According to Lenz's law, when a brushless DC motor rotates, its winding will generate a reverse voltage in the opposite direction to the voltage across the winding, that is, back electromotive force. Remember, the back EMF is the opposite of the voltage applied to the winding. The main factors that determine the back electromotive force are as follows:

(1) Angular velocity of the rotor;

(2) The magnetic field strength of the rotor permanent magnet;

(3) The number of coils wound on each stator winding.

The formula for calculating back electromotive force: Back EMF = (E) ∝ NlBw

in:

N- is the number of coils in each phase winding

L-the length of the rotor

B- is the magnetic flux density of the rotor

W-is the angular velocity of the rotor

Once the brushless DC motor is completed, the number of coils in its windings and the magnetic flux density of the permanent magnets will be determined. According to the formula, the only quantity that determines the back electromotive force is the angular speed of the rotor (which can also be converted into linear speed), and the angular speed is proportional to the back electromotive force. The manufacturer usually provides the back electromotive force constant of the motor, through which we can estimate the back electromotive force at a certain speed.

The voltage across the winding is equal to the supply voltage minus the back EMF. When designing a motor, the manufacturer will choose an appropriate back electromotive force constant so that the motor has enough voltage difference to reach the rated speed and has sufficient torque when working. When the brushless DC motor operates beyond the rated speed, the back electromotive force will continue to rise, and then the effective voltage applied between the motor windings will decrease, the current will decrease, and the torque will decrease. When the back electromotive force and the supply voltage are equal, the current will drop to 0, the torque will be 0, and the motor will reach its ultimate speed.