Electromagnetic basics: force, back-EMF and the torque constant
A current-carrying wire in a magnetic field feels a force, and a moving wire produces a voltage. Every motor runs on these two equations.
Two effects
| Effect | Equation | In a motor |
|---|---|---|
| Current → force (Fleming's left hand) | F = B·I·L | Produces torque |
| Motion → voltage (Faraday) | e = B·L·v | Produces back-EMF |
Torque constant and back-EMF constant
- Torque = Kt × current: torque is proportional to current. So to control torque, you control current.
- Back-EMF = Ke × speed: the faster it turns, the more the motor acts like a generator and produces an opposing voltage.
In SI units, Kt [N·m/A] and Ke [V·s/rad] have the same value.
RoadmapSee where this note sits in Motor Control→Motor electrical equation
V = R·I + L·dI/dt + Ke·ω
Only what is left of the supply voltage after subtracting the back-EMF drives current.
- Apply voltage at standstill and the back-EMF is 0, so a large inrush current flows.
- As speed rises and the back-EMF approaches the supply voltage, the current falls and the motor cannot go faster. This is the no-load top speed.
The KV value
"1000KV" on a drone motor means 1000 rpm per volt with no load, which corresponds to the inverse of Ke. A higher KV is faster but gives less torque for the same current.