# Number of pole pairs

The number of pole pairs ( symbol :) is the number of pairs of magnetic poles within rotating electrical machines . Therefore applies to Contacts . ${\ displaystyle p}$ ${\ displaystyle 2 \ cdot p}$

## Basics

Asynchronous machine with the number of pole pairs and 3 strands${\ displaystyle p = 1}$
Asynchronous machine with the number of pole pairs and 3 strands; the diagrams show the field strength in the air gap${\ displaystyle p = 2}$

Since magnetic poles can only occur in pairs, the smallest number of pole pairs is (1 north pole + 1 south pole). The number of poles is appropriately designated with . A four-pole machine thus has 2 pole pairs. This is to be understood as follows: In the simplest case, as in a DC machine, the number of pole pairs relates to its main pole field, i.e. the magnetic field which is generated in the stator by coils through which direct current flows. This constant magnetic field has a north and a south pole. The machine therefore has a number of pole pairs of 1. ${\ displaystyle p = 1}$${\ displaystyle 2 \ cdot p}$

For rotary field machines, an analogy to the DC machine was sought for the definition of the number of pole pairs . A rotating field is created with an arrangement of 3 coils , which are evenly offset by 120 ° in the stator and are traversed by a corresponding three-phase current . Alternatively, a bar magnet could be rotated on an axis at the appropriate speed. The same magnetic field is generated in both cases. Such a magnetic field has a rotating pole pair, i.e. a north and a south pole, which face each other. A rotating field machine that has a stator constructed in this way ( the rotor in the case of external pole machines ) has a number of pole pairs of 1.If, as shown in the example above, another triple coil is arranged exactly between the other three coils (the angle between two adjacent coils is now only 60 °) you would have 2 pole pairs.

The distance between two neighboring coils is called the pole pitch. It is measured from pole center to pole center. The higher the number of pole pairs, the closer the coils are to one another. In addition to the power factor and the level of the terminal voltage , the size of the pole pitch is decisive for the number of slots per pole in asynchronous machines. This has a great influence on the behavior of the air gap field. Machines always receive a corresponding number of coils according to their number of pole pairs.

Example: A 4-pole three-phase asynchronous motor has 2 pairs of poles (4 poles) each with 3 coils, i.e. a total of 6 individual coils.

## Number of pole pairs and air gap field

The air gap field receives a full cosine oscillation per pole pair. However, the wave does not move over the entire circumference during the passage of an electrical period. It only moves over the respective sector, which is occupied by a triple coil.

With a number of pole pairs , the shaft of the air gap field moves exactly one complete revolution over the circumference of the machine within one electrical period. With a number of pole pairs, the air gap field covers just a quarter of the circumference within one period. Thus, four periods are required to run through the full scope. ${\ displaystyle p = 1}$${\ displaystyle p = 4}$

## Number of pole pairs and speed

In motors operated directly on the mains , the mains frequency and the number of pole pairs determine the rotating field speed of a rotating field machine. Synchronous machines rotate exactly with the rotating field speed , asynchronous machines rotate with a slightly different speed depending on the load. The rotating field speed n s can be determined as follows:

${\ displaystyle n _ {\ text {s}} = {\ frac {f} {p}}}$

Source:

If you now relate the speed to one minute, the following formula results:

${\ displaystyle n _ {\ text {s}} = {\ frac {60 \ cdot f} {p}}}$

Since the maximum field speed at a mains frequency of 50  Hz precisely 3000 min -1 is, can be based on the on the nameplate stated rotation rate determine wievielpolig the machine.

Example: A 2-pole synchronous machine rotates at 50 Hz at 3000 min −1 , since two poles form a pole pair.

Explanation: A fictitious point on the shaft rotates to the next pole in the course of a half-wave. If there is only one pair of poles, i.e. 2 poles, it rotates once per period. (A sine period consists of two half waves). In the case of a motor with two pairs of poles, since there are four poles, it only rotates within 4 half-waves, i.e. 2 periods of 360 °. So the speed has halved.

## Number of pole pairs and torque

The mechanical power is calculated from the product of torque and speed :

${\ displaystyle P _ {\ text {mech}} = 2 \ cdot \ pi \ cdot n \ cdot M}$

For mains-operated motors with the same specified nominal power, the nominal torque is therefore proportional to the number of pole pairs. The motors of the same power with the larger number of pole pairs are larger than those with the smaller number of pole pairs. If you compare motors with the same basic principle and the same size, the achievable nominal torque is not fundamentally proportional to the number of pole pairs. Depending on the technology, the torque increases to a greater or lesser extent as the number of pole pairs increases, but always less than proportionally, and even decreases again when a higher number of pole pairs is exceeded.

## literature

• Ali Farschtschi: Electric machines in theory and practice . Structure, modes of operation, applications, selection and design criteria. 1st edition. VDE-Verlag, Berlin / Offenbach 2001, ISBN 3-8007-2563-0 .
• Karl Falk: The three-phase motor . A lexicon for practice. 1st edition. VDE-Verlag, Berlin / Offenbach 1997, ISBN 3-8007-2078-7 .

## Individual evidence

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6. ^ Julius Wolfgang Heubach (chief engineer, Kleinzschachwitz near Dresden ): The three-phase motor . A manual for study and practice. 1st edition. Published by Julius Springer, Berlin 1903.
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8. ^ Dierk Schröder: Electric drives . Basics. 3. Edition. Springer-Verlag (Springer textbook), Berlin 2007, ISBN 978-3-540-72764-4 .
9. Moeller (Eaton): Three-phase asynchronous motor . Electronic motor starters and drives. Bonn 2009 ( online [accessed July 12, 2011]).
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