Josh,

It might be better to examine the overall scene rather than just address 2 questions.

If you can say the there are many lifts and drops then presumably these are already there or at least estimated. So you have to accept the terrain and the hangingwall condition. Presumably the rock is stable enough to stand roof bolting.

Only the turnbuckle supplier can be happy with the selected adjustment. Bolt cutters and the shortest acceptable link will save a fortune. Radii of 1000m will not feel much disturbance if a few links are surplus to requirement. Then you can insert a few turnbuckles, if you must. Shortening claws are another aid to setting up the suspension chains but these must not remain in place after the preliminary stages of erection.

I would be more concerned with the achieved accuracy of the roof bolting.

Higher radius means better visibility and therefore better communication in the roadway. Thankfully, in these modern times the available radii are going to be governed by the heading machine (Dosco in my day) and its driver and your estimation of R=1000m is maybe high but not unrealistic.

You can run a string easier along a large radius to get the dip measurement. Record these dip measurements for posterity because your curve is unlikely to be truly circular and also because the ground might heave during construction. Finding an experienced installation crew might be difficult. This kind of work is part and parcel of mining. Miners used to do this kind of work quite regularly as faces got worked out or backfilled. I imagine they still do. Trust your own men: they know the surroundings. Any construction crew will have to follow the terrain as is: so there is no cause for concern except their safety. Your quoted route is comfortable and you really shouldn't need to lash out on so many turnbuckles. ■

Hello,

In case of belt conveyor, the vertical plane concave curve formula is as below. The formula calculates radius that the belt will acquire as a consequence of belt tension and belt plus material mass at that location. Now it is necessity that the idlers should be also placed along this minimum radius or radius more than this, so that belt remains supported by idlers in radial zone. This means radius so calculated signifies minimum radius.

Radius R = T divided by (M . g)

Where:

T is belt tension in Newton at the beginning of radial zone

M is (Belt mass kg/m) + (Material mass kg/m)

The g is acceleration due to gravity 9.81 m/(s^2)

Belt tension T can have 3 values viz. during steady running, starting and stopping. Use the one which is the largest. For this tension it can be considered that material is on entire belt length except at radial zone. This may signify worst situation most of the time. In short one has to see for situation which results into largest minimum radius.

As would be seen the required minimum radius becomes less by heavier belt. The radius will also become less by softer start (less acceleration) and by softer braking (less deceleration). The belt worn out mass can be considered about 80% of brand new weight.

In certain constrained situation, the construction radius is taken less than the minimum of worst case, and its consequences are investigated such as:

- Acceptability of belt lift-up magnitude during starting and stopping, as these are momentary status. The take-up should be responsive to take care of release of applicable belt length from curvature, otherwise there would be slip between belt and drive which is not good functionally and for belt life.

- Acceptability of belt lift-up magnitude such that belt does not get damaged by interference with skirt board, etc.

So to decide the conveyor radius for practical use, one should be able to design the conveyor and decide belt tension, etc. in varied situation and then decide the radius. If one is not well versed in design calculation, then take the services from external source.

The conveyor drive, etc. are chosen to suit the application situation.

The minimum radius for convex curves are quite less compared to concave radius. As an example, for 1200 mm wide belt, 40 degree trough, the radius could be around 40 m for textile fabric belt and around 100 m for steel cord belt.

The requirement of minimum radius also to suit mining activity and mining machinery will be another requirement, and to be taken care as per prevailing practice, for margin of compromises.

Ishwar G. Mulani

Author of Book: ‘Engineering Science And Application Design For Belt Conveyors’. Conveyor design basis ISO (thereby book is helpful to design conveyors as per national standards of most of the countries across world). New print Nov., 2012.

Author of Book: ‘Belt Feeder Design And Hopper Bin Silo’

Advisor / Consultant for Bulk Material Handling System & Issues.

Pune, India. Tel.: 0091 (0)20 25871916

Email: conveyor.ishwar.mulani@gmail.com

Website: www.conveyor.ishwarmulani.com ■

Isn’t the curve of a belt, lifted from the concave idler curve because of too much tensioning, a catenary?

If that is correct, then the curve is a cosinus hyperbolicus (cosh).

Placing the idlers in a circle with the calculated minimum radius should then be above the catenary.

Am I correct?

Have a nice day ■

A belt will definitely form a catenary if it is allowed to lift clear. Existing formulae, primitive as they may be, calculate a radius which the belt will sit in.

I think Josh's concern was ensuring clearances between the hanging wall and the footwalls encountered en route and the need to sympathise with the tangent points of the curves.

I am confident that Josh ran the conveyor successfully and hope he was able to chop the chains to length without too much trouble.

The preferred vertical radius for underground is infinity and as the starter realised the deviations to that ideal should be as small as possible within the tunnel heights available.

To sustain the high tensions it might be worth connecting ground anchors near transition points to limit fore and aft sway, pitching, rather than brace from the hanging. Just a thought to reduce the lateral/workout forces on the roofbolts. ■

Hello,

In the earlier posting, my focus was on belt conveyor design with respect to concave curve as per prevailing practice. So it did not dwell into intricacies of exact nature of the curve.

The actual shape of belt at concave curvature is catenary. So one can do exercise accordingly if he so decides. For catenary curve the known input to derive catenary specific formula would be 1) Belt tension at curve inlet 2) Curve end inclination at curve inlet and 3) Curve end inclination at its outlet. However, the exercise is likely to be cumbersome.

The reputed belt maker USA literature states that for belt conveyor concave curve; the difference between circular arc curve and actual catenary curve is small. Thus here the circular arc is engineering purpose catenary shape / curve.

Also belt conveyors are being constructed by considering circular arc since very long time. This implies that the circular arc must be on safer side (i.e. its curve must be obtuse or less sharp compared to catenary curve.

As for practical convenience; the circular arc can be drawn by usual engineers and draftsmen within 5 / 10 minutes. As against this catenary curve calculations and implementation will demand more time and will also need mathematical knowledge for its calculation. Thus it will be found to be expensive, because every hour spent for such work and time delay cost money to the company.

There is one more troubling point related to contractual matter. The calculation according to circular arc are well understood, recognised and accepted practice among suppliers, buyers and buyers’ consultant. The drawing made using the circular arc curve will get cleared quickly. As against this supplier / designer will have additional burden to convince / teach the other sides about the catenary method he has adopted ! This is likely to be expensive and unpleasant.

Finally choice is with the concerned designer about the nature of curve he intends to consider (whether exact catenary or engineering purpose catenary for belt conveyor).

Ishwar G. Mulani

Author of Book: ‘Engineering Science And Application Design For Belt Conveyors’. Conveyor design basis ISO (thereby book is helpful to design conveyors as per national standards of most of the countries across world). New print Nov., 2012.

Author of Book: ‘Belt Feeder Design And Hopper Bin Silo’

Advisor / Consultant for Bulk Material Handling System & Issues.

Pune, India. Tel.: 0091 (0)20 25871916

Email: conveyor.ishwar.mulani@gmail.com

Website: www.conveyor.ishwarmulani.com ■

The catenary formula is not that difficult.

All for now

Attachments

catenary equation (PDF)

■

Whatever formula is used is not an issue. If the belt lifts into a catenary then it is not resting on the idlers as intended, wherever. If a lifted belt is swaying about down a dark mine or fluttering about a wharf in the wind it is a hazard no matter what.

Although in this day and age computer generated CAD models can address catenary versus circular methods the slight refinement would cause resentment in most design reviewers. ■

Originally Posted by trophywalleye

Good Morning,

First I would like to introduce myself to the forum. My name is Josh, and I am a young mechanical engineer with about 8 years of experience - not all in the bulk handling side of things.

I'm reaching out to those familiar with the construction of conveyors, in particular those found in underground mines. I have spent some of my time in the field, however I have only seen a few conveyors constructed from start to finish.

I'm looking for some opinions on a few things:

1) How big of vertical curve is too big in practice underground (with respect to construction and achieving this radius - convex and concave)? How is it achieved considering I would be specifying a system by a supplier with channel rails, spreader bars, box framed idlers, and chains and turnbuckles hung from the back (roof)? Is it expected they can do it just with the turnbuckles? Are there any articles or references I can read up on...

2) I'm calculating in the range of 1000 to 1100 meter radius' (the tensions are high because the belts are extremely long, and there are many lifts and drops). I would suspect this seems very high and difficult to achieve. What should I expect an experienced installation crew to achieve for large radius'?

Thanks,

Josh

The conveyor vertical curve radii are depended on starting and steady state tension, belt weight, belt construction and its properties. For long and carrying larger bulk such radii are common and cannot be avoided. If the layouts are not proper, belt may lift and chances are material spillage occur , if loaded partially or belt edges are subjected to high tensions or belt buckling. It is desirable that expert to design such conveyors using large starting time with long delayed fluid couplings or variable speed drives.

Subash ■

Originally Posted by Subash Chander

.....with long delayed fluid couplings or variable speed drives.

Subash

Fluid couplings have recently, in these forums, been mentioned to overheat, boil and even explode. I would not recommend them for use in a high duty underground application unless the drive sits in open air above ground where it can be observed steaming along. For lower duty, completely underground, the fluid must be non-flammable. Presumably this will nullify the fire hazard after a coupling has gone bust. ■