Bulk Solids Processing, CEMA Screw/Auger Conveyors, Grain & Cement Silo Feeding
Screw Conveyor Flight Pitch & Trough Loading Capacity Formula
Calculate Net Annular Flight Area (m²), Inclined Volumetric Throughput Q_v (m³/h), Horizontal Zero-Incline Mass Rate (t/h), and Derated Inclined Mass Capacity Q_m (t/h).
Never flood a horizontal U-trough auger to 100% fill—above 30%–45% trough loading, powder packs against intermediate hanger bearings!
Sizing a helicoid screw (auger) conveyor as `PI()/4 * D_s^2 * Pitch * RPM` makes three classic plant-engineering errors: (1) it forgets to subtract the central Torque Pipe Shaft cross-section `d_p^2`, leaving Net Annular Flight Area `A_net = (PI()/4) * (D_s^2 - d_p^2)` (m²); (2) CEMA Trough Loading Factor `phi` restricts free-flowing grain to `0.45` (`45%`), sluggish flour/pellets to `0.30` (`30%`), and abrasive cement clinker/silica sand to `0.15` (`15%`) so solids stay well below intermediate hanger bearings!; and (3) tilting an auger uphill introduces fallback slip over the flight crest, multiplying output by Inclination Derating Factor `C_i` (`1.00` horizontal, `~0.85` at `10°`, `~0.55` at `20°`): `Q_v = 60 * A_net * S * N * phi * C_i` m³/h!
Verify on a 300 mm (`12"` Metric) Grain/Pellet Auger—Screw_OD `D_s` = 0.300 m (B2), Center_Pipe_OD `d_p` = 0.089 m (B3 -> Annular Area `A_net = 0.0645` m² in E2), Standard_Pitch `S` = 0.300 m (B4), Auger_Speed `N` = 65.0 RPM (B5), CEMA_Trough_Loading `phi` = 0.30 (`30%`, B6), Bulk_Density `rho_b` = 0.75 t/m³ (B7), and `10°` Incline_Factor `C_i` = 0.85 (B8): Inclined Volumetric Rate hits `19.23` m³/h (E3), Horizontal Mass Baseline equals `16.97` t/h (E4), and Derated `10°` Inclined Mass Capacity equals `14.42` t/h (E5)!
| CEMA Auger Capacity KPI (Ds=0.30 m, dp=0.089 m, Pitch=0.30 m, 65 RPM, 30% Fill) | Formula | Verified Output |
|---|---|---|
| Net Annular Flight Area (m²) | (PI() / 4) * ((Ds^2) - (dp^2)) | 0.0645 m² |
| Inclined Volumetric Rate (m³/h) | 60 * A_net * Pitch * RPM * Fill * Ci | 19.23 m³/h (9.62 m³/h @ 15% abrasive fill) |
| Horizontal Mass Rate (Ci=1, t/h) | 60 * A_net * Pitch * RPM * Fill * rho | 16.97 t/h (15.27 t/h @ cement 1.35 t/m³) |
| Derated Inclined Capacity (t/h) | Inclined_Volumetric_m3_hr * Bulk_rho | 14.42 t/h (12.98 t/h @ cement 15% fill) |
CEMA Annular Screw Displacement, Trough Fill & Inclination Derating Formula
Validate `Screw_OD > Pipe_OD > 0`, `Flight_Pitch > 0`, `RPM` in `(0, 300]`, `Trough_Loading phi` in `[0.10, 0.95]` (`0.15–0.45` for U-troughs, up to `0.90` only for shrouded flood-fed tubular feeder screws without hanger bearings!), `Bulk_Density > 0`, and `Incline_Derating` in `(0, 1]`!
=LET(ds_m, B2, dp_m, B3, pt_m, B4, nr_m, B5, ld_f, B6, rb_t, B7, ci_f, B8, IF(OR(dp_m <= 0, ds_m <= dp_m, pt_m <= 0, nr_m <= 0, nr_m > 300, ld_f < 0.1, ld_f > 0.95, rb_t <= 0, ci_f <= 0, ci_f > 1), "Invalid Auger Input", LET(an_m, (PI() / 4) * ((ds_m ^ 2) - (dp_m ^ 2)), qv_h, 60 * an_m * pt_m * nr_m * ld_f * ci_f, ROUND(qv_h * rb_t, 2))))Abrasive Portland Cement 15% Trough-Loading Restriction Check (Set Fill = 0.15 & Density = 1.35 t/m³)
Switch from free-flowing pellets to abrasive Portland cement (`rho_b` B7 = 1.35 t/m³), forcing CEMA `15%` trough loading (`phi` B6 = 0.15) to protect hanger bushings: Volumetric Throughput E3 halves to `9.62` m³/h, Horizontal Tonnage E4 adjusts to `15.27` t/h, and Inclined Capacity E5 settles at `12.98` t/h!
=IF(ISTEXT(E5), E5, LET(an_m, (PI() / 4) * ((B2 ^ 2) - (B3 ^ 2)), ROUND(60 * an_m * B4 * B5 * B6 * B8, 2)))Try the example
Use the original values or change them to test your understanding.