# Torque equation of Dc motor (for series, shunt and compound motor)

**Torque equation of Dc motor**

**Torque equation of dc motor** … Simply and as Dr. Hugh d Young explains torque is the propensity of force to cause a rotational motion, and here in Dc motor the torque develops between the armature and the stator, and it’s given by the product of the force and the radius at which the force acts.

**DC Motor Torque equation:**

It will be easy if we mathematically explain the torque, and we can start from:

**T=F.r.**

And;

**F=B.I.L.**

While:

B: is the flux density (in Wb/m^2).

I: the current flows through armature conductor (in Amp).

L: the length of armature conductor.

R: the radius of armature drum.

And as:

B=Φ /A.

While:

Φ: The total flux cut per pole (in Wb).

A: the area.

B=( Φ.P)/(2ϖ.r.Χ.L).

And;

I=Ia/A.

While:

Ia: is the total armature current.

A: the parallel path.

By substituting in torque equation, So we will have:

**T=(Φ.P/2.ϖ.r.X.L)*(Ia/A)*L*r.**

So;

**T=Φ.P.Ia/2ϖ.**

And as the total number of conductors is Z, so

**T=Φ.P.Ia.Z/2ϖ.A.**

So the torque will equal;

**T=0.159 Φ.Ia.Z.P/A.**

And as we know P, Z and A are constant so

**TαΦ.Ia**

Which means that the torque produced by a Dc motor is directly proportional to the main flux and the armature current.

**The torque of permanent magnet Dc motor:**

We said before that permanent magnet Dc motor uses a magnet to supply field flux, and that makes the motor have excellent starting torque capability with good speed regulation, and the torque is usually limited to 150% of rated torque which is a big disadvantage and that makes us use the permanent motor for low horsepower applications.

**Torque equation of Dc series motor:**

In series Dc motor we connect the field winding in series with the armature winding so we have a large amount of starting torque also the speed varies widely between no load and full load, and this high starting torque doesn’t allow us to use series motor where we require a constant speed under varying loads.

**Torque equation of** **shunt Dc motor:**

In shunt Dc motor we connect the field winding in parallel with the armature winding and we have a good speed regulation and also low starting torque which makes this motor suitable for belt-driven applications in industrial and automotive applications.

**Torque equation of compound Dc motor:**

In compound motor we have the benefits of both shunt and series motors, we have a better starting torque and a better speed regulation which makes it the best for many applications.