BIZOMAT MAKEOS · Fabrication
Drawn Shell Blank Diameter and Draws
What blank diameter is needed for this drawn cup, and how many draws will it take?
Blank diameter for a cylindrical drawn shell with or without a flange, the first drawing ratio against a limit, the estimated number of draws and the first-draw force.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Shell diameter (mean) | mm | Mean diameter of the finished shell. |
| Shell height | mm | Height of the shell (to the flange face if flanged). |
| Bottom corner radius | mm | Inside corner radius between wall and bottom. |
| Flange outside diameter (0 = no flange) | mm | Outside diameter of the flange; 0 for a plain cup. |
| Material thickness | mm | Sheet thickness. |
| Tensile strength | MPa | Ultimate tensile strength of the sheet. |
| Limiting first drawing ratio d ÷ D | Smallest first-draw ratio d ÷ D for your material and relative thickness, from drawing ratio tables (about 0.48–0.63). | |
| Limiting redrawing ratio | Smallest redraw ratio for later draws (about 0.73–0.82). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Shell diameter (mean)
- What it is
- The diameter of the finished cylindrical cup measured to the middle of its wall, halfway between inside and outside.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger shell diameter needs a larger blank.
- Get it right
- Use the mean diameter: inside diameter plus one wall thickness, or outside diameter minus one.
What this means: Shell height
- What it is
- The height of the shell wall from the bottom to the top edge, or to the flange face if the shell has a flange.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A taller shell needs a larger blank and is more likely to need more draws.
- Get it right
- Measure to the flange face, not the top of the flange, for a flanged shell.
What this means: Bottom corner radius
- What it is
- The radius of the curved corner where the shell wall meets the bottom, measured on the inside.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger corner radius slightly reduces the blank diameter.
- Get it right
- This is a radius, not a diameter.
What this means: Flange outside diameter (0 = no flange)
- What it is
- The outside diameter of the flat flange around the top of the shell, for a flanged shell.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger flange needs a larger blank.
- Get it right
- Leave it at 0 for a plain cup; any other value must be larger than the shell diameter.
What this means: Material thickness
- What it is
- The thickness of the sheet the shell is drawn from.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- First-draw force rises in direct proportion.
- Get it right
- Thickness is used for the draw force only; the blank formula assumes it does not change.
What this means: Tensile strength
- What it is
- The ultimate tensile strength of the sheet, from its mill certificate or material specification.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 350 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- First-draw force rises in direct proportion.
- Get it right
- Use the value for the temper you will draw, as annealed and hard tempers differ.
What this means: Limiting first drawing ratio d ÷ D
- What it is
- The smallest ratio of first-draw cup diameter to blank diameter your material can achieve in one draw without tearing, from drawing ratio tables for its relative thickness.
- Units and format
- Enter a plain number with no unit. The form accepts 0.3 to 0.95. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.55 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller limit allows a deeper first draw and can reduce the number of draws.
- Get it right
- Enter a ratio below one (cup diameter divided by blank diameter), not its inverse.
What this means: Limiting redrawing ratio
- What it is
- The smallest ratio of new diameter to previous diameter achievable in each redraw after the first, from drawing ratio tables.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 0.98. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.78 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller limit reduces the estimated number of draws.
- Get it right
- Enter a ratio below one; redraws usually reduce less than the first draw.
Method and formulas
- D = √(d_f² + 4 d h − 0.5 r d), with d_f = flange diameter (or d for a plain shell).
- First drawing ratio m = d ÷ D; one draw if m ≥ the limiting ratio.
- Further draws reduce the diameter by the redraw ratio each time.
- First-draw force ≈ π d₁ t UTS (D ÷ d₁ − 0.7), with d₁ the first-draw diameter.
- Example: a 60 × 50 mm cup needs a 124.42 mm blank and 2 draw(s).
Limitations
- Thin-wall, constant-thickness approximation; trim allowance (often 3–5 mm on the diameter) must be added.
- Corner radius correction is approximate.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size blanks for drawn cups and cans
- Plan the number of drawing operations
- Estimate first-draw press force
Who it is for
- Fabrication supervisors
- Manufacturing engineers
- Estimators
What you get
- Blank diameter
- First drawing ratio
- Estimated number of draws
- First-draw force
Interpreting the result
- Add trim allowance and confirm with a trial draw.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1353–1360. Topic reference; no source tables or recommended settings are reproduced.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.