Sheet-Metal Deep Drawing, Battery Cans, Beverage Shells & Stamping Forming Limits
Deep-Drawing Cup Blank Diameter, Draw Ratio & Force Formula
Calculate Surface-Area-Conserved Circular Blank Diameter D_b (mm), Actual Draw Ratio beta = D_b / d_p, Siebel Punch Drawing Force (kN), and First-Draw LDR Tear Check.
Push Draw Ratio beta = Db / dp past the ~2.10 Limiting Drawing Ratio and the cup bottom tears clean off!
Deep-drawing a seamless cylindrical battery can, filter housing, or kitchenware shell of diameter d_p (mm) and wall height h (mm) conserves sheet surface area (neglecting minor wall ironing): PI()*(D_b^2)/4 = PI()*(d_p^2)/4 + PI()*d_p*h, yielding Initial Circular Blank Diameter D_b = SQRT((d_p^2) + 4 * d_p * h)! Pulling that wide flange radially inward into the die throat induces severe circumferential compression resisted by the cylindrical cup wall under axial tension—governed by Draw Ratio beta = D_b / d_p! Whenever beta exceeds the alloy’s Limiting Drawing Ratio LDR (~2.00–2.15 for drawing-quality steel/aluminum), radial flange drawing force F_draw = (PI() * d_p * T * UTS * (beta - 0.7)) / 1,000 kN exceeds the cup wall’s tensile fracture strength, ripping the bottom out unless split into a first draw + redraw sequence!
Try this 80 mm Automotive Filter Can First-Draw Audit—Punch_Diameter d_p = 80.0 mm (B2), Cup_Wall_Height h = 55.0 mm (B3), Sheet_Thickness T = 1.50 mm (B4), Drawing_Steel_UTS = 320.0 MPa (B5), and Alloy_Limiting_Draw_Ratio LDR = 2.10 (B6): Required Flat Blank Diameter hits SQRT(6,400 + 17,600) = 154.92 mm (E2), Actual Draw Ratio equals 154.92 / 80 = 1.936 (E3), Siebel Punch Drawing Force reaches 149.17 kN (E4), and E5 confirms "SINGLE-DRAW SAFE" (1.936 <= 2.10)! In a shared Arte Sheets stamping process sheet, a `suggester` can test stretching the can height to 85 mm in Suggest Mode and leave a whole-cell comment `@mentioning` the die designer when E5 flips to a two-stage redraw.
| Deep-Drawing Cup KPI (dp=80 mm, h=55 mm, T=1.5 mm, UTS=320 MPa, LDR=2.10) | Formula | Verified Output |
|---|---|---|
| Initial Blank Diameter Db (mm) | SQRT(dp^2 + 4 * dp * Cup_Height_h) | 154.92 mm (183.30 mm @ h = 85 mm) |
| Actual Draw Ratio beta (Db / dp) | Blank_Diameter_Db / Punch_Diam_dp | 1.936 (2.291 @ h = 85 mm!) |
| Siebel Punch Draw Force (kN) | (PI() * dp * T * UTS * (beta - 0.7))/1000 | 149.17 kN (191.97 kN @ h = 85 mm) |
| First-Draw Tear Limit Check | beta <= LDR_Max (2.10) | SINGLE-DRAW SAFE (REDRAW @ h=85!) |
Area-Conserved Blank Diameter, Draw Ratio & LDR Feasibility Formula
Validate d_p > 5 mm, Cup_Height h > 0, Thickness T > 0, UTS in [60, 1200] MPa, and LDR in [1.60, 2.50]!
=LET(dp_m, B2, ch_m, B3, th_m, B4, ut_m, B5, ld_r, B6, IF(OR(dp_m <= 5, ch_m <= 0, th_m <= 0, ut_m < 60, ut_m > 1200, ld_r < 1.6, ld_r > 2.5), "Invalid Deep-Draw Input", LET(db_m, SQRT((dp_m ^ 2) + 4 * dp_m * ch_m), bt_r, db_m / dp_m, IF(bt_r <= ld_r, "SINGLE-DRAW SAFE", "EXCEEDS LDR (NEEDS REDRAW)"))))Tall 85 mm Cylindrical Can Wall-Tear Redraw Check (Set Cup Height h = 85.0 mm)
Increase target Cup_Height B3 from 55.0 mm to 85.0 mm: Blank Diameter E2 grows to 183.30 mm and Actual Draw Ratio E3 climbs to 2.291 (> 2.10 LDR!), flipping E5 immediately to "EXCEEDS LDR (NEEDS REDRAW)" so tooling engineers add a redraw station before cutting steel!
=IF(ISTEXT(E2), E2, LET(db_m, SQRT((B2 ^ 2) + 4 * B2 * B3), bt_r, db_m / B2, ROUND((PI() * B2 * B4 * B5 * (bt_r - 0.7)) / 1000, 2)))Try the example
Use the original values or change them to test your understanding.