Flat Rolling: Roll-Bite Deformation & Neutral Point

Rolling Parameters

Draft Δh (thickness reduction) 6.0 mm

Roll radius R 150 mm

Friction coefficient μ 0.25

Roll speed 20 rpm

⚠ Draft exceeds μ²R — the rolls cannot bite the strip on their own; an external push would be needed.

Roll-Bite Geometry

Bite angle α

0.0°

Contact length L

0.0 mm

Neutral point (from exit)

0.0 mm

Roll force / 300mm width

0 kN

Entry speed v₀

0 mm/s

Exit speed v₁

0 mm/s

Legend

Backward slip zone (roll faster — drags strip in) Forward slip zone (strip faster than roll) Neutral point marker

How it works

In flat (shape) rolling, two rolls of radius R squeeze a strip from entry thickness h₀ down to exit thickness h₁. The draft Δh = h₀ − h₁ sets the roll-bite geometry:

Bite angle:      cos α = 1 − Δh / (2R)
Contact length:  L = R·sin α  (≈ √(RΔh) for Δh ≪ R)
Max self-feeding draft: Δh_max = μ²R  (needs μ ≥ tan α to grip without an external push)

Inside the bite, the strip is thicker than the exit gap only at the entry, so it must speed up as it thins (constant volume flow at fixed width):

v(x)·h(x) = const  →  v₁ = v₀·h₀/h₁  (exit is faster than entry: "elongation")

Because the roll surface speed is constant but the strip accelerates through the bite, the two surfaces can only move together at one point — the neutral (no-slip) point. Before it the roll surface outruns the strip and friction drags the strip forward ("backward slip" zone, amber); after it the strip outruns the roll and friction resists it ("forward slip" zone, blue). Its approximate location:

φ_n ≈ α/2 − Δh/(4μR),  clamped to [0, α]

Roll-separating force is estimated with the classic "friction hill" approximation, using a fixed flow stress Y_f ≈ 200 MPa (mild steel) and an assumed 300 mm strip width w:

F ≈ Y_f · w · L · (1 + μL / (2·h̄)),  h̄ = (h₀+h₁)/2

Note: the 3D scene renders true roll and strip geometry to one consistent scale, but the strip is thin enough relative to the rolls that the thickness change is easiest to see near the gap — zoom in with the mouse wheel.

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Flat Rolling: Roll-Bite Deformation & Neutral Point Simulator