Dr. M Rivkin,

Congratulations for your research findings. It is true that actual maximum possible will be somewhat more than mentioned in technical literature. This is also reflected by the difference in recommended values amongst various literature / standards. So, there are two terms, safe maximum value and actual maximum value!

However, while choosing angle of maximum inclination for application engineering, the designer is handicapped by certain tolerance of uncertainties such as probable variation in material surface texture, lack of very precise data for material, monetary liability if the performance is inadequate etc. Therefore, they will generally opt for value:

A) Which is least among various literature.

B) Or the value as being used in existing plants, without problem.

C) Or slightly more than the normal value if purchaser agrees to the same. ■

Dr. M Rivkin,

Further to my earlier message, you can also investigate belt sag percentage vrs maximum inclination of conveyor; for say sag value say 0.65, 1, 1.5 and 2 percentage. Possibly you may find that permissible inclination slightly increases as the percentage sag of belt (between idlers) decreases, for same value of belt speed. ■

I would always advise caution when comparing the results of some specific materials handling trials with generalised published information in "technical literature".

My experience has shown that any piece of materials handling equipment can show significant variations in performance according the exact properties of the bulk material being tested. Indeed, if the same sample of material is used in tests over an extended period even this can result performance variations due to degredation, drying out or absorbing moisture.

Any published data must always be treated as a guideline and not exact, not least because the publisher will not want to be held responsible if equipment does not work!

It would be interesting if Dr Rivkin could give a fuller description of the range of bulk materials and belt sizes used in the trials. ■

A few comments on your observation:

1. The transport distance should be a factor - short conveyors can evacuate before the sliding effect becomes significant. H. Colijn did a lot of testing using powder fudicial indicators to map the degree of backward travel the ore takes. Many attributes were tested.

2. Loading configuation can stabilize or destabilize the load before a significant distance has been achieved -ie. your slow belt speed. As Mr. Mulani suggests the sag value can have a detrimental effect near the uphill load start point. Ore is agitated and destabilized with sag and speed and poor initial rock momentum.

3. Degrees of surface moisture affect the result- no moisture may cause rilling or test the sliding action of the ore to belt friction, as moisture increases the cohesive and adhesive properties may increase, making for a higher inclination, as moisture is further increased, the idler agitations may again unstabilize the ore.

4. Crossectional loading is usually adjusted by the cos (alpha)^3

to account for the inclination load capacity correction. Alpha is the slope angle. This does not imply the other factors are moot. This comes from DIN just stated a little differently.

5. Trough shape and spacing of idlers influence load stability

6. Belt construction influences load stability - thinner and more flexible belts agitate and destabilize the ore, while thicker and stiffer belts reduce the effect.

7. Calculate the rilling angle of a rock atop the center cross-section that reaches the limit of the dynamic repose angle or surcharge angle factored for the point of maximum stable inclination before the rock rolls. The is a 3-D problem. The surcharge angle, in crossection is exceded by a significant degree.

8. It would be of interest to see the device. Then we can all render an opinion as to whether it captures the point or may be its like the whale in Moby Dick from an earlier posting.

9. TUNRA and other Australian universities have also built vibrating tables to test inclination angles f various ores and ore properies. They do the testing as a service to the mining industry. Others around the world have done the same - Germany, USA, ....

10. Conveyors have been designed to 22 degree inclinations before. All depends on rock properties and moisture. What angles are you recommending and with what oreproperties and what belt conditions?

11. Change the surface configuration of the belt such as chevrons or cleats as in done. Now all the conditions are attributable to the internal granular properties of the ore.

Lawrence Nordell

Conveyor Dynamics, Inc.

www.conveyor-dynamics.com ■

Why do we want to increase the incline angle of an open trough belt when current typical inclines are unsafe against slide-back? The none-quantitative nature of this discussion is a good indication of the problem. Basis for safe, "maximum" inclne angles can be developed mathematically, experimentally and or emperically. The problem is that no one will accept the results because of the consequential cost. There are many high profile examples of failures in selecting a safe incline angle.

I will share with you here:

1.) A history that shows that this questions was investigated in depth many years ago.

2.) A true case where a major South African Coal Company looked for the answer, found it, implemented it, and then abandoned it because of the cost.

3. A modern proven solution, The Sandwich-Belt High-Angle Conveyor, that should make open trough inclined belts obsolete.

Let's begin

1.) In the 1940's A. Vierling and others investigated the incline angle problem in great depth. Basically if the dynamics could be supressed and the material to belt interface nearly elliminated then, under very controlled conditions, inclined angles could approach the materials natural angle of repose within 2 or 3 degrees. Wedging of the material load by steep V troughs helped to elliminate the material to belt interface as the weak link in the slide-back problem. Out of this work came the idea of belts with longitudinal ridges (grooves in the cover), for smaller sized materials and deep V troughs for larger sized materials. The basic question, "What is the maximum safe incline angle?", was not answered.

2.) A major South African Coal Company had long lived with the problem of material slide backs at their inclined conveyors. These were at inclines ranging from 15 to 17 degrees. Ironically this Company demonstrated a willingness to pay for reliabilty including, typically, 100% redundacy. In the 1990's this Company decided to address the question of conveying angle once and for all. They set up a commitee of experts and conducted an exhaustive study. The conclusion; conveying angles at their open trough inclined belt indstallations shall not exceed 12 degrees. A major coal handling installation was subsequently built compling to the new edict (max incline angle of 12 degrees). The cost of this new compliant installation turned out so high that the edict of 12 degrees max angle was abandoned after only one implementation. The problem is that we don't want to know "What is the max safe angle?" because we can't stand the answer.

As engineers we expect to develop a failure mode, determine a range of variance, then selct an appropriate safety factor against such failure. In this one case where such an approach was taken, in the end it was again abandoned.

3.) The writer developed the Sandwich-Belt High-Angle conveyor technology, beginning in 1978, along this approach including extensive study and research, technical rationalization, and testing. The testing included, intentionally, many slide-backs, with various materials at various angles with varying hugging pressures. Suitable safety factors, against such slide-backs, were determined.

More than 100 Sandwich-Belt High-Angle conveyors have been built pursuant to this technology. These have been for widely varying materials, at varying angles to 90 degrees (vertical), various rates beyond 6000 t/h, and various lifts to 175 meters. No material slide-back has been experienced in any commercial installation pursuant to this writers development.

Sandwich-Belt High-Angle conveyors can completely obsolete the conventional open trough inclined conveyor if these are compared at equal levels of safety against slide back.

Joseph A. Dos Santos, PE ■

Dear Dr M.Rivkin,

The ability to increase the angle is always qualified by various constraints such as reduced speed (which is the same as reduced capacity or increased cost for a desired rate), reduced belt sag (which means a higher belt tension basis and increased cost), reduced idler spacing, etc. Yet even with these constraints it remains a trial and error approach and no one will prescribe the rules to determine the allowed incline angle nor the minimum safety factor against slide-back, or the margin between allowed and slide-back angle (i.e. if slide-back will occur at 17 degrees then don't exceed 15 degrees etc). As I mentioned in my comments, when a major company did the in-depth study and determined the correct answer it chose the seat-of-the-pants approach because it refused to live with the up front cost of doing the right thing.

Joseph A. Dos Santos, PE ■

There are many valuable coments in this discussion but ultimately, the potential inclination is both product and its state dependent. That is, the condition in which the material is loaded can seriously influence how it behaves on the belt. For example, cement in a loose condition is virtually fluid but can settle to a stable condition that will travel up an incline. However, its potential to be disturbed and revert to a fluid is dependent on temperature, so it is not practical to utilise information from a data base to determine how it will behave.

Powder testing in relevant conditions can provide a useful guide to the way in which the material will behave. It is important to recognise the bounds of variation that the condition of the bulk material may be in and also consider the mechanics of the loading and transport conditions, to determine the feed condition and how this may be disturbed by defomation on the belt. Unless a very 'safe' angle of inclination is selected it would be prudent to consider facilties for reducing the feed to accomadate variable conditions. ■

Dear Dr. Rivkin,

The comments of Lyn Bates and Joseph Dos Santos are particularly relavent.

Although it is true that a conveyor can run at a steeper angle than that recommended in the technical literature, to design a system on a "best case" scenario is likely to create production problems when the environment changes, when the material being carried changes, or when the facility tries to increase production by overloading the belt.

To suggest that the angle of the conveyor can be increased by slowing the belt down is a viable production option ignors the desitre of most plants to move as mich product as quickly as possible.

The primary reason for an increased angle is to save floor space. If that is the main consideration, then solutions such as the Sandwich Belt, fold belt, or corrugated sidewall belts provide cost effective options.

Regards, ■

A crucial factor relating to the ‘safe’ working angle of inclination of a belt conveyor is the stability of the bulk material. The value may be easily established with loose solids that exhibit a consistent angle of repose in all circumstances of formation. Where the repose conditions vary according to how the material is prepared and tested, then to refer to a specific ‘angle of repose’ can be very misleading, unless the application conditions are most carefully specified. Fine and cohesive products fall into the category of bulk materials where their stability to form a stable pile or slope is sensitive to their specific condition at the time. The ambient temperature can be important because the influence of ambient air in the voids of the particles plays an important role in its behaviour and the viscosity of air changes with temperature.

In the case of products that vary considerably in shear strength, such as cement powder, the resistance to bulk deformation depends upon the inherent nature of the material, ambient and applied stress conditions and its specific state of dilatation. It is therefore most important to condition the substance at the loading point to achieve the most compact and strong form of bed, as deposited onto the belt surface where the boundaries are mainly unconfined. Account should also be taken of the degree and frequency of disturbance that is given to the layer of product in transit by the belt undulations over conveying idlers. The condition of the bulk material may not seem to be very significant in many belt conveying duties because it does not vary greatly with a lot of coarse bulk materials. It therefore tends not to receive the attention merited when inclined units are considered, particularly for transfer points when the initial loading point of the system accepts the product in an apparently stable and appropriate condition for conveying.

Flow streams that are subject to rapid changes of direction, long trajectories and locations involving ‘free fall’ will result in significant disturbance and dilatation of the bulk state and ‘loosening’ of the material condition. Feed hoppers, from which product is extracted directly onto the belt, ‘Live’ stream feed points and transfer points between belt conveyors, should therefore receive careful and expert study for inclined belt conveying duties.

Lyn Bates ■