Three-phase induction motor design calculator

Stator sizing for a three-phase induction motor, from the rated specification through to slot and tooth geometry. Enter your rated power, voltage, frequency and speed together with the magnetic and electric loading, and every derived quantity updates as you type.

The method is the classic output-equation approach: rated output gives the apparent power, the output coefficient and specific loadings fix the bore volume (with stack length taken equal to bore diameter), and the winding, slot and yoke dimensions follow from flux and current density.

Parameters, formulas and a worked example

The example column shows a worked 5 kW, 400 V, 50 Hz, 1500 rpm machine with 36 slots.

1. Rated Specifications

SymbolQuantityUnitFormulaExample
Po Rated Power kW input 5
V Rated Voltage V input 400
f Frequency Hz f = P·Ns/120 50
Ns Rated Speed rpm Ns = 120·f/P 1500
m Phases input 3
η Efficiency input 0.9
pf Power Factor input 0.85

2. Poles & Output

SymbolQuantityUnitFormulaExample
P No. of Poles P = 120·f/Ns 4
p Pole Pairs p = P/2 2
ns Speed Hz ns = Ns/60 25
Qo Output kVA Qo = Po/(pf·η) 6.5359

3. Magnetic & Electric Loading

SymbolQuantityUnitFormulaExample
Bav Air gap flux density T input 0.5
ac Ampere per metre A/m input 25000
Co Output Coefficient Co = 0.011·Bav·ac 137.5

4. Stator Geometry

SymbolQuantityUnitFormulaExample
D Stator Bore Dia m Qo = Co·D²·L·ns 0.123886
L Stack Length m L = D 0.123886
Фpp Flux per Pole Wb Фpp = π·Bav·D·L/P 0.006027

5. Electrical Parameters

SymbolQuantityUnitFormulaExample
E Phase Voltage V E = V/1.732 230.9401
I Phase Current A I = Po·1000/(1.732·V·pf·η) 9.4338
τ Torque Nm τ = 9550·Po/Ns 31.8333
σt Tangential Stress Pa σt = 2·τ/(π·D²·L) 10658.51

6. Winding Design

SymbolQuantityUnitFormulaExample
Q No. of Slots input 36
q Slots/pole/phase q = Q/(m·P) 3
qm Slots/phase qm = Q/m 12
α Slot angle ° α = 180·P/Q 20
τs Slot pitch m τs = π·D/Q 0.010811
τp Pole pitch m τp = π·D/P 0.0973
Cp Full Coil Pitch Cp = 180/α 9
Y Short Pitch Y = (Cp−1)/Cp 0.888889
ε Short coil angle ° ε = α (1 slot short) 20
kp Pitch Factor kp = cos(ε/2) 0.984808
kd Distribution Factor kd = sin(q·α/2)/(q·sin(α/2)) 0.959795
kw Winding Factor kw = kp·kd 0.945214
T Turns per phase T = E/(4.44·kw·f·Фpp) 182.605
Zs Conductors per slot Zs = T/qm 15.2171

7. Conductor & Slot Sizing

SymbolQuantityUnitFormulaExample
J Current Density A/mm² input 5
ff Fill Factor input 0.5
Bt Tooth flux density T input 1.5
By Yoke flux density T input 1.2
Ac Conductor Area mm² Ac = I/J 1.886766
Acu Copper Area mm² Acu = Zs·Ac 28.7111
As Slot Area mm² As = Acu/ff 57.4221
g Air Gap mm g = 0.18 + 0.006·Po^0.4 (Po in W) 0.361025
Qp Slots per pole Qp = Q/P 9
Фt Flux per tooth Wb Фt = Фpp/Qp 0.00066967
tw Tooth width mm tw = Фt/(Bt·L) 3.6037
sw Slot width mm sw = τs − tw 7.2074
hs Slot depth mm hs = As/sw 7.9671
ht Tooth height mm ht = hs 7.9671
yt Yoke thickness m yt = Фpp/(2·By·L) 0.020271
Do Outer stator dia m Do = D + 2·(hs + yt) 0.180362

8. Air Gap MMF

SymbolQuantityUnitFormulaExample
Hg Field intensity A·t/m Hg = Bav/µ₀ 397887.36
Ug Air gap MMF A·t Ug = Hg·g 143.6474

These are sound starting values for a design. Check them against your own specification, lamination data and manufacturing constraints.

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