Belt and screw feeders are commonly used to discharge bulk materials from hoppers.
Apart from controlling the rate of extraction, these offer the facility for extended hopper outlets that carry the additional benefits of holding extra storage capacity and adopting flat side walls shallower than required for cones or pyramids. However, to enable the flow and operational advantages of mass flow it is essential to extract material from the total hopper outlet area.
The can be achieved by geometric and frictional variation in the screw and casing, and hopper outlet variations in belt feeders, usually by progressive widening of the hopper outlet and/or raising the side skirt level.
When first loaded, the stresses imposed on the hopper contents act vertically to compact the material, but change as resistance to flow is opposed by the hopper wall in mass flow bins, or by the static product outside the flow route of a funnel flow bin.
A ‘stressed arch’ is generated over the outlet when discharge to take place, the span of the arch being such as to raise the stress in the arch to exceed the unconfined failure strength of the bulk material. The minimum width of the outlet must be greater than the ‘critical arching size’ required for reliable flow, so additional outlet width to provide incremental extraction, plus the safety margin allowed in design, result in an excess overpressures on the feeder that induces a shear load in the bulk material on starting and running.
It is well documented that starting loads can be considerably greater than running loads, Jenike indicated that this difference could even exceed a ratio of 10:1. This could well explain the conservative design values assess by Arnold, and the subject of an investigation by Sharp, and Holmes, following a thesis by Allen, suggesting that existing feeders were operating well below installed loads.
This has significance for drive design and operating efficiency. The extra cost of overdesign may be small against the risk of the equipment being unable to start but the capital and inefficient lifetime cost of excess power is wasteful, hence the designers dilemma.
Stressed arch conditions
The shape of the stressed arch that develops when flow takes place was shown by Hooke, to take the form of an inverted catenary. The inclination of the ends of the arch depends on the internal angle of friction of the bulk material in the case of a Funnel Flow hopper and on the combination of the hopper wall angle and the angle of contact friction between the bulk material and hopper wall in the case of the hopper contents moving in mass flow.
Figure 1. Inclination at end of arch
α = Wall inclination
? = angle of wall friction
W = Width of outlet
H = Height of arch
In practice, the shape of arch can be closely approximated by a parabola, which follows the form of -Ax2 + Bx + C, where B is zero, because the shape is central and C zero with origin as top of arch.
The gives form as –Ax2 and dy/dx as O + ?, which enables the cross sectional area of material under the arch, and hence the weight of this enclosed solid, to be determined.
To this must be added the weight of any unsupported material occupying the distance between the hopper outlet and the belt and the overpressure act-ing through an arch greater than the critical span.
Figure 2. Arch larger than critical span.
The underlying reason for the difference between starting and running loads clearly depends on the physical properties of the bulk material being handled.
Experience with screw feeders point to particle size and strength as being major factors influencing this value. Haupt’s study emphasises the rapid fall off in feeder load on the removal of a tiny amount of product from the interface region between the hopper outlet and belt.
This mirrors the rapid increase of force necessary to compress a confined bulk solid, especially if composed of hard, large particles. A granular bed will settle rapidly from a dilatant, loose-poured condition to a more dense stable structure as excess air in the voids can freely escape through the interstices between the particles. A confined mass in this state is very difficult to compact further because a network of load paths has developed through the bed.
Applied vibration can disturb the structure and cause further settlement, which creates temporary adjacent voids and reduce the local shear load but this approach is not recommended for recalcitrant feeders that refuse to start because if they do not start first time the situation is made much worse.
The core of the problem is that the degree of dilatation in a shearing layer is greater than that of a settled density because initially overlapping particles have to separate to pass each other. The degree of expansion is small, being limited to a layer thickness of up to five or 10 particles, but the effect is to convert the active stress to a passive stress and demanding the compaction of the adjacent settled and confined bed, for which the resisting stress can be massive.
This position can be seriously exacerbated if the feeder is mounted independently of the hopper as any deflection of the hopper when filled will place some of the weight of the hopper and contents on the interface material between the hopper outlet and the belt.
As with many problems in solids handling, brute force is not the best answer. It must be emphasised that there is not always a massive difference between the starting and running loads of a feeder and, for the very time necessary, there can often be overcome by temporary overloads on the drive system. However, passive failure stresses in confined hard, but relatively small, particles such as granular sugar and salt, can be exceedingly high and cause difficult starting conditions for feeders.
The first design task is therefore to determine if such a problem is likely. This can be established by measuring the distance raised by the lid of a shear cell when shearing occurs and the load required to compact the cell lid be a similar amount on a similar prepared sample.
If the potential load is high it is necessary to counter this by mitigating the passive stress condition by reducing the confining load or providing local voidage to accept the expansion of the shearing layer.
One way is to offset the discharge belt sideways a short from the hopper outlet and provide a void above the material on the belt. belt. Not only is the overpressure from the hopper outlet reduced, but confinement is avoided and local expansion can take place with little resistance from the material resting on the belt.
Two Rand investigations in the 1960s and 80s highlighted the general short-falls in commissioning time and performance efficiency between solids handling plant and plants handling liquids and gasses and the slow implementation of advances in the technology.
This was attributed to the lack of design taking account if the physical properties of the bulk material being handled and the fact that these were sensitive to many factors so, unlike liquids and gasses, could not be published in data banks.
Performance reliability is paramount in the design of solids handling equipment and for this the equipment must be designed to reflect operational values of the bulk material’s physical properties. However, the availability and cost of ‘standard’ machines entices users with rudimentary knowledge of the technology to purchase these without a flow audit of the project.
These is limited general understanding of bulk behaviour because it is not part of general education, but more importantly, rarely figures in university syllabuses despite solids handling being one of the largest industrial activities.
Much can be done with a basic understanding of the fundamental principles, such as wall friction and difference between active and passive stresses, but while byers base purchases on capital cost, rather than lifetime costs and performance insurance, serious performance failures will continue.
Read the article online at: https://www.drybulkmagazine.com/material-handling/28102019/the-feeder-dilemma/