Plastics Packaging, HDPE Blow Molding & Viscoelastic Die Swell
Blow Molding Parison Swell, Blow-Up Ratio & Wall Formula
Calculate Swollen Parison Diameter D_p (mm), Swollen Parison Wall Thickness t_p (mm), True Parison Blow-Up Ratio (BUR), and Finished Bottle Wall Thickness t_wall (mm).
Viscoelastic Barus die swell thickens AND widens the HDPE parison BEFORE air inflation thins it by 1 / BUR!
When high-density polyethylene (HDPE) exits an annular blow-molding die of mandrel-bushing mean diameter D_die (mm) and annular die gap t_gap (mm), elastic normal-stress recovery (Barus effect) causes the free-hanging tubular parison to expand radially by Diameter Swell Ratio S_d = D_parison / D_die (typically 1.20–1.40) AND thicken radially by Thickness Swell Ratio S_t = t_parison / t_gap (typically 1.40–1.80)! Neglecting S_d and S_t by computing Blow-Up Ratio directly from D_mold / D_die mispredicts container top-load crush wall thickness by 30%–60%! True Parison Blow-Up Ratio is BUR = D_mold / (D_die * S_d), and conserving annular polymer cross-section during radial inflation yields Average Finished Bottle Wall Thickness t_wall = t_parison / BUR = (t_gap * S_t * D_die * S_d) / D_mold!
Verify on an 80.0 mm Diameter HDPE Detergent Bottle—Annular_Die_Gap t_gap = 1.20 mm (B2), Die_Mean_Diameter D_die = 25.0 mm (B3), Diameter_Swell_Ratio S_d = 1.28 (B4 -> Swollen Parison Diameter = 32.00 mm in E2), Thickness_Swell_Ratio S_t = 1.50 (B5 -> Swollen Parison Wall = 1.80 mm in E3), and Bottle_Mold_Diameter D_mold = 80.0 mm (B6): True Parison Blow-Up Ratio hits 80.0 / 32.0 = 2.50 (E4, safely inside the 2.0–3.5 HDPE processing window), and Finished Bottle Wall Thickness equals 1.80 / 2.50 = 0.720 mm (E5)!
| HDPE Blow-Molding KPI (tgap=1.2 mm, Ddie=25 mm, Sd=1.28, St=1.50, Dmold=80 mm) | Formula | Verified Output |
|---|---|---|
| Swollen Parison Diameter Dp (mm) | Die_Diameter_mm * Diameter_Swell_Sd | 32.00 mm |
| Swollen Parison Wall tp (mm) | Die_Gap_mm * Thickness_Swell_St | 1.80 mm |
| True Parison Blow-Up Ratio (BUR) | Mold_Diameter_mm / (D_die * S_d) | 2.50 (3.00 @ Dmold = 96 mm) |
| Finished Bottle Wall twall (mm) | (t_gap * S_t) / True_BUR | 0.720 mm (0.600 @ Dmold = 96 mm) |
Viscoelastic Parison Swell & Finished Container Wall Thickness Formula
Validate Die_Gap > 0, Die_Diameter > 2 * Die_Gap, S_d >= 1.0, S_t >= 1.0, and Mold_Diameter > Swollen_Parison_Diameter (BUR > 1.0)!
=LET(tg_m, B2, dd_m, B3, sd_r, B4, st_r, B5, dm_m, B6, IF(OR(tg_m <= 0, dd_m <= 2 * tg_m, sd_r < 1, st_r < 1, dm_m <= dd_m * sd_r), "Invalid Parison Input", LET(dp_s, dd_m * sd_r, tp_s, tg_m * st_r, bu_r, dm_m / dp_s, ROUND(tp_s / bu_r, 3))))Wider Bottle Mold Corner-Thinning Check (Increase Mold Diameter D_mold to 96.0 mm)
Widen Bottle_Mold_Diameter B6 from 80.0 mm to 96.0 mm using the same die tooling: True Blow-Up Ratio E4 climbs from 2.50 to 3.00, thinning Finished Bottle Wall E5 from 0.720 mm down to 0.600 mm (requiring programmable axial parison die-gap profiling to protect pinch-off corners)!
=IF(ISTEXT(E5), E5, ROUND(B6 / (B3 * B4), 2))Try the example
Use the original values or change them to test your understanding.