Bulk Material Handling, CEMA Belt Conveyors, Mining & Aggregate Plant Engineering
Belt Conveyor Bulk Tonnage Capacity & Drive Power Formula
Calculate CEMA Mass Conveying Capacity Q_m (t/h), Potential Gravity Lift Power P_lift (kW), Horizontal Idler Rolling Friction Power P_fric (kW), and Required Drive Motor Shaft Power (kW).
Switching a belt conveyor from crushed limestone to dense iron-ore concentrate trips the gearbox breaker even at identical volumetric belt profile!
On a 3-roll troughed belt conveyor carrying CEMA Surcharge Cross-Sectional Ribbon Area `A_b` (m², set by belt width, troughing idler angle, and material surcharge angle) at Belt Speed `v` (m/s), Volumetric Capacity `Q_v = 3,600 * A_b * v` (m³/h) stays fixed—whereas Mass Tonnage Rate `Q_m = 3,600 * A_b * v * rho_b` (metric tons/hr, with Bulk Density `rho_b` in t/m³) AND Drive Power scale directly with material mass! Neglecting empty-belt tare and skirtboard drag for preliminary sizing, Lifting Material Through Net Elevation `H` (m) requires Gravity Potential Power `P_lift = (dot_m * g * H) / 1,000` kW (where `dot_m = A_b * v * rho_b * 1,000` kg/s and `g = 9.80665` m/s²), while Carrying Material Horizontally Over Projected Length `L` (m) against Artificial Idler Friction Factor `f` (~0.020–0.030) consumes `P_fric = (f * (A_b * rho_b * 1,000) * L * g * v) / 1,000` kW, divided by Reducer/Drive Efficiency `eta`!
Verify on a 1,000 mm Quarry Inclined Belt Conveyor—Troughed_Ribbon_Area `A_b` = 0.115 m² (B2), Belt_Speed `v` = 2.40 m/s (B3), Crushed_Stone_Bulk_Density `rho_b` = 1.60 t/m³ (B4 -> Mass Capacity = `1,589.76` t/h in E2), Horizontal_Center_Length `L` = 180.0 m (B5), Net_Vertical_Lift `H` = 18.0 m (B6), Idler_Friction `f` = 0.025 (B7), and Gearbox_Efficiency `eta` = 0.88 (B8): Gravity Lift Power equals `77.95` kW (E3), Material Friction Power equals `19.49` kW (E4), and Required Motor Shaft Power hits `110.73` kW (E5)!
| CEMA Belt Conveyor KPI (Ab=0.115 m², v=2.4 m/s, rho=1.60 t/m³, L=180 m, H=18 m) | Formula | Verified Output |
|---|---|---|
| Mass Tonnage Capacity Qm (t/h) | 3600 * Belt_Area_m2 * Speed_m_s * rho_t_m3 | 1,589.76 t/h (2,384.64 @ 2.40 t/m³ ore) |
| Gravity Elevation Power Plift (kW) | (Ab * v * rho*1000 * 9.80665 * H) / 1000 | 77.95 kW (116.93 kW @ 2.40 t/m³ ore) |
| Material Rolling Friction Power (kW) | (f * Ab * rho*1000 * L * 9.80665 * v)/1000 | 19.49 kW (29.23 kW @ 2.40 t/m³ ore) |
| Required Motor Shaft Power (kW) | (Plift_kW + Pfric_kW) / Drive_Efficiency | 110.73 kW (166.09 kW trips 132 kW drive!) |
CEMA Troughed Belt Tonnage, Elevation Lift & Idler Friction Power Formula
Validate `Belt_Area > 0`, `Belt_Speed` in `(0, 10]` m/s, `Bulk_Density > 0` t/m³, `Length > 0` m, `Lift >= 0` m (non-regenerative uphill/horizontal conveyor), `Friction f` in `[0.010, 0.100]`, and `Efficiency` in `(0, 1]`!
=LET(ab_m, B2, vb_s, B3, rb_t, B4, lh_m, B5, hv_m, B6, fr_i, B7, ef_d, B8, IF(OR(ab_m <= 0, vb_s <= 0, vb_s > 10, rb_t <= 0, lh_m <= 0, hv_m < 0, fr_i < 0.01, fr_i > 0.1, ef_d <= 0, ef_d > 1), "Invalid Conveyor Input", LET(ms_k, ab_m * vb_s * rb_t * 1000, pw_l, (ms_k * 9.80665 * hv_m) / 1000, pw_f, (fr_i * (ab_m * rb_t * 1000) * lh_m * 9.80665 * vb_s) / 1000, ROUND((pw_l + pw_f) / ef_d, 2))))Dense Iron-Ore Concentrate Campaign Overload Check (Set Bulk Density rho_b = 2.40 t/m³)
Feed dense iron-ore concentrate (`rho_b` B4 = 2.40 t/m³) at the same `0.115` m² belt profile: Tonnage E2 surges `50%` to `2,384.64` t/h, Lift Power E3 climbs to `116.93` kW, Friction Power E4 reaches `29.23` kW, and Required Shaft Power E5 jumps to `166.09` kW—explaining why a `132` kW limestone motor trips on thermal overload unless feeder gate area `A_b` is choked back!
=IF(ISTEXT(E5), E5, ROUND(3600 * B2 * B3 * B4, 2))Try the example
Use the original values or change them to test your understanding.