Dished end cap

The surface is faceted or triangulated, so the pattern is an approximation. The error is known and printed as a number on the drawing — it is not hidden.

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 sfærisk klokkebund: en øvre halvkugle (kappen) med et lige cylindrisk skørt under ækvator. Kappen er en ren kugleflade med radius lig halvdelen af diameteren.

Bunde og dæksler på tanke, beholdere og trykkar, hvor en kuppelform fordeler trykket og samtidig giver et lige skørt at svejse fast til den cylindriske kappe.

Smed, industritekniker og skibsmontør på tank- og apparatbyg; teknisk isolatør laver kappen udenom. Bunde og dæksler på tanke og beholdere.

Stål eller rustfri tankplade 2–8 mm, presset fra en ronde eller svejst af petaler. Isoleringskappen udenom er alu/rustfri 0,5–1,0 mm.

Source: Materialer/tykkelser: src/lib/kasse/materialer.ts (DIN 6935 for stål; massefylder og handelstykkelser; springback). Yderkappe: src/lib/sortiment.ts (pladekappe alu/alu-zink/rustfri 0,5–1,0 mm) + src/lib/calculations.ts (overlæg, «Faglig Regning», BAI 2024). Fremstillingsfælder: docs/PLAN-UDFOLDNINGSBIBLIOTEK.md §9.2/§4.

Diameter — Diameter

Ydre diameter over ækvator i mm; radius R = Diameter/2 og styrer hele kuplens krumning.

Skørt-højde — Skørt-højde

Højden i mm af det lige cylindriske stykke under ækvator (0 = ingen skørt).

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

1. 01Vælg antal blade N (fx 12). Kuplen deles i N ens lune-blade, der hver dækker 360°/N af omkredsen.
2. 02Sæt R = Diameter/2. Meridianbuen går fra ækvator (vinkel 0°) til polen (90°); dens sande længde er en kvart storcirkel = R·(π/2).
3. 03Tegn denne meridianbue som en lodret midterlinje på pappet i fuld størrelse (R·π/2) og del den i fx 6 lige stationer fra ækvator op mod polen.
4. 04Hver station svarer til en breddevinkel φ (0°, 15°, 30°, 45°, 60°, 75°, 90°). I hver station måles bladets halve bredde ud til BEGGE sider af midterlinjen: halv bredde = π·R·cos(φ)/N (bredest ved ækvator, 0 ved polen).
5. 05Forbind alle yderpunkterne med en jævn kurve til et spidst, symmetrisk blad, der ender i en spids ved polen.
6. 06Klip ét blad og brug det som skabelon til alle N ens blade. Buk dem let på langs og saml dem kant-mod-kant til kuplen.
7. 07Skørtet er en ren cylinder og udrulles for sig som et rektangel: bredde = π·Diameter, højde = Skørt-højde. Det svejses fast langs ækvator.

Flere blade (fx 16–24) giver en rundere kugle med mindre kantbukning, men mere svejsning; 12 er den klassiske afvejning. Husk svejsesvind på bladbredderne hvis pladen er tyk.

• ·En kugleflade har Gauss-krumning ≠ 0 og kan IKKE foldes rent fladt (Theorema Egregium) — den deles i lune-blade/petaler eller presses fra en ronde. Et «fladt mønster» af en kuppel lyver.
• ·Tykkelsen efter presning er IKKE t: 10–20 % tynding i knækket. Angiv «kontrolmål efter presning».
• ·Skørtet er en ren cylinder og udrulles for sig (bredde = π·D, højde = skørt-højde) — kun kuplen deles i blade.

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.

15 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 gives the GEOMETRY for an end head — it does not size for pressure. Pressure-bearing vessels are certified equipment and must be calculated in accordance with DS/EN 13445-3 (and above PED 2014/68/EU's class limits also approved accordingly).
• Crown and knuckle radius follow DIN 28011 (R = D, r = 0.1·D) or DIN 28013 (R = 0.8·D, r = 0.154·D) respectively. The standards' own tables of thicknesses, straight edge h₁ and tolerances are NOT reproduced here — look them up in the standard; the tool does not invent them.
• The thickness after pressing is not the sheet thickness: the material typically thins by 10–20% at the knuckle, most at the deepest part of the form. Strength and weight calculations must use the PRESSED thickness, measured on a finished piece.
• The blank-disc diameter is a RANGE and a STARTING dimension, not a definitive answer. Where between area preservation and meridian-arc the piece lands depends on tooling, blank-holder force and lubrication — that is why the head is trimmed after pressing.
• The segment variant (gores) is APPROXIMATE. Each gore is (π/n)/sin(π/n) − 1 wider than the chord it must span, and that difference must be formed into the sheet. The gores do not fit flat.
• The hygiene rules (fall ≥ 3° towards one low point, no crevices, circumferential seam clear of the knuckle) follow EHEDG's principles. They do not replace an approval under Regulation (EC) 1935/2004 or a HACCP assessment.
• The circumferential seam against the shell does not carry an edge allowance on a dished head: the engine does not yet have a mapping from rim to cutting contour for ‘cap’ and ‘non-developable’. Bead, overlap and root gap must be added by hand there.