Bellmouth Inlet: flat pattern
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. A flared entry to a round duct or a fan, the flare a quarter round or less, with a straight spigot to fit the duct: made in rings, each part of a cone, or in petals pressed to the curve.
Open the bellmouth inlet in SheetMorphConfigurations
- Rings. Bands round the flare, each the band of a cone through two of its circles, rolled and joined edge to edge.
- Petals. Equal petals from the throat to the lip, each flat across and curved along, pressed to the flare after cutting.
A worked example
The rings configuration with the sizes SheetMorph opens with, in mm. 4 rings, each part of a cone, and the spigot: 5 parts, 9 seams.
| Blank of P1 | 1257.8 mm × 100.0 mm |
| Blank of P2 | 1234.6 mm × 233.3 mm |
| Blank of P3 | 847.4 mm × 497.0 mm |
| Blank of P4 | 659.2 mm × 615.0 mm |
| Blank of P5 | 653.3 mm × 653.0 mm |
| Length of cut, every outline and hole | 15389.9 mm |
| Throat diameter | 401.00 mm |
| Lip diameter | 641.00 mm |
| Height of the flare | 120.00 mm |
| Overall height | 220.00 mm |
| Length of the flare, round its curve | 188.50 mm |
| Area of the flare | 289,107 mm² |
| Girth of the spigot | 1259.78 mm |
| Length | 100.00 mm |
| Number of rings | 4 |
| Angle of the flare each ring takes | 22.50 ° |
| Diameter at its lower circle | 401.00 mm |
| Diameter at its upper circle | 419.27 mm |
| Slant height | 46.82 mm |
| Diameter at its lower circle | 419.27 mm |
| Diameter at its upper circle | 471.29 mm |
| Slant height | 46.82 mm |
| Diameter at its lower circle | 471.29 mm |
| Diameter at its upper circle | 549.16 mm |
| Slant height | 46.82 mm |
| Diameter at its lower circle | 549.16 mm |
| Diameter at its upper circle | 641.00 mm |
| Slant height | 46.82 mm |
| P1 Spigot, long | 1257.76 mm |
| P1 Spigot, wide | 100.00 mm |
| P2 Ring 1, long | 1234.58 mm |
| P2 Ring 1, wide | 233.32 mm |
| P3 Ring 2, long | 847.44 mm |
| P3 Ring 2, wide | 497.02 mm |
| P4 Ring 3, long | 659.24 mm |
| P4 Ring 3, wide | 615.03 mm |
| P5 Ring 4, long | 653.26 mm |
| P5 Ring 4, wide | 652.96 mm |
| Plates | 5 |
| Triangular facets | 320 |
| Pattern extent X | 5910.02 mm |
| Pattern extent Y | 652.96 mm |
| Developed area | 412,962 mm² |
| Total cut length | 15389.87 mm |
| Longitudinal seam length | 287.29 mm |
How it is developed
Zone (polyconic) 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 ring is the band of a cone through two circles of the flare and unrolls to part of an annulus. The ring at the throat is nearly a cylinder, the one at the lip nearly flat.
- A ring is rolled to its cone and then pressed to the curve of the flare; the more rings, the less each is pressed.
- The spigot is a plain cylinder, rolled from a rectangle, to which the first ring is joined at the throat.
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): 320 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): 960 facet edges compared between the 3D surface and the flat pattern (max deviation 7.82e-13).
- Shared edges and seam closure (passed): 315 internal edges are shared vertex-for-vertex between adjacent facets; 5 seam(s) have mating edges of equal true length (max deviation 4.41e-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-11).
- Cut outlines closed and non-overlapping (passed): 5 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 flare is an arc of a circle, a quarter round at most; elliptical and conical (straight) entries are not modelled.
- A ring or a petal is cut flat and pressed or rolled to the flare: the pattern gives its size before forming.
- A rolled bead or a flange round the lip, and an inlet screen, are not modelled.
- The rings are joined edge to edge: no lap is added.
- 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.
Bellmouth. The bellmouth stands on the Z axis. End A is the foot of the spigot at Z = 0 (or the throat, with no spigot) and End B the lip. Above the spigot the wall turns outward on an arc of the flare radius, from upright at the throat through the flare angle; at 90 degrees the lip is flat.
Flare. The throat diameter is that of the duct, given as an inside, mid or outside size; the flare radius is taken to the mid-thickness of the plate. The lip diameter is the throat diameter and twice the flare radius times (1 - cos of the flare angle).
Rings. The flare is divided into equal angles; each ring is the band of the cone through the two circles that bound it, which unrolls to part of an annulus, and the spigot is a cylinder that unrolls to a rectangle. The rings are cut on the -X side.
Petals. A petal is as wide at any height as the girth there divided by the number of petals, and as long as the arc from the throat (or the foot of the spigot) to the lip; it is pressed across to the curve after cutting. With a spigot the petals run down it, so no separate spigot is cut.
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 bellmouth inletOther 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.
- Nozzle on Head: A round nozzle set onto a dished or hemispherical head, on its centre or off it: the nozzle unrolled with its saddle cut.
- 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.
- 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.