Presets
Playback
Brake and motor
A moving conductor in a magnetic field carries eddy currents that oppose the motion. The torque grows with the square of the field and, at low speed, with the speed.
Motor
Untick it to watch the free spin-down: the speed then falls and the disc warms up as its kinetic energy turns into heat.
Model checks
The science
What is modelled
A 0.72 m aluminium disc is driven by a proportional motor to a target speed and braked by the eddy currents induced under an electromagnet. The magnetic field saturates with coil current and falls with air gap. The brake torque grows with B squared, falls at high speed (skin effect) and falls as the disc warms (resistivity rises). Eddy heat warms the disc; a fan and natural convection cool it.
Equations
- Field:
B = Bmax tanh(I/Is) / tanh(8/Is) · 1/(1 + (g/g0)²). - Eddy torque:
τb = k (B/Bref)² ω / (1 + (ω/ωs)²) / (1 + α(T - 20)). - Rotor:
J dω/dt = τmotor - τb - τbearing; heat:m c dT/dt = τb ω - h A (T - Tamb).
Checks run in the page
- Work-energy balance over 60 s: change of kinetic energy = motor work - eddy heat - bearing loss.
- Heat bookkeeping: m c ΔT = eddy heat - cooling.
- An independent RK4 integration of the spin-down (with the heating) against the page's stepper.
- The B squared scaling of the torque between two currents.
Honest simplifications
A lumped, transparent engineering model, not a finite-element solution: a single effective pole, a made-up skin roll-off, uniform disc temperature, constant fan coefficient, no magnet heating, and a saturation curve rather than a measured B-I curve. It is not a certification model.
What to try
- Untick the motor, set 8 A and 3 mm: the disc stops within a few seconds and the temperature jumps.
- With the fan at 0 %, run the strong brake for a while and compare the temperature curve with a fan at 100 %.
- Open the gap to 25 mm: the field and the torque collapse.