David,

Good question. Wonder if it has been asked before. From my experience, I will identify some of the likely expectations of belt mal-tracking.

1. material load centering & ore irregularities- (gravity forces)

2. idler alignment (friction and gravity forces)

a) plan view - off normal (90 deg) to belt center - install. error

b) elev. xsection - roll - earth settling (gravity)

c) elev. side view - twist or yaw - (friction) - idler frame warp

d) installation errors/corrections - rain chgs friction=misalign.

3. broken cables, cable alignment (mfg. construction) press etc.

4. belt (fabric & steel cord)construction errors in uniform tension

5. storage - poor support, telescoping, causing permanent set

6. pulley alignment

7. belt wear - crossection wedge shape wear from ceramic pulleys

8. splice alignment and pattern errors

9. training idler negative influence - kinematics can cause mistrkg

10. thermal expansion - sun orientation on steel cord belts no cvr

11. harmonic vibration that causes load to shift - frame compliance

12. residual effects from horizontal and vertical concave curve rad.

13. wind

Hope this provides fodder for the mill. The above points drive design criteria for long overlands and become guidelines for limiting the errors from such.

One hint - friction alignment error and mal-steering force, to belt axis, reaches a natural limit at about 2 degree tilt in horizontal plane. You should find some of these effects are also solved by understanding horizontal curve engineering.

There are formulations for the above. I think it good to do the sums to appreciate the complexities.

I am sure others will have more to contribute. It is a big field.

Lawrence Nordell

President

Conveyor Dynamics, Inc.

1111 West Holly St.

Bellingham, Wa 98225

USA ■

David

If I understand the second resonse, you wish to analyze the belt's response to a condition that is causing mis-tracking by either gravity forces or friction forces.

To resolve this you must solve the local belt transverse bending behavior as an indeterminate beam with local transverse gravity and/or friction forces. This is a far bigger problem. Alas, it has been done in two ways.

First Approach of transverse Bending:

The first derivation of the belt (beam) in bending, with a flux variation between cables, was solved for steel cord belt construction by Profs. Oehem (father and son) at the Univ. of Hanover, Germany. He wrote a treatment of the strain field in the cords, due to actions of curving the belt, approximating an indeterminate beam solution.

Combine this with the horizontal curve analysis (gravity banking forces) of Hans Grimmer in 1963 (I believe also from Hanover) and you begin to approach the physics. If you derive Oehmen and Grimmer's works, you should find some flaws in their assumptions and results. Oehmen's work would take some explaining. Grimmer is easier.

To calculate the belts transverse equilibrium, Grimmer first placed the ore as a dense field mapped to the belt width. Both act as a singular membrane in cross section when the belt is symmetrically loaded. This produces a variable density along the belt width. As the belt moves transverse, the equilibrium forces are calculated from the shifting belt. This does not take into account the true ore motion above the belt or ore resettling from idler agitation. It will give a so-so approximation. Lots of designers use it.

The steering force equations of idler-to-belt during mis-alignment, have been solved, but I don't recall who or where. The function resembles a graph where the steering force (SF) is plotted against the angular misalignment (AM). Zero AM equals zero SF. Two degrees AM equals 100%SF. Pick your friction coef. and wa la.

Second Method for Tranverse Beam (Belt) Deflection:

The indeterminate beam is best solved using FEA. Ryan Lemmon (Conveyor Dynamics, Inc.) published a work on belt turnovers, for the Society of Mining Engineers (SME) that may be of some help in this area. He has one of Oehmen's references. I believe the proper belt reference from Oehmen (father or son) is in German published many years ago (1960-1970's).

Regards,

Lawrence Nordell

CDI ■

Dear Mr.David Pelc



I have written one book on belt conveyor. Its information is on bulk-online. This book also has one big topic on your subject. Please contact me if you intend to know about the topic etc.



IG Mulani

parimul@pn2.vsnl.net.in ■

Hello David,

As mentioned in the replies, there are a number of factors that can cause a belt to mistrack -- both external forces (idler misalignment, material buid-up on idlers and pulleys, frozen or sluggish bearings, uneven loading, load impact direction, side obstructions causing drag on the belt edges, over or under tensioning, et al) and internal forces (unevenly tensioned carcass, wavy carcass, crooked splice, belt bowing, et cetera).

There is a wealth of information available to you on belt mistraining causes and remedial actions (Mr. Mulani's book, CEMA, NIBA, most belt manufacturers, et cetera). Unfortunately there is little written on mathematical models concerning the various causes. Thus, if your thesis requires this, you will be conducting basic research and, thereby, doing the industry a favour. I would recommend that you contact belt manufacturers, conveyor manufacturers, idler manufacturers, and universities (such as the University of Hanover) to determine if they can offer assistance -- either in providing past study information or in conducting tests.

Basically, a belt reacts to the "braking" forces placed on it by the system and load, assuming good belt construction and splicing. The degree of belt reaction will depend on belt speed, load, tension, and braking (id est friction) force being applied. You should be focusing on models for each of the various mistracking causes, instead of attempting to develop an all-inclusive or unified model. For example, develop a model that shows the effect of a misaligned idler on a belt of a given weight (construction), travelling at a given speed, under a set load condition, and with a specific take-up tension. Show the effect of various misalignment angles for those conditions -- then change each of the

set conditions and repeat in turn. You can then follow this by repeating the exercise with a frozen idler and then with a sluggish idler. Further testing would be with material build-up of various amounts on one side of your test idler, through the same test range. Then do the same exercise with pulleys.

Further testing on uneven loading and impact direction would also be of use. As would side drag mistraining actions of skirting, side guide rollers, and structure contact. Finally, a study on the environmental effects of temperature, wind, moisture, dust storms, and icing would be of use.

Note that this list does not include internal causes.

Given the size of this field, you may want to limit your thesis to developing a mathematical model for just a few of the common belt mistraining causes -- my personal favorite is with the deleterious effect of over tensioning the belt, since this tends to increase the mistraining effects of all the other causes and a majority of users tend to run their belts too tight.

Good luck with your thesis, I hope to see the results in an article in Bulk Material Handling.

Regards, ■

Mr. Miller:

You note emphatically that mal-tracking may be caused by over tensioning. I beg to differ until proven otherwise. High tension in and of it self does not induce mal-tracking, in fact, it has just the opposite effect. If it did, then all attempts at high ST rated belts and belts under higher tension in horizontal curves would be at risk of controlling the tracking behavior. I have not witnessed such in high tension belts. El Abra, in Chile, has a rating of ST-6800 N/mm. The horizontal curves and the belt at-large tracks well at last inspection. The belt is designed to run with a safety factor SF= 5.5:1. This is 22% higher than the Safety Factor norm SF =6.7:1. Not many belts exceed this rating and none to my knowledge have high tension tracking sensitivity:

1. Selby (UK) ST-7000 SF= 5:1

2. Prosper Haniel ST-7500 SF= 5.5:1

3. Los Pelambres ST-7800 SF=5.51

4. Muskege River ST-7000 ??

However, too low a tension can cause mal-tracking. The irregularity of x-sectional loading and errors in belt construction can then dominate tracking response. Do a test, as we have done, measure the tracking of the belt edge in the high and low tesnion regions. You will find the high tension head station has a lower wander than the low tension tail station as the same section of belt passes.

Wish you well,

Lawrence Nordell

Conveyor Dynamics, Inc. ■

Dear David,

Misalignment of belt can be for varied reasons such as faulty structure, faulty belt, faulty material load, etc. The chapter in book discusses and have mathematical calculations for aligning force due to 1) Pivoted self aligning idlers 2) Trough shape 3) Forward tilt of side rollers 4) Bow string effect. All these calculation procedure is based on material plus belt pressure (grip) on idlers, in accordance with alternating plus / minus strains in bulk material, as it is being conveyed. The material force calculations are based on Rankine and Coulumb theories for bulk materials as applied to belt conveyors. The four methods described in book can be further extended to calculate aligning force due to idler banking in vertical plane or idler positioning in (skew) in horizontal plane. 20 pages in my book (page 96 - 115) have mathematical calculations to work out aligning force with numerical examples. These have many figures, formulae etc and cannot be reproduced here. However, if you inform me your email, I can email you calculation of one case. However, still it will not be adequate for undestanding, as material forces are based on one full chapter-8 (about 60 pages).

Regards,

I G Mulani

Author - Book on Engineering Science and Application Design for Belt Conveyors.

parimul@pn2.vsnl.net.in ■

Mr. Nordell:

With respect to belt overtensioning and its effect on mistraining. Highn tension systems and horizontal curves such as you described are designed, both system and belt, to run with the belt well placed when running within the designed tension parameters. However, if the take-up tension is increased so that the belt no longer makes contact with the center cans of the troughing idler sets, the return run is taut, and/or the belt lifts off idlers in concave vertical curves, the belt will be more sensitive to other mistraining sources.

An overly tight belt will run harder on the troughing cans than on the center can and will, thereby, be more sensitive to slight idler misalignments. Likewise, if pulleys are not square, the mistracking effect will be more pronouced if the belt is overly tight around them. Finally, belts that are overly tensioned cannot absorb mistraining sources such as material build-up on idlers and pulleys, off center loading, side loading, or uneven skirt rubber pressure.

Conversely, low tensioning allows the belt to react better to the system - with the caveat that the tension cannot be low enough to permit slippage on the drive pulley(s) or to "float" in horizontal turns or turnovers.

From this, I can only conclude that it is best to tension belts to the belt manufacturer's and conveyor designer's specifications (if given), or to follow the general guideline of setting the take-up tension to a point slightly greater than that required to prevent slippage at the drive. Although many engineers prefer to use the T2 calculation to set take-up tension, I've had better success by using the belt sag between idler measurement method (percentage changes depending on the system).

Having said this, I also realize that specialized conveyor systems may not follow this rule of thumb -- that's why it is important to gather information from the conveyor designer. Unfortunately, getting information from conveyor fabricators and designers can be difficult. It would be ideal if every conveyor system came with an Operation and Maintenance Manual that provided the operator (owner) with system information, preventive maintenance tables, maintenance procedures, and troubleshooting guides. However, most conveyor operators are not given this information in a useful format, if at all.

With regard to your comment on the relative belt tracking at high and low tension areas of the system -- this does not apply. I've studied the relative mistracking between drive pulleys and tail pulleys; and I've made the same observation. However, when you overtension the belt, this mistracking worsens on both pulleys. The point is, operating a conveyor in either an overtensioned or undertensioned mode is not good for belt training. I've highlighted overtensioning simply because most operators who run at improper belt tension levels do so on the high side, not on the low.

I suspect that we are not in disagreement, but that I did not adequately stress the over part of overtensioning. The tensioning forces that I am discussing are the same that lead to splice failures, puncturing at load zones, increased bearing wear, etc. That is, running the belt with take-up tensions at two to ten times that indicated by T2 calculations -- or running the belt through piles of spilled and hardened material.

Regards, ■