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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