Belt Feeder Load, Pull and Power
The belt pull and drive power a feeder needs to drag material out from under a loaded hopper.
Example
You enter
- Hopper outlet slot width B (in) 36
- Outlet slot length along the belt L (ft) 12
- Bulk density (lb/cu ft) 100
- Effective angle of internal friction (deg) 45
- Surcharge factor q, filled from empty 2.5
- Surcharge factor q, flowing 1
- Belt speed (fpm) 60
- Skirt and belt resistance, initial (lb, 0 to skip) 0
- Skirt and belt resistance, flowing (lb, 0 to skip) 0
- Drive efficiency (0 to 1) 0.9
You get
- Load initial (lb) 27000
- Pull initial (lb) 15273.5
- Pull flow (lb) 6109.4
- Drive power initial (hp) 30.856
- Drive power flow (hp) 12.342
Checked against published worked examples from: Bulk Solids Handling (Trans Tech Publications).
Details, formula, and sources
Scopeat the first start after filling and while running. The hopper load is the surcharge factor times bulk density times slot length times slot width squared, and shearing it takes 0.8 times the sine of the internal friction angle of that load. A 36 in by 12 ft slot under 100 lb/cu ft material with surcharge factors of 2.5 and 1.0 needs 15,270 lb of pull to start and 6,110 lb to run. The surcharge factors are entered from the hopper analysis. The feeder manufacturer and a flow-properties test govern.
Formula or tableFeeder load Q = q x bulk weight density x L x B^2 for a plane-flow slot outlet B wide and L long, with q the nondimensional surcharge factor, one value for the initial (filled from empty) condition and a smaller one for flow. Force to shear the material F = mu Q, mu = 0.8 sin(effective angle of internal friction). Shear power = F v; drive power = (F + other resistances) x v / efficiency. In US units: lb/cu ft x ft x ft^2 = lb; hp = lb x fpm / 33,000.
Source and editionA. W. Roberts and K. S. Manjunath, Wall Pressure-Feeder Load Interactions in Mass Flow Hopper/Feeder Combinations, Part II, Bulk Solids Handling vol. 6 no. 5, October 1986: Eqs. 21, 30, 32 and 42, and conclusion 5 for the 0.8 sin value. The surcharge-factor expressions (its Eqs. 24 to 29, after McLean and Arnold) are not reproduced; q is entered.
Free accessFree at bulk-online.com (BSH_1986_05_009.pdf). Its design example, section 12.2 (B 1.50 m, L 5.00 m, 0.95 t/m3, 50 degrees, q 2.54 and 1.05, 0.50 m/s, 90% efficiency), prints loads of 265.89 and 109.84 kN, shear forces of 162.94 and 67.31 kN, shear powers of 81.47 and 33.66 kW and total powers of 127.63 and 81.61 kW; converted to US units this tile returns each within 0.2% (the paper prints q to three figures, which is the whole gap).
What governsEstimate. AHJ and licensed professional govern.
API field namesslot_width_in, slot_length_ft, bulk_density_pcf, internal_friction_deg, surcharge_initial, surcharge_flow, belt_speed_fpm, other_resistance_initial_lb, other_resistance_flow_lb, drive_efficiency, load_initial_lb, pull_initial_lb, pull_flow_lb, drive_power_initial_hp, drive_power_flow_hp
- Surcharge factors are entered they depend on hopper half-angle, wall friction, head and filling methodthe hopper flow analysis
- Shear coefficient 0.8 x sin(effective angle of internal friction)Roberts and Manjunath (1986), conclusion 5
- Plane-flow slot Q = q x weight density x L x B^2Roberts and Manjunath (1986), Eq. 21
- Other resistances skirtplates, belt load, empty belt; entered as one figure per caseentered