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Mechanical Conveying of Bulk Solids

April 15, 2014
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Abstract
This article presents a brief overview of the various modes of conveying bulk solids with guidelines concerning factors to be considered regarding conveyor selection. Since the subject of mechanical conveying is indeed quite broad, the article focuses primarily, by way of example, on belt and screw conveyors and bucket elevators. Of paramount importance to the design and selection process is the characterization of the flow and handling properties of the bulk solid to be conveyed. This aspect of conveyor design forms the main theme of the article.

Introduction
Mechanical conveying and handling of bulk solids is a subject of broad industrial interest and importance. Applications range from long-distance overland transportation in which troughed belt conveyors, and sometimes cable conveyors, are widely used, to in-plant process operations where, apart from conventional troughed belt conveyors, there is a wide choice between special belt conveyors such as, aero belt, pipe, pocket, and pendant-type belt conveyors. Other widely employed mechanical conveyors include screw conveyors, drag chain conveyors, and bucket elevators. Furthermore, a choice often needs to be made between mechanical and pneumatic conveying, the latter involving a selection of lean, dense-phase or slug-type conveying. In some cases the choice of conveying system may involve a combination of various conveying modes. Much depends on the specific process requirements, the method of feeding and transfer, the need to prevent attrition and segregation, as well as the need for dust control. The economics of the various solutions will play a major role in the final decision.
    Of fundamental importance to the design and performance of mechanical conveyors is the characterization of the flow and handling properties of the bulk solid to be conveyed. The need for a thorough understanding of the way bulk solids interact with conveyors during transportation cannot be too strongly emphasized. This aspect of conveyor design and performance analysis is strongly emphasized. A selection of relevant references is included at the end of this article.

SELECTION CRITERIA

Factors Influencing the Selection Process
The selection of the appropriate mode of conveying for a particular application depends on a number of factors such as those listed in Table 1. As a further guide, the relationships between throughput, angle of elevation, and bulk solid lump size for several conveying modes are depicted in Figure 1. For example, the field of application for pneumatic conveyors is defined by the rectangular area bounded by the maximum particle lump size of 30mm, angle of lift ranging from 0° to 90°, and throughput of around 400 tn/hr. For conventional troughed belt conveyors and cable belt conveyors the nominal bounds are 300mm for lump size, angle of elevation 20°, and tonnage throughput of 10,000 tn/hr. For most cases, the bounds for in-plant operations are defined by the dotted rectangular area shown in Figure 3.

Figure 1: Comparison of Conveyor Zones

 

Figure 2: Conveyor Selection Based on Bulk Solid Cohesive Strength


Influence of Cohesive Strength on Conveyor Selection

The cohesive strength of bulk solids will have a marked influence on the ability of bulk solids to be conveyed and elevated. From flow property tests, the cohesive strength is normally expressed in terms of the bulk solid flow function, usually depicted as “FF”, which represents the functional relationship between the unconfined yield strength σc and the major consolidation stress σ1. That is

             FF=f(σ_c,σ_1) (10)

In order to compare bulk solids in terms of their cohesive strength in relation to their ability to be conveyed, the Flowability Index “Ff” is introduced as follows:  

Ff=  σ_c/(σ_1+10)                                        (2)

It is noted that during conveying, the major consolidation stress σ1 is normally low, in many cases, not greater than 10kPa. This forms the basis of the Ff lines shown in Figure 2, which represent the suggested upper bound limits for the various conveying modes indicated. For example, it is suggested that for pneumatic conveying, the flow function FF for the bulk solid should be bounded by the Ff = 0.15 line, which corresponds to bulk solids of low cohesive strength. For screw and chain conveyors the flow function is bounded by the Ff = 0.3 line. This represents the suggested limit for conveyors involving direct sliding of the bulk solid against the walls of the particular conveyor. As the cohesive strength of the bulk solid increases beyond the Ff = 0.3 limit, it becomes necessary to transport the bulk solid on vehicular type conveyors, such as a troughed belt conveyors, bucket elevators, or high-lift belt conveyors. The normal upper bound for elevating bulk solids by bucket elevators or high-lift conveyors is Ff = 0.45. In the case of belt conveyors, bulk materials of high cohesive strength can be readily conveyed, but the suggested upper bound is Ff = 0.6 in order to reduce the problems of belt cleaning due to carry-back and build-up of material in transfer chutes.

Belt Conveyors
Of the various modes of continuous conveying of bulk solids, belt conveyors are of considerable importance in view of their widespread use and proven reliability. In-plant applications often create many challenges for belt conveyor design due to space limitations and the need to employ high conveying angles without slip-back and spillage. The need for the relevant flow properties of the bulk solid to be considered in the design cannot be too strongly emphasized.


Correct Choice of Bulk Density
In the past, insufficient attention has been given to the correct choice of bulk density when determining the conveyor throughput. Bulk density varies with the consolidation stress or pressure, as illustrated by the results for a coal sample shown in Figure 3. Also shown is the packing ratio based on the measured solids density. When loading a bulk solid onto a belt conveyor, the bulk density will increase an amount Δρ from the initial loaded condition, ”L”, to the running condition, “R”, as illustrated in Figure 3. At the load point the bulk density corresponds to the major consolidation stress σ1L defined as

        σ1L  = kL ρ g h    (3)

During running, after the load has settled, the bulk density corresponds to the dynamic major consolidation stress 1D  defined as

    σ_(1R )= k_(L ) ρ g h (1+ a_v⁄g)                                (4)

where     a_v=  (2 π^2  〖V_b〗^2  K_s)/X                                          (5)

           Vb = belt velocity    Ks = sag ratio    X = idler spacing
h = average height of bulk solid on belt    kL = dynamic load factor, 0.5< kL<1.0.
 
    
Figure 3: Bulk Density and Packing for Coal

Figure 4: Conveyor Load Model

 

In general, the increase in bulk density, ∆ρ/ρ, is in the order of 12% to 14%. This corresponds to the amount of load settlement.


Slip Back and Lift-Off During Conveying
Referring to Figure 5, as the belt moves between the idlers, the bulk solid is subject to transverse acceleration in 'y' direction. As discussed in Ref. 6,7, this can result in reduced bulk solid and belt surface friction, leading to slip during inclined and declined conveying. If the belt speed is fast enough, then lift-off due to loss of contact of the bulk solids with the belt may occur. This applies mainly to the zone ahead of the idler where the inertia effects cause the bulk solid to lose contact with the belt. Both slip and lift-off can give rise to spillage. The problems become more pronounced at higher belt speeds indicating that higher belt tensions and/or lower sag ratios must be achieved and this may result in the need to employ reduced idler spacing. As an example, Figure 6 shows the belt velocities for slip and lift-off as a function of conveying inclination angle for a belt sag ratio of 2%, idler spacing of 1.5m, and an equivalent friction factor E = 0.5 for the troughed belt.  This shows that for a horizontal conveyor, for a 2% sag, both slip and lift-off will occur at belt velocities V¬b ≥ 6.1m/s. At a conveying elevation angle of 10°, slip will commence at the conveying speed of 4.8m/s and lift-off will commence at the conveying speed of 6.2m/s.

Figure 5: Belt Motion Model

 


Figure 6: Belt Velocities for Slip and Lift-Off



Screw Conveyors – Importance of Screw and Casing Friction
Screw conveyors are widely used for in-plant conveying of bulk solids. There are a number of different screw designs and configurations with the two principal types being the ‘open-trough’ type that operates either horizontally or at low angles of elevation usually at low speeds in the range up to 100 rev/min, and the fully enclosed screw conveyor that operates at all angles of elevation from the horizontal to the vertical over wide speed ranges, the maximum economical speed being a function of the screw diameter, D, in accordance with the following equation (Ref[1]):

        N_max=  C_s/√D rev/min                                (6)

where Cs  = constant which, for an enclosed screw conveyor with a one-to-one screw pitch to diameter ratio elevating grain, is Cs = 386 for the screw diameter D expressed in meters. The limiting factor in the screw performance is the loss in conveying efficiency due to the rotational or vortex motion of the material being conveyed. This loss is taken into account through the volumetric efficiency which is an integral component in the throughput prediction.
    Shaftless screws are now widely used, generally for conveying and feeding operations in the horizontal and lower elevation range of applications. Because of the very low bending and torsional or ‘wind-up’ stiffnesses of helical flights, it is necessary for the shaftless helical flights to be of robust design which, of necessity, requires large blade thicknesses to be employed.
    While the friction losses are high in the case of screw conveyors, particularly those that operate at high angles of elevation, the performance is totally dependent on friction, the lower the friction between the material being conveyed and the screw surface and the higher the resistive friction of the inner casing surface in reducing the vortex losses the better. The influence of screw and casing friction are illustrated in the following case study example:

Vertical Screw Case Study
Figure 7 shows a particular known type of vertical screw conveyor used at a port facility for unloading coal from bulk ships. The screw conveyor is forced fed by means of a counter rotating lower casing with feed vanes as illustrated. Hence the capacity of the screw conveyor is controlled by the feeding device and not by the conveyor itself. To avoid blockages in the screw intake, it is essential that the conveyor speed is high enough for the fill ratio ηF < 1.

Figure 7. Screw Conveyor for Ship Unloading


In the example being considered, the screw has a diameter of 790mm with pitch of 540 mm, and is 27 m high. The unloader failed to deliver the design throughput of 1400 tn/hr at 400 rev/min with the installed motor power of, nominally, 430, kW. Samples of the coal were delivered to the University of Newcastle for testing. The moisture content of the coal, as-supplied, was 27%, which was at the top end of the specified moisture level for acceptance. As it so happened, this moisture content corresponded to the level at which the coal gained its maximum bulk cohesive strength. It was the also the level at which the coal has its lowest bulk density which partly accounts for the possible shortfall in tonnage throughput.
    However, the most significant factors influencing the performance of such a screw elevator concerns the friction generated between the bulk solid, in this case the coal, and the screw and casing surfaces. The friction angles as functions of normal contact pressure for the coal in contact with steel surfaces deemed to be similar to that of the screw and casing of the actual unloader were determined. The friction angles for the screw and casing so determined gave a values of 25° corresponding to the relevant normal pressures. These values and the measured bulk densities were used to evaluate the screw unloader performance for the specified throughput of 1400 tn/hr. Under forced feeding at 1400 tn/hr, it was recommended that the feeder operate at or above 300 rev/min for which the fill ratio was calculated to be 74%. This fill ratio is deemed to provide a satisfactory margin against jamming or blockages. The chosen operating speed was 400 rev/min.
The power versus screw speed graphs are illustrated in Figure 8. Also shown is the variation of screw fill ratio as a function of speed. For the 400 rev/min, the required power for the screw is 600kW, this being the power that was finally installed. It is interesting to note that as polishing of the screw surface takes place with use, and at lower moisture levels of the coal which give rise to less cohesion, the friction angle for the coal on the screw surface could reduce. As an illustration, the power versus speed curve for the throughput of 1400 tn/hr for a screw surface friction angle of 20°, and casing friction angle of 25° is also illustrated in Figure 18. At 400 rev/min, a reduction of 5° in the screw surface friction angle reduces the power from 600 to 400kW, a reduction of 33%, which is quite significant.

Figure 8: Power and Fill Ratio for Ship Unloader Screw D = 790 mm, p = 540mm, H = 27m

 


Bucket Elevators – Discharge Characteristics
Bucket elevators are classified according to their speed and discharge characteristics. Referring to Figure 9, gravity discharge bucket elevators operate at low speeds with the buckets closely space as shown in Figure 9(a). In this case, the back face of each bucket acts as a chute for discharge of bulk solid from the trailing bucket. Centrifugal discharge occurs at higher speeds with the buckets spaced apart as illustrated in Figure 9(b). At the lower end of the speed range discharge commences after the buckets pass through the top dead center (TDC) position and commence their downward run. At the higher end of the speed range, discharge commences on the upward leg before the buckets reach the TDC position. High-speed centrifugal discharge is illustrated in Figure 10, which is from the work of Beverly et al [7]. In all cases, it is important to achieve efficient discharge without interference and fall back. Interference occurs when the discharging bulk solid from each bucket makes contact with the leading bucket. In the case of high-speed centrifugal discharge, the bulk solid has to be thrown clear of the moving buckets reaching the discharge chute of the elevator without contact with the buckets and the elevator casing.

Figure 9: Bucket Elevator Discharge Characteristics

                        

Figure 10: High-Speed Centrifugal Discharge



A useful way to classify bucket elevators is by means of the Froude Number defined as

    N_F=  (v_b^2)/(r_(g )  g)

For gravity discharge N_F<  r_b/r_t
For low-speed centrifugal discharge  r_b/r_t < N_(F )<1.0
For high-speed centrifugal discharge NF > 1.0
where  rb = radius at belt surface
rg = radius at center of gravity of the bulk solid in the bucket
rt = tip radius
Two important aspects of bucket elevator performance, namely the need for efficient feeding and discharge, are now illustrated. This is demonstrated in Figures 10 and 11, respectively, which are based on a case study of bucket elevator handling aluminum oxide. The elevator speed is 1.92 m/s.

Figure 11: Feeding of Buckets

 

Figure 12: Elevator Discharge
 

 

     Referring to Figure 11, with the chute angle at θ = 45°, the feed into the buckets was inefficient resulting in a bucket fill factor less than optimal. The filling of the buckets was improved by reducing the chute angle θ to 35°.
With the elevator speed of 1.92m/s, discharge commenced before the buckets reach their TDC position. In view of the geometry of the top section of the elevator casing, interference occurred as shown by the bulk solid trajectories in Figure 12. Some fall back of bulk solid to the boot of the elevator occurred. This reinforces the need to correctly design the top discharge section of the elevator casing in order to avoid such problems.


Concluding Remarks
In a review article such as this, it has not been possible to cover in detail the broad range of mechanical conveying equipment used by industry. Rather, the approach taken has been to highlight the basic objectives associated with the mechanical conveying of bulk solids and to review those more common types of conveyors, notably belt conveyors, screw conveyors, and bucket elevators. These are examples of the more widely used types of in-plant equipment used to move and elevate bulk materials. The need for the determination of the relevant flow properties of the bulk solid and conveyor materials is strongly stressed.
    The overriding message is that mechanical conveyors are often taken for granted, with their performance characteristics seeming to be obvious and simple. This is certainly not the case. They are all fascinating, intriguing devices that provide the opportunity for an in-depth understanding of the fundamental laws of mechanics and the basic flow properties of the bulk material being conveyed. The acceptance of mechanical conveying as a challenging academic study and research discipline for universities and colleges is strongly recommended.
    Alan W. Roberts is emeritus professor and founding director, TUNRA Bulk Solids, The University of Newcastle, Australia. He can be reached at Alan.Roberts@newcastle.edu.au.

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References
A.W. Roberts. Bulk Solid and Conveyor Belt Interactions for Efficient Transportation without Spillage. Bulk Solids Handling, Vol. 18 No. 1, January/March 1998 (pp.49-57)
A.W. Roberts, Mechanical Conveying Proc. From Powder to Bulk Conference,
The Institution of Mechanical Engineers, London, 200 (pp.377-410)
A.W. Roberts and M.G. Jones. Developments in Mechanical Transport of Bulk Solids. Relpowflo IV, Tromso, Norway, June, 2008
A.W. Roberts, and A.H. Willis. Performance of Grain Augers. Proc. Instn. of Mech. Engrs., Vol. 176 (8), 1962 (pp.165-194)
A.W. Roberts. The Influence of Granular Vortex Motion on the Volumetric Performance of Enclosed Screw Conveyors. Powder Technology, Vol. 104, 1999 (pp 56-67)
A.W. Roberts. Design and Performance Criteria for Screw Conveyors in Bulk  Solids Operations. Bulk Solids Handling, Vol. 21 No.6. 2002 (pp. 436-444)
G.J. Beverly, A.W. Roberts, and J.W. Hayes. Mechanics of High Speed Elevator Discharge. Bulk Solids Handling, Vol. 3, No. 4, November 1983 (pp.853-859)