Deep Drawing Calculator: Blank Diameter D0, LDR & Press Tonnage
By surface-area conservation (Romanowski / DIN 8584-3), the flat blank diameter for a cylindrical cup with punch corner radius rp is D0 = √(dp² + 4dph − 1.72dprp). Drawing an Ø60 × 45 mm cup (rp = 4 mm, t = 1.5 mm, DC04 steel) requires a 118.24 mm blank (β = 1.971) and 133.3 kN (15.0 US tons) total press force.
Cylindrical Deep Drawing Blank Diameter, LDR & Press Tonnage Calculator
Compute corner-corrected flat blank diameter D0 = √(dp² + 4dph − 1.72dprp), actual draw ratio β = D0/dp vs material LDR, Siebel punch drawing force, blankholder cushion load, and Oehler die clearance.
How Do You Calculate the Flat Blank Diameter (D_0) and Limiting Draw Ratio (LDR)?
In cylindrical sheet-metal deep drawing, a circular blank of diameter D0 is pulled radially inward over a die entry radius rd by a punch of diameter dp. Because plastic forming conserves metal volume and approximately conserves mid-surface area, equating the flat circle area (π/4)D0² to the sum of the flat bottom disk, toroidal corner fillet, and vertical wall yields the Romanowski equation: D0 = √(dp² + 4dph − 1.72dprp). Omitting the corner-radius term (as crude sharp-corner formulas do) overestimates our Ø60 × 45 mm blank by more than 3.4 mm (120.00 mm vs. 118.24 mm), adding unnecessary flange area that increases drawing tonnage and tearing risk.
Once D0 is known, divide by punch diameter to find the actual Draw Ratio β = D0 / dp (or North American percent reduction %R = 100(1 − dp/D0)). Every alloy tested under ISO 6892-1 (Metallic Tensile Testing) has a maximum safe first-draw ratio (Limiting Draw Ratio, LDR, typically 1.88 to 2.15) before the axial tensile stress in the vertical cup wall exceeds the ultimate strength of the sheet and tears the bottom off the punch, as documented in the Schuler Metal Forming Handbook, Machinery's Handbook (31st Ed., Industrial Press), and The Fabricator's deep drawing guidelines.
| Cup Ø dp × Height h | Blank Diameter D0 | Draw Ratio β (% Red.) | DC04 Steel Total Force | 304 Stainless Total Force | Die Clearance ud |
|---|---|---|---|---|---|
| Ø40 × 25 mm (t=1, rp=3) | Ø73.42 mm (2.891") | β = 1.835 (45.5%) | 52.1 kN (5.9 US tons) | 97.5 kN (11.0 US tons) | 1.22 mm/side |
| Ø50 × 35 mm (t=1.2, rp=4) | Ø95.66 mm (3.766") | β = 1.913 (47.7%) | 84.5 kN (9.5 US tons) | 157.7 kN (17.7 US tons) | 1.44 mm/side |
| Ø60 × 45 mm (t=1.5, rp=4) | Ø118.24 mm (4.655") | β = 1.971 (49.3%) | 133.3 kN (15.0 US tons) | 248.5 kN (27.9 US tons) | 1.77 mm/side |
| Ø80 × 60 mm (t=1.5, rp=5) | Ø157.81 mm (6.213") | β = 1.973 (49.3%) | 186.5 kN (21.0 US tons) | 343.6 kN (38.6 US tons) | 1.77 mm/side |
| Ø100 × 75 mm (t=2, rp=6) | Ø197.37 mm (7.771") | β = 1.974 (49.3%) | 308.0 kN (34.6 US tons) | 568.8 kN (63.9 US tons) | 2.31 mm/side |
| Ø120 × 95 mm (t=2.5, rp=8) | Ø241.51 mm (9.508") | β = 2.013 (50.3%) | 474.1 kN (53.3 US tons) | 876.5 kN (98.5 US tons) | 2.85 mm/side |
How Are Siebel Punch Force, Blankholder Pressure, and Oehler Die Clearance Sized?
Following Siebel's DIN 8584-3 equation, peak punch drawing force is Fd = π × dp × t × UTS × ((β / ηdef) − 0.7), where deformation efficiency ηdef ≈ 0.72 accounts for circumferential hoop compression in the flange plus friction and unbending over the die radius. Simultaneously, a nitrogen or hydraulic die cushion must apply specific pressure pbh (1.4 to 3.5 MPa, converted in SI units per NIST SI Units Reference and NIST Special Publication 811) across the outer flange annulus to suppress radial wrinkling. Finally, because hoop compression thickens the outer rim of the blank, die radial clearance per side must be enlarged via Oehler's formula ud = t + ck√(10t) so the thickened upper wall clears the die throat without galling or ironing.
| Sheet Metal Alloy | Tensile UTS | Limiting Draw Ratio (LDR) | Blankholder Pressure pbh | Die Clearance Formula | Ref Force (Ø60×45×1.5) |
|---|---|---|---|---|---|
| DC04 / 1008 deep-draw steel | 320 MPa | βmax ≤ 2.05 (51.2% max 1st draw) | 2.5 MPa | t + 0.07√(10t) (1.77 mm at t=1.5) | 133.3 kN (15.0 US tons) |
| SAE 1018 / CS mild steel | 410 MPa | βmax ≤ 1.90 (47.4% max 1st draw) | 2.8 MPa | t + 0.08√(10t) (1.81 mm at t=1.5) | 167.9 kN (18.9 US tons) |
| 304 austenitic stainless | 620 MPa | βmax ≤ 2.10 (52.4% max 1st draw) | 3.5 MPa | t + 0.10√(10t) (1.89 mm at t=1.5) | 248.5 kN (27.9 US tons) |
| 5052-O / 3003-O aluminum | 195 MPa | βmax ≤ 1.88 (46.8% max 1st draw) | 1.4 MPa | t + 0.06√(10t) (1.73 mm at t=1.5) | 80.4 kN (9.0 US tons) |
| C260 cartridge brass | 345 MPa | βmax ≤ 2.15 (53.5% max 1st draw) | 2.2 MPa | t + 0.06√(10t) (1.73 mm at t=1.5) | 140.1 kN (15.8 US tons) |
Worked Examples: Single-Stage Cup vs. Multi-Stage Redraw Planning
Worked Example 1 (Ø60 × 45 mm Cup in 1.50 mm DC04 Steel): With dp = 60.0 mm, h = 45.0 mm, and rp = 4.0 mm in DC04 steel (LDR = 2.05), the developed blank is 118.24 mm (4.655 in) and the draw ratio is β = 1.971 (49.3% reduction). Because 1.971 ≤ 2.05, this shell forms in a single draw stage, requiring Fd = 115.0 kN punch force plus Fbh = 18.4 kN cushion force (total 133.3 kN / 15.0 US tons) with radial die clearance 1.77 mm.
Worked Example 2 (Ø50 × 65 mm Deep Can Requiring Redraw): Changing the shell to dp = 50.0 mm and h = 65.0 mm (rp = 4.0 mm) yields D0 = 123.09 mm and β = 2.462 > 2.05 (needs_redraw = True)—which requires a 2-stage draw. Before stamping, size the blanking die on our sheet metal punch & blanking tonnage calculator, check flange bends on the press brake tonnage chart and bend deduction K-factor calculator, and weigh coil stock on the metal stock weight calculator.
Cite this page
ToolSpecVault Engineering Data Team. (2026, October 29). Deep Drawing Calculator: Blank Diameter D0, LDR & Press Tonnage. ToolSpecVault. https://toolspecvault.com/sheet-metal-deep-drawing-blank-diameter-tonnage-calculator/