Truncated cone and reducer

The surface is developable and the flat pattern is solved in closed form. Cut the part to the drawing and it fits — the whole uncertainty sits in the K-factor, which belongs to the material and the machine, not to the geometry.

Dimensions are entered as: Inside dimensions. The flat pattern itself is always computed on the neutral fibre — at Ø800 in 3 mm sheet the difference between the inside and the outside dimension is 18.8 mm of developed width, and then the seam does not meet.

En lige (akse-symmetrisk) keglestub: en åben konisk skal med en mindre topåbning og en større bundåbning, der deler samme lodrette akse. Når top-radius sættes til 0, bliver den til en ren kegle.

Koniske overgange mellem to runde diametre i ventilation og procesanlæg — reduktioner på kanaler, tragt-overgange, cyklon-toppe, lamper og emhætter.

VVS-energi og teknisk isolatør — reduktioner mellem to kanaldiametre, tragt-overgange og cyklon-toppe; smed/metalsmed på procesudstyr.

Galvaniseret eller rustfri tyndplade 0,7–2 mm til ventilation; slidfast stål til cyklon-toppe. Valses til konus.

Source: Materialer/tykkelser: src/lib/kasse/materialer.ts (DIN 6935 for stål; massefylder og handelstykkelser; springback). Ventilation: DS 447:2021 + BR18 §§ 420–452 (src/lib/vvs/artikler.ts). Fremstillingsfælder: docs/PLAN-UDFOLDNINGSBIBLIOTEK.md §9.2/§4.

Top-radius — Topåbningens radius

Radius af den lille (øverste) cirkelåbning i mm. 0 mm giver en spids kegle.

Bund-radius — Bundåbningens radius

Radius af den store (nederste) cirkelåbning i mm.

Højde — Vertical height

Den lodrette afstand mellem top- og bundåbningen i mm (ikke sidelængden).

Sider — Facettering

Antal flader modellen tegnes med (visning). Et højt tal ser glat/rundt ud; et lavt tal viser tydelige gjæringer som i en facetteret udfoldning.

Step by step with compass and square — in cardboard first, in sheet metal after.

1. 01Tegn opstalten (tværsnit) af keglestubben i 1:1: bundlinjen lig fuld bunddiameter, topåbningen centreret over den, adskilt af den lodrette højde.
2. 02Forlæng de to skrå sider opad til de mødes i toppunktet (apex). Mål den sande sidelængde (slanklængden) fra apex til bundkanten og fra apex til topkanten.
3. 03Slå med passeren en bue med den ydre slanklængde (apex→bund) som radius fra et centrum på pappet, og en mindre bue med den indre slanklængde (apex→top) fra samme centrum.
4. 04Afsæt langs den ydre bue en buelængde lig bundcirklens omkreds (π·d for bunden). Det fastlægger sektorvinklen — træk de to ydre radiale grænselinjer ind mod centrum.
5. 05Del bueafsnittet i 12 lige store dele og træk radiale linjer fra centrum; de bliver fals-/stationslinjer i mønstret.
6. 06Klip sektoren ud mellem den indre og ydre bue. Tilføj sømtillæg langs den ene radiale kant, og fals langs stationslinjerne, før du runder den til keglestub.

Sektoren er symmetrisk, så sømmen kan lægges ved en hvilken som helst stationslinje — vælg den der giver mindst spild på pladen. Husk at mønstret bygger på den SANDE slanklængde, ikke den lodrette højde.

• ·Radial-linje-metoden slår slanklængden som radius til den NEUTRALE fiber (middeldiameter), ikke ydre — ellers mødes sømmen ikke.
• ·Deler du omkredsen i for få stationer, bliver mønstret for lille: korden er kortere end buen. 12 dele er nok til pap, men til plade skal antallet højt (relativ mangel ≈ π²/6N²).
• ·Skal keglen flanges i kanten, er det KRYMPNING, ikke bukning: Ø1000 med 40 mm skørt = 8 % omkredskrympning. Giv 2–4 % ekstra materiale.

The words and formulas the trade uses for a flat pattern. The symbols are the same throughout Discebo: α is the bend angle in degrees, R the inside bend radius, t the sheet thickness and K the K-factor — all in millimetres.

Flat pattern (development)

The part's surface laid out flat as one continuous cutting outline — the way the sheet looks BEFORE it is bent or rolled. Only a developable surface can be unfolded exactly; a doubly curved surface cannot be laid flat without stretching the material.

Flat length

The flat length the part must be cut to so the dimensions come out right once it is bent. It is either the sum of the outside dimensions minus the bend deductions, or the sum of the flat legs plus the bend allowances — both routes must give the same number.L = Σ(udvendige mål) − Σ(BD) = Σ(flade ben) + Σ(BA)

Bend allowance

The length of material that sits in the bend itself, measured along the neutral fibre. The bend allowance is always positive and is added to the flat legs.BA = (π/180) · α · (R + K · t)

Bend deduction

The amount subtracted from the sum of the outside dimensions, because the two outside dimensions between them count the corner twice. Here the bend deduction is taken as POSITIVE and subtracted; DIN 6935 writes the same quantity as the compensation value v with the opposite sign.BD = 2 · OSSB − BA

Outside setback

The distance from the theoretical outside corner point in to where the bend starts. Above 90°, tan(α/2) is clamped to at most 1 per DIN 6935, so the number does not explode towards 180°.OSSB = tan(α/2) · (R + t)

Compensation value v to DIN 6935

The standard's own way of writing the same corner loss: the flat length is a + b + v, where v is negative. Our bend deduction is therefore the same quantity with the opposite sign — never flip one without the other.L = a + b + v ⇒ v = −BD

K-factor

Where the neutral fibre sits in the sheet, given as a fraction of the sheet thickness. DIN 6935 writes the correction factor k, which applies to the neutral line in the form (R + t·k/2); the American CAD convention writes (R + K·t), so K = k/2.k = 0,65 + 0,5 · log₁₀(R/t), k ≤ 1,0 ⇒ K = k/2

Neutral fibre

The layer in the sheet that is neither stretched nor compressed when the part is bent. The flat pattern is always computed on the neutral fibre — which is why it matters whether the drawing's dimensions are inside or outside.

Bend angle

The angle the material is turned through, not the angle between the legs. The bend angle is 180° minus the included angle, so a square corner is 90° and a seam fold is 180°.α = 180° − åbningsvinklen

Inside bend radius

The radius on the inside of the bend. It is set by the tooling and the material, not by the drawing — too small a radius cracks the part in the outer fibre.

Sheet thickness

The thickness of the material. It enters every single bend allowance, so sheet delivered 0.2 mm thicker than ordered shifts the flat length at every bend.

Fold line

The line on the flat pattern where the part is to be bent. It is drawn but never cut through — in a laser file it therefore sits on its own layer.

Test bend

A strip of known raw length, bent in the material and the tooling that production will use. Measure the two outside legs afterwards and the bend deduction and K-factor can be worked back. The machine's own measured bend table beats any table.BD_målt = (A + B) − L₀

DIN 6935 covers only cold bending of flat products in structural steel. Stainless, aluminium, copper, brass and titanium zinc are not included — there the formulas are an extrapolation, and a test bend in the actual material settles it.

19 fields. The starting values belong to the figure itself — they live in one place in the code, so the tool, the share link and the smoke test can never disagree about what «default» means.

A preset sets every dimension at once. The name is often the word the part goes by in the workshop — the library's search knows them all.

Read them before the part is cut. They are here because they cannot be calculated away — not as legal text, but as craft.

• The figure calculates GEOMETRY. A conical shell in pressure-bearing equipment must be verified in accordance with EN 13445-3 (conical shell and knuckle reinforcement) — a half apex angle above 30° requires a separate verification of the knuckle ring, and the tool does not do that.
• The tightness of a ventilation reducer is not geometry. Round ducts must meet the leakage class in EN 12237, and a seamed joint without sealing does not hold class C.
• Chimney and flue pipes are certified equipment (EN 1856-1/-2). A conical transition in a flue must not be manufactured according to this figure.
• The angle of repose for a bulk material is an INPUT from the supplier. The tool does not invent it — a cone that is steep enough for dry grain will bridge over with damp wood chips or sticky sludge.
• Eccentric and offset-top transitions have UNEQUAL generatrices. If the piece is to be rolled, the roller must be set to each individual generatrix; a cone roller with one setting produces a right cone.
• The K-factor is DIN 6935's suggestion and is NOT standard-backed for stainless steel, aluminium and titanium zinc. At R_n/t < 5 the figure uses D_n = D_i + 2·K·t — check it against a trial bend in the material you are using.
• The insulation shell's overlap against the adjoining piece follows BAI's trade agreement (20/35/50 mm depending on finished Ø) and is set in the workshop's overlap rule — the figure does not calculate it itself.
• Wind load, snow load and support of a free-standing cone (silo roof, Chinese hat, hood) are NOT covered. It is a building component and must be verified in accordance with EN 1991-1-3 and EN 1991-1-4.