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 $𝐸_{𝐢1}$ and $𝐸_{𝐢2}$ are the voltages generated in the coil sides and $𝐸_{𝐢}$ is the resultant coil voltage. Then,

$$\mathrm{𝑬_{π‘ͺ} = 𝑬_{π‘ͺ𝟏} + 𝑬_{π‘ͺ𝟐}}$$

Since $𝐸_{𝐢1}$ and $𝐸_{𝐢2}$ are in phase, the resultant coil voltage is equal to their arithmetic sum (Refer the figure of full-pitch coil).

$$\mathrm{∴\:𝐸_{𝐢} = 𝐸_{𝐢1} + 𝐸_{𝐢2}}$$

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 $𝐸_{𝐢}$ is equal to the phasor sum of $𝐸_{𝐢1}$ and $𝐸_{𝐢2}$.

If the coil span is decreased by an angle of electrical, the coil span is (180 − α) electrical degree. The voltages generated $𝐸_{𝐢1}$ and $𝐸_{𝐢2}$ in the two coil sides will be out of phase with respect to each other by an angle of 𝛼° electrical. The phasor sum of $𝐸_{𝐢1}$ and $𝐸_{𝐢2}$ is $𝐸_{𝐢}$ = 𝐴𝐢(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.

$$\mathrm{Coil\:Span\:Factor, π‘˜_{𝐢} =\frac{Voltage \:generated\:with\:short − pitch\:coil}{Voltage \:generated\:with\:full\:pitch\:coil}}$$

Refer the phasor diagram,

$$\mathrm{π‘˜_{𝐢} =\frac{Phasor\:sum\:of\:voltages \:of\:two\:coil\:sides}{Arithmetic\:sum\:of\:voltages \:of\:two\:coil\:sides}=\frac{𝐴𝐢}{2𝐴𝐡}}$$

$$\mathrm{\Rightarrow\:π‘˜_{𝐢} =\frac{2𝐴𝐷}{2𝐴𝐡}= cos\left(\frac{α}{2}\right)}$$

For a full pitch coil,

$$\mathrm{α = 0°;\:\:\:cos\frac{α}{2}= 1;\:\:\:or\:\:\: π‘˜_{𝐢} = 1}$$

For a short pitch coil,

$$\mathrm{π‘˜_{𝐢} < 1}$$

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.