To demonstrate the efficacy of proposed method, a prototype machine of FSPMM with specified geometric is assessed that Dimension of this machine is placed in table 3. Rotor pole/stator 10/12 that two scenarios (only PM, only 2-layer) are considered for this sample geometric to prove our claim. The layout of winding for 2 layer winding is based on right and left side of each slot that A,B,C are respectively reference phase, another phase with 120 electrical degree lag and the third phase with 120 electrical degree lead shown in Table 2.
Table 2
Layout of 2-layer winding
Number of slot
|
Right side
|
Left side
|
1
|
A-
|
B+
|
2
|
B-
|
C+
|
3
|
C-
|
A+
|
4
|
A-
|
B+
|
5
|
B-
|
C+
|
6
|
C-
|
A+
|
7
|
A-
|
B+
|
8
|
B-
|
C+
|
9
|
C-
|
A+
|
10
|
A-
|
B+
|
11
|
B-
|
C+
|
12
|
C-
|
A+
|
Table 3
Specifications of prototype FSPM with inner and outer rotor
Inner Rotor FSPM
|
Item |
Value |
Number of outer phases, Nph
|
3
|
Number of inner rotor slots, Nr
|
10
|
Number of outer stator slots, Ns
|
12
|
Relative permeability of permanent magnet, µrpm
|
1
|
Residual flux density, Brem
|
1.2T
|
Outer rotor yoke radius, Rry
|
102mm
|
Outer stator yoke radius, Ry
|
75mm
|
Outer radius of outer stator, Rs
|
92.09mm
|
Inner radius of outer rotor, Rr
|
96mm
|
Outer radius of flux barrier, Rnmi
|
72.67mm
|
Width of outer rotor slot, wr
|
27.01π/180 rad
|
Width of outer stator slot, ws
|
6.92 π/180 rad
|
Width of outer PM, wpm
|
5.41 π/180 rad
|
Filling factor, Kf
|
1
|
Stack length, Ls
|
100 mm
|
Outer Rotor FSPM
|
Item Value
|
rotor yoke radius, Rry
|
26mm
|
stator yoke radius, Ry
|
60mm
|
radius of inner stator, Rs
|
38mm
|
radius of inner rotor, Rr
|
35mm
|
radius of exterior, Rnm
|
63.63mm
|
Number of outer phases, Nph
|
3
|
Number of inner rotor slots, Nr
|
10
|
Number of outer stator slots, Ns
|
12
|
Relative permeability of permanent magnet, µrpm
|
1
|
Residual flux density, Brem
|
1.2T
|
Width of outer rotor slot, wr
|
27.01π/180 rad
|
Width of outer stator slot, ws
|
6.92 π/180 rad
|
Width of outer PM, wpm
|
5.41 π/180 rad
|
Filling factor, Kf
|
1
|
Stack length, Ls
|
100 mm
|
A. Only PM
B. Only 2-layer winding
C. Cogging torque
Cogging torque of electrical motors is the torque due to the interaction between the permanent magnets of the rotor and the stator slots of a Permanent Magnet (PM) machine. It is also known as detent or 'no-current' torque. This torque is position dependent and its periodicity per revolution depends on the number of magnetic poles and the number of teeth on the stator. Cogging torque is an undesirable component for the operation of such a motor. It is especially prominent at lower speeds. Cogging torque results in torque as well as speed ripple; however, at high speed the motor moment of inertia filters out the effect of cogging torque. Relationship cogging torque is obtained (in presence of only PM) as follow:
$$Tcogging\left(t\right)={\int }_{-\pi }^{\pi }\frac{{L}_{s}{{R}_{c}}^{2}}{{\mu }_{0}}{B}_{r} {B}_{\theta } d\theta$$
4
Where, Br and \({B}_{\theta }\) respectively are the radial and tangential flux density components in the air-gap, due to the PMs and Rc is radius of the center of airgap.
D. Electromagnetic torque
Electromagnetic torque is due to presence of both winding and PM therefore, resultant torque is like below:
$$T\left(t\right)={\int }_{-\pi }^{\pi }\frac{{L}_{s}{{R}_{c}}^{2}}{{\mu }_{0}}{B}_{r} {B}_{\theta } d\theta$$
5
Where, Br and \({B}_{\theta }\) respectively are the radial and tangential flux density components in the air-gap, due to both PMs and winding.
E. Inductance
The integral constants are also calculated when only coil j is carrying current without the effect of PMs. Having assumed the series connections of all coils in each phase, the self-inductance of phase k is calculated using the summation of the flux linked with the coils of phase k due to solely the corresponding coil current of phase k divided by the corresponding coil current of phase k. For self-inductance:
![](data:image/png;base64,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)