BIZOMAT MAKEOS · Fabrication
Rolled Plate Plan (Roll-To Radius for Springback, Blank Length, Radius Inspection)
To what radius must I roll this plate so it springs back to the radius I want, how long is the blank, and does my roll-gauge measurement show the radius is within tolerance?
Plan for rolling a plate or sheet to a radius: the radius to roll to so that after springback it opens to the target radius, found by solving the springback relation (as the bending springback tool), the springback change, the blank length along the mid-thickness for the arc angle, and inspection of the rolled radius from a measurement over two rolls (as the arc radius from rolls tool), against the radius tolerance.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Target inside radius | mm | Inside radius the finished part must have. |
| Plate thickness | mm | Thickness of the plate. |
| Yield strength | MPa | Yield strength of the plate. |
| Elastic modulus | GPa | Elastic modulus of the plate. |
| Arc angle of the part | ° | Angle of arc the part covers (360° for a full shell). |
| Inspection over rolls | ||
| Surface measured | choice | Which surface the roll gauge measures. |
| Gauge set-up | choice | How the rolls and height reading are arranged (as the arc radius from rolls tool). |
| Roll diameter | mm | Diameter of the two gauge rolls. |
| Measurement over the rolls | mm | Measurement over the two rolls. |
| Height measured | mm | Height reading of the arc. |
| Radius tolerance (±) | mm | Plus-or-minus tolerance on the radius. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Target inside radius
- What it is
- The inside radius the finished, rolled part must have after it springs back, from the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the inside radius; if the drawing gives the outside or mean radius, convert it first.
What this means: Plate thickness
- What it is
- The thickness of the plate or sheet being rolled.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thicker plate springs back less, so the roll-to radius moves closer to the target.
- Get it right
- Use the actual measured thickness if it differs from nominal.
What this means: Yield strength
- What it is
- The yield strength of the plate material, ideally from the mill certificate for the actual batch.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher yield strength gives more springback, so the plate must be rolled tighter.
- Get it right
- Use the certificate value; actual yield is often above the minimum specified.
What this means: Elastic modulus
- What it is
- The elastic modulus of the plate material, from material data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type gigapascals; 1 GPa = 1000 MPa.
What this means: Arc angle of the part
- What it is
- The angle of arc the rolled part covers, used for the blank length along the mid-thickness.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 180° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Blank length is proportional to the arc angle.
- Get it right
- A full cylindrical shell is a full circle.
Inspection over rolls
What this means: Surface measured
- What it is
- Whether the roll gauge measures the inside (concave) surface or the outside (convex) surface of the rolled part. The target radius is adjusted to match.
- Units and format
- Choose one of 2 options from the list: Inside (concave) surface; Outside (convex) surface.
- Example
- The form opens with “Inside (concave) surface” selected as a worked example. Choose the option that matches your case.
- Get it right
- For the outside surface the target is the inside radius plus the thickness.
What this means: Gauge set-up
- What it is
- How the two gauge rolls and the height reading are arranged against the arc: the arc bridging the rolls, or the arc resting on them, as described in each option.
- Units and format
- Choose one of 2 options from the list: Arc bridges the rolls; H = height of the arc’s top; Arc rests on the rolls; H = height of the arc’s lowest point.
- Example
- The form opens with “Arc bridges the rolls; H = height of the arc’s top” selected as a worked example. Choose the option that matches your case.
- Get it right
- Pick the arrangement that matches how you took the height reading; the wrong one gives a wrong radius.
What this means: Roll diameter
- What it is
- The diameter of each of the two precision gauge rolls used for the radius measurement. Both rolls must be the same size.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the measured or certified roll size.
What this means: Measurement over the rolls
- What it is
- The measurement across the outside of the two gauge rolls, which fixes the chord between their centres.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be greater than the roll diameter.
What this means: Height measured
- What it is
- The height reading of the arc relative to the rolls, as defined in the gauge set-up option chosen.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 34.3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it at the middle of the span between the rolls.
What this means: Radius tolerance (±)
- What it is
- How far the measured radius may differ from the target either way, from the drawing tolerance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Final radius R_f = R_i ÷ (4x³ − 3x + 1) with x = R_i S_y ÷ (E t) (as the bending springback tool), solved for the roll-to radius R_i that gives the target.
- Blank length = (R + t ÷ 2) × arc angle in radians along the mid-thickness.
- Measured radius from the rolls: (c_b² + c_e²) ÷ 2c_e ± D ÷ 2 (as the arc radius from rolls tool), compared with the target for the surface measured.
- Example: roll to 218.84 mm so it springs back to 300 mm; cut the blank 947.19 mm long; the gauge reads 300.37 mm.
Limitations
- Elastic–perfectly plastic material; work hardening makes the springback larger.
- Ends of rolled plates stay flat unless pre-bent.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set plate rolls for a shell or curved panel
- Develop the blank for a rolled part
- Inspect a rolled radius with rolls and a height gauge
Who it is for
- Boilermakers
- Fabrication supervisors
- Inspectors
What you get
- Roll-to radius and springback
- Blank length
- Measured radius and deviation
Interpreting the result
- Thin, high-strength plate rolled to a large radius springs back most: roll tighter in small steps and gauge often.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1351–1352, 687–688. Topic reference; no source tables or recommended settings are reproduced.
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