# Torque Equation of DC Motor

When a DC machine is loaded either as a motor or as a generator, the rotor conductors carry current. These conductors lie in the magnetic field of the air gap. Thus each conductor experiences a force. The conductors lie near the surface of the rotor at a common radius from its center. Hence torque is produced at the circumference of the rotor and rotor starts rotating. The term torque as best explained by Dr. Huge d Young is the quantitative measure of the tendency of a force to cause a rotational motion, or to bring about a change in rotational motion. It is in fact the moment of a force that produces or changes a rotational motion.The equation of torque is given by,
Where, F is force in linear direction.
R is radius of the object being rotated,
and θ is the angle, the force F is making with R vector
The DC motor as we all know is a rotational machine, and
But keeping in mind that our purpose is to derive the
Now I
The mechanical power P
Where ω is speed in rad/sec.
Now for simplifying the torque equation of DC motor we substitute.
Where, P is no of poles,
φ is flux per pole,
Z is no. of conductors,
A is no. of parallel paths,
and N is the speed of the D.C. motor.
Substituting equation (6) and (7) in equation (4), we get:
The torque we so obtain, is known as the electromagnetic torque of DC motor, and subtracting the mechanical and rotational losses from it we get the mechanical torque.
Therefore, T
Which is constant for a particular machine and therefore the torque of DC motor varies with only flux φ and armature current I
Current / conductor I
Hence, the total torque developed of a DC machine is,
This torque equation of DC motor can be further simplified as:
Which is constant for a particular machine and therefore the torque of DC motor varies with only flux φ and armature current I

**torque of DC motor**is a very important parameter in this concern, and it’s of utmost importance to understand the**torque equation of DC motor**for establishing its running characteristics.To establish the torque equation, let us first consider the basic circuit diagram of a DC motor, and its voltage equation.
Referring to the diagram beside, we can see, that if E is the supply voltage, E_{b} is the back emf produced and I_{a}, R_{a} are the armature current and armature resistance respectively then the voltage equation is given by,

**torque equation of DC motor**we multiply both sides of equation (2) by I_{a}._{a}^{2}.R_{a}is the power loss due to heating of the armature coil, and the true effective mechanical power that is required to produce the desired torque of DC machine is given by,_{m}is related to the electromagnetic torque T_{g}as,Now equating equation (4) & (5) we get,

_{m}= T_{g}- mechanical losses. This is the torque equation of DC motor. It can be further simplified as:_{a}. The Torque equation of a DC motor can also be explained considering the figure below._{c}= I_{a}/ A Therefore, force per conductor = f_{c}= BLI_{a}/A Now torque T_{c}= f_{c}.r = BLI_{a}.r/A_{a}.Closely Related Articles

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