Eccentric Round Reducer: flat pattern
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. A round pipe reducer flat along its bottom, with a straight length at each end: the two straights rolled from their own plates and the oblique cone between them developed, in one plate or two halves.
Open the eccentric round reducer in SheetMorphConfigurations
- Flat on the bottom. End B is moved down until the bottoms of the two circles are level, so the bottom runs straight from end to end, as under a pump inlet or along a pipe rack.
A worked example
The flat on the bottom 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 | 1070.4 mm × 522.8 mm |
| Blank of P3 | 787.3 mm × 100.0 mm |
| Length of cut, every outline and hole | 7235.1 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 |
| Axis of End B below the axis of End A | 75.00 mm |
| Shortest line of the cone, along the flat bottom | 300.00 mm |
| Longest line of the cone, along the top | 335.41 mm |
| Slope of the top from the axis | 26.57 ° |
| 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 | 1070.42 mm |
| P2 Cone, wide | 522.80 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 | 1034.20 mm |
| Developed area | 587,843 mm² |
| Total cut length | 7235.09 mm |
| Longitudinal seam length | 550.00 mm |
How it is developed
Triangulation of the oblique cone; straight lengths unrolled. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.
- The cone is oblique: its bottom is flat, as long as the taper, and its top is the longest line. Its plate is laid out from the true length of every line between the points of its two circles, which all meet at the apex, so it is exact.
- 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 4.90e-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 2.27e-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 1.16e-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 moved toward -Y until the bottoms of the two circles are level, so the bottom (-Y) runs straight from end to end. 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 an oblique cone: the lines between the points of its two circles all meet at its apex, so it 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 eccentric round reducerOther reducers
- Concentric Round: A round pipe reducer on one centreline, with a straight length at each end: the 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.