Oilseed Screw Press

What is modelled

A power screw converts crank torque into axial force. With lead p per turn and thread efficiency η, one turn does torque work 2πT and delivers force work F p, so F = 2πηT/p. The seed cake is modelled as a bed whose pressure rises logarithmically as it is compressed; the platen stalls when the screw force equals the cake force.

Equations

• Axial force F = 2π η T / p; cake pressure P = F / A, A = π (D/2)².
• Cake law (illustrative) P(s) = K ln(h0 / (h0 - s)), initial height h0 = m / (ρb A) with bulk density 550 kg/m³.
• Torque needed at travel s: T(s) = F(s) p / (2π η); work W = ∫ F ds.
• Thread friction: η = tanλ / tan(λ + φ), λ = atan(p / (π dm)), d_m = 70 mm, friction angle φ = atan μ. A square thread self-locks when η < 0.5.

Checks run in the page

• Torque rebuilt from the force, F p / (2π η), against the set torque.
• Input and output power at the set crank speed.
• Stall work from numerical integration against the closed form.
• Friction coefficient derived from η returns the same η.

Honest simplifications

The cake law, its stiffness and the bulk density are illustrative: real oil expression depends on seed type, temperature, moisture and a draining cage, and no oil yield is predicted. Collar friction, frame stiffness and screw wind-up are ignored. A teaching model, not a press design tool.

• Press Heavy crank: the same press stalls later and reaches a higher cake pressure.
• Press Low efficiency and watch the torque you need climb for the same pressure.
• Raise the cake stiffness to make the cake stall earlier, with less travel.