⚙️DC Motor Simulator - Lorentz Force, Torque–Speed Curve, Inrush Current

How to use DC Motor Simulator & Torque–Speed Curves

1. 1Pick a preset (toy motor, drill motor, e-bike hub motor) or edit the voltage, resistance, inductance, k, inertia and friction
2. 2On the cutaway tab, watch the coil, commutator, brushes and force arrows, and compare torque ripple for different numbers of coils
3. 3Drag the load torque slider and read the operating point, no-load speed, stall torque, peak power and peak efficiency on the characteristic curves
4. 4Check the inrush current and time constants on the start-up tab, and set a driven speed and load resistor in generator mode

FAQ

Why does a motor draw so much current when it starts?

The current is I = (V − E)/R, where E = kω is the back-EMF. At switch-on the rotor isn’t turning, so E = 0 and only the armature resistance (and inductance) limits the current to roughly V/R, often several times the rated current. As the speed builds, the back-EMF cancels most of the supply voltage and the current falls. That’s why large motors need soft starters or current limits, and why a stalled motor overheats.

Why are the back-EMF constant and the torque constant the same k?

In SI units the motor turns electrical power E·I into mechanical power T·ω (losses aside). Substituting E = k_e·ω and T = k_t·I into E·I = T·ω gives k_e = k_t, so V·s/rad and N·m/A are the same number. Datasheets often quote k_e in V/krpm; multiply by 60/(2π×1000) to convert.

What does the commutator do?

After half a turn each wire has moved to the other pole. If the current kept its direction, the force would reverse and the coil would just rock back and settle. The commutator is a split ring that turns with the coil and slides against fixed brushes. It swaps the current exactly when the coil plane is perpendicular to the field (where the torque is zero), so the torque always acts the same way. Brushless motors replace it with Hall sensors and electronic switches.

At what load is a DC motor most efficient?

Speed falls almost linearly with load torque. Output power peaks at about half the stall torque, but copper losses are large there and efficiency is only around 50%. Peak efficiency sits at a much lighter load, typically 10–20% of stall torque, set by the balance between friction and copper losses: the lower the friction, the higher the peak and the closer it is to no load. Both points are marked on the curves.

Why can the same motor work as a generator?

Turn the coil by hand and the wires cut the field lines, producing an EMF E = kω. With nothing connected there is no current and it spins freely. Connect a load resistor and a current I = E/(R + R_L) flows; the force on that current opposes the rotation (Lenz’s law), so you have to supply a torque kI. Output power is greatest when the load resistance equals the armature resistance, but efficiency is then only about 50%.