Pottery Wheel (2D): Cross-Section, Plan View and Stress Gauges

What is simulated

A fixed mass of wet clay is thrown on an electric potter's wheel: a solid lump is opened and pulled up into a vessel. The page follows the shape through the throw, computes the moment of inertia of the clay, runs the wheel with a speed controller, and checks the two things that ruin a pot: the clay flying outward when the wheel is too fast for the vessel's width, and a tall thin wall buckling under its own weight and the potter's hand.

Shape and volume

The outer wall is ro(s) = R + b sin(πs) − d s with s = z/h: base radius R, belly b, taper d. The clay never changes volume (V = m/ρ, ρ = 1900 kg/m³), so the wall thickness t follows from V = ∫ π[ro2 − max(ro − t, 0)2] dz plus a 12 mm floor: the taller or wider the vessel, the thinner the wall.

Spin and angular momentum

The wheel obeys d(Iω)/dt = τmotor − τbearing − τhand with I = Iwheel + Iclay(p). A PI controller drives the motor (limited to 6 N m and 400 W) toward the set speed; bearing friction is 0.04 + 0.0004ω N m and the hand drag is 0.3 F r. With the motor off the product Iω is conserved: pulling the clay outward raises I and slows the wheel, which is why heavy flywheels are used.

Centrifugal limit and wall buckling

A free ring of clay at radius r spinning at ω carries the hoop stress σ = ρ ω2 r2; it holds while this stays below the tensile strength of wet clay, which gives ωmax = √(σt/ρ)/r. The wall also has to carry its own weight ρ g h plus the hand load F/(2π r t) without buckling; the classical thin-cylinder value E t / (r √(3(1−ν2))) is reduced by a knockdown factor of 0.3, as for real shells.

Simplifications

• The shape is given by three numbers and a smooth morph from the lump; the potter's hands do not shape the clay in the simulation, they only add a friction torque and an axial load.
• The ring model for the centrifugal limit is conservative: in a real vessel the belly is supported by the rest of the shell. The values for wet-clay strength (2 to 8 kPa), modulus (0.4 MPa) and the knockdown factor are round figures of the right order, not measurements of a given clay body.
• The wall thickness is horizontal and uniform above the 12 mm floor; slip, water, wobble from an uncentred lump and clay viscosity are not modelled.
• Where the limits are exceeded the 3D clay is drawn flaring or slumping as a warning; it does not simulate the failure.

Checks

Five boxes: the clay volume from an exact revolved integration of the drawn cross-section against the mass over the density; the sliced moment of inertia of a hollow cylinder against the closed form; conservation of Iω through a whole throw with the motor off; the ring stress from adding up centrifugal forces on half a ring against ρ ω2 r2; and a motor spin-up integrated with RK4 against the exponential solution.