# Number of poles used for calculating synchronous speed

I am a bit confused in the formula used to determine the synchronous speed $$\N_S\$$. Following is the formula used to determine the speed:

$$\N_S = \frac{120f}{p}\$$

Now for a 6 pole motor there are some sites where 6 is first divided by 2 and then the answer got is used for $$\p\$$ and there are some sites that use 6 for $$\p\$$. Can somebody clear this confusion? Also do the number of poles affect the phase difference? Like for 6 pole three-phase motor the phase difference would be 120 irrespective of the number of poles or would it be 60?

More than one winding and more than one phase contributes to the formation of one pole. In a three phase motor, the magnetic effects of each of the three phase windings are added together to form each pole. Within a phase, several distributed windings may be part of a phase. In single-phase motors, a main winding and an auxiliary winding or a shaded-pole winding forms each pole.

The formula in which p is the number of poles, $$\N_S = \frac{120f}{p}\$$, is the formula that is most often used. In the few texts or articles where p is the number of pole-pairs, the formula $$\N_S = \frac{60f}{p}\$$ is used. Of the dozen or so motor texts that I have, I believe that only one does calculations with pole-pairs. In the 60 years that I have been studying or working with AC motors, I have very rarely encountered any calculations using pole-pairs.

Can somebody clear this confusion?

Poles effectively come in pairs (pole-pairs). You need to consider that a machine with 6 numerical poles is in fact a 3 pole-pair machine. Some sites will use the pole-pair count and some (fewer) will count all poles and then divide by 2.

do the number of poles affect the phase difference?

No, the phase difference between the three supply phases is always nominally 120°. However, the physical angle rotated by the rotor gets smaller per cycle as the number of pole-pairs increases.

• but the book i have been reading also used 6 for $p$. Aug 21, 2021 at 11:21
• Maybe you need to find a book that clearly states what p is i.e. numerical poles or pole pairs. Aug 21, 2021 at 11:25
• Check Hughes Electrical technolgy Aug 22, 2021 at 7:50