Dished Head in Petals: flat pattern
A vessel head in petals round a crown plate: torispherical, hemispherical, semi-elliptical (2:1), or a cone with a knuckle. A vessel head made of petals round a crown plate, for heads too large to press in one piece: torispherical, hemispherical or semi-elliptical (2:1), or a cone with a knuckle at its large end.
Open the dished head in petals in SheetMorphConfigurations
- Torispherical. A crown of large radius joined to the shell by a knuckle of small radius.
- Hemispherical. Half a sphere: the crown radius is half the diameter and there is no knuckle.
- Semi-elliptical (2:1). Half an ellipsoid: with a depth of a quarter of the diameter it is the 2:1 elliptical head.
- Cone with a knuckle. A cone joined to the shell by a knuckle at its large end, open at its small end.
A worked example
The torispherical configuration with the sizes SheetMorph opens with, in mm. 8 petals, all alike, round a crown plate: 8 parts, 0 seams.
| Blank of G1 | 891.7 mm × 789.7 mm |
| Blank of G2 | 891.7 mm × 789.7 mm |
| Blank of G3 | 891.7 mm × 789.7 mm |
| Blank of G4 | 891.7 mm × 789.7 mm |
| Blank of G5 | 891.7 mm × 789.7 mm |
| Blank of G6 | 891.7 mm × 789.7 mm |
| Blank of G7 | 891.7 mm × 789.7 mm |
| Blank of G8 | 891.7 mm × 789.7 mm |
| Length of cut, every outline and hole | 21678.5 mm |
| Diameter of the head | 2001.00 mm |
| Crown radius | 2000.50 mm |
| Knuckle radius | 200.50 mm |
| Straight flange | 50.00 mm |
| Depth of the dish | 388.05 mm |
| Height over all | 438.05 mm |
| Angle from the axis where the knuckle meets the crown | 26.39 ° |
| Number of petals | 8 |
| Width of a petal at the rim | 785.79 mm |
| Width of a petal at the crown plate | 314.16 mm |
| Length of a petal, along its middle | 791.13 mm |
| Diameter across, as pressed | 800.00 mm |
| Flat blank, diameter | 805.63 mm |
| G1 Petal, long | 891.69 mm |
| G1 Petal, wide | 789.67 mm |
| Plates | 8 |
| Triangular facets | 272 |
| Pattern extent X | 891.69 mm |
| Pattern extent Y | 7699.27 mm |
| Developed area | 3,652,043 mm² |
| Total cut length | 21678.54 mm |
| Longitudinal seam length | 0.00 mm |
How it is developed
Gore (polycylindric) development. This is a triangulated approximation: the curved surface is divided into small flat triangles, each laid out at its true size. The finer the division, the closer the pattern is to the surface; SheetMorph states the deviation it found.
- Each petal is laid out flat across and curved along: at every point its width is the girth of the head there divided by the number of petals, and its length is the length of the profile from the rim to the crown plate. All petals are alike.
- Along a petal come the straight flange, the knuckle and the crown. The petal is pressed to both curves after cutting.
- The crown plate is a round plate pressed to the crown radius. It is not drawn: its flat blank is listed.
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): 272 facets form one closed band: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
- Developed edges equal true 3D lengths (passed): 816 facet edges compared between the 3D surface and the flat pattern (max deviation 5.51e-12).
- Shared edges and seam closure (passed): 264 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 1.54e-8).
- Cut outlines closed and non-overlapping (passed): 8 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
- A dished head cannot be laid flat: the petals are cut flat and pressed to shape, and the pattern gives their size before pressing.
- The crown plate is not drawn; the diameter of its flat blank is listed.
- An elliptical head, and a cone with a knuckle, are made with the elliptical and toriconical head; a 2:1 elliptical head is close to a torispherical one with a crown radius of 0.9 and a knuckle radius of 0.17 of the diameter.
- 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.
- Neither head can be laid flat: the petals are cut flat and pressed to shape, and the pattern gives their size before pressing.
- The crown plate of an elliptical head is not drawn; the diameter of its flat blank is listed.
- A cone with a knuckle has one at its large end only; a knuckle or a flare at the small end is not modelled. Its cone alone, without the knuckle, unrolls exactly with the cone.
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.
Head. The head stands on the Z axis, open downward: End A is its rim at Z = 0, and the dish rises to End B, the edge of the round crown plate. A straight flange, when there is one, stands between the rim and the knuckle.
Crown and knuckle. The crown is part of a sphere of the crown radius, centred on the axis. The knuckle is part of a torus of the knuckle radius, whose centre is the knuckle radius inside the wall. They meet where the line through both centres cuts them. Petal j lies between the meridians at j and j + 1 times 360 / petals degrees.
Elliptical head. The meridian is a quarter of an ellipse whose half width is half the diameter and whose height is the depth of the dish. A depth of a quarter of the diameter gives the 2:1 head, and a depth of half the diameter a hemisphere.
Cone with a knuckle. The knuckle is part of a torus of the knuckle radius, whose centre is the knuckle radius inside the wall at the top of the flange. It turns through the half angle of the cone, measured from the axis, and the cone leaves it on the tangent. Petal j lies between the meridians at j and j + 1 times 360 / petals degrees.
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 dished head in petalsOther vessels
- Shell with Nozzles: A cylindrical shell unrolled to a rectangle, with the holes for up to four radial nozzles marked in their developed shape.
- Tank Shell: The shell of a storage tank or silo in courses and plates from stock, the vertical seams staggered, with a nozzle or manway marked on its plate.
- Silo: A silo, bin or hopper as one job: the body, the cone bottom from its wall angle, the spout, a support skirt and a cone roof, with what it holds.
- Reinforcing Pad: The pad welded round a nozzle on a shell or a pipe: rolled to the shell, with the hole for the nozzle and a tell-tale hole, whole or in two halves.
- Sphere: A sphere made of plates: gores from pole to pole, or zones round it, with a round cap at each pole.