Flat-Oval Bend: flat pattern
A segmented bend in flat-oval duct, bent the easy way or the hard way: every gore unrolled, with the mitre at each joint. A segmented bend in flat-oval duct, bent the easy way or the hard way: every gore unrolled, with the mitre at each joint.
Open the flat-oval 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: 3 middle gores alike and 2 end gores: 5 parts, 14 seams.
| Blank of P1 | 1430.4 mm × 139.3 mm |
| Blank of P2 | 1430.4 mm × 278.7 mm |
| Blank of P3 | 1430.4 mm × 278.7 mm |
| Blank of P4 | 1430.4 mm × 278.7 mm |
| Blank of P5 | 1430.4 mm × 139.3 mm |
| Length of cut, every outline and hole | 15943.7 mm |
| Major size | 601.00 mm |
| Minor size | 201.00 mm |
| Length of each flat | 400.00 mm |
| Girth of every plate | 1431.46 mm |
| Radius to the centreline | 600.00 mm |
| Radius of the throat | 499.50 mm |
| Radius of the heel | 700.50 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 |
| Length at the throat | 198.71 mm |
| Length at the heel | 278.68 mm |
| Length at the throat | 99.36 mm |
| Length at the heel | 139.34 mm |
| P1 Gore 1, long | 1430.45 mm |
| P1 Gore 1, wide | 139.34 mm |
| P2 Gore 2, long | 1430.45 mm |
| P2 Gore 2, wide | 278.68 mm |
| Plates | 5 |
| Triangular facets | 360 |
| Pattern extent X | 1430.45 mm |
| Pattern extent Y | 1393.38 mm |
| Developed area | 1,365,761 mm² |
| Total cut length | 15943.69 mm |
| Longitudinal seam length | 794.85 mm |
How it is developed
Parallel-line development of each gore. 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 gore is a length of straight flat-oval duct cut on the mitre at its joints. Every line along it is as long as its distance from the centre of the bend makes it: shortest at the throat and longest at the heel.
- Bent the easy way the throat and the heel are the two flats, each cut square across, and the round ends are the cheeks.
- The middle gores are all alike, and an end gore is half of one, cut square at its outer end. Reverse alternate gores end for end to keep the seams in line along 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): 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 1.01e-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 2.33e-10).
- 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 section is the same all the way round the bend; a bend that also changes shape is the oval-to-rectangle or oval-to-round bend.
- 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 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 flat-oval 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.
- Oval to Rectangle: 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.
- 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.