Axial Flux Permanent Magnet
Brushless Machines
Numerical Example 2.3
m1 := 3
Number of phases
Pout := 75000
Output power, W
V1L := 460
Line voltage (Y connection), V
f := 100
Frequency, Hz
rpm := 1500
Speed, rpm
Calculations
n :=
p :=
rpm
Number of pole pairs
n
p=4
1
3
Inner-to-outer diameter ratio (assumption)
⋅ 1 + kd ⋅  1 − kd

8
1
(
epf := 0.9
V1 :=
n = 25
f
k d :=
k D :=
Speed, rev/s
60
)
2

Parameter kD dependent of inner and outer
diameters of PMs
k d = 0.577
k D = 0.131
Assumed efficiency x power factor product
V1L
3
Pout
Ia :=
m1 ⋅ V1 ⋅ epf
Bmg := 0.65
Input voltage per phase (two stators
connected in series), V
V1 = 265.6
Phase rms current, A
Ia = 104.6
Magnetic flux density in the air gap (assumption), T
J.F. Gieras, R.J. Wang, M.J.
Kamper
1
Axial Flux Permanent Magnet
Brushless Machines
Am := 40000
Peak ine current density (assumption), A/m
ε := 0.9
EMF to voltage ratio (assumption)
k w1 := 0.96
Winding factor for fundamental (assumption)
3
Dout :=
ε ⋅ Pout
2
π ⋅ k D⋅ k w1⋅ n ⋅ Bmg⋅ Am⋅ epf
Din := k d ⋅ Dout
Inner diameter, m
 π ⋅ Dout⋅ ( 1 + k d) ⋅ Am

4 ⋅ m1 ⋅ 2 ⋅ Ia


N1 := round 

Φ f :=
2
π
⋅ Bmg⋅


π ⋅ 2 ⋅ f ⋅ k w1⋅ Φ f

N1
m1
s1 := n c⋅ m1
q 1 :=
2
2
 Magnetic flux density, Wb
aw := 4
Din = 0.261
N1 = 51
Φ f = 0.00555
The number of turns estimated on the
basis of the EMF and magnetic flux
N1 = 51
Selected number of turns assuming double layer winding
and n c = 16 coils per phase.
Number of coils per phase
Number of slots (number of coils per phase times
number of phases
s1
2 ⋅ p ⋅ m1
Dout = 0.452
Tentatively estimated number of turns
per phase
⋅ Dout ⋅  1 − k d

ε ⋅ 0.5⋅ V1
N1 := 48
n c :=
π
8⋅ p

N1 := round 

Output diameter, m
Number of slots per pole per phase
n c = 16
s1 = 48
q1 = 2
Number of stator parallel conductors (assumption)
J.F. Gieras, R.J. Wang, M.J.
Kamper
2
Axial Flux Permanent Magnet
Brushless Machines
Nc :=
aw⋅ N1
s1
Number of conductors in a single coil
Nc = 12
m1
s1
Nc :=
⋅a
nc w
6
Ja := 4.5⋅ 10
Ia
sa :=
aw⋅ Ja
k fill
π ⋅ Din
s1
b sl := 0.0119
h t1 :=
ssl
c1min := t1min − b sl
t1max :=
Cross section area of the slot
(the number of conductors in each slot = 2N c)
ssl = 0.000232
Minimum stator slot pitch, m
t1min = 0.0171
Slot width (chosen), m
Stator slot depth (height of tooth), m
b sl
B1tmax :=
sa = 0.00000581
Slot fill factor for rectangular conductors and
lowe voltage machine (assumtion)
2 ⋅ Nc⋅ sa
t1min :=
Nc = 12
Current density (assumption for totally enclosed
machine with air cooling), A/m2
Crooss section area of the stator conductor, m2
k fill := 0.6
ssl :=
Alternatively
Bmg⋅ t1min
c1min
π ⋅ Dout
s1
h t1 = 0.02
Narrowest stator tooth width, m
c1min = 0.0052
Magnetic flux density in teh narrowest
part of the stator tooth, m
B1tmax = 2.14
Stator slot pitch at Dout (maximum slot pitch), m
J.F. Gieras, R.J. Wang, M.J.
Kamper
t1max = 0.02962
3
Axial Flux Permanent Magnet
Brushless Machines
B1tmin :=
Bmg⋅ t1max
t1max − b sl
Magnetic flux density in the widest
part of the stator tooth, T
J.F. Gieras, R.J. Wang, M.J.
Kamper
B1tmin = 1.09
4