Presets
Playback
Parameters
Layers
Model check
The science
What is simulated
A heavy-duty apron feeder: overlapping steel pans on a chain carry a bed of run-of-mine ore out from under a hopper. The leveling gate sets the bed depth h; the pans set the speed v. The ore you see is a set of tracer rocks that follow the material: the hopper stock sinks at w = Qv / (B Lo) and then rides the pans at v.
Capacity
Volume flow Qv = B h v η (width B = 1.8 m, bed fill factor η), mass flow Q = ρ Qv, shown in t/h. Doubling the speed or the gate opening doubles the capacity; η is the share of the gate section the ore really fills.
Stress at the outlet (Janssen)
A slice of stock of height dz in a bin of hydraulic radius Rh = A / perimeter has weight ρ g A dz and wall friction μw K σ P dz, so dσ/dz = ρ g - μw K σ / Rh and σ(z) = (ρ g Rh / (μw K)) (1 - e-μw K z / Rh). The stress saturates instead of growing as ρ g z, because the walls carry part of the weight. K = 0.4 and μw = tan of the wall friction angle.
Drive
Force F = μp σo B Lo + μr (mbed + mchain) g: the stock over the outlet drags on the pans (μp = 0.45), the loaded run and the chain roll on the rails (μr = 0.035). Power P = F v / ηdrive with ηdrive = 0.88; the motor is rated 45 kW. The 8-tooth sprocket gives a chordal speed ripple of 1 - cos(π/N).
Simplifications
- The hopper flow is a uniform plug (mass flow): real stock can arch, rat-hole or segregate.
- The whole outlet stress is assumed to act on the pans; real feeders reduce it with relieving hoppers and skirt geometry.
- Friction and rolling coefficients are constants; wear, wet ore and fines change them a lot.
- The rocks are tracers of the material, not a particle-contact (DEM) simulation. Their sizes do not enter the capacity.
- Impact loads from the truck or loader that fills the hopper are not modelled.
Checks
Four boxes run the page's own code against independent results: a tracer mass balance (Little's law), the Janssen ODE solved by RK4 against its closed form, the chordal speed ratio of a polygonal sprocket, and the mean chain speed with the drive work.