Silo or Bin with a Cone Bottom: flat pattern

A silo, bin or hopper as one job: the body, the cone bottom from its wall angle, the spout, a support skirt and a cone roof, with what it holds. A silo, bin or hopper as one job: the cylindrical body, the cone bottom from its wall angle down to the outlet, the outlet spout, a support skirt, and a cone roof or an open top, with what it holds.

Configurations

• Cone roof. Closed by a cone roof of the pitch given, in two halves, each rolled from a sector.
• Open top. Open at the top, as a hopper or a bin under a feeder.

A worked example

The cone roof configuration with the sizes SheetMorph opens with, in mm. 6 plates: the spout, the hopper, the body, the roof in two halves and the skirt: 6 parts, 8 seams.

How it is developed

Development of rolled plates: cylinders and cones. This is an exact development: the surface unfolds without stretching, so the pattern closes exactly.

• It holds 35.676 cubic metres to the top of the roof: the hopper 6.115, the body 28.274, under the roof 1.286.
• The hopper is a cone 2338.2686 high, from the outlet up to the body at 60 degrees from level; it unrolls to part of an annulus.
• The roof is a cone of 20 degrees in two halves, each rolled from a sector of 169.1447 degrees; the two meet on seams over -X and +X.
• The skirt is a cylinder of the body’s diameter, welded round the body where the hopper meets it.
• The body may be made in courses of stock plate with the Tank Shell module, to the same diameter.

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): 288 facets form the spout, hopper and body under a cone roof, and the skirt round it: every edge inside a part joins exactly two facets, every open edge one (V - E + F = 1).
• Developed edges equal true 3D lengths (passed): 864 facet edges compared between the 3D surface and the flat pattern (max deviation 1.00e-11).
• Shared edges and seam closure (passed): 282 internal edges are shared vertex-for-vertex between adjacent facets; 4 seam(s) have mating edges of equal true length (max deviation 4.55e-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 3.58e-7).
• Cut outlines closed and non-overlapping (passed): 6 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 hopper is a concentric cone; an eccentric (flat-sided) hopper, a hopper with a second, steeper cone, or a square hopper (see Pyramid Hopper) is not modelled here.
• The roof has no hatch, vent or manway drawn: mark them on the roof plate as needed. The body may be made in courses with the Tank Shell module.
• The skirt has no access opening; the legs, ring beam and base plate are not modelled.
• No flow, pressure or wall-thickness design is done: the angle and the plate are as given.
• 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.

Levels. The silo stands on the Z axis with the foot of its spout at Z = 0. Above the spout the hopper rises at its wall angle to where it meets the body, the body rises its height, and the roof rises to its apex.

Hopper. The hopper’s wall angle is measured from level: the steeper it is, the more freely the material flows, and the taller the hopper for the same outlet. Its height follows from the angle, the diameter and the outlet.

Skirt. The skirt is a cylinder the diameter of the body, welded round it where the hopper meets it and standing down from there to carry the silo. Its height is measured down from that line; it may reach below the spout.

Capacity. What the silo holds is worked out from the sizes as given: the hopper as a frustum, the body as a cylinder, and the space under a cone roof, each listed. The usable volume depends on how the material lies, which is not worked out.

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 vessels

• Shell with Nozzles: A cylindrical shell unrolled to a rectangle, with the holes for up to four radial nozzles marked in their developed shape.
• Tank Shell: The shell of a storage tank or silo in courses and plates from stock, the vertical seams staggered, with a nozzle or manway marked on its plate.
• Reinforcing Pad: The pad welded round a nozzle on a shell or a pipe: rolled to the shell, with the hole for the nozzle and a tell-tale hole, whole or in two halves.
• Sphere: A sphere made of plates: gores from pole to pole, or zones round it, with a round cap at each pole.
• Dished Head: A vessel head in petals round a crown plate: torispherical, hemispherical, semi-elliptical (2:1), or a cone with a knuckle.