# Principles of Rotation of 3-Phase Full-Wave Brushless Motors

2023.06.21

Points of this article

・The inflow and outflow of currents into and out of three coils change the magnet field, causing the rotor to rotate.

In succession to the outer appearance and structure described in the previous article, here the principles of motor rotation are explained.

## Principles of Rotation of 3-Phase Full-Wave Brushless Motors

The principles of rotation of a brushless motor are here explained in the following steps ① to ⑥. To aid understanding, a permanent magnet is simplified from a disc shape to two rectangular shapes.

## ①

Of the 3 phase coils, coil 1 is fixed in the 12:00 direction (upward), coil 2 is at 4:00, and coil 3 is fixed at 8:00. Of the 2 poles of the permanent magnet, the N pole is on the left and the S pole is on the right, and the magnet can rotate.

A current Io is made to flow into coil 1, causing a magnetic field the S pole of which is outside coil 1. Currents Io/2 are caused to flow out from coils 2 and 3, generating a magnetic field with the N pole on the outside of those coils.

Taking the vector resultant of the magnetic fields of coils 2 and 3, the magnetic field at the downward-directed N pole occurs with an intensity that is 0.5-fold that when the current Io flows in one coil; added to the magnetic field of coil 1, the intensity is 1.5-fold. This creates a resultant magnetic field at a 90° angle with respect to the permanent magnet, so that the maximum torque can be generated, and the permanent magnet rotates in the clockwise direction.

When the current in coil 2 is reduced and the current in coil 3 is increased according to the rotation position, the resultant magnetic field also rotates clockwise, and so the permanent magnet continues to rotate.

## ②

In the state of rotation by 30°, the current Io is made to flow into coil 1 and the current in coil 2 is reduced to zero, while the current Io is caused to flow out of coil 3.

The S pole is then outside of coil 1, and the N pole is outside of coil 3. Taking the vector resultant, a magnetic field occurs with intensity equal to √3 (≈1.72)-fold of that when the current Io is made to flow in one coil. This also creates a resultant magnetic field at an angle of 90° to the magnetic field of the permanent magnet, so that the permanent magnet rotates in the clockwise direction.

The current Io flowing into coil 1 is reduced according to the rotation, the current flowing into coil 2 is increased from zero, and the current flowing out of coil 3 is increased to become Io; the resultant magnetic field rotates clockwise, and the permanent magnet continues to rotate.

※If the current for each phase is represented as a sinusoidal waveform, then these current values become Io×sin(π⁄3) = Io×√3/2. Taking the vector resultant of the magnetic field, the overall intensity is (√3/2)2×2 = 1.5 times the magnetic field that occurs for one coil. When the current for each phase is sinusoidal, the magnitude of the vector resultant magnetic field is 1.5-fold times the magnetic field that occurs for one coil regardless of the position of the permanent magnet, and the magnetic field is at 90° to the magnetic field of the permanent magnet.

## ③

Having rotated another 30°, the current Io/2 is made to flow into coil 1, Io/2 is made to flow into coil 2, and Io is made to flow out from coil 3.

The S pole is outside of coils 1 and 2, and the N pole is outside of coil 3. Taking the vector resultant, a magnetic field occurs equal to 1.5 times that occurring when the current Io flows in one coil (the same as in ①). A resultant magnetic field is formed that is at a 90° angle with respect to the magnetic field of the permanent magnet, and the permanent magnet rotates clockwise.

## ④ to ⑥

Rotation is similar to that in ① to ③.

When in this way the supply of current to the coils is switched according to the sequential positions of the permanent magnet, the permanent magnet is caused to rotate in one direction. If the current directions are reversed, reversing the direction of the resultant magnetic field, rotation is in the counterclockwise direction.

The diagram below shows the continuous change in the current in each of the coils through the above steps ① to ⑥. The reader should be able to understand the relation between the changes in the currents as explained above and the permanent magnet rotation.

## 【Download Documents】Overview of Brushed DC Motor Structure, Operating Principle, Drive Method, Characteristics, Features, and Applications

Basic overview of brushed motors, including structure, principle of operation, drive method, and features.

### Overview of Brushed DC Motor Structure, Operating Principle, Drive Method, Characteristics, Features, and Applications

Basic overview of brushed motors, including structure, principle of operation, drive method, and features.