Concentric Rectangular Reducer: flat pattern

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. A rectangular duct reducer on one centreline, with a straight length at each end: each side is one plate, folded where the taper begins and ends.

Configurations

• Tapered on four sides. Both the width and the depth reduce, equally on each side of the centreline.
• Tapered on two sides. The width is kept: the top and the bottom slope and the two sides are flat.

A worked example

The tapered on four sides configuration with the sizes SheetMorph opens with, in mm. 4 plates: the bottom, the top and the two sides, each a straight length, the taper and a straight length: 4 parts, 4 seams.

How it is developed

True-shape development of flat sides. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.

• Each side is laid out to its true shape: the straight length at End A, the taper as long as its slant length, and the straight length at End B, one above the other, folded where the taper begins and ends.
• The reducer is on one centreline: the top and the bottom are alike, and so are the two sides.
• 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): 4 stations: opposite sides and the two diagonals of each compared (max deviation 0).
• Plates flat, rolled or triangulated (passed): 0 flat, 4 folded or rolled from flat pieces (both develop exactly), 0 twisted and split along a diagonal.
• Surface connectivity (passed): 24 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): 72 facet edges compared between the 3D surface and the flat pattern (max deviation 3.41e-13).
• Shared edges and seam closure (passed): 20 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 2.33e-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

• Both ends are square to the axis; for an inclined end, or a centre moved by any amount, use the rectangle-to-rectangle transition.
• No flanges, drive cleats or slips are drawn at the ends.
• 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.

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. From End A each side is a straight length, the taper and a second straight length, in one plate folded twice. End B is on the axis of End A.

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.

Other 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.
• 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.
• 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.