BIZOMAT MAKEOS · Fabrication
Deep Drawing Plan (Blank, Draws, Forces and Press)
What blank does this drawn cup need, how many draws will it take, and what punch and blank-holder forces must the press supply?
Plan for drawing a cylindrical shell: blank diameter from the shell diameter, height, corner radius and any flange (as the shell blank tool), the diameter after each draw from your first and later drawing ratios (as the draw reductions tool), the drawing force for each draw by the handbook-style formula F = π d t UTS (D ÷ d − 0.7) (as the deep draw force tool), the blank-holder force on the flange annulus at your holding pressure, and the press check for the heaviest draw.
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 finished shell. |
| Bottom corner radius | mm | Corner radius at the bottom of the shell. |
| Flange diameter (0 = none) | mm | Outside diameter of a flange left on the shell (0 for no flange). |
| Sheet thickness | mm | Sheet thickness. |
| Tensile strength | MPa | Tensile strength of the sheet. |
| First drawing ratio (d₁ ÷ D) | Largest reduction in the first draw as a ratio of cup to blank diameter (your value for the material; lower is more severe). | |
| Redrawing ratio (dₙ ÷ dₙ₋₁) | Ratio for each redraw (your value for the material and annealing). | |
| Blank-holder pressure | MPa | Pressure on the flange from the blank holder (your value; roughly 1–3 MPa for steel, less for aluminium). |
| Die entry radius | mm | Radius of the die entry, which sets the inner edge of the flange under the holder. |
| Press capacity | kN | Rated capacity of the press. |
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 drawn cup measured to the middle of the wall, halfway between the inside and outside surfaces. The draws continue until the cup reaches this size.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 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 gives a larger blank and higher drawing forces.
- Get it right
- Use the mean diameter, not the inside or outside: outside diameter minus one sheet thickness gives it.
What this means: Shell height
- What it is
- The height of the finished cup from the bottom to the top edge, before any trimming allowance you may add.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 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, so it can need more draws.
- Get it right
- Add any trim allowance to the height yourself; the blank is calculated for exactly this height.
What this means: Bottom corner radius
- What it is
- The radius of the corner between the cup bottom and its wall, as drawn on the part. The blank formula subtracts a small amount of material for it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 200 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 the bottom corner of the cup, not the die entry radius, which has its own input.
What this means: Flange diameter (0 = none)
- What it is
- The outside diameter of a flat flange left around the top of the cup. It replaces the shell diameter in the blank formula, so the blank includes the flange material.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 4000 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 increases the blank diameter and the area under the blank holder.
- Get it right
- Use 0 for a plain cup with no flange. Any flange must be larger than the shell diameter or the tool reports an error.
What this means: Sheet thickness
- What it is
- The thickness of the sheet the blank is cut from, which the drawing force formula treats as unchanged through the draws.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 20 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
- The drawing force rises in direct proportion to thickness.
- Get it right
- Measure the actual sheet with a micrometer; nominal gauge and real thickness can differ.
What this means: Tensile strength
- What it is
- The ultimate tensile strength of the sheet material, which sets how hard the punch must pull the metal through the die.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 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
- The drawing force for every draw is directly proportional to it.
- Get it right
- Take it from the mill certificate or material data sheet for the grade and temper you will draw.
What this means: First drawing ratio (d₁ ÷ D)
- What it is
- How far the first draw reduces the blank: the first cup diameter divided by the blank diameter. A smaller ratio means a deeper, more severe first draw.
- Units and format
- Enter a plain number with no unit. The form accepts 0.4 to 0.9. 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 ratio makes a smaller first cup, which can save draws but raises the first drawing force.
- Get it right
- Type it as a ratio below 1, not as a percentage. Use the value proven for your material, lubricant and tooling.
What this means: Redrawing ratio (dₙ ÷ dₙ₋₁)
- What it is
- The reduction applied in each redraw after the first: the new cup diameter divided by the previous one. The same ratio is used for every redraw.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 0.95. 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 ratio reaches the final diameter in fewer redraws.
- Get it right
- Redraw ratios are normally less severe than the first draw ratio; use the value for whether the part is annealed between draws.
What this means: Blank-holder pressure
- What it is
- The pressure the blank holder applies on the flat ring of sheet still outside the die, to stop wrinkles forming as the metal flows in.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0 MPa to 20 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.5 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The blank-holder force rises in direct proportion to this pressure.
- Get it right
- This is a contact pressure on the sheet, not the hydraulic or cushion pressure of the press.
What this means: Die entry radius
- What it is
- The radius on the edge of the die opening that the sheet bends over as it enters the die. In this tool it sets the inner edge of the ring held under the blank holder.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 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 die radius shrinks the held ring and lowers the blank-holder force.
- Get it right
- Do not confuse it with the bottom corner radius of the cup; this one is on the die.
What this means: Press capacity
- What it is
- The rated force the press can deliver at the working part of the stroke, compared with the heaviest draw plus its blank-holder force.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Check the press rating at the point in the stroke where drawing happens; many presses reach full rating only near the bottom.
Method and formulas
- Blank D = √(d_f² + 4 d h − 0.5 r d), with d_f the flange diameter or d (as the shell blank tool).
- Draw diameters: d₁ = max(m₁ D, d), then dₙ = max(m₂ dₙ₋₁, d) until the shell diameter is reached.
- Drawing force Fₙ = π dₙ t UTS (dₙ₋₁ ÷ dₙ − 0.7) with d₀ = D (as the deep draw force tool).
- Blank-holder force = p_BH × π ÷ 4 × [dₙ₋₁² − (dₙ + 2r_d)²] where positive; press load = drawing + holder force.
- Example: a 60 × 50 mm shell needs a 124.42 mm blank and 2 draws; the first draw takes 101.83 kN with the holder.
Limitations
- Thin-wall cups without ironing; ironing and tapered shells need other formulas.
- Drawing ratios are material- and lubricant-dependent: use your proven values.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan the draws and tooling for a drawn shell
- Choose a press for a deep-drawn part
- See how the drawing ratios change the number of draws
Who it is for
- Press tool designers
- Sheet-metal engineers
- Manufacturing engineers
What you get
- Blank diameter and first drawing ratio
- Diameter and force for each draw
- Blank-holder force and press check
Interpreting the result
- If the first draw is close to the press capacity, a lower blank-holder pressure or a larger first ratio helps.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1353–1361. 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.
Open the Deep Drawing Plan (Blank, Draws, Forces and Press) calculator