Analysis of Stator-Slot Circumferentially Magnetized PM Machines with Full-Pitched Windings

: Stator-slot circumferentially magnetized PM machines (SSCMPMMs) have high fault-tolerant capability. In this paper, the SSCMPMMs with full-pitched windings and different stator slot/rotor pole numbers are investigated, together with the inﬂuence of key geometric parameters. It shows that the 12 stator-slots 7 rotor-poles (12S7R) machine delivers the highest torque. It is then compared with the SSCMPMM with tooth-coil windings. The results show that when they have the same active length, the 12S7R machine delivers signiﬁcantly higher torque and higher efﬁciency. Furthermore, when the machine length is over around 140 mm, the 12S7R machine is more advantageous in producing high torque and high efﬁciency. A prototype is manufactured and tested to validate the theoretical analyses.


Introduction
Electrical machines with permanent magnets (PMs) mounted in the stator, i.e., stator PM machines, have been attracting interests for the last several decades. The stator PM machines have some inherent advantages over the rotor PM machines, e.g., robust salient pole-rotor structure and easy thermal management for the magnets if the forced liquid cooling is employed.
In doubly salient PM machines, PMs are circumferentially magnetized and located in the stator yoke separated by the interval of number of stator teeth equal to the phase number. Hence, they usually use less number and also amount of PMs but have relatively low torque density, although they may exhibit good torque per PM volume. Switched-flux PM machines have circumferentially magnetized PMs sandwiched between the stator teeth and can enhance the airgap flux density by flux focusing, which is favourable for high torque. However, the overload capability of switched-flux PM machines is deteriorated due to high stator core saturation. The airgap flux density in flux-reversal PM machines with a pair of PMs mounted on stator tooth surface relies on the magnet remanence and thickness, and no flux focusing effect can be utilized. It was found that changing the PM arrangement from NSSN type to NSNS type helps to improve the performance almost at no extra cost [16]. Meanwhile, by employing consequent pole PM structure, the PM utilization and electromagnetic performance are both improved [17].
Stator-slot radially magnetized PM machine cannot produce high torque density due to large magnetic reluctance. This issue can be solved by employing Halbach array PM in the stator slot [15]. The side magnets can help to conduct and enhance magnetic flux. due to low induced back electromotive force (EMF) on open circuit [18]. However, torque density of the SSCMPMMs needs to be improved, especially at a light load con tion.
Coil pitch has a significant influence on the torque performance since it affe slot/pole number combination and winding pitch factor. The authors of [19] analytica investigated the influence of coil pitch of 1, 2, and 3 slot pitches on the back EMF of flu reversal and switched-flux PM machines. It is also found that for both flux-reversal a switched-flux PM machines, distributed windings help to improve torque density co pared with tooth-coil windings [20,21]. Therefore, it is necessary to investigate the inf ence of coil pitch in SSCMPMMs, which is the subject of this paper.
(a) 12S10R with TCW [14] (b) 12S8R with FPW (c) 12S7R with FPW This paper is arranged as follows: Firstly, the machine topology, operation princip and slot/pole number combinations are introduced in Section 2. The influence of key g metric parameters of SSCMPMMs is investigated in Section 3. The 12 stator-slots 7 rot poles (12S7R) machine with full-pitched windings (FPW) is identified to exhibit the hig est torque density and then compared with a 12S10R machine with tooth-coil windin (TCW) in Section 4. Finally, a prototype is manufactured and tested in Section 5, and so conclusions are drawn in Section 6. Coil pitch has a significant influence on the torque performance since it affects slot/pole number combination and winding pitch factor. The authors of [19] analytically investigated the influence of coil pitch of 1, 2, and 3 slot pitches on the back EMF of flux-reversal and switched-flux PM machines. It is also found that for both flux-reversal and switched-flux PM machines, distributed windings help to improve torque density compared with tooth-coil windings [20,21]. Therefore, it is necessary to investigate the influence of coil pitch in SSCMPMMs, which is the subject of this paper. This paper is arranged as follows: Firstly, the machine topology, operation principle, and slot/pole number combinations are introduced in Section 2. The influence of key geometric parameters of SSCMPMMs is investigated in Section 3. The 12 stator-slots 7 rotor-poles (12S7R) machine with full-pitched windings (FPW) is identified to exhibit the highest torque density and then compared with a 12S10R machine with tooth-coil windings (TCW) in Section 4. Finally, a prototype is manufactured and tested in Section 5, and some conclusions are drawn in Section 6.  Figure 2b. The amount of PM flux forced into airgap and rotor side depends on the armature field strength. Therefore, the average torque under I d = 0 control can be expressed as

Machine Topology, Operation Principle, and Slot/Pole Number Combination
in which N r is the rotor-pole number, ψ PM (i q ) is the PM flux linkage and affected by the armature current i q , and ϕ PM (F q ) is the PM flux and affected by the armature magnetomotive force (MMF) F q .  Stator-slot PM machines consist of three parts as other flux modulation machin armature, PM excitation (PM MMF), and modulation poles (rotor slots). Although MMF is closely related to the armature MMF, stator-slot PM machines still comply principle of flux modulation effect. The pole-pair number of armature windings the rotor-pole number, and their relationships are determined by [9] Nr = iNs/2 ± Pa (i = 1, 3, 5···) in which Nr is the rotor-pole number, Ns is the stator-slot number, i is the odd n and Pa is the pole-pair number of armature windings. 12S-4R/8R/10R/11R/13R/1 stator-slot PM machines are mentioned in [14], and the corresponding Pa is 2, 2, 4, and 2, respectively, but all with tooth-coil windings. However, there are other co tions, e.g., 12S-5R/7R, whose armature pole-pair number is 1, as shown in Table 1. paper, 12 stator-slots machines with FPW and different number of rotor poles are i gated. The coil pitches are 3, 6, 6, and 3 slot pitches, respectively. It should be not FPW is not restricted to 12 stator-slots machines.
Taking 12S7R machine for example, as shown in Figure 3, the coil positions chanical degree and electrical degree are shown in Figure 3b and Figure 3c, respe Figure 4 shows the winding layout and back EMF phasors of 12S-4R/5R/7R/8R ma 12S-5R/7R machines have two sets of balanced three-phase windings that are shifted by 30 electrical degrees. For 12S-4R/8R stator rotor-pole machines, there is n angle between two sets of windings.  Stator-slot PM machines consist of three parts as other flux modulation machines, i.e., armature, PM excitation (PM MMF), and modulation poles (rotor slots). Although the PM MMF is closely related to the armature MMF, stator-slot PM machines still comply to the principle of flux modulation effect. The pole-pair number of armature windings affects the rotor-pole number, and their relationships are determined by [9] N r = iN s /2 ± P a (i = 1, 3, 5···) (2) in which N r is the rotor-pole number, N s is the stator-slot number, i is the odd number, and P a is the pole-pair number of armature windings. 12S-4R/8R/10R/11R/13R/14R/16R stator-slot PM machines are mentioned in [14], and the corresponding P a is 2, 2, 4, 5, 5, 4, and 2, respectively, but all with tooth-coil windings. However, there are other combinations, e.g., 12S-5R/7R, whose armature pole-pair number is 1, as shown in Table 1. In this paper, 12 stator-slots machines with FPW and different number of rotor poles are investigated. The coil pitches are 3, 6, 6, and 3 slot pitches, respectively. It should be noted that FPW is not restricted to 12 stator-slots machines.  Taking 12S7R machine for example, as shown in Figure 3, the coil positions in mechanical degree and electrical degree are shown in Figure 3b,c, respectively. Figure 4 shows the winding layout and back EMF phasors of 12S-4R/5R/7R/8R machines. 12S-5R/7R machines have two sets of balanced three-phase windings that are phase shifted by 30 electrical degrees. For 12S-4R/8R stator rotor-pole machines, there is no shift angle between two sets of windings.    The winding factor kw can be expressed as where kd is the winding distribution factor, and kp is the pitch factor. kd is given by where Q is the number of coil-EMF phasors per phase, α is the angle between two adjacent coil-EMF phasors, and v is the harmonic order. The pitch factor kp is given by [16] kp = cos(θc/2 − π/2) where θc is the angular difference between two adjacent slot conductors for the v th harmonics and is expressed as v(2πNr/Ns). The efficiency can be predicted by considering the total copper loss (Pcu_total), iron loss (Piron), PM eddy current loss (Ppm_eddy), as η = Pem/(Pem + Pcu_total + Piron + Ppm_eddy) (6) where Pem is the output power. The total copper loss includes the effective copper loss Pcu_eff and the end-winding copper loss Pcu_end. The end-winding length per turn lend is calculated as where τc is the average coil pitch of the machine. For FPW, τc is calculated as For TCW, τc is calculated as τc =π(r3 − yk − 0.5hslot)/Ns + 0.5tw (9) where r3 is the stator outer radius, yk is the stator yoke width, hslot is the slot depth, tw is the tooth width, and y is the coil pitch in slot pitch.

Influence of Key Geometric Parameters
Before investigating the influence of key geometric parameters, optimal models are obtained by global optimization under the following conditions.
(1) Both machines have the same stator outer diameter, stack length, PM material, and iron steel. The effective copper loss is fixed to 20 W. The winding factor k w can be expressed as where k d is the winding distribution factor, and k p is the pitch factor. k d is given by where Q is the number of coil-EMF phasors per phase, α is the angle between two adjacent coil-EMF phasors, and v is the harmonic order. The pitch factor k p is given by [16] k p = cos(θ c /2 − π/2) where θ c is the angular difference between two adjacent slot conductors for the v th harmonics and is expressed as v(2πN r /N s ). The efficiency can be predicted by considering the total copper loss (P cu_total ), iron loss (P iron ), PM eddy current loss (P pm_eddy ), as η = P em /(P em + P cu_total + P iron + P pm_eddy ) (6) where P em is the output power. The total copper loss includes the effective copper loss P cu_eff and the end-winding copper loss P cu_end . The end-winding length per turn l end is calculated as where τ c is the average coil pitch of the machine. For FPW, τ c is calculated as For TCW, τ c is calculated as where r 3 is the stator outer radius, yk is the stator yoke width, h slot is the slot depth, tw is the tooth width, and y is the coil pitch in slot pitch.

Influence of Key Geometric Parameters
Before investigating the influence of key geometric parameters, optimal models are obtained by global optimization under the following conditions. (1) Both machines have the same stator outer diameter, stack length, PM material, and iron steel. The effective copper loss is fixed to 20 W. (2) All the optimizations are based on genetic algorithm (GA), and 30 individuals in each population with 35 generations have been employed. (3) The optimized parameters are stator yoke width, stator inner radius, stator tooth width, rotor tooth width, rotor slot depth, and PM thickness. Parameters of the optimized machines are listed in Table 2. The influence of key geometric parameters, i.e., rotor-pole number, stator yoke width, stator tooth width, stator inner diameter, PM thickness, and rotor tooth width, is investigated. As listed in Table 1, when P a is fixed, there are different rotor-pole numbers that can satisfy (2). For example, when P a = 1, the rotor-pole number can be chosen as 5, 7, 17, or 19. Figure 5 shows that when the rotor pole number is 5 or 7, higher torque can be generated. Then, the influence of other geometric parameters in 12S-4R/5R/7R/8R machines is further investigated. The influence of key geometric parameters, i.e., rotorstator tooth width, stator inner diameter, PM thickness, a gated. As listed in Table 1, when Pa is fixed, there are di can satisfy (2). For example, when Pa = 1, the rotor-pole n or 19. Figure 5 shows that when the rotor pole number generated. Then, the influence of other geometric param chines is further investigated.  Figure 6 shows that larger stator yoke width is re torque for 12S5R and 12S7R, because the armature pole pa yoke width is required to avoid high saturation. In contras  Figure 6 shows that larger stator yoke width is required to generate the highest torque for 12S5R and 12S7R, because the armature pole pair number is 1 and larger stator yoke width is required to avoid high saturation. In contrast, 12S4R and 12S8R need smaller optimum stator yoke widths.
ctr. Veh. J. 2021, 12, x FOR PEER REVIEW Figure 6. Influence of stator yoke width on average torque when Stator tooth width affects the stator tooth saturation shown in Figure 7, the optimum stator tooth widths range f that there exists an optimum stator inner radius to maximize balance is achieved between electrical loading and magnet the optimum values are around 20, 18, 19, and 20 mm, respe split ratios between the stator inner radius to outer radius of Stator tooth width affects the stator tooth saturation and flux modulation effect. As shown in Figure 7, the optimum stator tooth widths range from 3.5-4.5 mm. Figure 8 shows that there exists an optimum stator inner radius to maximize the average torque, when a better balance is achieved between electrical loading and magnetic loading.  Figure 7, the optimum stator tooth widths range f that there exists an optimum stator inner radius to maximize balance is achieved between electrical loading and magnet the optimum values are around 20, 18, 19, and 20 mm, respe split ratios between the stator inner radius to outer radius of  Figure 9 shows that thicker PMs are favourable to produce maximum torque for 12S-5R/7R machines compared to 12S-4R/8R machines. To explain this, the armature MMF of stator windings is analysed. For simplicity, the input current is normalized, and the turn number per slot is 1. Figure 10 compares the MMFs of the two stator windings with P a = 1 and P a = 2. When P a is smaller, the armature MMF is stronger, and more PM flux can be forced into the airgap and the rotor side under load condition. (1) shows that the average torque is greatly affected by the armature MMF. Hence, the stronger the armature MMF, the higher the PM flux and the thicker the PMs.  Figure 9 shows that thicker PMs are favourable to produce 5R/7R machines compared to 12S-4R/8R machines. To explain stator windings is analysed. For simplicity, the input current is number per slot is 1. Figure 10 compares the MMFs of the two s and Pa = 2. When Pa is smaller, the armature MMF is stronger, forced into the airgap and the rotor side under load condition. torque is greatly affected by the armature MMF. Hence, the str the higher the PM flux and the thicker the PMs.
When the PM thickness is larger than the optimum value electrical loading are reduced. Meanwhile, the reduced electric creased PM flux φPM(Fq), as shown in (1). As can be observed from Figure 11, 12S-4R/5R machines have larger values of optimum rotor tooth width than 12S-7R/8R machines. The former needs wider rotor tooth to collect more flux due to smaller rotor pole number. When the PM thickness is larger than the optimum values, the copper area and the electrical loading are reduced. Meanwhile, the reduced electrical loading also means decreased PM flux ϕ PM (F q ), as shown in (1).
As can be observed from Figure 11, 12S-4R/5R machines have larger values of optimum rotor tooth width than 12S-7R/8R machines. The former needs wider rotor tooth to collect more flux due to smaller rotor pole number.
(c) Spectra As can be observed from Figure 11, 12S-4R/5R machines h mum rotor tooth width than 12S-7R/8R machines. The former n collect more flux due to smaller rotor pole number. Figure 11. Influence of rotor tooth width on average torque when Pcu_e Figure 12 compares the torque waveforms of 12S machine numbers. The corresponding geometric parameters are listed chines deliver higher torque than 12S-4R/8R machines. In addi 12R-5R/7R machines are much lower than those of 12S-4R/8R numbers of least common multiple of stator-slot number and ro

Torque (Nm)
Rotor tooth width (mm) Figure 11. Influence of rotor tooth width on average torque when P cu_eff = 20 W. Figure 12 compares the torque waveforms of 12S machines with different rotor pole numbers. The corresponding geometric parameters are listed in Table 2. 12S-5R/7R machines deliver higher torque than 12S-4R/8R machines. In addition, the torque ripples of 12R-5R/7R machines are much lower than those of 12S-4R/8R machines, due to larger numbers of least common multiple of stator-slot number and rotor-pole number.

Comparison of Stator-Slot PM Machines with Tooth-Coil and Full-Pitched Windings
In this section, the 12S7R machine with FPW is compared with 12S10R with TCW,

Comparison of Stator-Slot PM Machines with Tooth-Coil and Full-Pitched Windings
In this section, the 12S7R machine with FPW is compared with 12S10R with TCW, based on globally optimized topologies. Figure 13 shows the cross sections of compared stator slot PM machines. M1 (12S7R with FPW) and M2 (12S10R with TCW) are globally optimized. M3 (12S10R with TCW) is optimized under the same PM volume as M1. The parameters are listed in Table 2.

Comparison of Stator-Slot PM Machines with Tooth-Coil and Full-Pitched Windings
In this section, the 12S7R machine with FPW is compared with 12S10R with TCW, based on globally optimized topologies. Figure 13 shows the cross sections of compared stator slot PM machines. M1 (12S7R with FPW) and M2 (12S10R with TCW) are globally optimized. M3 (12S10R with TCW) is optimized under the same PM volume as M1. The parameters are listed in Table 2. On open circuit, Figure 14a-c, the PM flux linkage only circulates within the stator, if neglecting magnetic saturation. However, there is some "leakage" flux linking the stator and the rotor due to nonlinear BH characteristics of the iron core laminations. Hence, negligible back EMFs and cogging torques can be expected.
On load, Figure 14d-f, the PM flux is forced into the airgap and the rotor side by the armature MMF, and the PM flux has improved saturation in the flux path, i.e., the stator tooth of M1 and the stator yoke of M2. This also explains the small stator yoke width in M2. Although more space is used to accommodate the copper wire, the stator yoke is not saturated on load.
By comparing Figure 14e,f, it can be observed that the on-load flux density in the stator teeth increases when increasing the PM volume. This is due to the fact that the armature MMF Fq can only force PM flux φPM(Fq) into the airgap, and excess PM flux makes On open circuit, Figure 14a-c, the PM flux linkage only circulates within the stator, if neglecting magnetic saturation. However, there is some "leakage" flux linking the stator and the rotor due to nonlinear BH characteristics of the iron core laminations. Hence, negligible back EMFs and cogging torques can be expected. the flux path more saturated. Aside from that, the stator slot area is reduced, and so is the armature MMF Fq. Therefore, M3 generates lower torque than M2, as shown in Figure 15.  Figure 15 compares the torques of the three machines. As can be observed, M1 delivers the highest torque, together with the lowest torque ripple. On load, the slot/pole number combination plays an important role in affecting the torque ripple. For M1, the least common multiple LCM is 84, while that of M2 and M3 is 60, which explains the lowest torque On load, Figure 14d-f, the PM flux is forced into the airgap and the rotor side by the armature MMF, and the PM flux has improved saturation in the flux path, i.e., the stator tooth of M1 and the stator yoke of M2. This also explains the small stator yoke width in M2. Although more space is used to accommodate the copper wire, the stator yoke is not saturated on load.
By comparing Figure 14e,f, it can be observed that the on-load flux density in the stator teeth increases when increasing the PM volume. This is due to the fact that the armature MMF F q can only force PM flux ϕ PM (F q ) into the airgap, and excess PM flux makes the flux path more saturated. Aside from that, the stator slot area is reduced, and so is the armature MMF F q . Therefore, M3 generates lower torque than M2, as shown in Figure 15.   Figure 15 compares the torques of the three machines. As can be observed, M1 delivers the highest torque, together with the lowest torque ripple. On load, the slot/pole number combination plays an important role in affecting the torque ripple. For M1, the least common multiple LCM is 84, while that of M2 and M3 is 60, which explains the lowest torque ripple of M1. Regarding other electromagnetic performance, only M1 and M2 are compared.
In Figure 16, the airgap flux densities of the two machines are shown. M1 exhibits higher airgap flux density than M2, due to the thicker PMs resulting in more "leakage" flux, which can also be observed in Figure 14.
Similarly, the tendency of the back EMFs of the two machines can be explained. As shown in Figure 17, M1 has higher back EMF than M2.
In Figure 16, the airgap flux densities of the two machines are shown. M1 higher airgap flux density than M2, due to the thicker PMs resulting in more " flux, which can also be observed in Figure 14.
Similarly, the tendency of the back EMFs of the two machines can be expla shown in Figure 17, M1 has higher back EMF than M2.  Cogging torque is mainly affected by the slot/pole number combination strength of airgap magnetic field, i.e., the amount of "leakage" flux. M1 exhibi cogging torque than M2 due to higher "leakage" flux, as shown in Figure 18.
The least common multiple (LCM) between the stator-slot number and the r number of M1 and M2 is 84 and 60, respectively. Therefore, the dominant coggin harmonics in one electrical period are 12th and 6th, respectively, as shown in Fig  Cogging torque is mainly affected by the slot/pole number combi strength of airgap magnetic field, i.e., the amount of "leakage" flux. M1 cogging torque than M2 due to higher "leakage" flux, as shown in Figure The least common multiple (LCM) between the stator-slot number an number of M1 and M2 is 84 and 60, respectively. Therefore, the dominant harmonics in one electrical period are 12th and 6th, respectively, as shown  Cogging torque is mainly affected by the slot/pole number combination and the strength of airgap magnetic field, i.e., the amount of "leakage" flux. M1 exhibits higher cogging torque than M2 due to higher "leakage" flux, as shown in Figure 18.  Figure 19 shows that both the machines rely on PM torque, and they reluctance torque. Figure 20 compares the torques versus armature curr control. It should be noted that the SSCMPMMs have antisaturation capa saturation capability is due to the fact that most of the PM flux circulates w core on open circuit, and the armature MMF forces the PM flux into the rotor side at load condition. The magnetic flux path firstly becomes less the armature current increases. Then, the PM MMF and the armature M ance, at which point the main flux path is least saturated. Afterward, th comes more and more saturated if the armature current is further incre nomenon is indicated by the inductance variation versus armature curre Figure 21. The inductance variations also indicate that M2 has better over The least common multiple (LCM) between the stator-slot number and the rotor-pole number of M1 and M2 is 84 and 60, respectively. Therefore, the dominant cogging torque harmonics in one electrical period are 12th and 6th, respectively, as shown in Figure 18b. Figure 19 shows that both the machines rely on PM torque, and they have negligible reluctance torque. Figure 20 compares the torques versus armature current under I d = 0 control. It should be noted that the SSCMPMMs have antisaturation capability. This antisaturation capability is due to the fact that most of the PM flux circulates within the stator core on open circuit, and the armature MMF forces the PM flux into the airgap and the rotor side at load condition. The magnetic flux path firstly becomes less saturated when the armature current increases. Then, the PM MMF and the armature MMF reach a balance, at which point the main flux path is least saturated. Afterward, the flux path becomes more and more saturated if the armature current is further increased. This phenomenon is indicated by the inductance variation versus armature current, as shown in Figure 21. The inductance variations also indicate that M2 has better overload capability. Figure 22 compares the power factor of the two machines. M2 exhibits the slightly higher power factor on rated load, due to the smaller inductance. Although M1 has much larger inductance, its electrical frequency is lower. the armature current increases. Then, the PM MMF and the armatur ance, at which point the main flux path is least saturated. Afterward comes more and more saturated if the armature current is further in nomenon is indicated by the inductance variation versus armature cu Figure 21. The inductance variations also indicate that M2 has better o   the armature current increases. Then, the PM MMF and the armature MM ance, at which point the main flux path is least saturated. Afterward, the comes more and more saturated if the armature current is further increas nomenon is indicated by the inductance variation versus armature curren Figure 21. The inductance variations also indicate that M2 has better overlo    Figure 22 compares the power factor of the two machines. M2 exhi higher power factor on rated load, due to the smaller inductance. Althoug  Figure 22 compares the power factor of the two machines. higher power factor on rated load, due to the smaller inductance. larger inductance, its electrical frequency is lower.            Figure 26 compares the torques versus machine length. The machine leng hend is the height of end-winding. The volume of the end-winding Vend and th the effective winding Veff satisfy (10).
where rb is the radius of slot bottom, rt is the radius of slot top, and Sslot is area.
As can be observed, when the machine length is smaller than 145 mm, lower torque than M2. However, when the machine length is larger than 14 more advantageous in producing high torque. Similar efficiency tendency served in Figure 27. M1 is more efficient when the machine length is over 14  V end /V eff = l end /l s (10) V end = π(r b 2 − r t 2 )h end (11) V eff = S slot l s (12) where r b is the radius of slot bottom, r t is the radius of slot top, and S slot is the total slot area. As can be observed, when the machine length is smaller than 145 mm, M1 delivers lower torque than M2. However, when the machine length is larger than 145 mm, M1 is more advantageous in producing high torque. Similar efficiency tendency can be observed in Figure 27. M1 is more efficient when the machine length is over 140 mm.

Experiment Validation
The 12S7R SSCMPMM with y = 3 is prototyped, as shown in are inserted into the stator slot after winding the stator. Due to th teeth, the magnets can be stuck in the stator slots. Such practice mass production. The geometric parameters of the prototype are Although the open-circuit performance is produced by the " affected by magnetic saturation and material imperfections, it is back EMF. Figure 29 compares the 2D/3D FEA calculated and me which we can observe that 2D/3D FEA calculated values are clos

Experiment Validation
The 12S7R SSCMPMM with y = 3 is prototyped, as shown in Figure 28. The magnets are inserted into the stator slot after winding the stator. Due to the employment of parallel teeth, the magnets can be stuck in the stator slots. Such practice may be not applicable to mass production. The geometric parameters of the prototype are listed in Table 3.

Experiment Validation
The 12S7R SSCMPMM with y = 3 is prototyped, as shown in Figure 28. The m are inserted into the stator slot after winding the stator. Due to the employment of p teeth, the magnets can be stuck in the stator slots. Such practice may be not applic mass production. The geometric parameters of the prototype are listed in Table 3.
Although the open-circuit performance is produced by the "leakage" flux, and affected by magnetic saturation and material imperfections, it is still worth check back EMF. Figure 29 compares the 2D/3D FEA calculated and measured back EMF which we can observe that 2D/3D FEA calculated values are close to the measured  Although the open-circuit performance is produced by the "leakage" flux, and easily affected by magnetic saturation and material imperfections, it is still worth checking the back EMF. Figure 29 compares the 2D/3D FEA calculated and measured back EMFs, from which we can observe that 2D/3D FEA calculated values are close to the measured ones.
Stator yoke width (mm) 7 Rotor tooth width (mm) 7.8 Rotor slot depth (mm) 7.5 The static torque versus rotor position is measured by injecting dc current ( = 10 A) into the three phase windings [22]. The FEA calculated and measured are shown in Figure 30. The measured static torque is around 23.6% and 18% lo 2D and 3D FEA calculated values. Similarly, larger difference can be observed FEA calculated and measured torque versus current curves, as shown in Figure   (  The static torque versus rotor position is measured by injecting dc current (I a = −2I b = −2I c = 10 A) into the three phase windings [22]. The FEA calculated and measured static torques are shown in Figure 30. The measured static torque is around 23.6% and 18% lower than the 2D and 3D FEA calculated values. Similarly, larger difference can be observed between 2D FEA calculated and measured torque versus current curves, as shown in Figure 31.
Stator inner radius (mm) Stator tooth width (mm) Stator yoke width (mm) Rotor tooth width (mm) Rotor slot depth (mm) The static torque versus rotor position is measured by injecting dc c = 10 A) into the three phase windings [22]. The FEA calculated and me are shown in Figure 30. The measured static torque is around 23.6% and 2D and 3D FEA calculated values. Similarly, larger difference can be o FEA calculated and measured torque versus current curves, as shown in

Conclusions
In this paper, stator slot circumferentially magnetized PM mach with full-pitched windings (FPW) are analysed. The influence of key ters is investigated for the 12 stator-slots and 4/5/7/8 rotor-poles SSCM tor-slots 7 rotor-poles (12S7R) and 12S5R machines need larger stat thicker PMs. The 7 poles rotor can produce the highest torque and th ple.
Compared with 12S10R SSCMPMM with tooth-coil windings (TC chine with FPW can deliver around 5.5 times higher torque. Meanwh chine length is over around 140 mm, the 12S7R machine can produce sity and higher efficiency compared with its 12S10R counterpart.

Conclusions
In this paper, stator slot circumferentially magnetized PM machines (SSCMPMMs) with full-pitched windings (FPW) are analysed. The influence of key geometric parameters is investigated for the 12 stator-slots and 4/5/7/8 rotor-poles SSCMPMMs. The 12 statorslots 7 rotor-poles (12S7R) and 12S5R machines need larger stator yoke width and thicker PMs. The 7 poles rotor can produce the highest torque and the lowest torque ripple.
Compared with 12S10R SSCMPMM with tooth-coil windings (TCW), the 12S7R machine with FPW can deliver around 5.5 times higher torque. Meanwhile, if the total machine length is over around 140 mm, the 12S7R machine can produce higher torque density and higher efficiency compared with its 12S10R counterpart.