θ is the angle between the current and magnetic field
Essential Components
1. Coil and Armature
Multiple wire turns (n) wound around the armature
Carries current to produce mechanical energy
Force is proportional to the number of turns
Forms the main conducting surface interacting with magnetic flux
2. Axle
Central rotation point
Transfers rotational energy
Supports the armature assembly
3. Magnets
Create external magnetic field
Can be permanent or electromagnetic
Radial magnets preferred for smooth operation
4. Split-ring Commutator
Semi-crescent shaped conductive segments
Rotates with the coil
Reverses current direction every half-revolution
Maintains continuous rotation
5. Brushes
Made of conductive materials (typically carbon)
Stationary components
Connect power source to commutator
Require regular maintenance due to wear
6. Battery
Provides direct current
Creates electromotive force (emf)
Powers the entire system
Torque Production
The total torque in a DC motor is given by:
τ=nIABsinθ
where:
n is the number of coil turns
I is the current
A is the coil area (m²)
B is the magnetic field strength
θ is the angle between the area vector and magnetic field lines
This equation is derived from:
Force on multiple turns: F=nIlBsinθ
Basic torque equation: τ=rFsinθ
Considering coil geometry: τ=2wF (where w is coil width)
Accounting for both arms: τ=wnIlBsinθ
Final form using area (A = lw)
[Insert Torque Diagram]
The Role of the Split-ring Commutator
The split-ring commutator is crucial for maintaining continuous rotation. Here's how it works:
Initially, current flows through the coil, creating motor forces
Every half-revolution, the commutator switches contact points
This reverses current direction in the coil
Maintains consistent torque direction
Enables continuous rotation
Force Magnitude Characteristics
The motor force magnitude remains constant throughout rotation, while its direction changes periodically every 180°. This is true for both parallel and radial magnet configurations.