Pitch Factor or Coil Span Factor in Alternator

Coil span or coil pitch is defined as the distance between the two sides of a coil.

Pole pitch is defined as the angular distance between the central line of one pole to the central line of the next pole. A pole pitch is always 180° electrical regardless of the number of poles on the machine.

• When a coil is having a span of 180° electrical, it is called as a full-pitch coil.
• When the coil is having a span less than 180° electrical, it is known as a short-pitch coil or fractional-pitch coil.

The fractional-pitch coil is also known as chorded coil. A stator winding using fractional pitch coil is called as a chorded winding.

If the span of the coil is reduced by an angle of electrical, then the coil span will be (180 − α) electrical degrees.

In case of a full-pitch coil, the two coil sides span a distance exactly equal to the pole pitch of 180° electrical. Consequently, the voltage generated in a full pitch coil is such that the coil-side voltages are in phase.

Let E_C1 and E_C2 are the voltages generated in the coil sides and E_C is the resultant coil voltage. Then,

$$\mathrm{E_{C} \:=\: E_{C1} \:+\: E_{C2}}$$

Since E_C1 and E_C2 are in phase, the resultant coil voltage is equal to their arithmetic sum (Refer the figure of full-pitch coil).

$$\mathrm{∴ \: E_{C} \:=\: E_{C1} \:+\: E_{C2}}$$

If the coil span of a single coil is less than the pole pitch of 180° electrical, i.e., the case of short-pitch coil, the voltages generated in each coil side are not in phase. The resultant coil voltage $E_{C}$ is equal to the phasor sum of E_C1 and E_C2.

If the coil span is decreased by an angle of electrical, the coil span is (180 − α) electrical degree. The voltages generated E_C1 and E_C2 in the two coil sides will be out of phase with respect to each other by an angle of a° electrical. The phasor sum of E_C1 and E_C2 is E_C = AC (Refer the figure of short pitch coil).

The coil span-factor or pitch factor is defined as the ratio of the voltage generated in the short-pitch coil to the voltage generated in the full-pitch coil. The coil span factor is also known as chording factor.

$$\mathrm{\text{Coil Span Factor, } \:k_{C} \:=\:\frac{\text{Voltage generated with short - pitch coil}}{\text{Voltage generated with full pitch coil}}}$$

Refer the phasor diagram,

$$\mathrm{k_{C} \:=\: \frac{\text{Phasor sum of voltages of two coil sides}}{\text{Arithmetic sum of voltages of two coil sides}} \:=\: \frac{AC}{2AB}}$$

$$\mathrm{\Rightarrow \: k_{C} \:=\: \frac{2AD}{2AB} \:=\: \cos\left(\frac{\alpha}{2}\right)}$$

For a full pitch coil,

$$\mathrm{\alpha \:=\: 0°;\:\: \cos \frac{\alpha}{2} \:=\: 1;\:\: or \:\: k_{C} \:=\: 1}$$

For a short pitch coil,

$$\mathrm{k_{C} \:\lt\: 1}$$

Advantages of Chording

The advantages of the chorded winding are as follows −

• There is a saving in the conductor material because the chording shortens the ends of the winding.
• The chording or short-pitching reduces the effects of distorting harmonics and hence the waveform of the generated voltage is improved and making it approach a sine wave.