Polymer Sheet Processing, Vacuum/Pressure Thermoforming & Packaging Gauge Thinning
Vacuum Thermoforming Areal Draw Ratio & Wall Formula
Calculate Rectangular Mold Areal Draw Ratio Ra = A_mold / A_clamp, Volume-Conserved Average Part Wall Thickness t_avg (mm), Deepest Bottom-Corner Minimum Wall (mm), and Retained Corner Gauge (%).
Drawing a 4.5 mm ABS sheet into a deep tub thins average walls to 1.64 mm—and female mold corners down to 0.90 mm without plug-assist!
During single-sheet vacuum or pressure thermoforming, a heated thermoplastic sheet (`ABS`, `PETG`, `HDPE`, `HIPS`) of Initial Extruded Gauge `t_0` (mm) is locked around Clamping-Frame Footprint `A_clamp = L * W` (`mm²`) and stretched pneumatically against a 3D mold surface of Total Developed Area `A_mold = L * W + 2 * (L + W) * H` (`mm²` for a rectangular tub of depth `H`)! Because solid/rubbery polymer volume inside the clamp frame is strictly conserved (`A_clamp * t_0 = A_mold * t_avg`), **Areal Draw Ratio `R_a = A_mold / A_clamp = 1 + (2 * (L + W) * H) / (L * W)`** divides starting gauge down to **Mean Formed Wall `t_avg = t_0 / R_a`**! Worse yet, sheet touching the cold mold walls first freezes immediately while the remaining free bubble stretches into deep female corners—leaving Minimum Corner Gauge `t_corner = c_f * t_avg` (`c_f ≈ 0.45–0.65` straight vacuum vs `0.75+` syntactic-foam plug-assist)!
Verify on a 400 x 300 x 150 mm ABS Medical-Tray Female Mold—Clamp_Length `L` = 400.0 mm (B2), Clamp_Width `W` = 300.0 mm (B3), Cavity_Draw_Depth `H` = 150.0 mm (B4 -> Areal Draw Ratio `R_a = 2.750` in E2), Starting_Sheet_Gauge `t_0` = 4.50 mm (B5 -> Mean Part Wall `t_avg = 1.64` mm in E3), and Corner_Distribution_Factor `c_f` = 0.55 (B6): Thinnest Bottom-Corner Gauge equals `0.90` mm (E4 = `20.0%` of starting sheet thickness in E5)!
| Vacuum Thermoforming KPI (400x300 mm Clamp, Depth H=150 mm, t0=4.50 mm, cf=0.55) | Formula | Verified Output |
|---|---|---|
| Areal Draw Ratio Ra (Amold / Aclamp) | 1 + (2 * (L_mm + W_mm) * H_mm) / (L * W) | 2.750 (3.917 @ deep 250 mm tub!) |
| Volume-Conserved Mean Wall (mm) | Starting_Gauge_t0_mm / Areal_Draw_Ra | 1.64 mm (1.15 mm @ deep 250 mm tub) |
| Minimum Bottom-Corner Wall (mm) | Mean_Wall_mm * Corner_Factor_cf | 0.90 mm (0.63 mm paper-thin @ 250 mm!) |
| Retained Corner Gauge (%) | (Corner_Wall_mm / Starting_t0_mm) * 100 | 20.0% (14.0% @ deep 250 mm tub) |
Incompressible Sheet Areal Draw Ratio & Corner Wall-Thinning Formula
Validate `Clamp_Length L > 10` mm, `Clamp_Width W > 10` mm, `Draw_Depth H > 0` mm, `Starting_Gauge t_0 > 0.1` mm, and `Corner_Factor c_f` in `(0.15, 1.0]`!
=LET(ln_m, B2, wd_m, B3, ht_m, B4, tz_m, B5, cf_r, B6, ad_r, 1 + (2 * (ln_m + wd_m) * ht_m) / (ln_m * wd_m), tc_m, (tz_m / ad_r) * cf_r, IF(OR(ln_m <= 10, wd_m <= 10, ht_m <= 0, tz_m <= 0.1, cf_r <= 0.15, cf_r > 1), "Invalid Thermoforming Input", ROUND((tc_m / tz_m) * 100, 1)))Deep-Draw 250 mm Tote Bin Corner Webbing/Tearing Check (Set Cavity Depth H B4 = 250.0 mm)
Deepen the mold cavity from `150.0` to `250.0` mm (`B4 = 250`): Areal Draw Ratio E2 jumps to `3.917`, Average Wall E3 drops to `1.15` mm, and Unassisted Bottom Corners E4 thin down to `0.63` mm (`14.0%` retained in E5)—confirming why `R_a > 3.0` requires syntactic-foam plug-assist pre-stretching or starting gauge `t_0 >= 6.0` mm!
=IF(ISTEXT(E5), E5, LET(ad_r, 1 + (2 * (B2 + B3) * B4) / (B2 * B3), ROUND((B5 / ad_r) * B6, 2)))Try the example
Use the original values or change them to test your understanding.