Oval-to-Rectangle Bend: flat pattern
A segmented bend that changes from flat-oval duct to rectangular duct as it turns, bent the easy way or the hard way: every gore developed, with the mitre at each joint. A segmented bend that changes from flat-oval duct at End A to rectangular duct at End B as it turns, bent the easy way or the hard way: every gore developed, with the mitre at each joint.
Open the oval-to-rectangle bend in SheetMorphConfigurations
- Easy way. The bend turns across the flats: the long axis of the oval is square to the plane of the bend.
- Hard way. The bend turns across the round ends: the long axis of the oval lies in the plane of the bend.
A worked example
The easy way configuration with the sizes SheetMorph opens with, in mm. 5 plates, one per gore, each a little nearer the rectangle than the one before: 5 parts, 14 seams.
| Blank of P1 | 1430.2 mm × 140.2 mm |
| Blank of P2 | 1431.2 mm × 281.2 mm |
| Blank of P3 | 1452.1 mm × 283.7 mm |
| Blank of P4 | 1482.2 mm × 286.2 mm |
| Blank of P5 | 1502.3 mm × 143.7 mm |
| Length of cut, every outline and hole | 16140.2 mm |
| Major size | 601.00 mm |
| Minor size | 201.00 mm |
| Width of End B, along the major size | 501.00 mm |
| Depth of End B, along the minor size | 251.00 mm |
| Length of each flat | 400.00 mm |
| Girth of the oval at End A | 1431.46 mm |
| Girth of the rectangle at End B | 1504.00 mm |
| Radius to the centreline | 600.00 mm |
| Radius of the throat at End A | 499.50 mm |
| Radius of the heel at End A | 700.50 mm |
| Radius of the throat at End B | 474.50 mm |
| Radius of the heel at End B | 725.50 mm |
| Bend angle | 90.00 ° |
| Gores, the two end gores included | 5 |
| Turn at each joint | 22.50 ° |
| Mitre angle of each joint, from square | 11.25 ° |
| Length of the bend along its centreline | 942.48 mm |
| Length on the centreline | 238.69 mm |
| P1 Gore 1, long | 1430.21 mm |
| P1 Gore 1, wide | 140.23 mm |
| P2 Gore 2, long | 1431.15 mm |
| P2 Gore 2, wide | 281.23 mm |
| P3 Gore 3, long | 1452.09 mm |
| P3 Gore 3, wide | 283.72 mm |
| P4 Gore 4, long | 1482.16 mm |
| P4 Gore 4, wide | 286.20 mm |
| P5 Gore 5, long | 1502.26 mm |
| P5 Gore 5, wide | 143.75 mm |
| Plates | 5 |
| Triangular facets | 360 |
| Pattern extent X | 1502.26 mm |
| Pattern extent Y | 1421.33 mm |
| Developed area | 1,385,976 mm² |
| Total cut length | 16140.24 mm |
| Longitudinal seam length | 775.37 mm |
How it is developed
Triangulation of each gore (true-length unfolding). 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.
- The bend changes from the oval at End A to the rectangle at End B as it turns. At each joint the section is that far from the oval toward End B as the joint is through the angle of the bend, so the change is shared evenly among the gores.
- Each gore is therefore a short transition cut on the mitre at its joints: its plate is unfolded from the true lengths of the narrow triangles between its two joints. No two gores are alike; mark each with its number.
- Bent the easy way, the flats of the oval are at the throat and the heel.
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): 360 facets form 5 gores joined end to end: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 0).
- Developed edges equal true 3D lengths (passed): 1080 facet edges compared between the 3D surface and the flat pattern (max deviation 1.04e-12).
- Shared edges and seam closure (passed): 355 internal edges are shared vertex-for-vertex between adjacent facets; 5 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 0).
- 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
- Each gore changes shape, so it is not a cylinder: it is divided into narrow triangles and unfolded from their true lengths, and no two gores are alike.
- The gores meet in plain mitre joints: no lap, bead or flange is added. Add a seam allowance under Fabrication.
- A smooth pressed or spiral-wound flat-oval bend is a different part: this one is made of straight gores.
- 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.
Section. A flat oval is two half circles of the minor size joined by two flats; the major size is over the round ends. End A is at Z = 0, square to the Z axis. Bent the easy way its long axis is along Y; bent the hard way it is along X.
Bend. The bend turns in the XZ plane from +Z toward +X, about a centre the bend radius from the Z axis. Its gores are counted with the two end gores, which are half gores, and each joint turns the duct by the bend angle divided by the gores less one. Every gore is cut along its throat, the line nearest the centre of the bend.
Change of shape. End B is a rectangle, its width along the long axis of the oval and its depth along the short axis. Each point of the oval is matched to one of End B: the tips of the oval to the middles of the ends of the rectangle, the middles of the flats to the middles of its sides, and the half circles round the corners, with a point at every corner. At every joint the section is part of the way from the oval to End B, in proportion to the angle turned, so each gore is a short transition as well as a part of the bend.
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 oval-to-rectangle bendOther pipe bends
- Round: Segmented round bends, at a constant diameter or reducing and expanding, one plate per gore.
- S-Offset: An S-bend of round pipe: two opposed miter bends with a straight between, from the offset or the straight you give.
- Flat Oval: A segmented bend in flat-oval duct, bent the easy way or the hard way: every gore unrolled, with the mitre at each joint.
- Oval to Round: A segmented bend that changes from flat-oval duct to round duct as it turns, bent the easy way or the hard way: every gore developed, with the mitre at each joint.