figure 6a addition, it can be seen from Figure 6a that the distortion of no-load back-EMF is serious, leads that the distortion of no-load back-EMF is serious, which leads to torque harmonics when which a sinusoidal to torque a sinusoidal currentto is make fed into windings. It is necessary to make the current is harmonics fed into thewhen windings. It is necessary thethe positive magnetic flux path symmetrical positive flux pathflux symmetrical with the magnetic flux path toTherefore, obtain lowthe no-load with the magnetic negative magnetic path to obtain lownegative no-load back-EMF distortion. tooth back-EMF Therefore, thesegments tooth width of the “V”-shaped laminated segments that adjoin width of thedistortion. “V”-shaped laminated that adjoin with non-magnetic blocks should be reduced, with non-magnetic blocks reduced, and the reduced width (Vtw) is also optimized. and the reduced width (Vtwshould ) is alsobeoptimized.

ht

hh

I

rectangle

II

hh

hw

hw

trapezoid

Vt

w

w rp

Non-magnetic block 12S/10P MSOR-FSPM Figure 7. Main optimized parameters of 12S/10P MSOR-FSPM motor. motor.

4.1. 4.1. Stator Stator Pole Pole Shoe Shoe There two available available pole pole shoe There are are two pole shoe shoe shapes—rectangle shapes—rectangle pole shoe and and trapezoid trapezoid pole pole shoe—which shoe—which are shown in Figure 7. h h and hw are the height and width of the pole shoe, respectively. hh and hw are are shown in Figure 7. hh and hw are the height and width of the pole shoe, respectively. hh and hw no thanthan 2 mm to ensure the appropriate slot slot area.area. ht is hthe thickness of trapezoid pole shoe and arelarger no larger 2 mm to ensure the appropriate t is the thickness of trapezoid pole shoe it is itequal to 2tomm. TheThe combinations of of different parameters are and is equal 2 mm. combinations different parametersand andshapes shapesofofthe the pole pole shoe shoe are expressed as “h w_hh rectangle” and “hw_hh trapezoid”. Cogging torque and electromagnetic torque of expressed as “hw _hh rectangle” and “hw _hh trapezoid”. Cogging torque and electromagnetic torque of the combinations are are shown shown in in Figure Figure 8. 8. the main main combinations Figure 8a shows that the cogging torque a Figure 8a shows that the cogging torqueof ofthe themotor motorwith withpole poleshoe shoeisissmaller smallerthan thanthat thatofof motor without pole shoe. Figure 8b also shows that the torque ripple of a motor with pole shoe is a motor without pole shoe. Figure 8b also shows that the torque ripple of a motor with pole shoe is smaller of aa motor motor without without pole pole shoe. shoe. When combination is mm_1 mm mm smaller than than that that of When the the pole pole shoe shoe combination is “2 “2 mm_1 rectangle”, the cogging torque of the motor is the minimum. When the pole shoe combination is rectangle”, the cogging torque of the motor is the minimum. When the pole shoe combination is “2 mm_2 mm rectangle”, the torque ripple 25.47% of motor is the minimum. Moreover, when the “2 mm_2 mm rectangle”, the torque ripple 25.47% of motor is the minimum. Moreover, when the pole pole shoe combination is “2 mm mm_1 mm trapezoid”, theripple torque ripple is of26.98%, motor which is 26.98%, which is shoe combination is “2 mm_1 trapezoid”, the torque of motor is close to the close to the minimum value. Using Fast Fourier Transform (FFT) to analyze cogging torque and minimum value. Using Fast Fourier Transform (FFT) to analyze cogging torque and electromagnetic electromagnetic torque,period and transform based on the back-EMF period, the of each torque, and transform is basedperiod on theisback-EMF period, the amplitude ofamplitude each harmonic is harmonic is shown in Figure 9. shown in Figure 9.

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Cogging torque (N.m) Cogging torque (N.m)

4 34 23 12 01

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Electromagnetic torque (N.m) Electromagnetic torque (N.m)

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30 27 27 24 24 21 21 18

-10

18 15

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(a) Rotor position (elec.deg)

40

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Rotor position (elec.deg)

80

120 160 200 240 280 320 360

(b) Rotor position (elec.deg)

(a) (b) Figure 8. Cogging torque and electromagnetic torque: (a) Cogging torque of 12S/10P MSOR-FSPM Figure 8. Cogging torque and electromagnetic torque: (a) Cogging torque of 12S/10P MSOR-FSPM motor; Electromagnetic torque of 12S/10P MSOR-FSPM Figure(b) 8. Cogging torque and electromagnetic torque: (a) motor. Cogging torque of 12S/10P MSOR-FSPM motor; (b) Electromagnetic torque of 12S/10P MSOR-FSPM motor. Cogging torque amplitude (N.m) Cogging torque amplitude (N.m)

4.5

No pole shoe 2mm_2mm rectangle No pole shoe 2mm_1mm rectangle 2mm_2mm rectangle 2mm_1mm trapezoid 2mm_1mm rectangle 2mm_1mm trapezoid

4.5 4.0 4.0 3.5 3.5 3.0 3.0 2.5 2.5 2.0 1.5 1.0

4

3 3 2

1

1.0 0.5 0.0

No pole shoe 2mm_2mm rectangle No pole shoe 2mm_1mm rectangle 2mm_2mm rectangle 2mm_1mm trapezoid 2mm_1mm rectangle 2mm_1mm trapezoid

4

2

2.0 1.5

0.5 0.0

Electromagnetic torque amplitude (N.m) Electromagnetic torque amplitude (N.m)

motor; (b) Electromagnetic torque of 12S/10P MSOR-FSPM motor.

1st 2nd 3rd 4th 5th 6th 7th 8th 9th

Harmonic order

1st 2nd 3rd 4th 5th 6th 7th 8th 9th

(a) Harmonic order (a)

1

0 0

1st 2nd 3rd 4th

5th

6th

Harmonic order

1st 2nd 3rd 4th

5th

6th

7th

(b) order Harmonic

7th

8th 8th

9th 9th

(b)

Figure 9. FFT results of cogging torque and electromagnetic torque: (a) Amplitude of each harmonic in cogging torque; (b) of Amplitude of eachand harmonic in electromagnetic torque. Figure 9. FFT results cogging torque electromagnetic torque: (a) Amplitude of each harmonic

Figure 9. FFT results of cogging torque and electromagnetic torque: (a) Amplitude of each harmonic in in cogging torque; (b) Amplitude of each harmonic in electromagnetic torque. cogging (b) Amplitude each harmonic in electromagnetic torque. Thetorque; FFT results of coggingof torque and electromagnetic torque show that the main harmonics of

all combinations are the 3rd order, the 6th and the 9thtorque order.show The 6th The FFT results of cogging torque andorder electromagnetic thatharmonic the mainamplitude harmonicsof of cogging torque and electromagnetic torque of all combinations is close. In the motor without pole all combinations are the 3rd order, the 6th order and the 9th order. The 6th harmonic amplitude of The FFT results of cogging torque and electromagnetic torque show that the main harmonics the 3rd harmonic amplitude is notably than that of the motor with pole shoe. Exceptpole for cogging torque and electromagnetic torque of all combinations close.The In the motor without of allshoe, combinations are the 3rd order, the 6thhigher order and the 9th isorder. 6th harmonic amplitude the motors whose pole shoe combinations are higher “2 mm_2 mm rectangle” and “2 mm_1 trapezoid”, shoe, the 3rd harmonic amplitude is notably than that of the motor with polemm shoe. Except for of cogging torque and electromagnetic torque of all combinations is close. In the motor without the 3rd harmonic amplitude of electromagnetic torque in motors and whose pole mm shoetrapezoid”, is other the motors whose pole shoe combinations are “2 mm_2 mm rectangle” “2 mm_1 pole combinations shoe, the 3rd harmonic amplitudethat is notably higher than that ofit the motor with pole shoe. is muchamplitude larger thanoftwice of cogging torque. can be deduced the the 3rd harmonic electromagnetic torque in Therefore, motors whose pole shoe that is other Except for the motors whose pole shoe combinations are “2 mm_2 mm rectangle” and “2 mm_1 armature reaction of motors pole shoe are “2Therefore, mm_2 mmitrectangle” and “2that mm_1 combinations is much largerwhose than twice that combinations of cogging torque. can be deduced the mm trapezoid”, thereaction 3rd harmonic amplitude electromagnetic torque in motors whose pole shoe is other mm trapezoid” is slight. Furthermore, the average torque are and slot area of motor whose shoe armature of motors whose poleof shoe combinations “2 mm_2 mm rectangle” andpole “2 mm_1 combinations is is much larger than twice the that of cogging torque. it shoe can be deduced combination “2ismm_1 mm trapezoid” are average larger than that of motor whose pole combination mm trapezoid” slight. Furthermore, torque and slotTherefore, area of motor whose pole shoe that iscombination “2 mm_2 mm on the “2 trapezoid” is and is “2rectangle”. mm_1 mmBased trapezoid” areabove larger than that ofresults, motor polemm shoe combination the armature reaction of motors whose pole shoecomparison combinations arewhose “2mm_1 mm_2 mm rectangle” chosen as the pole shoe scheme. is “2 mm_2 mm rectangle”. Based on the above comparison results, “2 mm_1 mm trapezoid” is “2 mm_1 mm trapezoid” is slight. Furthermore, the average torque and slot area of motor whose chosen as the pole shoe scheme. pole shoe combination is “2 mm_1 mm trapezoid” are larger than that of motor whose pole shoe 4.2. Rotor Pole Arc Coefficient combination is “2 mm_2 mm rectangle”. Based on the above comparison results, “2 mm_1 mm 4.2. Rotor Pole Arc Coefficient The poleasarc is scheme. equal to wrp/τp, which varies from 0.35 to 0.7 when the rotor pole trapezoid” is rotor chosen thecoefficient pole shoe pitch The τp isrotor constant. Variation of average torque torque ripple shown Figure pole arc coefficient is equal to wrp/τpand , which varies fromis0.35 to 0.7inwhen the10a. rotorWith pole increasing rotor pole arc coefficient, the torque ripple is first decreased and then increased. The pitchPole τp isArc constant. Variation of average torque and torque ripple is shown in Figure 10a. With 4.2. Rotor Coefficient average torque reduced because thethe fluxtorque leakage of the outer radius becomes more and increasing rotoris pole arc coefficient, ripple is magnet first decreased and then increased. The The rotor pole arc coefficient is equal to w /τ , which varies from 0.35 to 0.7 when the rp p more serious, as shown in Figure 10b.the In order to obtainofathe torque ripple as low as possible andmore average average torque is reduced because flux leakage magnet outer radius becomes androtor pole torque pitch τasp large is constant. average torquea torque and torque ripple shown inripple Figure possible, the rotor pole arcto coefficient is chosen asas 0.45, torque is 10a. more serious, asas shown inVariation Figure 10b.ofIn order obtain ripple lowwhose asispossible and average Withreduced increasing rotor pole arc coefficient, the torque ripple is first decreased and then increased. to large 24.92% average 20.66 torque as asand possible, thetorque rotor is pole arcN·m. coefficient is chosen as 0.45, whose torque ripple is reduced torque to 24.92% average torque is 20.66 The average is and reduced because the fluxN·m. leakage of the magnet outer radius becomes more

and more serious, as shown in Figure 10b. In order to obtain a torque ripple as low as possible and average torque as large as possible, the rotor pole arc coefficient is chosen as 0.45, whose torque ripple is reduced to 24.92% and average torque is 20.66 N·m.

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24 36 20 32 0.35

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0.65

(a)

0.70

16 28

Torque ripple (%) ripple (%) Torque

Average torque (N.m)torque (N.m) Average

56

Average torque Torque ripple

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24 20

(b)

16

12

0.35 10. 0.40 0.45 torque, 0.50 torque 0.55 0.60 0.70 leakage of magnet outer radius: (a) Average torque Figure Average ripple0.65 and flux

Pole arctorque coefficient Figure 10. Average torque, ripple and flux leakage of magnet outer radius: (a) Average torque and torque ripple with increasing rotor pole arc coefficient; (b) the flux leakage of magnet outer radius and torque ripple increasing rotor pole arc coefficient; (b) the flux leakage (a) (b)of magnet outer radius in module MAwith . in module MA .

Figure 10. Average torque, torque ripple and flux leakage of magnet outer radius: (a) Average torque

4.3. “V”-Shaped Laminated Segment Tooth Width and torque ripple with increasing rotor pole arc coefficient; (b) the flux leakage of magnet outer radius

4.3. “V”-Shaped Laminated Segment Tooth Width in module MA. back-EMF The no-load waveform of winding A after the above optimizations is shown in

No-load back EMFback (V) EMF (V) No-load

Figure 11a. It can be seen that the distortion of no-load serious. Consequently,isit shown leads in The no-load back-EMF waveform of winding A back-EMF after the is above optimizations 4.3. “V”-Shaped Laminated Segment Tooth Width to torque harmonics when a sinusoidal current is fed into the windings, which is one of the main Figure 11a. It can be seen that the distortion of no-load back-EMF is serious. Consequently, it leads reasons causing torque ripple. The magnetic flux module A are shown in no-loadhigh back-EMF waveform of winding A lines afterofthe aboveMoptimizations isFigure shown11b, to torque The harmonics when a sinusoidal current is fed into the windings, which is one of theinmain where it canItbe thatthat thethe positive magnetic flux path and theisnegative flux path are Figure 11a. canfound be seen distortion of no-load back-EMF serious. magnetic Consequently, it leads reasons causing high torque ripple. The magnetic flux lines of module MA are shown in Figure 11b, nottorque completely symmetrical, results in distortion of the no-load back-EMF. In of order to to harmonics when a which sinusoidal current is fed into thecoil windings, which is one the not main where it can be found that the positive magnetic flux path and the negative magnetic flux path are reduce the statorhigh slot torque area, the toothThe width of the flux “V”-shaped laminated that reasons causing ripple. magnetic lines of module MAsegments are shown in adjoin Figure with 11b, not completely symmetrical, which results in distortion of the coil no-load back-EMF. In order not non-magnetic reduced to improve the symmetry the the magnetic fluxmagnetic path, andflux the path reduced where it can beblocks foundisthat the positive magnetic flux pathofand negative are to reduce the stator slot area, the tooth width of distortion the “V”-shaped laminated segments width Vtw is optimized. Total harmonic (THD) variation of theback-EMF. no-load back-EMF with not completely symmetrical, which resultsdistortion in of the coil no-load Inthat orderadjoin not to with increasing V tw is shown in Figure 12a.width It is first decreased and then increased, reaching the minimum non-magnetic is reduced improve the symmetry of the magnetic flux path, and thewith reduced reduce theblocks stator slot area, thetotooth of the “V”-shaped laminated segments that adjoin value Vtwblocks is 2.75ismm. Average torque and torque ripple with increasing tw are and shown Figurewith reduced to improve the symmetry of variation the magnetic thein reduced widthnon-magnetic Vtw when is optimized. Total harmonic distortion (THD) of flux theVpath, no-load back-EMF 12b. Average torque is reduced, torque ripple is first decreased and then increased, reaching the width V tw is optimized. Total harmonic distortion (THD) variation of the no-load back-EMF with increasing Vtw is shown in Figure 12a. It is first decreased and then increased, reaching the minimum minimum value when Vin tw Figure is 2.0 mm. The THD is just slightly greater than thereaching minimum value when increasing V tw is shown 12a. It is first decreased and then increased, the minimum value when Vtw is 2.75 mm. Average torque and torque ripple with increasing Vtw are shown in Vtw is when 2.0 mm, itsmm. average torque is larger torque than that when Vtwincreasing is 2.75 mm. Hence, theinreduced value Vtw and is 2.75 Average torque ripple with Vtw are shown Figure Figure 12b. Average torque is reduced, torqueand ripple is first decreased and then increased, reaching the width Vtw is chosen mm, whose torque ripple is reduced to 15.61%, THD of no-load back-EMF 12b. Average torqueasis2.0 reduced, torque ripple is first decreased and then increased, reaching the minimum value when V is 2.0 mm. The THD is just slightly greater than the minimum value when tw is reducedvalue from 19.67 by 44.89%. minimum whento Vtw10.84% is 2.0 mm. The THD is just slightly greater than the minimum value when Vtw isV2.0 mm, and its average torque is larger than that when Vtw is 2.75 mm. Hence, the reduced tw is 2.0 mm, and its average torque is larger than that when Vtw is 2.75 mm. Hence, the reduced widthwidth Vtw isVtw chosen as 2.0 mm, whose torque ripple reduced to 15.61%, THD of no-load back-EMF is is chosen as 2.0 mm, whose torque rippleis No-load back EMF of winding Ais reduced to 15.61%, THD of no-load back-EMF 100 reduced from 19.67 to 10.84% by 44.89%. is reduced from 19.67 to 10.84% by 44.89%. 50

No-load back EMF of winding A

100 0 50 -50 0

-100 -50

-100

0

40

80

120 160 200 240 280 320 360

Rotor position (elec.deg)

(a)

(b)

0 11.40 80 back-EMF 120 160 waveform 200 240 and 280 magnetic 320 360flux lines: (a) No-load back-EMF waveform of Figure No-load Rotor position (elec.deg) winding A; (b) Magnetic flux lines of module MA.

(a)

(b)

Figure 11. No-load back-EMF waveform and magnetic flux lines: (a) No-load back-EMF waveform of

Figure 11. No-load back-EMF waveform and magnetic flux lines: (a) No-load back-EMF waveform of winding A; (b) Magnetic flux lines of module MA. winding A; (b) Magnetic flux lines of module MA .

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Average torque (N.m)

THD (%)

18 16 14 12 10 8

21.0

THD of no-load back EMF

26

Average torque Torque ripple

20.5

24

20.0

22

19.5 20

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20

0.0

0.5

1.0

(a)

1.5

2.0

Vtw (mm)

2.5

3.0

3.5

14

(b)

Figure 12. THD, average torque and torque ripple: (a) THD of no-load back-EMF with increasing Vtw;

Figure 12. THD, average torque and torque ripple: (a) THD of no-load back-EMF with increasing Vtw ; (b) Average torque and torque ripple with increasing Vtw. (b) Average torque and torque ripple with increasing Vtw .

4.4. Analysis and Discussion

4.4. Analysis and Discussion

The cogging torque, average electromagnetic torque, and torque ripple of the initial motor and

optimized motor are compared in Table 3. It can be seen that statorripple pole shoe, pole arc and The cogging torque, average electromagnetic torque, and torque of therotor initial motor coefficient, and width in of Table “V”-shaped laminated have significant influences on optimized motor aretooth compared 3. It can be seen segments that statorallpole shoe, rotor pole arc coefficient, cogging torque, electromagnetic torque, and torque ripple. Therefore, these parameters should and tooth width of “V”-shaped laminated segments all have significant influences on coggingbe torque, carefully chosen in the original design. After optimizations, reduces theshould coggingbe torque by 20.43% electromagnetic torque, and torque ripple. Therefore, these itparameters carefully chosen in and torque ripple by 66.84% but the average torque loss is only 1.80%. the original design. After optimizations, it reduces the cogging torque by 20.43% and torque ripple by 66.84% but the average loss is only 1.80%. Tabletorque 3. Torque performances in the initial motor and the optimized motor. Table 3. Torque Performance

Initial in hwthe , hh =initial “2 mm_1 mm and the optimized motor. Optimized performances motor Vtw = 2.0 mm wrp/τp = 0.45

Motor Trapezoid“ Cogging torque (N·m) 4.60 3.64 5.29 Initial hw , hh = “2 mm_1 mm AveragePerformance electromagnetic torque (N·m) 19.97 19.15 wrp20.66 /τ p = 0.45 Motor Trapezoid“ Torque ripple (%) 47.08 26.98 24.92 Cogging torque (N·m) 4.60 3.64 5.29 Average electromagnetic torque (N·m) 19.97 19.15 20.66 5. Comparison of (%) the MSOR-FSPM Motor and COR-FSPM Motor24.92 Torque ripple 47.08 26.98

3.66 V19.61 tw = 2.0 mm 15.61 3.66 19.61 15.61

Motor 3.66 Optimized 19.61 Motor 15.61 3.66 19.61 15.61

5.1. Parameters of the MSOR-FSPM Motor and COR-FSPM Motor

5. Comparison of the MSOR-FSPM Motor and COR-FSPM Motor Although the operation principle of the MSOR-FSPM motor is the same as that of the COR-FSPM

5.1. Parameters the MSOR-FSPM and COR-FSPM Motor motor, the of magnetic flux path ofMotor each phase and some properties have been changed. In order to evaluate the utilization of PM, the average electromagnetic torque of the two motors are compared.

Although the operation principle of the MSOR-FSPM motor is the same as that of the COR-FSPM Several rules must be observed to make the comparison results fair: (1) outside diameter, air gap motor, the magnetic flux path ofmotors each phase some properties haveofbeen order to length, and stack length of both are theand same; (2) material properties eachchanged. part are theIn same; evaluate the utilization of PM, the average electromagnetic torque of the two motors are compared. (3) current density of both motors is the same; (4) phase current value of both motors is the same. The Several rules mustviews be observed to make the comparison (1) outside diameter, cross-sectional of both motors are shown as Figure 13.results Except fair: the partial parameters shown air in gap length, and4,stack length ofdesign both motors are the same; (2) material properties of each Table the other main parameters of both motors are the same with Table 1. part are the same; (3) current density of both motors is the same; (4) phase current value of both motors is the same. Table 4. MSOR-FSPM motor13. andExcept COR-FSPM The cross-sectional views ofPartial both parameters motors areofshown as Figure the motor. partial parameters shown Machine Parameter MSOR-FSPM COR-FSPM Unit in Table 4, the otherSymbol main design parameters of both motors are the same with Table 1. α

Rotor pole arc coefficient

0.45

rp Partial parameters Rotor pole width 17.8 Tablew4. of MSOR-FSPM motor and COR-FSPMmm motor.

Symbol α wrp ht hw hh Ncoil Sslot Vpm

ht Pole shoe thickness 2 mm Pole shoe width 2 hw Machine Parameter MSOR-FSPM COR-FSPMmm hh Pole shoe height 1 mm pole arc coefficient 0.45 coil Number of turns per coil 70 35 NRotor Areawidth per phase 955.44 17.8 785.28 mm2 Sslot Rotor pole thickness 2 179,850 Vpm Pole shoe Volume of PMs 97,185 mm2

Pole shoe width Pole shoe height Number of turns per coil Area per phase Volume of PMs

2 1 70 955.44 97,185

35 785.28 179,850

Unit mm mm mm mm mm2 mm2

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__

-

+

__

++

+

__

+ + -+

+

_ _ _+_ +

++ ++ _

_

+

_

+

-

+

++

__

-

+

+

+

_

+

_

+

_

+

++

__

+

-

(b)

+

+ -

-

(a)

__ __

C1

+

B2

C1

+

C2

B2

++

-

C1 C2

B1

_+_ +

A1

_

A2

B1 B2

+

C2 +

A1 C4 B1 __ ++ C1 _ B4 _ + _ ++ B1 A1 C4 A4_ A2 + C1 B1 A1 C4 B4 C3 B2 C1 C2 A2 B3 B4A4 A3 A2B2 A4 C3 C2 B3 C3 B2 A3 C2 B3 A3

++ _

A1

_ _

+ A2

-+ -

A1 -

-B1

A2 +

++

+

+

+ -

-

Figure 13. Cross-sectional views: Cross-sectional view of MSOR-FSPM (b) Cross-sectional (a)(a)(a)Cross-sectional (b) motor; Figure 13. Cross-sectional views: view of MSOR-FSPM motor; (b) Cross-sectional view of COR-FSPM motor. (a) (b) view of COR-FSPM motor. views: (a) Cross-sectional view of MSOR-FSPM Figure 13. Cross-sectional motor; (b) Cross-sectional view of13. COR-FSPM motor. Figure views: Circuit (a) Cross-sectional view of MSOR-FSPM motor; (b) Cross-sectional 5.2. Analysis of Cross-sectional Theory and Magnetic view COR-FSPM motor. 5.2. Analysis ofofTheory and Magnetic Circuit

Figures 14–17 show no-load magnetic field distributions and the local magnetic circuits of 5.2. Analysis of Theory andthe Magnetic Circuit MSOR-FSPM motor and COR-FSPM motor at two typical rotor positions, where themagnetic PM flux linkage Figures 14–17 showand theMagnetic no-loadCircuit magnetic field distributions and the local circuits of 5.2. Analysis of Theory Figures 14–17 show the no-load magnetic fieldand distributions and extreme the local value, magnetic circuits of of phase A reaches the positive extreme value the negative respectively. MSOR-FSPM motor and COR-FSPM motor at two typical rotor positions, where the PM flux linkage of Figures the 14–17 show the of no-load magnetic field distributions and thewhere local magnetic circuits of MSOR-FSPM motor and COR-FSPM motor atflux two typical rotor positions, the flux linkage periodicity the value magnetic the circumference, only thePM magnetic flux phaseConsidering A phase reaches the positive extreme and the along negative extreme value, respectively. Considering MSOR-FSPM motor and COR-FSPM motor at two typical rotor positions, where the PM flux linkage of A reaches the positive extreme value and the negative extreme value, respectively. circuits of phase A with markings in these Figures are analyzed. the periodicity of reaches the periodicity magnetic flux along the circumference, the magnetic flux of flux phase A of phase A the positive extreme value and the negative extreme value, respectively. Considering the of the magnetic flux along theonly circumference, only thecircuits magnetic with markings in the these Figures are analyzed. Considering periodicity of the flux along the circumference, only the magnetic flux circuits of phase A with markings inmagnetic these Figures are analyzed. circuits of phase A with markings in these Figures are analyzed. A2 B1

A1

A2

A1 C2

A2

A1

B1 B2 B1

C1 C2 C2

B2

C1

B2

C1

(a)

F F

Φ F A2

RMp

RMp

Mp ΦRMp

RMp Φ

F RMp ΦA1F

RMp

ΦMp ΦA2 ΦMp ΦA2

F

(b)

ΦMp ΦMp ΦA1 ΦA1

Figure 14. Positive extreme (a) value of phase A flux linkage produced by (b)PMs in MSOR-FSPM motor: (a) No-load magnetic field distributions; (b) Local equivalent magnetic (a) (b)circuit. Figure 14. Positive extreme value of phase A flux linkage produced by PMs in MSOR-FSPM motor: Figure 14. Positive extreme value of phase A flux linkage produced by PMs in MSOR-FSPM motor: (a) No-load magnetic field distributions; (b)ALocal magnetic Figure 14. Positive extreme value of phase flux equivalent linkage produced bycircuit. PMs in MSOR-FSPM motor: (a) No-load magnetic field distributions; (b) Local equivalent magnetic circuit. (a) No-load magnetic field distributions; (b) Local equivalent magnetic circuit. ΦA1(ΦA2、ΦA3、ΦA4) A1 A2

A1

A4

A1 A2 A2

A3 A3

A4 A4

ΦA1(ΦA2、ΦA3、ΦA4) Cp Φ、CpΦA4) ΦA1Φ (Φ A2、 ΦA3 RCpCp Φ RCp Φ Cp F F ΦCp ΦCp F F

RCp RCp

RCp RCp

F F

A3

(a)

(b)

Figure 15. Positive extreme value PMs in COR-FSPM motor: (a) (a) of phase A flux linkage produced by(b) No-load magnetic field distributions; (b) Local equivalent magnetic circuit. (a) (b) Figure 15. Positive extreme value of phase A flux linkage produced by PMs in COR-FSPM motor: (a) No-load distributions; (b) Local equivalent magnetic by circuit. Figure 15.magnetic Positive field extreme value of phase A flux linkage produced PMs in COR-FSPM motor: (a) Figure 15. Positive extreme value of phase A flux linkage produced by PMs in COR-FSPM motor: No-load magnetic field distributions; (b) Local equivalent magnetic circuit.

(a) No-load magnetic field distributions; (b) Local equivalent magnetic circuit.

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A2 A2

ΦA2 ΦA2

A1 A1 C2 C2

B1 B1 B2 B2

RMn RMn

C1 C1

ΦA1 ΦA1 F F

F F

ΦMn ΦMn

ΦMn ΦMn

(a) (a)

RMn RMn

(b) (b)

Figure 16. Negative extreme value of phase-A flux linkage produced by PMs in MSOR-FSPM motor:

Figure 16. Negative extreme value flux linkageproduced produced by PMs in MSOR-FSPM motor: Figure 16. Negative valueofofphase-A phase-A fluxequivalent linkage bycircuit. PMs in MSOR-FSPM motor: (a) No-load magneticextreme field distributions; (b) Local magnetic (a) No-load magnetic field distributions; (b) Local equivalent magnetic circuit. (a) No-load magnetic field distributions; (b) Local equivalent magnetic circuit.

A1 A1 A2 A2

A4 A4 A3 A3

(a) (a)

lst lst

F F

RCn RCn

RCn RCn

ΦCn ΦCn ΦCn ΦCn ΦA1(ΦA2、ΦA3、ΦA4) ΦA1(ΦA2、ΦA3、ΦA4)

F F

(b) (b)

Figure 17. Negative extreme value of phase A flux linkage produced by PMs in COR-FSPM motor: Figure 17. Negative value of phase A fluxequivalent linkage produced PMs in COR-FSPM motor: (a) No-load magneticextreme field distributions; (b) Local magneticby circuit. Figure 17. Negative extreme value of phase A flux linkage produced by PMs in COR-FSPM motor: (a) No-load magnetic field distributions; (b) Local equivalent magnetic circuit.

(a) No-load magnetic field distributions; (b) Local equivalentbymagnetic circuit. As is seen from Figure 14a, the magnetic flux produced PMA1 and PMA2 in MSOR-FSPM motor

As is seen from Figure 14a,ofthe magnetic flux produced by PMand A1 and A2 in MSOR-FSPM motor are added at the middle tooth “W”-shaped laminated segment thePM width of the magnetic flux are added at the middle tooth of “W”-shaped laminated segment and the width of the magnetic flux path for one PM is half of this tooth. The corresponding equivalent magnetic circuit is shown in As is seen from Figure 14a, the magnetic flux produced by PMA1 and PMA2 in MSOR-FSPM path for one PM is half of this tooth. The corresponding equivalent magnetic circuit shown in Figure 14b. As is seen from Figure 15a, the magnetic flux produced by PM A1 and PM C4 is in the CORmotor are added at the middle tooth of “W”-shaped laminated segment and the width of the magnetic Figure 14b. As is seen from Figure 15a, tooth the magnetic flux pole, produced byis PM A1 and PM C4 winding in the CORFSPMfor motor at the righttooth. end the stator which surrounded by flux path oneare PMadded is half of this Theofcorresponding equivalent magnetic circuit isA1, shown FSPM at the right end tooth ofPM theisstator pole, surrounded by winding A1, and themotor widthare of added the magnetic flux path for one half of thiswhich tooth. is The corresponding equivalent in Figure 14b. As is seen from Figure 15a, the magnetic flux produced by PMA1 and PMC4 in the and the width of is the magnetic flux path one PM the is half of this tooth. Theofcorresponding magnetic circuit shown in Figure 15b.for Therefore, magnetoresistance MSOR-FSPM equivalent motor and COR-FSPM motor are addedin atFigure the right end tooth of stator pole, which is surrounded by winding magnetic circuit is shown 15b. Therefore, thethe magnetoresistance of MSOR-FSPM COR-FSPM motor in the equivalent magnetic circuits is almost equal to each other, i.e., motor and A1, and the width of in the path circuits for oneisPM is half The corresponding COR-FSPM motor themagnetic equivalentflux magnetic almost equaloftothis eachtooth. other, i.e., R  R (13) Mp Cp equivalent magnetic circuit is shown in Figure 15b. Therefore, the magnetoresistance of MSOR-FSPM RMp  RCp (13) motorwhere and COR-FSPM motor in the equivalent magnetic circuits is almost equal to each other, i.e., of the equivalent magnetic circuit in the MSOR-FSPM motor, and RMp is the magnetoresistance is the magnetoresistance of the equivalent magnetic in the MSOR-FSPM where RMpmagnetoresistance RCp is the of the equivalent magnetic circuitcircuit in the COR-FSPM motor. motor, and R Mp ≈as RCp RCp isIfthe of the equivalent magnetic in the COR-FSPM motor. themagnetoresistance magnetomotive force per PM is defined Fmcircuit , the positive extreme value of phase A flux (13) If the magnetomotive per PM is defined as Fmand , the COR-FSPM positive extreme A flux linkage produced by PMs force in the MSOR-FSPM motor motorvalue can of be phase obtained by wherelinkage RMp isproduced the the equivalent magnetic circuit inmotor the MSOR-FSPM motor, PMs in the of MSOR-FSPM motor and COR-FSPM can be obtained by and Equations (14)magnetoresistance andby (15), respectively. (14) and (15), respectively. RCp isEquations the magnetoresistance of the equivalent magnetic circuit in the COR-FSPM motor.

Fm 2 N M _ coil Φas m140  Fpositive If the magnetomotive force  per PM is defined , the extreme value of(14) phase A M _ phaseA_p Mp F m RMp   2 N Φ  140  (14) M phaseA_p M coil Mp _ _ flux linkage produced by PMs in the MSOR-FSPM motor and COR-FSPM motor can be obtained by RMp Equations (14) and (15), respectively. F  C_ phaseA_p  4 N C _ coil 2ΦCp  280  Fm (15) m Fm  C_ phaseA_p  4 N C _ coil 2ΦCp  280  RCp (15) (14) ψ M_phaseA_p = 2NM_coil ΦMp = 140 × RCpR Mp

ψC_phaseA_p = 4NC_coil ·2ΦCp = 280 ×

Fm RCp

(15)

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where Ψ M_phaseA_p is the positive extreme value of phase A flux linkage produced by PMs in the MSOR-FSPM motor, Ψ C_phaseA_p is the positive extreme value of phase A flux linkage produced by PMs in the COR-FSPM motor, NM_coil is the number of turns per coil in the MSOR-FSPM motor, NC_coil is the number of turns per coil in the COR-FSPM motor, ΦMp is the positive extreme value of PM flux in the MSOR-FSPM motor, ΦCp is the positive extreme value of PM flux in the COR-FSPM motor. It can be seen from Equations (14) and (15) that Ψ M_phaseA_p is about 50% of Ψ C_phaseA_p . However, this relationship is not suitable for the negative extreme value of flux linkage produced by PMs in both motors. As is seen from Figure 16a, the magnetic flux produced by PMA1 and PMA2 in the MSOR-FSPM motor are independent, and the width of the magnetic flux path for one PM is the tooth width. The corresponding equivalent magnetic circuit is shown in Figure 16b. As is seen from Figure 17a, the magnetic flux produced by PMA1 and PMB1 in the COR-FSPM motor are added at the left end tooth of the stator pole, which is surrounded by winding A1, and the width of the magnetic flux path for one PM is half of this tooth. The corresponding equivalent magnetic circuit is shown in Figure 17b. The saturation degree of the MSOR-FSPM motor is greatly changed. The magnetoresistance of the MSOR-FSPM motor in the equivalent magnetic circuit is far less than that of the COR-FSPM motor, and it is close to 50% that of the COR-FSPM motor, i.e., R Mn ≈ 0.5RCn

(16)

where RMn is the magnetoresistance of the equivalent magnetic circuit in the MSOR-FSPM motor, and RCn is the magnetoresistance of the equivalent magnetic circuit in the COR-FSPM motor. The negative extreme value of phase A flux linkage produced by PMs in the MSOR-FSPM motor and the COR-FSPM motor can be obtained by Equations (17) and (18), respectivelyL ψ M_phaseA_n = 2NM_coil ΦMn = 140 ×

Fm Fm = 280 × R Mn RCn

(17)

Fm RCn

(18)

ψC_phaseA_n = 4NC_coil · 2ΦCn = 280 ×

where Ψ M_phaseA_n is the negative extreme value of phase A flux linkage produced by PMs in the MSOR-FSPM motor, Ψ C_phaseA_n is the negative extreme value of phase A flux linkage produced by PMs in the COR-FSPM motor, ΦMn is the negative extreme value of PM flux in the MSOR-FSPM motor, ΦCn is the negative extreme value of PM flux in the COR-FSPM motor. It can be seen from Equations (17) and (18) that Ψ M_phaseA_n is close to 100% of Ψ C_phaseA_n . Based on the above analysis, the average PM flux linkage produced by PMs in the MSOR-FSPM motor is close to 75% of that in the COR-FSPM motor, even if the volume of PMs in the MSOR-FSPM motor is about half of that in the COR-FSPM motor. When the same vector control is adopted, the average electromagnetic torque in the MSOR-FSPM motor could be close to 75% of that in the COR-FSPM motor. 5.3. Validation by FEM The results of theoretical analysis are verified by the FEM. No-load PM flux linkage waveforms of phase A and their FFT results calculated by the Maxwell 2D FEM software are shown in Figure 18. Since the reluctance torque Trm in the FSPM motor can be eliminated by adopting vector control of id = 0, the average electromagnetic torque of the FSPM motor in d-q coordinate system can be calculated from Equation (19): 3 Tem_average = Nr ψPM_d Im (19) 2 where Ψ PM_d is the amplitude of PM flux linkage, Im is the amplitude of phase current. For these two motors, Nr is equal to 10 and Im is equal to 15.4 A. Ψ PM_d of the MSOR-FSPM motor, and the COR-FSPM motor are 0.09586 Wb and 0.12039 Wb, respectively. Even if the PM volume of the MSOR-FSPM motor is only 54.04% of that in the COR-FSPM motor, the amplitude of the fundamental

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flux linkage in the MSOR-FSPM motor is about 79.62% of that in the COR-FSPM motor. Based on Based on the fundamental flux linkage, the corresponding average electromagnetic torque of the the fundamental flux linkage, the corresponding average electromagnetic torque of the MSOR-FSPM MSOR-FSPM motor calculated indirectly by Equation (19) is 22.14 N·m and that of the COR-FSPM motor calculated motor is indirectly 27.81 N·m. by Equation (19) is 22.14 N·m and that of the COR-FSPM motor is 27.81 N·m. Energies 2017, 10, 937

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0.20

0.14

0.05

b

0.00 0.20 -0.05 0.15 -0.10 0.10 -0.15 0.05 -0.20 0.00 0

-0.05 -0.10

a

a

MSOR-FSPM COR-FSPM

40

d

MSOR-FSPM Fundamental COR-FSPM Fundamental

c

b

d

80 120 160 200 240 280 320 360 Rotor position (elec.deg)

(a)

Amplitude (Wb) Amplitude (Wb)

Flux linkage (Wb) Flux linkage (Wb)

Based on the fundamental linkage,Fundamental the corresponding average electromagnetic torque of the MSOR-FSPM flux MSOR-FSPM MSOR-FSPM 0.15 COR-FSPM Fundamental MSOR-FSPM motor calculatedcCOR-FSPM indirectly by Equation 0.12 (19) is 22.14 N·m and that ofCOR-FSPM the COR-FSPM 0.10 0.10 motor is 27.81 N·m. 0.08 0.14 0.06 0.12 0.04 0.10 0.02 0.08 0.00

0.06

MSOR-FSPM COR-FSPM

1st

2nd 3rd Harmonic order

4th

(b)

0.04

0.02 of no-load flux linkage: (a) No-load flux Figure -0.15 18. No-load flux linkage waveforms and FFT results

Figure 18.linkage No-load flux linkage andofFFT results of no-load flux linkage: (a) No-load flux waveforms of phasewaveforms A; (b) FFT results phase A no-load flux linkage. 0.00 -0.20 1st 2nd 3rd 4th 0 40 80 120 160 200 240 280 320 360 linkage waveforms of Rotor phase A; (b) FFT results of phase A no-load flux linkage. Harmonic order position (elec.deg)

Electromagnetic torque (N.m) Electromagnetic torque (N.m)

The electromagnetic(a) torque waveforms calculated directly by Maxwell(b) 2D are shown in Figure 19. Their average torques are 20.97 N·m for the MSOR-FSPM motor and 27.61 N·m for the COR-FSPM The electromagnetic torque waveforms calculated directly by motor Maxwell 2D(a)are shown in Figure 19. Figure 18. average No-load flux linkage waveforms and of no-load flux linkage: No-load motor. The electromagnetic torque ofFFT theresults MSOR-FSPM is 75.95% of thatflux in the Their average torques are 20.97 N · m for the MSOR-FSPM motor and 27.61 N · m for the COR-FSPM linkage waveforms of phase A; (b) FFT results of phase A no-load flux linkage. COR-FSPM motor, which is close to the theoretical value of 75%. Compared with the results of Maxwell 2D, theelectromagnetic errors of average electromagnetic torque in the MSOR-FSPM motor and COR-FSPM motor. The average torque of the MSOR-FSPM motor is 75.95% of that in the The calculated electromagnetic torque calculated directly by Maxwell 2D are The shown in Figurethe 19. motor indirectly by waveforms Equation (19) are 5.58% and 0.72%, respectively. reason COR-FSPM motor, which is close to the theoretical value of 75%. Compared with for the results of Their average torques are 20.97 N·m forcomponent the MSOR-FSPM motor and N·m when for the COR-FSPM errors is that the influences of harmonic on average torque are27.61 neglected Equation (19) Maxwell 2D, the of average electromagnetic torque in the MSOR-FSPM motorthat andinCOR-FSPM motor. Theerrors average torque the 75.95% the is adopted. For theelectromagnetic COR-FSPM motor, the of ratio ofMSOR-FSPM fundamentalmotor wave is and other of harmonics is motor calculated indirectly by Equation (19) are 5.58% and 0.72%, respectively. The reason for COR-FSPM motor, which is close to the theoretical value of 75%. Compared with the results of errors 99.27:0.73, the influences of harmonic component on average electromagnetic torque are small andthe Maxwell 2D, the errors of average electromagnetic torque intorque MSOR-FSPM motor and COR-FSPM is that the influences of harmonic component average are neglected when Equation the average electromagnetic torque based onon Equation (19) isthe almost equal to the Maxwell 2D result. (19) is motor calculated indirectly bythe Equation 5.58%wave and and 0.72%, respectively. reason for the For motor, ratioratio of (19) fundamental other harmonics is 89.37:10.63. The adopted. Forthe theMSOR-FSPM COR-FSPM motor, the ofare fundamental wave and other The harmonics is 99.27:0.73, errors is that the influences of harmonic component on average torque are neglected when Equation (19) harmonic component is higher than that of the COR-FSPM motor, and the error of the average the influences of harmonic component on average electromagnetic torque are small and the average torque calculatedmotor, indirectly Equation (19) is larger thanand thatother in theharmonics COR-FSPMis is electromagnetic adopted. For the COR-FSPM the by ratio of fundamental wave electromagnetic torque both based on Equation (19) is almost equal that to the Maxwell 2D result. For the motor. However, the and Maxwellon 2Daverage results show the average electromagnetic 99.27:0.73, the influences ofcalculation harmonic component electromagnetic torque are small and MSOR-FSPM motor, the ratio of motor fundamental other harmonics 89.37:10.63. The of the MSOR-FSPM isbased far larger than and half(19) that the COR-FSPM motor, even if2D the PMharmonic thetorque average electromagnetic torque onwave Equation isofalmost equal toisthe Maxwell result. in the than MSOR-FSPM motor is of about half motor, of that inand the COR-FSPM which verifies the component is higher that ofthe theratio COR-FSPM the error ofmotor, the average electromagnetic Forvolume the MSOR-FSPM motor, fundamental wave and other harmonics is 89.37:10.63. The results ofcomponent our theoretical analysis. harmonic is by higher than that ofisthe COR-FSPM motor, and COR-FSPM the error of the average torque calculated indirectly Equation (19) larger than that in the motor. However, electromagnetic torque calculated indirectly by Equation (19) is larger than that in the COR-FSPM both the calculation and Maxwell 2D results show that the average electromagnetic torque of the MSOR-FSPM results COR-FSPM motor. However, both the calculation and Maxwell show that the average electromagnetic 32 MSOR-FSPM motor is far larger than half that of the2D COR-FSPM motor, even if the PM volume in the torque of the MSOR-FSPM motor 28 is far larger than half that of the COR-FSPM motor, even if the PM MSOR-FSPM motor is about half of that in the COR-FSPM motor, which verifies the results of our volume in the MSOR-FSPM motor 24 is about half of that in the COR-FSPM motor, which verifies the theoretical analysis. results of our theoretical analysis. 20 16

12 32 8 28 4 24 0 20 0

16

MSOR-FSPM

40

COR-FSPM

80 120 160 200 240 280 320 360 Rotor position (elec.deg)

Figure 19. Electromagnetic 12torque waveforms of the MSOR-FSPM motor and COR-FSPM motor. 8

However, the above comparison is based on the same number of turns per phase. Actually, the 4 slot area per phase of the MSOR-FSPM motor is enlarged because of the reduction of PMs, and its 0 0 that 40 of 80the 120 160 200 240 280 The 320 average 360 stator slot fill factor is smaller than COR-FSPM motor. electromagnetic torque Rotor position (elec.deg)

Figure 19. Electromagnetic torque waveforms of the MSOR-FSPM motor and COR-FSPM motor.

Figure 19. Electromagnetic torque waveforms of the MSOR-FSPM motor and COR-FSPM motor. However, the above comparison is based on the same number of turns per phase. Actually, the slot area per phase the MSOR-FSPM motoron is enlarged of the reduction PMs, and its However, the aboveofcomparison is based the samebecause number of turns perofphase. Actually, the stator slot fill factor is smaller than that of the COR-FSPM motor. The average electromagnetic torque

slot area per phase of the MSOR-FSPM motor is enlarged because of the reduction of PMs, and its stator slot fill factor is smaller than that of the COR-FSPM motor. The average electromagnetic torque in the MSOR-FSPM motor is calculated when the stator slot fill factor of the MSOR-FSPM motor is the

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same as that of the COR-FSPM motor. The compared performances of the three motors are shown as Table 5, in which MSOR-FSPM-1 motor has the same number of turns per phase as the COR-FSPM motor and MSOR-FSPM-2 motor has the same stator slot fill factor as the COR-FSPM motor. It can be seen that the average electromagnetic torque in the MSOR-FSPM motor is further enlarged to 86.53% of that in the COR-FSPM motor when they have the same stator slot fill factor. The PM utilization in the MSOR-FSPM motor is further improved. Table 5. Compared performances of the MSOR-FSPM motor and COR-FSPM motor. Performance

MSOR-FSPM-1

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MSOR-FSPM-2

COR-FSPM 17 of 19

Ratio of PM volume (%) 54.04 54.04 100 Ψ PM_d (Wb) 0.12039is in the MSOR-FSPM motor is calculated when the0.09586 stator slot fill factor 0.11092 of the MSOR-FSPM motor Ratio of Ψ PM_d (%) 79.62 92.13 100 the same as that of the COR-FSPM motor. The compared performances of the three motors are shown Average torque calculated indirectly (N·m) 22.14 25.62 27.81 5, in which MSOR-FSPM-1 motor per phase as the COR-FSPM Ratioas ofTable average torque calculated indirectly (%) has the same 79.61number of turns 92.12 100 motor and MSOR-FSPM-2 motor has the same stator slot fill factor as the COR-FSPM motor.27.61 It can Average torque calculated directly (N·m) 20.97 23.98 thattorque the average electromagnetic the MSOR-FSPM motor Ratiobeofseen average calculated directly (%) torque in 75.95 86.53 is further enlarged 100 to

86.53% of that in the COR-FSPM motor when they have the same stator slot fill factor. The PM utilization in the MSOR-FSPM motor is further improved.

5.4. Inductance of the MSOR-FSPM Motor and COR-FSPM Motor

Table 5. Compared performances of the MSOR-FSPM motor and COR-FSPM motor. The waveforms of self-inductance and mutual-inductance in the MSOR-FSPM motor and Performance MSOR-FSPM-1 MSOR-FSPM-2 COR-FSPM motor are COR-FSPM motor are shown in Figure 20. The inductance characteristics of the COR-FSPM Ratio of PM volume (%) 54.04 54.04 100 the same as the conventional FSPM motor where the self-inductance and mutual-inductance change ΨPM_d (Wb) 0.09586 0.11092 0.12039 twice in one electrical period, and the average self-inductance value is equal to two times that of Ratio of ΨPM_d (%) 79.62 92.13 100 Average But torque calculated indirectly (N·m)motor, self-inductance 22.14 25.62 mutual-inductance 27.81 mutual-inductance. for the MSOR-FSPM and change of average torque and calculated indirectly (%) 79.61 92.12 100 two times that once in oneRatio electrical period, the average self-inductance value is far more than Average torque calculated directly (N·m) 20.97 23.98 27.61 of mutual-inductance. Ratio of average torque calculated directly (%) 75.95 86.53 100 It is worth noting that the self-inductance is increased and mutual-inductance is reduced Inductance of theisMSOR-FSPM and COR-FSPM Motor when a5.4. module stator adopted. Motor The self-inductance of the MSOR-FSPM motor is larger than two times that of the COR-FSPM motor, and mutual-inductance is smaller motor than and halfCORthat of the The waveforms of self-inductance and mutual-inductance in the MSOR-FSPM COR-FSPM When an in open circuit occurs in onecharacteristics phase in theofMSOR-FSPM motor, remaining FSPMmotor. motor are shown Figure 20. The inductance the COR-FSPM motor the are the same as the conventional FSPM motor where the self-inductance change two-phase windings have greater potential to continue to work dueand to mutual-inductance the smaller mutual-inductance. one electrical and the the average self-inductance value is equal to two times that is of smaller When atwice shortincircuit occurs period, in one phase, short-circuit current of the MSOR-FSPM motor mutual-inductance. But for the MSOR-FSPM motor, self-inductance and mutual-inductance change than that of the COR-FSPM motor due to the larger self-inductance. Therefore, it is deduced that the once in one electrical period, and the average self-inductance value is far more than two times that of fault tolerance capability of the MSOR-FSPM motor is better than that of the COR-FSPM motor. mutual-inductance. 0.006

Inductance (H)

0.005 0.004

Laa MSOR-FSPM Lab MSOR-FSPM Lac MSOR-FSPM

0.003 0.002

Laa COR-FSPM Lab COR-FSPM Lac COR-FSPM

0.001 0.000

-0.001 -0.002

0

40

80

120 160 200 240 280 320 360

Rotor position (elec.deg)

Figure 20. Waveforms of self-inductance and mutual-inductance in the MSOR-FSPM motor and

Figure 20. Waveforms of self-inductance and mutual-inductance in the MSOR-FSPM motor and COR-FSPM mot COR-FSPM mot It is worth noting that the self-inductance is increased and mutual-inductance is reduced when a module 6. Conclusions stator is adopted. The self-inductance of the MSOR-FSPM motor is larger than two times that of the COR-FSPM motor, and mutual-inductance is smaller than half that of the COR-FSPM A novel motoroccurs withinmodular is researched in this paper. The motor motor.MSOR-FSPM When an open circuit one phasestator in the structure MSOR-FSPM motor, the remaining two-phase windings have greater potential to continue to work due to the smaller mutual-inductance. When a structure is illustrated in great detail, and its operation and design principles are explained. short circuit occurs in one phase, the short-circuit current of the MSOR-FSPM motor is smaller than that of the COR-FSPM motor due to the larger self-inductance. Therefore, it is deduced that the fault tolerance capability of the MSOR-FSPM motor is better than that of the COR-FSPM motor.

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The influences of rotor pole number on motor torque characteristics are discussed. The MSOR-FSPM motor topology with 12-slot/10-pole is chosen to be researched further due to the minimum and period cogging torque. The magnetic performances of the MSOR-FSPM motor are optimized from the aspects of stator pole shoe, rotor pole arc coefficient, and the tooth width of “V”-shaped laminated segments. After optimizations, the torque ripple is reduced from 46.63 to 15.61% or 66.52%, and average electromagnetic torque is only reduced from 19.97 N·m to 19.61 N·m or 1.80%. Finally, utilization of PM in the MSOR-FSPM motor and COR-FSPM motor is analyzed from the point of view of the magnetic flux path. It is verified by FEM results. Even if the PM volume in the MSOR-FSPM motor is 54.04% of that in the COR-FSPM motor, when they have the same number of turns per phase, the average electromagnetic torque of the MSOR-FSPM motor is more than 75% of that in the COR-FSPM motor; when they have the same stator slot fill factor, the average electromagnetic torque of the MSOR-FSPM motor can reach 86.53% of that in the COR-FSPM motor. It is thus indicated that the utilization of PM in the MSOR-FSPM motor is much improved by adopting the proposed modular stator. This paper is mainly concerned with the design principles and fundamental theoretical research of a new outer-rotor FSPM motor topology, which provides good references for the prototype manufacturing and further research. Acknowledgments: This work was supported in part by the National Natural Science Foundation of China under Projects 51677005. Author Contributions: All authors contributed to this work by collaboration. Jing Zhao is the main author of this manuscript; Yun Zheng assisted to establish the finite element model and perform the simulations; Congcong Zhu, Xiangdong Liu and Bin Li provided some useful suggestions in the construction of paper. All authors revised and approved the publication. Conflicts of Interest: The authors declare no conflict of interest.

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