Chapter B

Q. B.1

Calculate the breadth, pitch, and winding factors for the distributed fractional-pitch winding of Fig. B.2.



Verified Solution

The winding of Fig. B.2 has two coils per phase belt, separated by an electrical angle of 30°. From Eq. B.6 the breadth factor is

k_{\mathrm{b}}=\frac{AD}{nAB}=\frac{\sin (n \gamma / 2)}{n \sin (\gamma / 2)} \quad \quad \quad (B.6)

k_{\mathrm{b}}=\frac{\sin (n \gamma / 2)}{n \sin (\gamma / 2)}=\frac{\sin \left[2\left(30^{\circ}\right) / 2\right]}{2 \sin \left(30^{\circ} / 2\right)}=0.966

The fractional-pitch coils span 150° = 5π/6 rad, and from Eq. B.14 pitch factor is

k_{\mathrm{p}}=\cos \left(\frac{π  –  ρ}{2}\right)=\sin \left(\frac{\rho}{2}\right) \quad \quad \quad (B.14)

k_{\mathrm{p}}=\sin \left(\frac{\rho}{2}\right)=\sin \left(\frac{5 \pi}{12}\right)=0.966

The winding factor is

k_{\mathrm{w}}=k_{\mathrm{b}} k_{\mathrm{p}}=0.933