Short Answer:

Torque in a DC motor develops when current flows through the armature conductors placed in a magnetic field. Due to the interaction between the magnetic field and the current-carrying conductor, a mechanical force is generated. This force acts tangentially and causes the rotor to rotate, producing torque.

The amount of torque produced depends on the strength of the magnetic field, the current flowing through the armature, and the number of conductors. This torque is responsible for turning the load connected to the motor shaft, making the DC motor useful for various mechanical applications.

Detailed Explanation:

Torque development in a DC motor

Torque is the turning force that causes rotation in a motor. In a DC motor, torque is developed due to the electromagnetic force that acts on the armature conductors when current flows through them in the presence of a magnetic field. This is a direct application of Lorentz Force Law, which states that a current-carrying conductor placed in a magnetic field experiences a mechanical force.

When a DC voltage is applied to the motor, current flows through the armature windings. These windings are placed in the magnetic field created by the field magnets (either permanent magnets or electromagnets). According to Fleming’s Left-Hand Rule, if:

• the forefinger shows the direction of the magnetic field,
• the middle finger shows the direction of the current,
• then the thumb shows the direction of the force (torque).

In a DC motor, this force acts on every conductor in the armature, and since these conductors are arranged around a cylindrical rotor, the forces combine to produce a torque that rotates the armature. This torque continues to act as long as the current flows and the magnetic field is present.

Now, let’s understand the factors that affect torque:

1. Armature current (Ia):
   The more current that flows through the armature, the more force is experienced by the conductors, and thus more torque is produced.
2. Magnetic flux (Φ):
   Torque is directly proportional to the magnetic field strength. A stronger field results in greater force on the conductors.
3. Number of conductors (Z):
   More conductors mean more paths for current and more points where force is applied.
4. Armature radius (r):
   The larger the distance of the conductor from the center of the shaft, the more torque it can produce.
5. Constant motor design factors (K):
   Each motor has a design constant based on its physical construction.

The torque equation of a DC motor is:
T = K × Φ × Ia
Where:

• T is torque
• K is a constant
• Φ is the magnetic flux per pole
• Ia is the armature current

This shows that torque is directly proportional to both the flux and the armature current. That’s why in applications like cranes or electric trains, where high torque is required at the start, series motors (which allow large armature current and high flux) are commonly used.

Types of Torque in DC Motors:

• Starting Torque (or Breakaway Torque):
  Torque required to start the motor from rest. This is usually the highest.
• Running Torque:
  Torque needed to keep the motor rotating at a steady speed under load.
• Load Torque:
  Torque needed to overcome the load connected to the motor.

Why Torque is Important:

Without torque, a DC motor would not be able to rotate and perform any mechanical work. Torque is what drives the wheels of an electric vehicle, moves the belts in a conveyor system, or lifts a weight in an elevator. DC motors are popular in many industries because they can provide high starting torque and precise speed control.

Conclusion:

Torque in a DC motor is developed due to the interaction of the magnetic field and the current flowing through the armature conductors. This electromagnetic force causes the rotor to rotate, which is the motor’s output. The strength of the torque depends on armature current and magnetic flux, and it plays a vital role in determining the motor’s ability to drive mechanical loads effectively.