# Induction motor electrical and mechanical angle

How do we reach the relation between mechanical angle($\theta m$) and electrical angle($\theta e$) as: $\theta e = (P/2)\theta m$ ? ; where P is the number of poles.

• By comparing electrical frequency with rotational speed.
– user16324
Aug 28, 2015 at 10:46

How do we reach the relation between mechanical angle(θm) and electrical angle($θ_e$) as: $θ_e$=(P/2)$θ_m$ ? ; where P is the number of poles.

An electrical machine is simply an electrical<>mechanical energy conversion device which utilises magnetic fields as the exchange medium.

When an electrical machine is operating as a motor, the idea is to create a traveling, rotating magnetic field, via the stator and "hope" 1 that this moving flux attracts the rotor (be it via an equivalent magnetic field or via an affinity to reduce the reluctance)

So a stator: A 3 phase, single pole pair topology. If the stator was now unrolled you can now see that for 360degree electrical we have equally achieved 360degree mechanical.

As the number of pole-pairs is increased, the point at which an electrical cycle is completed becomes a fraction of the main mechanical cycle & this factor is the pole-pair count

1 hope is used because there are some prerequisites that must be met that are machine specific. freq, voltage, load, supply ...

In a multipolar electrical machine (motor or generator), relationship between the mechanical angle and electrical angle is given by: Electrical angle = (P/2) x Mechanical angle where: P = Number of poles

So:

• In a two-pole motor (P = 2): Electrical Angle = Mechanical Angle
• In a four-pole motor (P = 4): Electrical Angle = 2 times Mechanical Angle
• In a six-pole motor (P = 6): Electrical Angle = 3 times Mechanical Angle

etc.

Hope this helps

• I should consider this an unprofessional answer since the question has been rewritten as it is without explanation. Oct 7, 2017 at 14:32

Mechanical degrees in a motor refers to the rotation of the shaft. 1 revolution of the shaft equals 360 mechanical degrees. Electrical degrees in a motor has to do with the magnetic position of the rotor. One transition from "North" to "South" to "North" again equals 360 electrical degrees.

From this, it should be easy to picture. A 2 pole motor has 1 "North" pole and 1 "South" pole on the rotor. So in order for it to turn 360 electrical degrees ("North" to "South" to "North"), it needs to rotate 360 ($\frac{360}{1}$) mechanical degrees. A 4 pole motor has 2 "North" poles and 2 "South" poles. That means that 360 electrical degrees will occur when the shaft has rotated only 180 ($\frac{360}{2}$) mechanical degrees. A 6 pole motor has 3 "North" poles and 3 "South" poles. That means that 360 electrical degrees will occur when the shaft has rotated only 120 ($\frac{360}{3}$) mechanical degrees. You can see that each time we divide the mechanical degrees by the number of pole pairs (or, the number of poles divided by 2).

So in general we can say that $\theta_e=\frac{P}{2}\theta_m$.

• So its like a magnetic poles being induced on the rotor, and how quickly it reverses the polarity determines electrical angle. Right? Then electrical angle is only rotor-side quantity? Aug 29, 2015 at 6:45

The mechanical angle is angle of rotor shaft vs stator, meanwhile the electrical angle is the angle between poles (rotor vs stator). If you have one pole pair only, then electric = mechanical.

• Angle between poles? I did not get you completely. Aug 29, 2015 at 6:44
• The rotor is supposed to induce both a North pole and a South pole, or multiple numbers of them. The angle between poles is the smallest angle between two similar poles. Oct 7, 2017 at 14:34