Water-Wheel Fulling Mill

What is modelled

An overshot wheel supplies the power eta rho g Q H; its torque falls linearly with speed. Cams on the shaft lift hammers and let them drop on the cloth. The shaft obeys I dw/dt = torque of the wheel - cam torque - bearing drag.

Equations

• Power available P = eta rho g Q H, maximum at half the free-running speed; stall torque 4 P / w_f.
• Cam torque m g dh/dtheta while a cam lifts a hammer by h(theta) = lift (1 - cos(pi s)) / 2.
• Work per turn N m g h; blows per second N w / 2 pi.
• Drop t = sqrt(2h/g), impact speed sqrt(2 g h).

Checks run in the page

• Power curve scanned for its maximum.
• Cam work per turn against the lifted potential energy.
• Time-stepped steady speed against the torque balance and counted blows.
• Free fall and impact energy per blow.

Honest simplifications

Linear wheel characteristic, cam lift of 70 degrees, hammers lifted by their centre of mass without lever ratio, a flywheel inertia of 6000 kg m2 and bearing drag of 80 N m s are assumed values; stock-to-cloth friction and water level changes are not modelled.

• Press Weak stream, heavy hammers: the wheel slows at every cam and may stall.
• Press Flood: strong flow to see the wheel run near its free speed.
• Add hammers with the slider and watch the torque ripple smooth out.