Short answer
Lay out rolled and formed parts on the mean line, the middle of the sheet, because that layer keeps its length. For a cylinder the mean diameter is the inside diameter plus one thickness. Each layout mistake costs π × t on the blank: 15.7 mm for 5 mm plate.
A flat pattern is drawn for a sheet with no thickness. The sheet you cut has thickness, and when it is rolled or pressed, the inside of the bend gets shorter and the outside gets longer. Somewhere in between is a layer that keeps its length. If the pattern is laid out on that layer, the formed part comes out at its sizes. If it is laid out on the inside or the outside, it does not.
On thin duct work the difference hides in the seam. On 4, 6 or 10 mm plate it does not.
The mean line
For rolled shells and cones, the layer that keeps its length sits very close to the middle of the sheet. That is why plate shops lay out on the mean diameter: the inside diameter plus one thickness, or the outside diameter minus one thickness.
Take a shell with an inside diameter of 500 mm in 5 mm plate:
| Laid out on | Diameter | Blank length (π × D) |
|---|---|---|
| Inside | 500 mm | 1570.8 mm |
| Mean | 505 mm | 1586.5 mm |
| Outside | 510 mm | 1602.2 mm |
Cut on the inside diameter, the blank is 15.7 mm short. Rolled up, the seam does not close, or it closes and the shell comes out about 5 mm small in diameter. Cut on the outside diameter, it is 15.7 mm too long and has to be trimmed after a test roll. Laid out on the mean, it closes at the size on the drawing.
Here is the same shell worked out by Unfoldo, with the 500 mm given as an inside size. Change the diameter or the height and the blank follows:
| Mean diameter | 505 mm |
|---|---|
| Circumference (mean) | 1,586.5 mm |
| Pattern size | 1,586.5 × 600 mm |
| Area (bbox) | 0.9519 m² |
| Press lines | 23 |
| Parts | 1 |
The rule of thumb is that each layout mistake is worth π × t, a little over three times the thickness. At 10 mm plate that is more than 31 mm on one shell.
Which size do you have?
The drawing usually tells you, if you look at why the size is there:
- Inside size when something goes inside the part: a pipe that slides in, a liner, a flow area that must not shrink. Hoppers and chutes are often given inside.
- Outside size when the part goes into something: a sleeve, a flange bore, a hole in a wall, or a duct that slips into the next one.
- Mean size when someone has already done the work, which is common on plate drawings for shells and cones.
Cones, transitions and elbows
The same idea carries over to every shape, but it is less obvious than on a cylinder.
On a cone, the mean surface sits half a thickness from the inside surface, measured square to the sheet, and the cut edges at the ends are square to the sheet too. Seen at the ends, the diameters move by one thickness times the cosine of the slope from vertical. On a tall, steep cone that is nearly a full thickness, as on a cylinder; on a flat cone, such as a shallow hopper bottom, it is much less. Adding one thickness to the diameters of every cone overshoots on the flat ones.
Here is a cone 800 mm across the bottom and 400 mm across the top, 300 mm high, in 6 mm plate with inside sizes. The mean diameters come out 4.99 mm larger, not 6:
| Mean base diameter | 804.99 mm |
|---|---|
| Mean top diameter | 404.99 mm |
| Slant height | 360.56 mm |
| Outer radius (R1) | 725.61 mm |
| Inner radius (R2) | 365.06 mm |
| Sector angle (each part) | 199.6921° |
| Chord across the outer ends | 1,429.85 mm |
| Pattern size | 1,451.22 × 849.69 mm |
| Area (bbox) | 1.2331 m² |
| Press lines | 23 |
| Parts | 1 |
On a square to round, the flat triangles and the corner pieces are worked out from the mean surface too. A rectangle given as an inside size moves out by half a thickness square to each side, and the round end gets its own correction.
On a segmented elbow, the centre line radius does not change, but the diameter of every segment does, and so do the throat and heel lengths of each cut.
Working these out by hand is where most of the time on a thick part goes, and where most of the mistakes are made.
What Unfoldo does with it
Every shape page asks for the sheet thickness and whether the sizes you type are inside, mean or outside. The pattern is then worked out on the mean surface of the sheet, so the formed part meets the sizes you entered. If you give inside sizes, the part's inside is at those sizes; if you give outside sizes, its outside is.
On parts with two ends, the setting applies to the sizes as you entered them, which is the usual way drawings are dimensioned. If your drawing mixes inside and outside sizes on one part, convert the odd one before you enter it: add one thickness to an inside diameter to get the outside, or subtract one to go the other way.
When the mean line is not enough
For rolled shells and cones, laying out on the mean line is the standard practice, and it holds well while the bend radius is large compared with the thickness. On tight press brake bends, the layer that keeps its length moves towards the inside of the bend, which is what bend allowance tables and K factors describe. That is a different job from shell and transition work, and a different calculation.
Questions
Should I lay out a rolled shell on the inside, mean or outside diameter?
On the mean diameter: the inside diameter plus one thickness, or the outside diameter minus one thickness. The middle of the sheet keeps its length when it is rolled, so a blank cut to the mean circumference closes at the size on the drawing.
How much does one thickness change the blank length of a cylinder?
π × t, a little over three times the thickness. For 5 mm plate that is 15.7 mm on one shell, for 10 mm plate more than 31 mm.
Does the mean line rule work for press brake bends?
Not exactly. On tight bends the layer that keeps its length moves towards the inside of the bend, which is what bend allowance tables and K factors describe. The mean line is right for rolled shells, cones and transitions with large radii.
How does thickness change a cone's diameters?
The mean surface sits half a thickness from the inside, square to the sheet. Seen at the ends, the diameters move by one thickness times the cosine of the slope from vertical: nearly a full thickness on a tall, steep cone and much less on a flat one.
What if my drawing gives one end inside and the other outside?
Correct each end on its own, or convert the odd one before you enter it: add one thickness to an inside diameter to get the outside, subtract one to go the other way.