A Fundamental Approach to Belt Feeder Loads

Belt Feeder Design

A Fundamental Approach to Belt Feeder Loads

How to assess loads on Feeders, (practically)
Feeders are widely used for metering bulk solids and discharging the contents of hoppers and silos. Numerous attempts have been made to describe the process of feeding but quite often they only cover certain products and hopper construction. In this article the reader will find a more general approach to this field of problems.
(ed. WoMaMarcel - 01/9/2015)
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The arches themselves follow a network of continuous load path between contacting particles and roughly adopt a catenary shape, small deviations being possible because contact friction between particles allows slight angular deviations of particle-to-particle contact forces from straight lines of action. Surface tension, cohesive, tensile, electrostatic, molecular and other inter-particle forces may allow other particles to stick on the underside of this arch at the outlet and be subjected to this stress relieving action of the unstable arch, but these effects can normally be neglected for practical purposes.

The line of action at the toes of the arch is dictated by the slope of the hopper wall and angle of wall friction in the case of mass flow hoppers, or by the internal angle of friction of the bulk solid for a funnel flow regime. The arch shape can be closely approximated by a parabola, allowing simple calculations to establish the height of the arch and the mass of material between the stressed arch and the feeder that is solely borne by the feeder. Added to this downward value acting on the feeder is the force acting through the stressed arch in either the static or discharge condition. Stresses in the static arch can be calculated by the method used to establish the ‘critical arching size’. It follows that spans exceeding this size are not capable of bearing the compressive stress applied and that, to prevent failure, the arch must be supported by a force equivalent to the value by which the principle stress in the arch exceeds the compressive failure stress, multiplied by the principle stress ratio of the bulk material.

Once flow has started the material dilates to a weaker bulk state and lower density. Pressures decrease towards the outlet, by an amount depending on the degree of flow restraint offered by the rate at which the feeder extracts material. However, the shear value also decreases due to the extra freedom of movement allowed by the dilatation, so the ‘drag-out’ resistance offered to the feeder also diminishes.

The rub is that the recognised Jenike type method of measuring the initial shear force to ‘drag out’ material from under a hopper outlet is applicable to fine powders, but is not appropriate for coarse, firm granular material, because the confining force does not reflect passive stresses that firmly oppose an expansion of the shear plane in totally confined conditions. For initial shear to take place the mass must dilate locally so that particles that were overlapping in a close-nested, settled structure can move past each other. This dilatation is significantly for large particles. If expansion is resisted by confinement, passive stresses can be exceptionally high, in some cases requiring failure of the particles to allow shear to take place, even though the material in a loose condition may be very free-flowing, as with granular sugar or salt. This condition may be avoided operational by extracting a tiny amount of material at an early stage of initial loading to develop a shear plane in lightly stressed conditions and retaining a small heel of material before re-filling. It also may be avoided by providing a local region of voidage into which the shear plane expansion may move, by way of inserts in the hopper outlet or offsetting the outlet to remove the compacting stresses on the shear plane or providing a local void region.

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