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 nature of the bulk material handled has an important influence on the power required by a feeder, particularly:

  • Wall friction on the hopper contact surface. (Incipient value).
  • Wall friction on the hopper contact surface. (Sustained value).
  • Bulk density in differing conditions of compaction.
  • Internal shear strength. (Incipient value). In specific state of compaction.
  • Internal shear strength. (Sustained value). In specific state of compaction.

Note that moisture, chemical, thermal and time effects may bear significantly on these values, in which case historical and ambient conditions may be relevant.

It will be seen that combinations of the above factors results in many permutations that makes research on this topic an extensive subject to investigate and be tedious and involve considerable overlapping to devise a formula to suit each case. A correctly designed hopper will have outlet dimensions that exceeds the ‘critical arching size’ for the product in the given bin geometry by a comfortable, but not excessive, margin that is sufficient to satisfy the required discharge rate and accommodate foreseeable adverse operating conditions. A hopper outlet of ‘critical arch’ dimensions would offer no additional load on the feeder from material above the arch, but flow reliability would be very suspect unless the ‘worst’ operating circumstances on which a design allowance was made was very unlikely to occur.

Clearly, the amount by which the size of opening exceeds the critical arching size has a great influence on the superimposed loads passing through the outlet.

A calculated ‘safe’ hopper opening dimension for reliable flow itself is likely to incorporate a degree of safety, but an additional factor is also usually applied as a form of insurance and to accommodate and uncertainty. The resulting dimension must relate to the minimum size of opening specified, so a taper slot outlet that is incorporated to provide an incremental extraction by a belt feeder in order to generate live flow along the whole length of a slot outlet, will present a further increase in span that allows additional over-pressure to develop. Also, if the condition to be stored has a variable condition due to source, process, age or time consolidation, then the design must be based on the ‘worst’ flow conditions. When then handling the ‘easiest’ flow conditions that would pass through a smaller opening, an even greater over-pressure will be generated. In practice, therefore, a hopper outlet size is likely to be significantly larger than the critical arching span dimension.

A key concept is that material in a hopper with outlet larger than the ‘critical arch span’ will collapse and flow out, as the principle stress in the arch exceeds the failure strength of the bulk material. The magnitude of the excess principle stress, times the principle stress ratio of the bulk solid, produces a normal force to the surface of the arch that acts down onto the feeder when flow is not taking place.

The force acting on the hopper outlet may be considered to have two components:

  • The force acting down from the failing arch, which is partially supported by the hopper walls in the case of a mass flow discharge pattern, or by mobilised shear stress on the adjacent static material in a funnel flow regime.
  • The weight of the mass under the stressed arch that is totally unsupported by the hopper walls. i.e. from the material in the space between the stressed arch and the feeder belt.

The force acting from the arch is the most important as this determines the ‘drag-out’ load on the feeder. The weight of the mass under the arch is part of the conveying load of the equipment, combined with the continuing load from any extension of the belt from the feeder exit.

An important consideration is that, even if flow has not taken place, there is usually some degree of settlement in the lower region of the contents as the bin fills due to the increasing load on the prior contents. The degree to which settlement takes place will be much less for hard, granular material that settle quickly to a stable structure than it is for powders, which tend to land in a dilated condition and consolidate to settle to a higher density as excess air escapes by percolating through the bed. The compacting load on the contents will be limited by Janssen effects, but any settlement will cause a reaction at the bins walls as microscopic slip takes place and develops stressed arches across the bin walls. Through these arches are not sufficiently robust to prevent flow taking place when the feeder allows extraction, they do offer some support for the material above the stressed arches when flow is not occurring.

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