Sheet metal
Plate pre-bending in plate rolling
In short
Pre-bending forms the plate ends that the plate roll leaves flat. The residual flat is about half the lower roll centre distance on a pyramid roll, 1.8 to 2.0 × t on a 3-roll initial pinch, 1.2 to 1.5 × t on a 4-roll; without pre-bending, the seam peaks by δ = √(R² + f²) − R.
Calculation
Example calculated with the tool’s default values.
Inputs
- Diameter
- 1000 mm
- The diameter entered is
- Inside
- Thickness
- 6 mm
- Yield strength Re
- 235
- Plate roll
- 3-roll pyramid (symmetric)
- Lower roll centre distance
- 300 mm
- Pitch between hits (press)
- 25 mm
- Checking template chord
- 500 mm
Results
- Length to pre-bend (per end)
- 150 mm
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Seam peaking without pre-bending
- 21.9 mm
- Hits per end (press)
- 6pitch 25.0 mm, 2.85° per hit
- Angle over the pre-bent length
- 17.09°
- Maximum die opening
- 50 mm
- Radius under load
- 393 mmfor 503 mm after springback
- Inside template sagitta
- 66.99 mmchord 500 mm, radius 500.0 mm
- Blank (π × Dn)
- 3160.4 mmwithout pre-bending: + 2 × 150 mm to trim
- Pyramid roll: it cannot pre-bend the ends; pre-bend on a press brake (die to radius) or leave the blank long and trim the flats.
- Springback: estimate at minimum Re (actual yield varies by heat); roll in passes and check with the template.
- Flat and hit pitch to be confirmed by the machine manual and a trial piece.
Step-by-step calculation
Neutral-fibre diameter
Dn = Dint + e
Dn = 1006.0 mm ; Rn = 503.0 mm
Residual flat
f ≈ centre distance / 2
f ≈ centre distance / 2 = 300 / 2 = 150.0 mm
Seam peaking
δ = √(R² + f²) − R
√(503.0² + 150.0²) − 503.0 = 21.89 mm
Angle over the pre-bent zone
θ = f / Rn
150.0 / 503.0 = 0.2982 rad = 17.09°
Hits
n = ⌈f / pitch⌉; actual pitch = f / n; V die ≤ 2 × pitch
n = ⌈150.0 / 25.0⌉ = 6; pitch 25.0 mm; V die ≤ 50 mm
Springback
Ri / Rf = 4x³ − 3x + 1 ; x = Ri·Re / (E·t) ; E = 210 000 MPa
Rf = 503 → Ri = 393 mm (limite élastique 2681 mm)
Checking template
s = R − √(R² − (c/2)²)
500.0 − √(500.0² − 250.0²) = 66.99 mm
How to use it
- Enter the shell diameter and say whether it is inside, outside or on the neutral fibre.
- Enter the thickness and the yield strength Re of the plate.
- Pick the plate roll: 3-roll pyramid (with the lower roll centre distance), 3-roll initial pinch or universal, or 4-roll.
- Enter the pitch between press hits and the chord of the checking template.
- Read the length to pre-bend at each end.
Frequently asked questions
What is pre-bending in plate rolling?
It is the forming of the plate ends before or during rolling: the plate roll leaves a flat at each end, and pre-bending removes it. A 3-roll pyramid roll cannot pre-bend the ends: pre-bend them on a press brake with a die to radius, or leave the blank long and cut off the flats after rolling.
How long is the pre-bent end of a plate?
The length of the residual flat. On a pyramid roll, f ≈ centre distance / 2: with 300 mm, 300 / 2 = 150.0 mm per end. On a 3-roll initial pinch or universal roll, 1.8 to 2.0 × t; on a 4-roll double pinch, 1.2 to 1.5 × t (Hengdeli). Without pre-bending, add 2 × 150 mm to the blank, to cut off.
How many press hits for plate pre-bending?
Pre-bending must give the angle θ = f / Rn over the pre-bent length. Example: 1000 mm inside Ø shell in 6 mm plate, Rn = 503.0 mm: θ = 150.0 / 503.0 = 0.2982 rad = 17.09°. With a 25 mm pitch: n = ⌈150.0 / 25.0⌉ = 6 hits of 2.85°, and a V opening of at most 2 × pitch, so 50 mm.
Which plate rolling formula gives peaking and springback?
Peaking is δ = √(R² + f²) − R: √(503.0² + 150.0²) − 503.0 = 21.89 mm in the example. For springback, Ri / Rf = 4x³ − 3x + 1 with x = Ri·Re / (E·t) and E = 210 000 MPa: for Rf = 503 mm in S235, roll under load to Ri = 393 mm. The 500 mm chord template has a sagitta s = R − √(R² − (c/2)²) = 66.99 mm.
Limits
Indicative results: the flat and the hit pitch are to be confirmed by the machine manual and a trial piece. Springback is estimated at minimum Re, while actual yield varies by heat: roll in passes and check with the template. Beyond the elastic limit radius E·t / (2 Re), the plate springs back flat.
Sources
- Kevos : roulage, plats d’extrémité, retour élastique, gabarits : Flat ends, peaking, springback Ri/Rf, sweep templates (link)
- Hengdeli : croquage sur rouleuse : Plat résiduel selon la machine (× t) (link)
- Planichapa : longueur de flan d’une virole roulée : Flan = π × Dm ; plats à chuter (link)
- sheetmetal.me : pliage par frappes successives : Pas = arc / frappes ; vé ≤ 2 × pas (link)
- The Fabricator : pliage par frappes (bump bending) : Arc, pas, ouverture de vé = 2 × pas (link)
- EN 1993-1-1 : module d’élasticité de l’acier : § 3.2.6, E = 210 000 MPa