Formula & Calculator
Torque of a DC Motor
Relates a DC motor's output torque to its magnetic flux and armature current.
Interpretation
Torque of a DC motor T = k·Φ·I_a is proportional to the product of magnetic flux Φ and armature current I_a.
Increasing either the field flux or the armature current increases the torque.
Example: k=0.5, Φ=0.02Wb, I_a=10A → T = 0.5 × 0.02 × 10 = 0.1 N·m.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| T | Torque | N·m |
| k | Motor constant | N·m/(Wb·A) |
| Φ | Flux per pole | Wb |
| I_a | Armature current | A |
What it means
The torque T of a DC motor is given by T = k·Φ·I_a, where k is a constant depending on motor construction, Φ is the magnetic flux per pole, and I_a is the armature current. Torque is proportional to the product of flux and armature current. In a shunt motor, Φ is nearly constant, so torque is directly proportional to armature current. In a series motor, Φ is proportional to I_a, so torque is proportional to I_a². This is used in traction applications where high starting torque is needed. The torque equation is derived from the Lorentz force on the armature conductors. Example: A motor with k=0.5, Φ=0.02Wb, and I_a=10A produces T = 0.5 * 0.02 * 10 = 0.1 N·m. To increase torque, either increase flux or armature current.
Worked example
DC Motor Torque – Practical Example
Real‑World| Parameter | Value |
|---|---|
| k·Φ | 0.05 N·m/A |
| Ia | 4 A |
| Formula | T = k·Φ·Ia |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
Torque of a DC motor T = k·Φ·I_a is proportional to the product of flux and armature current. This shows how torque is produced by the interaction of the magnetic field and the current. Engineers use it to design motors, to select ratings, and to control torque by adjusting current or field flux. This formula is fundamental to motor design and performance analysis.
- DC motor sizing and torque requirement calculation
- Field‑weakening control for high‑speed operation
- Torque control in servo systems
- Motor performance optimisation
- Educational understanding of electromechanical torque
Frequently Asked Questions
The torque is T = k·φ·I_a, where k is a constant, φ is the flux per pole, and I_a is the armature current. For a shunt motor, φ is constant, so T ∝ I_a.
Newton‑meters (N·m) in SI.
Torque is directly proportional to armature current for a given flux. This is why starting current is high (to produce high starting torque).
Starting torque is the torque at zero speed; it depends on the starting current. Running torque is the torque at operating speed, determined by the load.
Common errors: 1) forgetting the flux term, 2) using the wrong constant, 3) applying to series motors where flux depends on I_a, 4) confusing with generator torque, 5) not accounting for saturation.
Motor selection for loads, designing motor drives, and analyzing acceleration.
Reducing φ (field weakening) reduces torque for the same armature current, but allows higher speed (since E_b = kφω).
Mechanical power P = T·ω, where ω is angular speed. In terms of electrical input, P = E_b·I_a.