Blank Diameter for Cup
Calculate the blank (initial flat disc) diameter needed to draw a cylindrical cup, D = √(d² + 4·d·h), from the cup diameter d (mm) and the cup height h (mm), by area conservation. The calculation rests on a fundamental drawing principle: the operation does NOT significantly change the sheet thickness (ideally drawing conserves volume and, with constant thickness, conserves surface AREA). So the flat disc area must equal the cup surface area (bottom + side wall). Equating π·D²/4 = π·d²/4 + π·d·h and solving for D gives the formula. This is the starting point of any drawn-part design: it sets the disc size to cut from the coil or sheet, which determines material consumption (and thus cost and yield, optimized by blank arrangement — nesting). For cups with flange, rounded bottom or non-straight walls, add the corresponding areas. Correct blank calculation avoids waste (disc too big) and incomplete parts (disc too small). Enter the cup diameter and height.
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Diâmetro do blank para copo
O diâmetro do blank (disco plano inicial) necessário para embutir um copo cilíndrico é D = √(d² + 4·d·h), a partir do diâmetro do copo d e da altura do copo h, pela conservação da área da chapa. O cálculo se baseia em um princípio fundamental do embutimento: a operação não muda significativamente a espessura da chapa (idealmente, o embutimento conserva o volume e, com espessura constante, conserva a área da superfície). Assim, a área do disco plano deve igualar a área da superfície do copo (fundo + parede lateral). Igualando π·D²/4 = π·d²/4 + π·d·h e resolvendo para D, obtém-se a fórmula. Esse cálculo é o ponto de partida de qualquer projeto de peça embutida: define o tamanho do disco a recortar da bobina ou chapa, o que determina o consumo de material (e portanto o custo e o aproveitamento da matéria-prima, otimizado pelo arranjo dos blanks na chapa — o nesting, que minimiza o refugo entre discos). Para copos com flange, fundo arredondado ou paredes não retas, somam-se as áreas correspondentes à fórmula básica. O cálculo correto do blank evita tanto o desperdício (disco grande demais) quanto as peças incompletas (disco pequeno demais, que não fecha a altura do copo). Informe o diâmetro e a altura do copo.
Related Tools
Cup Deep-Drawing Force
Calculate the deep-drawing force to form a cylindrical cup, F = π·d·t·σ_r·(D/d − 0.7), from the punch (cup) diameter d (mm), the sheet thickness t (mm), the material tensile strength σ_r (N/mm²) and the blank (disc) diameter D (mm). Deep drawing turns a flat disc into a hollow body (cup, can, pot, fuel tank, body panel): a punch pushes the disc center through a die, and the rim material flows radially inward, forming the cup wall. Force grows with the drawing ratio D/d (the larger the disc relative to the cup, the more material must flow and the higher the force), with material strength and thickness. The (D/d − 0.7) term is a classic empirical approximation (Siebel's formula) including friction and deformation work. Computing the force is essential to select the press and avoid RUPTURE of the cup bottom (if the force exceeds the already-formed wall's strength, the bottom tears). It is a central calculation in metal packaging, appliances and auto parts. Enter the punch diameter, thickness, tensile strength and blank diameter.
Drawing Ratio (LDR)
Calculate the drawing ratio, β = D ÷ d, from the blank (initial disc) diameter D (mm) and the punch (cup) diameter d (mm). The drawing ratio measures how 'deep' the draw is — how much the disc is reduced to form the cup. It is the fundamental parameter determining a draw operation's FEASIBILITY: there is a maximum ratio, the Limiting Drawing Ratio (LDR), above which the cup CANNOT be formed in one operation, because the required force would exceed the cup wall's strength, tearing the bottom. For most steels and aluminums the LDR is around 1.8-2.2 (depends on material anisotropy, the Lankford r value — high-r materials draw better). If the desired ratio exceeds the LDR, the cup must be formed in SEVERAL successive operations (redrawing), reducing the diameter gradually, possibly with intermediate annealing to restore ductility. The drawing ratio is thus the first check in any drawn-part design: it sets whether it is possible in one pass, in how many passes, and guides material choice. Enter the blank and punch diameters.
Blank Holder Force
Calculate the blank holder force in deep drawing, F_s = p·(π/4)·(D² − d²), from the blank holder specific pressure p (N/mm²), the blank diameter D (mm) and the punch diameter d (mm). In drawing, besides the punch forming the cup, there is a BLANK HOLDER pressing the disc rim (the annular area between blank and punch) against the die, with a controlled force. Its role is CRITICAL: to prevent WRINKLE formation on the rim. As it draws, the rim material flows inward and, reducing its perimeter, tends to wrinkle (like crumpled fabric), because it is under circumferential compression. The blank holder grips the rim with enough pressure to prevent wrinkles, but NOT so much as to stop the material from flowing (which would tear the bottom). It is a delicate balance: too little pressure → wrinkles; too much → rupture. The specific pressure p is typically a small fraction of the material strength (0.5-3 N/mm² for steels), and the total force is that pressure times the annular area where the holder acts. Computing this force is essential in drawing-tool design and press setup (which applies the holder via springs, pneumatic or hydraulic cushions). Enter the specific pressure and the blank and punch diameters.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.