Cutterhead Thrust and Torque

What is modelled

A disc cutter of radius R pressed a depth p into rock contacts it over a chord and an arc. In the simplified crushing-zone model the normal force is proportional to the rock strength, the tip width and the contact chord. The rolling force that resists the cutter turning is the normal force times tan(phi/2), phi being the contact angle. Cutters on a spiral between a small and the outer radius add up to total thrust and torque.

Equations

• Contact chord l = √(2 R p - p²), angle φ = arccos(1 - p/R).
• Normal force FN = κ σc w l, rolling force FR = FN tan(φ/2).
• Thrust n FN cos(φ/2); torque Σ FR ri; power T ω.
• Specific energy SE = 2πT / (A p) per revolution; advance rate p N.

Checks run in the page

• Contact angle from two geometric forms.
• Torque as a sum over cutters against n F r-mean.
• Specific energy from work per turn against power over excavation rate.
• Cutter-rating penetration against the closed form.

Honest simplifications

A single-parameter crushing model instead of a full empirical machine model, no cutter wear, no muck, no groundwater or face support pressure, no gauge cutters. Educational civil-engineering mechanics, not a TBM design or selection tool.

• Press Hard rock, thin cut and watch the thrust stay in rating at low penetration.
• Press Overloaded to see the cutter load pass its rating.
• Raise the number of cutters: thrust and torque scale linearly while the force per cutter stays.