Rolled Ring: flat pattern
A ring, a hoop or part of one rolled from flat bar or strip: the length to cut on the neutral line, with the gap for the weld and the flat ends. A ring, a hoop or part of one rolled from flat bar or a strip of plate: the length to cut, measured on the neutral line, with the gap for the weld and the flat ends the rolls leave.
Open the rolled ring in SheetMorphConfigurations
- Full ring. A closed ring or hoop, with a gap for the weld if one is wanted.
- Part of a ring. A bar rolled to a given angle of the circle.
A worked example
The full ring configuration with the sizes SheetMorph opens with, in mm. One bar 1885.0972 long by 50 wide: 1 part, 1 seam.
| Blank, the rectangle the plate is cut from | 1885.1 mm × 50.0 mm |
| Length of cut, every outline and hole | 3870.2 mm |
| Diameter on the neutral line | 601.00 mm |
| Inside diameter | 600.00 mm |
| Outside diameter | 602.00 mm |
| Width of the bar | 50.00 mm |
| Neutral diameter over thickness | 601 |
| Gap at the joint | 3.00 mm |
| Length to cut | 1885.10 mm |
| Flat end, each end | 0.00 mm |
| Length of stock to roll | 1885.10 mm |
| Length if the bar is rolled on edge instead | 2039.04 mm |
| P1 Ring, long | 1885.10 mm |
| P1 Ring, wide | 50.00 mm |
| Plates | 1 |
| Triangular facets | 64 |
| Pattern extent X | 1885.10 mm |
| Pattern extent Y | 50.00 mm |
| Developed area | 94,255 mm² |
| Total cut length | 3870.19 mm |
| Longitudinal seam length | 0.00 mm |
How it is developed
Length of the neutral line of a rolled bar. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.
- The bar is 1885.0972 long: the circle through the middle of its thickness, 601 in diameter, less the gap of 3.
- No flat ends are allowed for: set the two ends to the curve in a press before rolling, or allow for them.
- The plate is the bar laid flat, with a line across it at every division of the circle to check the curve against as it is rolled.
Checked before it can be exported
Every pattern SheetMorph draws is checked against the 3D part it comes from. For this example:
- Surface connectivity (passed): 64 facets form one open sheet: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 1).
- Developed edges equal true 3D lengths (passed): 192 facet edges compared between the 3D surface and the flat pattern (max deviation 3.91e-13).
- Shared edges and seam closure (passed): 63 internal edges are shared vertex-for-vertex between adjacent facets; 0 seam(s) have mating edges of equal true length (max deviation 0).
- Developed facets consistently oriented (passed): All developed facets are counter-clockwise (outside face up); none is mirrored or degenerate.
- Developed area equals surface area (passed): Facet area in 3D and in the flat pattern agree (difference 1.16e-10).
- Cut outlines closed and non-overlapping (passed): 1 closed outline(s); no outline crosses itself or another outline.
Assumptions
- The pattern is developed on the mid-thickness surface; inside or outside sizes are converted to it by the thickness.
- Curves are chains of chords between division points.
- No seam, lap, weld-preparation or pressing allowance is added.
Limits of this module
- The neutral line is taken at the middle of the thickness, which holds for a ring more than about ten thicknesses in diameter. A tighter ring is a little shorter: make a trial piece.
- The bar is rolled on the flat, its width along the axis. For a bar rolled on edge the length on the middle of its width is listed, but the pattern is not drawn that way.
- Springback, and the stretch of thin strip, are not modelled.
- Curves are chains of straight chords between division points.
- No seam, lap, weld-preparation or pressing allowance is added, and plates are not nested onto stock sheets.
Conventions
Coordinate system. The part stands on the Z axis with End A at Z = 0. Angles round the axis are measured from +X toward +Y, counter-clockwise seen from +Z.
Divisions and thickness. A circle is divided into 4N equal chords. Sizes are inside, mid-thickness or outside sizes; the pattern is developed on the mid-thickness surface and the views show the sizes as entered.
Ring. The ring stands on the Z axis, its width along the axis: End A is its lower edge at Z = 0 and End B its upper edge. A full ring is cut on the -X side, where its gap is; a segment starts on the +X axis and runs counter-clockwise seen from above.
Length. A bar rolled on the flat neither stretches nor shortens along the middle of its thickness, so its length is that of the circle there: pi times the inside diameter plus the thickness, or the outside diameter less it. The diameter is read as the reference of the sizes says.
Flat ends. Rolls cannot curve the last part of a bar at each end. The flat end entered is added twice to the length for the stock, to be cut off after rolling; leave it at zero where the ends are set first in a press.
Change the sizes to your own in SheetMorph, check the drawing, add seam and flange allowances, and export DXF, PDF, SVG, CSV or G-code. Check every pattern against your own standards before cutting.
Open the rolled ringOther rings and helicals
- Segmented Flange: A flat ring, as a flange, a stiffener or a base ring, made in equal segments so that it nests on the plate, with or without its bolt holes.
- Screw Flight: One flight of a screw conveyor or auger, right or left hand: standard, tapered or ribbon, as the flat blank that is pulled out to one pitch.
- Spiral Chute: A spiral chute: a floor that winds round an axis as it falls, with or without walls on its edges.
- Stair Stringer: The stringer of a spiral or helical stair: a plate rolled to stand on a cylinder as it climbs, alone or as a pair, with a line for every tread.