2.2 kW 400 V cage motor (star-delta) design

Data: 2.2 kW, 400 V, 50 Hz, 1420 rpm, so 4 poles and $n_s = 25$ rps; $\eta = 0.8$, $\cos\phi = 0.825$. Assumptions: $K_w = 0.955$; star-delta starting, so the stator runs in delta ($E_{ph} = 400$ V); tooth flux density limit 1.7 Wb/m²; iron factor 0.9.

i) Main dimensions

$$\begin{aligned} Q &= \frac{2.2}{0.8 \times 0.825} = 3.333\ \text{kVA} \\ C_0 &= 11 \times 0.44 \times 21000 \times 0.955 \times 10^{-3} = 97.07 \\ D^2L &= \frac{3.333}{97.07 \times 25} = 1.374 \times 10^{-3}\ \text{m}^3 \end{aligned}$$

$L = 1.5\tau = 1.5 \times \pi D/4 = 1.178D$:

$$D^3 = \frac{1.374\times10^{-3}}{1.178} = 1.166\times10^{-3} \Rightarrow D = 0.1053\ \text{m}, \quad L = 0.124\ \text{m}$$

ii) Stator turns per phase

$$\begin{aligned} \tau &= \pi \times 0.1053/4 = 0.0827\ \text{m} \\ \Phi &= 0.44 \times 0.0827 \times 0.124 = 4.51 \times 10^{-3}\ \text{Wb} \\ T_s &= \frac{400}{4.44 \times 50 \times 4.51\times10^{-3} \times 0.955} = 418.3 \end{aligned}$$

iv) Number of stator slots

Slot pitch 12–15 mm. $q = 2$: $S_s = 3 \times 4 \times 2 = 24$; slot pitch $= \pi \times 105.3/24 = 13.78$ mm (OK). 24 slots. Conductors per slot $= 6 \times 418.3/24 = 104.6$, take 105: $Z_s = 2520$, $T_s = 420$.

iii) Size of stator conductor

$$I_{ph} = \frac{3333.3}{3 \times 400} = 2.778\ \text{A}, \qquad a_s = \frac{2.778}{4} = 0.694\ \text{mm}^2$$

Bare diameter $= \sqrt{4 \times 0.694/\pi} = 0.94$ mm.

v) Area and dimensions of each slot

$$A_{slot} = \frac{105 \times 0.694}{0.4} = 182.3\ \text{mm}^2$$

$d = 4w$: $4w^2 = 182.3$, $w = 6.75$ mm, $d = 27.0$ mm.

vi) Minimum width of stator teeth

$L_i = 0.9 \times 0.124 = 0.1116$ m; teeth per pole $= 24/4 = 6$:

$$W_{ts(min)} = \frac{4.51\times10^{-3}}{1.7 \times 6 \times 0.1116} = 3.96\ \text{mm}$$

Actual tooth width at the gap $= 13.78 - 6.75 = 7.0$ mm, so tooth density is safe.

Answer: $D = 10.53$ cm, $L = 12.4$ cm; $T_s = 420$; $a_s = 0.694$ mm² (0.94 mm dia); 24 slots; slot 182.3 mm² ($6.75 \times 27.0$ mm); $W_{ts(min)} = 3.96$ mm.