A Fundamental Approach to Belt Feeder Loads
A Fundamental Approach to Belt Feeder Loads
Subject to the proviso that wall friction has been mobilised, the approach below may be used to assess starting and restarting forces. The force required to extract product through a flowing bed is lower than the force needed to initiate discharge because mass dilated by a flowing condition is easier to shear; the higher the rate of flow, the lower the transverse shear strength.
It may be difficult to assess the shear strength of a bulk material in dynamic flow condition because of its sensitivity to flow rate, but any feeder capable of initiating flow can sustain discharge continuously.
Rise at hopper exit to lower inclined edges of hopper walls = R
Width of hopper outlet at start = W
Width of hopper outlet at exit W_{exit}
Average width of hopper outlet w_{av}
The overpressure from the stressed arch O_{p}
Hence Dragout force F_{do}
where:
 ∫_{p} = principle stress in arch
 ∫_{f} = failure stress of the bulk material
 P_{r} = principle stress ratio
 L = length of hopper outlet
(The value of (∫_{p } ∫_{f}) at the hopper outlet is taken for a factor of safety).
Considering the conveying load of material under the stressed arch, for practical purposes a catenary arch can be considered as a parabola, which has the general form of
or, in this case, the maximum height of arch, H
The slope at any point
Hence
where
 α = angle of hopper wall from vertical
 φ = angle of wall friction
 w = half the width of the hopper outlet, W.
Note that the minimum hopper outlet width, W, is generally greater than 1.1 · ‘critical span’ for flow reliability.
Area, A, under a parabola = 2/3 · W · H, where H = height of centre of stressed arch. So area A under stressed arch at hopper outlet
Hence the weight of unsupported load under stressed arch is
where
 ξ = bulk density
The load acting from material in clearance space is
and the repose from side skirts is
Hence the total conveying load on feeder is
To minimise the feeder load, the width of the exit from the hopper should be based on the critical arching span of the bulk material, with a suitable safety factor and allowance for the increased span incorporated over the hopper outlet length to secure progressive extraction.
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