Nozzle on a Dished Head: flat pattern

A round nozzle set onto a dished or hemispherical head, on its centre or off it: the nozzle unrolled with its saddle cut. A round nozzle set onto a torispherical or hemispherical head, parallel to its axis, on the centre or off it: the nozzle unrolled with its saddle cut.

Configurations

• Torispherical head. A crown of large radius joined to the shell by a knuckle of small radius.
• Hemispherical head. Half a sphere: the crown radius is half the diameter and there is no knuckle.

A worked example

The torispherical head configuration with the sizes SheetMorph opens with, in mm. One plate: the nozzle unrolled, with its saddle cut: 1 part, 2 seams.

How it is developed

Parallel-line development (unrolled cylinder). 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 line of the nozzle runs from its end down to the head. Its length is the height of the end less the height of the head under it, which is on the crown, a sphere, or beyond it on the knuckle.
• Off the axis the saddle is lowest on the side away from the axis, so the nozzle is longest there.
• The saddle is the joint between the nozzle and the head. The hole is marked on the pressed head from the nozzle, or as a circle of the diameter of the nozzle seen along the axis.

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 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): 192 facet edges compared between the 3D surface and the flat pattern (max deviation 1.10e-12).
• Shared edges and seam closure (passed): 63 internal edges are shared vertex-for-vertex between adjacent facets; 1 seam(s) have mating edges of equal true length (max deviation 1.14e-13).
• 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 5.82e-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 nozzle is parallel to the axis of the head; a nozzle square to the surface of the head (radial) or inclined is not modelled.
• The hole in the head is not developed: a pressed head is not flat. It is round in plan, of the diameter of the nozzle, and is marked on the head from the nozzle itself.
• The nozzle is set onto the head, not through it, and the saddle is taken on the mid-thickness surfaces of both.
• 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.

Head. The head stands on the Z axis, open downward, with its rim at Z = 0 and no straight flange. It is shown by its outline and its rim, and is not developed here: use the dished head in petals for its plates.

Nozzle. The nozzle is parallel to the axis of the head, its own axis moved along X by the offset. End A is its saddle, where it meets the head, and End B its square end. Its length is measured along its axis, from where the axis meets the head. It is cut along the line nearest the axis of the head, which is its shortest.

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.

Other pipe ends and nozzles

• Angled Cut: A length of round pipe with one or both ends cut at an angle: mitered ends, wedges and oblique lengths.
• Pipe on Plate: A round pipe standing on a flat or sloping plate, such as a roof: the pipe cut to the slope, and the plate with its hole.
• Pipe on Elbow: A round branch set onto a segmented bend, on its outside or on its side: the branch unrolled with the saddle that fits the gores.
• Nozzle on Sphere: A round nozzle on a sphere made in zones, radial or upright: the nozzle unrolled with its cut, and the zone it stands on with the hole marked.
• Bellmouth: A flared inlet to a round duct or a fan, with a straight spigot: made in rings, each part of a cone, or in petals pressed to the curve.
• Roof Flashing: The flashing where a flue or vent passes through a pitched roof: the base plate on the slope with its hole, and the sleeve cut to the pitch.