[Dear Oscar,

Pulley Diameter is selected based on the steel cord belt construction as a function of wrap angle and belt properties for a given belt safety factor and whether clean or dirty side contact. The below has many caveates a designer must consider.

First, the wrap angle forces the wire construction to become torsionally and axially solid beyond about 70 degrees. That is the wire strands stop flexing when the internal friction is sufficiently large to stop torsional flexure and elongation between wire groups and betwee wires. Thus, bending stiffness changes to a set value beyond a 70 degree wrap and the combined bending and axial stress must be factored with this in mind.

Second, the belt safety factor selection must be included in the pulley diameter selection. Given the above comment, a SF=6.7:1 can have a high tension pulley diameter ( bending or torsional stress and axial stress) where the pulley diameter is 150 times the wire cord diameter. At SF = 5.5:1 the number is close to pulley diameter = 200 x wire cord diameter. These are at 100% operation tension. The pulley diameter can be reduced to 70% of this value for low tension diameter pulleys when the belt working tension is less than 70% of the maximum operating tension.

By example: A ST-2000 N/mm belt rating designed for SF=6.7:1 will likely have a wire rope diameter = 6.5 mm (6.5 mm x 150 = 975 mm). Then a 1000 mm high tension pulley would be acceptable. The low tension pulley could be 700 mm. These values also depend on wire rope construction. In low steel cord ST values this may need adjustment when the steel cord construction becomes less flexible such as a semi-Warrington weave or reduced wire strand count such as 7X7, et al.

The slight wrap angles such as < 15 degrees can be further modified by the lower bending stress. First, you must know the contribution to the overall wire rope fatigue limit. How much goes to axial fatigue and how much to bending fatigue? You must also be cognizant of the stress the wire rope size has upon the shear stress between steel cord and pulley as a function of the pulley diameter. So, no simple and single valued answer. Belt suppliers, that know these answers, and there are only a few, tend to be very conservative. The engineer must interrogate the belt supplier for what they know and how they have tested and analyzed these conditions.

It is always easier to specify a slightly larger diameter except:

A) Means larger gear ratios and may require an additional gear stage which in turn means low reducer reliability

B) Means belt is more difficult to clean with a scraper give belt cover has less surface flexure

C) Means belt can operate with lower safety factor (SF) - cannot use the published belt ST value with published Pulley Diameter with lower SF. ■

Originally Posted by ONgubane

Dear Lawrance,

Thank you for your elaborate reply.

Do you have similar comment for fabric belts?

Kind Regards,

Oscar Ngubane (Mech Eng, TWP Projects, South Africa)

More difficult with the muliple plys, type of weaves, type of carcass, splice designs - stretch length will dictate stress at axial edge of splice, how step lengths are configured, finger splices, et. al.

I prefer to keep to the things we have exhautively studied. Fabric reinforcements of pipe conveyors is the grey area for us. We do study the type of carcass constructions needed to reinforce pipe conveyor designs.

Sorry for the brief comment. ■

Originally Posted by ONgubane

Dear Experts,

Most, if not all, belt manufacturers have tables recommending pulley diameters for snub pulleys (15 to 30 degree wrap angle).

Has anyone come across litarature on Deflector pulleys. That is, "tail snub pulleys" with wrap angles of 2 to 15 degrees? Surely these could be made smaller diameters than conventional snub pulleys.

Your assistance will be greatly appreciated.

Regards,

Oscar Ngubane

Mech Eng (TWP Projects, South Africa)

Why redefine a snub pulley? If you drive the tail drum then the snub drum must go on the top strand which keeps it on the slightly dirty side. If it isn't a tail drive then you are talking about a bend pulley and should adhere (dirty talking) to the manufacturers' sizing for bend pulleys. If you persist and deviate you will be contradicting the published guidelines and that would throw warranty out of the window. Why make work? ■

I think there is more depth to this post then is being acknowledged. Belt manufacturers list the recommended pulley diameters according to the belt tension. Some list a lesser diameter allowed for snub pulleys of limited wrap angle. These don't address the issue of what are the pulley diameters required as a function of both tension and wrap angle. Indeed if we logically extrapolate the belt manufacturers guidelines then we could not use 5", 6", 7" or even 8" diameter idler rolls. The answer is in the shear lag of the rubber but this has never been developed and presented. Larry makes a good point in fixing the pulley diameter to wrap relationship beyond 70 degrees of wrap though I must say that I did not quite follow the longitudinal and torsional constraint argument. The pulley diameters is related to the diameter of the outer wires and is depended on the freedom of the wires to slide past each other, otherwise the pulley diameter would depend on the wire rope diameter as if it were a solid steel round bar. Too often we use pulleys or live shaft roller to force a modest deflection of the belt line and for these there are no logical rules or guidelines.

Joe Dos Santos ■

Hello,

Standards and belt manufacturers provide pulley diameter for belt deflection less than 30 degree (i.e. belt wrap around snub pulley will have angle less / equal to 30 degree).

If the belt deflection is very low opt for convex radial zone for return belt instead of snub pulley. Convex radius is as per rule / calculation.

In case of shiftable conveyor, there is no space to mount snub pulley at tail terminal (return station). Belt (having huge tension) is snubbed in by convex curve i.e. return idler level rises gradually as per convex profile and it reaches required level in reasonable / suitable distance.

I think this obviates the need for snub pulley and its size if belt wrap is 10 - 15 degree.

Regards,

Ishwar G. Mulani

Author of Book : Engineering Science And Application Design For Belt Conveyors (new print November, 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 ■

Anyone who puts in a tail snub pulley with 2 degrees wrap should be taken ouside and severly dealt with!

You have to "earn a pulley" as the best conveyor designs have the least number of them.

Regards

LSL Tekpro ■

Amen to that Graham. I too am a pulley minimalist. I do sympathize with the principal of the question however, which I don't believe has been addressed and I wish that a belt manufacturer (the ones that write these rules) would chime in.

In my previous post I asked what is the required pulley diameter for a given belt construction as a function of the wrap angle? I posed that extrapolation of the pulley criteria would invalidate the use of return idlers as these do have a wrap angle and their diameter is in violation. Qualitatively I know the answer, there is shear lag through the rubber allowing plies to behave as independent. The continuum between this case and a pulley (where the wrap is sufficient to develop the shear forces that cause plane sections to remain plain at the interior of the wrap) has never been developed and presented and this is at the heart of the question.

Lets go in the other direction. Does this mean that if a return idler can support the load of a 10 degrees wrap than it is ok regardless of the diameter? ■

Dear Joe:

Regarding your question of "longitudinal and torsional" design criteria for steel cord belt I offer the fact that the steel cord are stressed due to axial loading and, when bent over a pulley the cords must also carry the bending stress windup. The windup is a function of the wrap angle. It takes about 70 degrees to fully lock the individual wires within one cord. The cords never reach a state where their sectional modulus becomes the OD of the cord. Take a wire rope connected between hands and bend into a loop. Feel the resistance as the circle closes to a smaller radius. However, the sectional modulus migrates from near zero with no wrap to a much higher number, depending on the cord construction (i.e. 7x7 is different than 7x19). Much has been written about this when wire ropes were fatigue tested for use in Nuclear Plants such as Hanford Works here in Washington State.

Return idlers used in place of bend pulleys is another - more complex problem than meets the eye. At small wrap angles, the compression of the bottom cover and the internal belt construction produces an artificial radius larger than the bend pulley diameter. We have used the criteria of up to 2 degrees with success for T2 belt loads. Thus, a 10 degree bend will require 5 idlers to do the same, providing the resultant force does not appreciably reduce the idler's life. To go further, we invoke IP. ■

Here are some notes on pulley (sheave) diameters vs. cord (rope) diameter. Note: they do not account for wrap angle.http://www.wwwrope.com/productpdfs/ELTB09.pdf

http://www.slingchoker.com/sling2/crosby/vii/vii177.htm

Graduating to bending fatigue see FIG. 8-6:

http://www.unols.org/publications/wi...pescables.PDF

More recent analysis:http://nopr.niscair.res.in/bitstream...%20189-195.pdf

These articles do not evaluate the rope as it applies to a steel cord belt. They are only interested in sheaves a rope construction. The sheave applies an additional stress component that does not occur in the belt.

You can do academic analysis from text book entitled: Theory of Wire Rope University of Illinois at Urbana Champagne (we have at office) has some flaws.

Tension Member Technologies (TMT) have made bending fatigue their science. The owner came from Hanford.

Anyway, happy reading. ■

Morning Joe..

I simply can't remember when I last put a snub pulley at a tail, other than when I needed some wrap for conveyors fitted with tail drive(s).

The idea is to gradually bring the belt to the return belt line over a suitable distance. None of this wrap over idler stuff.

At the head end, you can go to 800mm head pulley diameter before you need to think about a snub.

I have just done a couple of conveyors with 1000mm diameter head pulleys. No snubs though. The profiles were with concave radii, so I simply selected suitable return belt tangent points, so the belts made straight for the under side of the pulleys.

No snubs.. have our Forum readers ever tried to change one out? I suppose it's OK if you are a life sized bat that can work upside down, and can borrow the gear that the aliens used to lift stone blocks out of remote cliff faces 4 000 years ago.

The trouble is that we have conveyor designers out there, that have never even pulled the engine out of a pick-up truck, or even taken out a gearbox!

Cheers

LSL Tekpro ■

Larry,

You are absolutely right in what you are describing for steel cords and steel cord belts. With the slip between wires and the twist of the strands the overall path length of each wire is equal. The situation is quite different at multiple plies as the plies don't twist around each other and they do have different path lengths. As I have said, qualitatively I know the answer why return rolls don't act like pulleys. I have said shear lag in the rubber between plies. You mention compression of the rubber. Indeed the return roll locally becomes an indent into the rubber cover and the effective curve radius at the carcass/cords is much larger.

You mention break angle limitations over each return roll, of 2 degrees. This is very good. I too have created such rules which I refer to generally as continuity criteria. All of this makes the point that the pulley diameter criteria should bridge the gap between idlers and pulleys. Indeed, rather than three or four set values (T>0.8Tr, 0.6Tr

Graham,

I know that I have turned this into an academic exercise to some extent but it would be nice to have guidelines from the belt manufacturers on low wrap pulleys or live shaft rolls regardless of why they are being used, say as snubs ore deflectors, etc.

Joe Dos Santos■

Larry,

For whatever reason, the second paragraph of my post got cut off when posted. Here it is complete:

You mention break angle limitations over each return roll, of 2 degrees. This is very good. I too have created such rules which I refer to generally as continuity criteria. All of this makes the point that the pulley diameter criteria should bridge the gap between idlers and pulleys. Indeed, rather than three or four set values (T greater than 0.8Tr, 0.6Tr Less than T less than 0.8Tr, T less than 0.6Tr) for a belt construction, the minimum pulley diameter guideline should also be a graph as a function of wrap angle, from 0 deg to the wrap angle (say 70 degrees in steel cord belts) that requires the max pulley diameter.

Joe Dos Santos ■

Joe,

I see a problem giving out such a formula. Then every text reader will be pushing for pulley sizes for each wire cord diameter. All these diameters will drive a normal man to do abnormal things, and abnormal men to go beyond hope.

We could publish pulley diameters for each cord size by cord construction type, safety factor, and tension range till each diameter graduates up 100 mm or 200 mm and then for groups of wrap angles, ..... Who will buy the effort?

There are so many quirks that wanabe engineers practice. They do not read standards, design reports, publications some present as a better design, ..... How many times have we answered the same question in this forum to those that are too lazy to make an effort to find the answer already available.

On a separate note, I interchanged the note on bending, which is really torque. When you bend wire cords (ropes) most naturally twist as they are bent, introducing a torsional response, not to different from pulley a cord axially and notice that it also twists. Typically, when the cord is bent over a pulley, it takes about 70 degrees of wrap to fully lock the wire strands within the cord - for most steel cord constructions. There is a body of research on what happens between wires during these events, but, it never becomes a solid. ■

Larry,

I agree with most of what you say. The sins are already being committed. on the one hand the responsible designer, that does not know the answer will not budge from the recommended pulley diameters. The reckless designer may not care, rationalizing that if the roll, per CEMA, can support the deflecting load, regardless of wrap angle, than it must be ok. Extend this to the use of live shaft rolls, with very high load capability, then the sins can be deadly. That is why I wish the belt manufacturers would take this on, with the same guidelines that they already use, just relate it to wrap angle.

Joe Dos Santos ■