Torque equations and motor constants
How k_t, k_e and winding design combine into the torque a motor can actually deliver.
- Explain torque equations and motor constants at engineering level
- Read the numbers that define the behaviour
- Apply the idea to a real drive unit
Overview
Behind every motor's torque-per-amp figure sits a small set of design constants that link the electromagnetic theory to a number an engineer can actually use.
In depth
For a well-designed machine, torque is proportional to current through the torque constant k_t, which bundles up pole count, flux and winding turns.
The torque constant and the back-EMF constant are numerically equal when both are expressed in consistent SI units — a direct consequence of energy conservation in an ideal machine.
Lab: Build a motor
Choose pole count, winding turns and magnet strength, then hit the torque and speed targets.
Torque in a permanent-magnet machine scales with magnetic flux, the number of conductor turns and the current in them. Speed is limited by the back-EMF the same flux and turns generate: at some speed the back-EMF equals the DC-link voltage and the machine can turn no faster without field weakening. Every design is therefore a trade between torque and speed for a fixed voltage.
Key takeaways
- Torque is proportional to current via the torque constant k_t.
- k_t and k_e are the same physical quantity expressed two ways.
- Raising torque per amp inherently lowers the achievable top speed.
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