Reducing Rectangular Bend: flat pattern
A rectangular bend whose width, or width and depth, change steadily from one end to the other. A rectangular duct bend whose width, or width and depth, change steadily from one end to the other.
Open the reducing rectangular bend in SheetMorphConfigurations
- Width changes. The throat is a true arc; the heel runs in or out as the width changes. The depth is constant and the cheeks stay flat.
- Width and depth change. The depth changes as well, so the cheeks lean and are split into triangles.
A worked example
The width changes configuration with the sizes SheetMorph opens with, in mm. 4 plates: two cheeks, the throat and the heel, 8 pieces round the bend: 4 parts, 4 seams.
| Blank of P1 | 680.8 mm × 381.7 mm |
| Blank of P2 | 234.5 mm × 201.0 mm |
| Blank of P3 | 672.5 mm × 379.0 mm |
| Blank of P4 | 760.6 mm × 201.0 mm |
| Length of cut, every outline and hole | 6088.3 mm |
| Width at End A | 401.00 mm |
| Width at End B | 251.00 mm |
| Depth | 201.00 mm |
| Throat radius | 149.50 mm |
| Heel radius at End A | 550.50 mm |
| Heel radius at End B | 400.50 mm |
| Bend angle | 90.00 ° |
| Length of the throat arc | 234.83 mm |
| Pieces round the bend | 8 |
| P1 Cheek 1, long | 680.77 mm |
| P1 Cheek 1, wide | 381.74 mm |
| P2 Throat, long | 234.46 mm |
| P2 Throat, wide | 201.00 mm |
| P3 Cheek 2, long | 672.46 mm |
| P3 Cheek 2, wide | 379.04 mm |
| P4 Heel, long | 760.63 mm |
| P4 Heel, wide | 201.00 mm |
| Plates | 4 |
| Triangular facets | 64 |
| Pattern extent X | 760.63 mm |
| Pattern extent Y | 1506.35 mm |
| Developed area | 520,752 mm² |
| Total cut length | 6088.33 mm |
| Longitudinal seam length | 0.00 mm |
How it is developed
Parallel-line development: flat cheeks, rolled throat and heel. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.
- The throat is rolled to a true arc. The heel is rolled to a curve that runs in or out as the width changes, so its radius is not constant.
- The cheeks are flat and are cut to their true shape.
- The throat and heel are straight between stations; more pieces bring them closer to the true curves.
- Each side is a separate plate. The four corner edges of a duct are joints between plates, drawn as plain edges without allowance.
Checked before it can be exported
Every pattern SheetMorph draws is checked against the 3D part it comes from. For this example:
- Every station is a rectangle (passed): 9 stations: opposite sides and the two diagonals of each compared (max deviation 0).
- Plates flat, rolled or triangulated (passed): 2 flat, 2 folded or rolled from flat pieces (both develop exactly), 0 twisted and split along a diagonal.
- Surface connectivity (passed): 64 facets form one closed duct: 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 4.62e-13).
- Shared edges and seam closure (passed): 60 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 1.75e-10).
- Cut outlines closed and non-overlapping (passed): 4 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 one thickness across each opening.
- Folds are sharp lines; no bend allowance is applied.
- No seam, lap or weld allowance is added.
Limits of this module
- The throat is a single arc; the heel is not a true arc when the width changes.
- When the depth changes the cheeks are not flat: they are triangulated approximations.
- No seam, lap, lock-seam, flange or weld allowance is added unless the module says so; corner joints are drawn as plain edges.
- Bend allowance and springback are not modelled; folds are sharp lines on the mid-thickness surface.
- No stiffening, tie rods, access doors or nesting onto stock sheets.
Conventions
Coordinate system. End A is at Z = 0, centred on the Z axis, with its width along X and its depth along Y. A duct that turns or is offset does so in the XZ plane, toward +X.
Corners and sides. Corners are numbered 0 (-X, -Y), 1 (+X, -Y), 2 (+X, +Y), 3 (-X, +Y), seen from +Z at End A. Rj_c is corner c of station j. Each of the four sides is its own plate; the plates are joined along the four corner edges.
Plates. Plates are drawn outside face up and stacked in the order of their numbers. The blank sizes listed are the bounding rectangle of each plate.
Material thickness. Say whether the sizes are inside, mid-thickness or outside sizes. The pattern is developed on the mid-thickness surface, one thickness larger or smaller across each opening; the views show the sizes as entered.
Bend. The bend turns from +Z toward +X about a centre on the +X side of End A. The throat keeps the radius entered; the width, measured from the throat outward, changes in proportion to the angle turned, and so does the depth when it changes.
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 reducing rectangular bendOther duct bends
- Elbow: Elbows of rectangular duct, rolled to a radius or in mitered segments: two cheeks, a throat and a heel.
- Square-Throat Elbow: A rectangular elbow with a square inside corner, joined on one mitre, with or without turning vanes.
- Offset: A rectangular duct moved sideways between two parallel ends: an ogee of two curves, or a slanted piece on two mitres.
- Round to Rectangle: A square-to-round whose two ends are at an angle: it changes shape and direction in one piece.