Question

D.C. Motors - Relationship between Speed, Back E.M.F., and Flux

Answer 1

In a DC (direct current) motor, the relationship between speed, back electromotive force (EMF), and flux is described by the motor's fundamental operating principle, known as the motor equation. This equation helps us understand how changes in these parameters affect each other.

Back Electromotive Force (EMF):
When a DC motor operates, it generates a voltage called the back electromotive force (EMF) or back voltage. This voltage is produced due to the rotation of the armature coil within the magnetic field created by the stator. The back EMF is proportional to the speed of the motor and opposes the applied voltage, acting as a counter-electromotive force.

Mathematically, the back EMF (Eb) is given by:
Eb = kω, where:

Eb is the back EMF
k is a constant specific to the motor (motor's back EMF constant)
ω is the angular velocity (rotational speed) of the motor in radians per second

Flux (Magnetic Field Strength):
The magnetic field strength or magnetic flux (Φ) in the motor is determined by the current flowing through the field windings of the stator. The strength of the magnetic field affects the amount of torque generated by the motor and, consequently, its speed.

Relationship between Speed, Back EMF, and Flux:
The motor equation relates the speed of the motor (N), the back EMF (Eb), and the flux (Φ) as follows:

Eb = kω
Eb = V - IaRa
Φ ∝ Ia

Where:

N is the speed of the motor in revolutions per minute (RPM) or radians per second (rad/s).
V is the applied voltage to the motor terminals.
Ia is the armature current.
Ra is the armature resistance.

From the motor equation, we can deduce some relationships:

a. Speed and Back EMF: The speed of the motor is directly proportional to the back EMF. As the motor speeds up, the back EMF increases proportionally.

b. Back EMF and Applied Voltage: The back EMF opposes the applied voltage. As the back EMF increases (due to an increase in speed), the effective voltage across the armature decreases, which in turn affects the current and torque produced by the motor.

c. Flux and Armature Current: The magnetic flux is proportional to the armature current. As the armature current increases, the magnetic field strength (flux) also increases.

Overall, these relationships play a critical role in governing the behavior of a DC motor. Adjusting the applied voltage, armature current, or load on the motor will affect the speed, back EMF, and flux, thus influencing its performance and efficiency.