Wooden Screw Press

What is modelled

A square-thread screw is an inclined plane wrapped around a cylinder. The pressman pulls the end of a bar of length L with force F, giving a torque F L. The thread converts this torque into an axial load P on the platen. Friction in the thread takes a large share: it sets the efficiency and decides whether the screw holds its load or lets it drive the bar backward.

Equations

• Lead angle tan λ = lead / (2 π r), friction angle tan φ = μ.
• Load P = F L / (r tan(λ + φ)), frictionless P0 = 2 π F L / lead.
• Efficiency η = tan λ / tan(λ + φ); self-locking when φ > λ (efficiency below 50 percent).
• Platen travel P / k and bar turn 2 π (P / k) / lead.

Checks run in the page

• Force balance on the helix against P tan(λ + φ).
• Energy: work at the bar against stored energy plus thread friction.
• Back-off force and the sign that decides locking or overhauling.
• Frictionless limit against 2 π L / lead.

Honest simplifications

A square thread with one friction coefficient, no friction in the platen bearing or the screw collar, a linear spring for frame and paper, a static pull rather than the pressman's swinging motion, and a pressure spread evenly over the form. The wooden press in the 3D exhibit is an interpretive model of a period screw press; its proportions here are illustrative.

• Press Oiled screw to see the load rise with lower friction.
• Press Fast screw (self-releasing): the lead angle exceeds the friction angle and the bar kicks back.
• Press Slow screw, self-locking and read the efficiency below 50 percent.