Rolling Calculator
Rolling 25 mm plate to 20 mm takes a draft of 5 mm, more than the 3 mm the 300 mm rolls can bite at μ = 0.1.
5 mm
- Maximum possible draft μ²R
- 3 mm
- Can the rolls bite?
- no: the draft exceeds μ²R, the strip will not be drawn in
- Reduction
- 20 %
- True strain ln(h₀/h₁)
- 0.2231435513
- Projected contact length √(RΔh)
- 38.72983346 mm
- Approximate roll force σ̄ w L
- 2323.790008 kN
Step-by-step solution
- Δh = h₀ − h₁ = 5 mm; Δh_max = μ²R = 3 mm
- L = √(RΔh) = 38.72983346 mm
- F ≈ σ̄ × w × L = 200 × 300 × 38.72983346 = 2323.790008 kN
Rolling Formula
Δh_max = μ²R, L = √(RΔh)
F ≈ σ̄ w L (no friction hill); true strain ln(h₀/h₁)
Worked Example
Rolling 25 mm plate to 20 mm with 300 mm radius rolls and μ = 0.1:
- Δh = h₀ − h₁ = 5 mm; Δh_max = μ²R = 3 mm
- L = √(RΔh) = 38.72983346 mm
- F ≈ σ̄ × w × L = 200 × 300 × 38.72983346 = 2323.790008 kN
Can the rolls bite?: no: the draft exceeds μ²R, the strip will not be drawn in · Reduction: 20 % · True strain ln(h₀/h₁): 0.2231435513 · Projected contact length √(RΔh): 38.72983346 mm · Approximate roll force σ̄ w L: 2323.790008 kN
GATE tip
The neutral point, where strip and roll surface speeds match, lies between entry and exit; forward slip is the exit speed excess over the roll speed.
More Processing and Materials Calculators
-
Chvorinov's Rule Calculator
t = B (V/A)ⁿ
B mould constant, n ≈ 2; riser modulus ≥ 1.2 × casting modulus
Example: A 200 × 100 × 50 mm block with B = 2 s/mm² and n = 2: Solidification time t = 6.80272 min.
-
Rule of Mixtures Calculator
Isostrain: E_c = V_fE_f + V_mE_m
isostress: 1/E_c = V_f/E_f + V_m/E_m
Example: Carbon fibre (230 GPa) in epoxy (3.5 GPa) at 60 % fibre volume: Longitudinal modulus (isostrain) E_c = 139.4 GPa.
-
Polymer Molecular Weight Calculator
Mₙ = Σ xᵢMᵢ, M_w = Σ xᵢMᵢ² / Σ xᵢMᵢ
xᵢ number fraction; PDI = M_w/Mₙ ≥ 1; DP = Mₙ/m₀
Example: Fractions of 10, 20, 30 and 40 kg/mol with number fractions 0.1, 0.3, 0.4 and 0.2: Number-average molecular weight Mₙ = 27000 g/mol.
-
Radius Ratio Calculator
r_c / r_a → coordination number
limits 0.155 (3), 0.225 (4), 0.414 (6), 0.732 (8), 1.0 (12)
Example: Sodium chloride: Na⁺ 1.02 Å and Cl⁻ 1.81 Å: Radius ratio r_c/r_a = 0.563536.
Frequently asked questions
Why is there a maximum draft?
The rolls must drag the strip in by friction; if the contact angle exceeds the friction angle (tan α > μ), the strip skids.
How can a larger draft be taken?
Rough or larger rolls, or several passes. Hot rolling uses higher friction and takes larger drafts than cold rolling.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Rolling Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/rolling-calculator/
IEEE
Scientific Converters, "Rolling Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/rolling-calculator/