Concentric Round Reducer: flat pattern
A round pipe reducer on one centreline, with a straight length at each end: the cone and the two straights, each its own plate. A round pipe reducer on one centreline, with a straight length at each end: the two straights rolled from their own plates and the cone between them developed, in one plate or two halves.
Open the concentric round reducer in SheetMorphConfigurations
- Concentric. Both ends on one centreline.
A worked example
The concentric configuration with the sizes SheetMorph opens with, in mm. 3 plates: the straight at End A, the cone, the straight at End B: 3 parts, 8 seams.
| Blank of P1 | 1257.8 mm × 150.0 mm |
| Blank of P2 | 1140.0 mm × 451.9 mm |
| Blank of P3 | 787.3 mm × 100.0 mm |
| Length of cut, every outline and hole | 7253.6 mm |
| Diameter of End A | 401.00 mm |
| Diameter of End B | 251.00 mm |
| Straight length at End A | 150.00 mm |
| Length of the taper | 300.00 mm |
| Straight length at End B | 100.00 mm |
| Overall length | 550.00 mm |
| Slant height of the cone | 309.23 mm |
| Half angle of the cone | 14.04 ° |
| Outer radius of the sector | 826.68 mm |
| Inner radius of the sector | 517.45 mm |
| Angle of the sector | 87.31 ° |
| Girth at End A | 1259.78 mm |
| Girth at End B | 788.54 mm |
| P1 Straight at End A, long | 1257.76 mm |
| P1 Straight at End A, wide | 150.00 mm |
| P2 Cone, long | 1139.99 mm |
| P2 Cone, wide | 451.90 mm |
| P3 Straight at End B, long | 787.27 mm |
| P3 Straight at End B, wide | 100.00 mm |
| Plates | 3 |
| Triangular facets | 192 |
| Pattern extent X | 1257.76 mm |
| Pattern extent Y | 927.85 mm |
| Developed area | 583,497 mm² |
| Total cut length | 7253.55 mm |
| Longitudinal seam length | 559.23 mm |
How it is developed
Radial-line development of the cone; straight lengths unrolled. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.
- The cone is a right cone: its plate is a sector of a ring, 826.6827 and 517.4498 in radius, through 87.3128 degrees.
- Each straight length is a rectangle as long as its circle is round, rolled and joined to the cone round the circle.
- The cone is cut along its bottom.
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): 192 facets form one band from End A to End B: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
- Developed edges equal true 3D lengths (passed): 576 facet edges compared between the 3D surface and the flat pattern (max deviation 6.39e-13).
- Shared edges and seam closure (passed): 189 internal edges are shared vertex-for-vertex between adjacent facets; 3 seam(s) have mating edges of equal true length (max deviation 1.71e-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): 3 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
- Both ends are square to the axis; for an inclined end, or a centre moved by any amount, use the circle-to-circle transition (cone).
- No flanges, swages or beads are drawn at the ends.
- 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.
Reducer. End A, the larger end, is at Z = 0 and End B at the far end of the straight lengths and the taper, along Z. End B is on the axis of End A. A straight length of zero is left out.
Plates and seams. Each straight length is rolled from a plate as wide as the circle is round. The cone is a right cone and is developed from its true lengths. Every plate is cut along the bottom (-Y). Under Pattern the cone is laid out in one plate, or in two halves cut along its top as well, for a reducer too big for one sheet.
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 concentric round reducerOther reducers
- Eccentric Round: A round pipe reducer flat along its bottom, with a straight length at each end: the oblique cone and the two straights, each its own plate.
- Concentric Rectangular: A rectangular duct reducer on one centreline, with a straight length at each end: each side one plate, folded where the taper begins and ends.
- Eccentric Rectangular: A rectangular duct reducer flat along one side or two, with a straight length at each end: each side one plate, folded where the taper begins and ends.