Two involute spur gears mesh at a single pitch point where their surfaces roll without sliding. Everywhere else along the line of action the tooth flanks slide across each other — the "specific sliding" that the 3D version hints at with its meshing-point sparks and steam pipe, but never quantifies. This companion computes it directly:
v_slide(x) = (ω1 + ω2) · x // x = distance from pitch point along the line of action
σ_H = sqrt(F·E* / (π·b·Reff)) // Hertzian contact stress, two curved surfaces
q = μ·F·|v_slide| // frictional heat generation rate
dT/dt = q/C_th − k_cool·(T − T_amb) // lumped thermal model
Output speed and torque follow the ideal gear-ratio relations ω2 = ω1·N1/N2 and, once the heat loss is subtracted from input power, τ2 = η·τ1·N2/N1. Raising the load or the driver speed raises the tangential force and sliding velocity together, so heat generation grows roughly with their product — push it far enough (or hit "Overload spike") and the temperature readout crosses into spark territory, exactly the failure mode the flavor text of the original gears describes.
- Sliding-velocity trace — oscillates once per tooth pass; zero at the pitch point, maximum at the tips of engagement.
- Temperature history — rises while heat generation exceeds cooling, falls once the steam-vent cooling wins.
- Sparks — spawn at the mesh point once contact stress or temperature crosses the danger threshold.