Polymer Processing & Battery Electrode Coating, Gaskell Two-Roll Calendering Nip
Polymer Two-Roll Calendering Gaskell Nip Force Formula
Calculate Post-Nip Exit Sheet Gauge 1.226*H0 (mm), Peak Hydrodynamic Nip Pressure (MPa), Gaskell Roll Separating Force (kN), and Two-Roll Viscous Drive Power (kW).
Set a calender nip gap to 0.60 mm and the PVC sheet exits 22.6% THICKER—while generating 188 tonnes of roll-bending separating force!
Rigid/flexible PVC film, rubber conveyor belting, and dry-process battery electrode lines squeeze high-viscosity melt (`mu` Pa·s) between counter-rotating heated steel rolls of Radius `R` (m), Surface Speed `U` (m/s), Face Width `W` (m), and Minimum Nip Gap `H_0` (`mm`, `h_0 = H_0 / 1,000` m). R. E. Gaskell’s classic **Lubrication-Approximation Calender Nip Theory** (deep flood-fed bank where dimensionless leave-off coordinate `lambda = 0.475`) proves two critical shop-floor phenomena: (1) Conservation of mass from peak-pressure stagnation to zero-pressure detachment swells **Sheet Exit Gauge `H_{exit} = (1 + lambda^2) * H_0 = 1.226 * H_0`** (`+22.6%` thicker than `H_0` even BEFORE viscoelastic die swell!), AND (2) **Peak Nip Pressure `P_{max} = (0.755 * mu * U * SQRT(R / h_0)) / h_0`** (`Pa`) and **Roll Separating Force `F_{sep} = (1.22 * mu * U * R * W) / h_0`** (`N`) explode inversely with `h_0`—bowing un-crowned steel rolls in the center ("oxbow" thick-center gauge defect) while consuming **Two-Roll Viscous Power `P_{drive} = 2.18 * mu * U^2 * SQRT(R / h_0) * W`** (`W`)!
Verify on a `1.60` m Wide PVC Flooring Calender Nip—Apparent_Melt_Viscosity `mu` = 4,200 Pa·s (B2), Chilled-Iron_Roll_Radius `R` = 0.30 m (`600` mm diameter, B3), Roll_Surface_Speed `U` = 0.45 m/s (B4), Minimum_Nip_Gap `H_0` = 0.60 mm (B5), and Sheet_Width `W` = 1.60 m (B6): Sheet Exit Gauge equals `0.736` mm (E2), Peak Nip Pressure hits `53.18` MPa (E3), Roll Separating Force reaches `1,844.6` kN (`188.1` tonnes-force requiring roll crossing or hydraulic roll-bending compensation! E4), and Viscous Nip Power equals `66.33` kW (E5)!
| Gaskell Calender Nip KPI (mu=4,200 Pa·s, R=0.30 m, U=0.45 m/s, W=1.60 m, H0=0.60 vs 0.35 mm) | Formula | Verified Output |
|---|---|---|
| Post-Nip Sheet Gauge H_exit (mm) | 1.226 * Min_Nip_Gap_H0_mm | 0.736 mm (0.429 mm @ H0=0.35 mm) |
| Peak Nip Pressure P_max (MPa) | (0.755 * mu * U * SQRT(R/h0)) / (h0 * 1e6) | 53.18 MPa (119.36 MPa @ H0=0.35 mm!) |
| Roll Separating Force F_sep (kN) | (1.22 * mu * U * R * W) / (h0 * 1000) | 1,844.6 kN (3,162.2 kN roll bow @ 0.35 mm!) |
| Two-Roll Viscous Power (kW) | (2.18 * mu * U^2 * SQRT(R/h0) * W) / 1000 | 66.33 kW (86.85 kW @ H0=0.35 mm) |
Gaskell Flood-Fed Newtonian Calendering Pressure, Separating Load & Power Formula
Validate `Viscosity mu > 10` Pa·s, `Roll_Radius R > 0.05` m, `Speed U > 0.01` m/s, `Nip_Gap H_0` in `(0.02, 20.0]` mm, and `Width W > 0.1` m!
=LET(mu_p, B2, rr_m, B3, us_m, B4, hz_m, B5 / 1000, wf_m, B6, IF(OR(mu_p <= 10, rr_m <= 0.05, us_m <= 0.01, B5 <= 0.02, B5 > 20, wf_m <= 0.1), "Invalid Calender Nip", ROUND((2.18 * mu_p * (us_m ^ 2) * SQRT(rr_m / hz_m) * wf_m) / 1000, 2)))Thin-Gauge 0.35 mm Nip Closing `h0^(-3/2)` Pressure Spike Check (Set Nip Gap B5 = 0.35 mm)
Screw down the hydraulic nip cylinders from `0.60` to `0.35` mm (`B5 = 0.35`): Exit Gauge E2 thins to `0.429` mm, Peak Pressure E3 more than DOUBLES (`h_0^{-1.5}` scaling!) to `119.36` MPa, and Separating Force E4 surges to `3,162.2` kN (`322` tonnes!)—requiring roll-crown adjustment so center thickness stays flat!
=IF(ISTEXT(E5), E5, LET(hz_m, B5 / 1000, ROUND((1.22 * B2 * B4 * B3 * B6) / (hz_m * 1000), 1)))Try the example
Use the original values or change them to test your understanding.