Screw Flight: flat pattern

One flight of a screw conveyor or auger, right or left hand: standard, tapered or ribbon, as the flat blank that is pulled out to one pitch. One flight of a screw conveyor or auger, right or left hand: an ordinary flight round the shaft, a tapered flight whose outside diameter changes along it, or a ribbon that stands clear of it. Each is the flat blank that is pulled out to one pitch.

Configurations

• Standard flight. A flat ring round the shaft, of one outside diameter, pulled out to one pitch.
• Tapered flight. The outside diameter changes along the shaft from the start of the flight to one pitch on, as in a tapered feed screw.
• Ribbon flight. A ribbon of the width given, from its outer edge inward, standing clear of the shaft, as in a ribbon mixer or a conveyor for sticky material.

A worked example

The standard flight configuration with the sizes SheetMorph opens with, in mm. One flight of one pitch; 10 needed for a screw 3000 long: 1 part, 9 seams.

How it is developed

Triangulation (true-length unfolding) of a helicoid. 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 flight is divided into narrow triangles between its inner and outer edges and unfolded from their true lengths. The plate that results is very nearly a ring with a piece cut out, whose sizes are listed: cut the ring, slit it, and pull the two ends apart to the pitch.
• Flights are welded end to end along the shaft. The radial ends of the plate are those joints.
• The weight shown is for one flight.

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): 64 facets form one open sheet: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 1).
• Developed edges equal true 3D lengths (passed): 192 facet edges compared between the 3D surface and the flat pattern (max deviation 7.46e-14).
• Shared edges and seam closure (passed): 63 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 4.37e-11).
• Cut outlines closed and non-overlapping (passed): 1 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

• A helicoid cannot be laid flat exactly: the flight is stretched as it is pulled to pitch, and the blank is the size before forming. Allow for the shop’s own forming practice.
• The flight is of constant pitch and diameter, with its inner edge on a round shaft; tapered, variable-pitch, ribbon and cut flights are not modelled.
• Thickness is used for the weight only: a flight is flat plate, so the reference of the sizes does not change the blank.
• 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.
• The pitch is constant along a flight, and the taper is even; variable-pitch, cut and folded flights are not modelled.

Conventions

Hand. A right-hand flight winds like an ordinary screw thread: seen along the shaft, it turns clockwise as it goes away from you. A left-hand flight is its mirror image. The blank is the same shape either way, turned over.

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.

Flight. The shaft is the Z axis. One flight makes one turn and rises one pitch, starting on the +X side at Z = 0. End A is its inner edge, on the shaft, and End B its outer edge.

Blank. With the lengths of the inner and outer edges of one turn, Li and Lo, and the width of the flight w, the blank is a ring of inner radius w Li / (Lo - Li). The outer edge takes up Lo / outer radius of a turn; the rest of the ring is the gap that closes when the flight is pulled out.

Tapered flight. The inner edge is on the shaft. The outer edge starts at the first diameter and reaches the second one pitch on, changing evenly with the angle turned, so it lies on a cone. A screw that tapers over several pitches is made of flights that each start at the diameter the one before ended at.

Ribbon flight. The outer edge is at the outside diameter and the inner edge the width of the ribbon inside it, clear of the shaft. The ribbon is carried on arms from the shaft, which are not drawn; the gap between the ribbon and the shaft is listed.

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 rings and helicals

• Segmented Flange: A flat ring, as a flange, a stiffener or a base ring, made in equal segments so that it nests on the plate, with or without its bolt holes.
• Rolled Bar: A ring, a hoop or part of one rolled from flat bar or strip: the length to cut on the neutral line, with the gap for the weld and the flat ends.
• Spiral Chute: A spiral chute: a floor that winds round an axis as it falls, with or without walls on its edges.
• Stair Stringer: The stringer of a spiral or helical stair: a plate rolled to stand on a cylinder as it climbs, alone or as a pair, with a line for every tread.