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Sheet-Metal Stamping & Press-Shop Die Cushions, Siebel Blank-Holder Pressure & LDR Gate

Deep-Drawing LDR & Siebel Blank-Holder Cushion Formula

Calculate First-Draw Ratio Beta (D0 / dp), Siebel Anti-Wrinkling Blank-Holder Pressure pbh (MPa), Required Nitrogen/Pneumatic Die-Cushion Force (kN), and LDR Single-Stage Gate.

Too little blank-holder cushion pressure buckles cup flanges into radial wrinkles—too much or exceeding beta = 2.10 LDR rips the bottom right off the punch nose!

Drawing a flat sheet-metal disc (`Blank Diameter D_0` mm, `Thickness t` mm, `Ultimate Tensile Strength UTS` MPa) into a seamless cup over **Punch Diameter `d_p`** (`mm` with Die-Throat Clearance `d_d ~= d_p + 2.5 * t`) subjects the shrinking outer flange to intense circumferential hoop compression! **Erich Siebel (`1954`)** quantified the **Minimum Anti-Wrinkling Blank-Holder Contact Pressure `p_{bh} = k * ((beta - 1)^2 + (d_p / (200 * t))) * UTS`** (`MPa`, where **Draw Ratio `beta = D_0 / d_p`** and **`k ~= 0.0020–0.0030`**), which acts across Initial Annular Binder Ring Area `A_{bh} = (pi / 4) * (D_0^2 - (d_p + 2.5 * t)^2)` (`mm²`) to set **Die-Cushion Clamp Force `F_{bh} = (p_{bh} * A_{bh}) / 1,000`** (`kN`)! Even with ideal binder lubrication, deep-drawing quality steels (`DDQ`, normal anisotropy `r_m ~= 1.6–1.8`) hit **Limiting Draw Ratio `LDR = beta_{max} ~= 2.10`**—beyond which radial flange drawing force exceeds cup-wall tensile strength and **tears the punch bottom clean off** unless split into a two-stage first draw + redraw!

Verify on a `100` mm Diameter Automotive Filter Housing Cup—Blank_Diameter `D_0` = 195 mm (B2), Punch_Diameter `d_p` = 100 mm (B3), Sheet_Thickness `t` = 1.20 mm (B4), Steel_`UTS` = 360 MPa (B5), and Siebel_Constant `k` = 0.0025 (B6): First-Draw Ratio `beta` equals **`1.95`** (E2), Siebel Blank-Holder Pressure equals **`1.187` MPa** (E3), Required Die-Cushion Force equals **`25.56` kN** (`2.61` tf, E4), passing `"SINGLE-STAGE DRAW SAFE (<=2.10)"` in E5!

Siebel Cushion & LDR Gate KPI (dp=100 mm, t=1.2 mm, UTS=360 MPa, k=0.0025)FormulaVerified Output
First-Stage Draw Ratio BetaBlank_Diameter_D0_mm / Punch_Diameter_dp_mm1.95 (2.35 @ 235 mm oversize blank!)
Siebel Holder Pressure pbh (MPa)k * (((beta - 1) ^ 2) + (dp / (200 * t))) * UTS1.187 MPa (2.015 MPa flange friction)
Die-Cushion Clamp Force (kN)(pbh * (PI/4) * (D0^2 - (dp + 2.5*t)^2)) / 100025.56 kN (70.62 kN cushion load)
Limiting Draw Ratio GateIF(beta <= 2.10, "SINGLE-STAGE...", "EXCEEDS LDR...")SINGLE-STAGE DRAW SAFE (<=2.10)

Erich Siebel (1954) Anti-Wrinkling Binder Pressure & 2.10 LDR Redraw Formula

Validate `Punch_Diameter d_p` in `[10, 1,500]` mm, `Blank_Diameter D_0` in `(1.05 * d_p, 3.50 * d_p]`, `Sheet_Thickness t` in `[0.1, 15.0]` mm, `UTS` in `[80, 1,500]` MPa, and `Siebel_Factor k` in `[0.001, 0.006]`!

=LET(dz_m, B2, dp_m, B3, th_m, B4, ut_m, B5, sk_f, B6, IF(OR(dp_m < 10, dp_m > 1500, dz_m <= dp_m * 1.05, dz_m > dp_m * 3.5, th_m < 0.1, th_m > 15, ut_m < 80, ut_m > 1500, sk_f < 0.001, sk_f > 0.006), "Invalid Draw Input", ROUND(dz_m / dp_m, 2)))

Taller Cup Blank (`D_0 = 235` mm -> `beta = 2.35 > 2.10`) Bottom-Split Redraw Check

Enlarge the blank to `B2 = 235` mm to form a deeper housing in one hit: Draw Ratio `beta` E2 climbs to **`2.35`**, Cushion Force E4 nearly triples to **`70.62` kN** (`2.015` MPa in E3), and E5 flags **`"EXCEEDS LDR — REDRAW REQUIRED"`** (`use a 125 mm first draw @ beta1 = 1.88 followed by a 100 mm redraw @ beta2 = 1.25`)!

=IF(ISTEXT(E2), E2, LET(bt_r, B2 / B3, pb_m, B6 * (((bt_r - 1) ^ 2) + (B3 / (200 * B4))) * B5, ROUND((pb_m * (PI() / 4) * ((B2 ^ 2) - ((B3 + 2.5 * B4) ^ 2))) / 1000, 2)))

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