For the most part we agree. CDI parses the concave curve into smaller intervals. The lift tension is calculated at about the 75-80% of the concave vertical curve arc length, assuming the belt is horizontal before the curve. This means we extend the loading beyond the point of initial tangency to about 80% of the arc's length. Therefore more tension is applied than at the initial tangency.

We generally agree with using worn belt, however, the top cover is worn to within 3mm of the steel cord over about 70% of the top cop cover's belt width and half the top cover wear over the bottom cover at its full width.

To determine the belt tension, we also use partial loading schemes. A maximum of three largest non-sequential uphill or downhill flights are loaded for uphill at minimum operating temperature, with new belt, and visa-verse for the downhill plus the loss of idler drag and minimum belt covers to apply minimum rolling resistance. ■

Dear Derek and Lawrence,

Not being really familiar with conveyor belts, I find the discussions about this subject in this forum very interesting and intriguing.

In this thread, I understand that in a concave belt section, there is a possibility that the belt is,

under certain circumstances, lifted from the rollers.

At that moment, the belt is not guided anymore by the rollers and is following a “chain curve”.

This “chain curve” has the same mathematical form as f.i. an anchor chain on which a ship is moored and an arch in a (stuck) silo.

The mathematical equation is a cosinus hyperbolicus (cosh).

This can be calculated for the belt and then be checked against the built roller curve.

Any loading condition then can be investigated.

Or is this old news?

have a nice day

teus ■

dear Derek,

The equation : R=T/wg

T = tension in Newton

w=mass of load and belt in kg

g=gravity constant in m/sec2

results in R=Radius in (Newton)/(kg * m/sec2) = dimensionless

Or is there a factor 1 involved with the dimension "meter"

Is the catenary between 2 rollers not less important than the catenary that is created when the belt is lifted over a long distance?

Since when get calculations too difficult for designers?

All for now

teus ■

Dear All,

1. Derived concave vertical curve radius "lift" formula used which estimates the true catenary hyperbolic function is derived from the same formula used to estimate the sag between two idlers, except for the 1.1 (1.08) factor. The 1.1 factor accommodates the lift at near the end of the curvature for all included angles.

Radius = (1.1 x Tension) / (belt mass x g) per Teus

2. Concave curve can be modified by using a spiral analysis which reduces the radius (curvature) at the lower tension zone to allow a greater radius at the higher tension zone within the same total arc length.

3. Normal criteria, set by project management firms, that there be no belt lift off until the belt has reached end-of-life, including during starting and stopping. Sometimes this must be relaxed, such as at tripper approach radii. Two reasons: belt tracking and spillage. With highly undulating geometry paths, criteria for which flights are loaded and unloaded becomes a probability of likelihoods.

4. Starting/stopping forces to analyze lift off, in my opinion is not conservative. Often belts have hood covers, wind hoops, side guide rollers, tolerances in rolling resistance, belt mass, and variations in start/stop control algorithms, which either need analysis or some allowance to assure a reliable installation.

5. Clients' Design Criteria set guidance rules for Design and Supply firms to conform too. This results in acceptable design standards which can easily be evaluated by the Vendor Bid review team in order to standardize the cost impact on civil/structural route. This cost can be very large when taken in proportion to the total capital investment. ■

Dear Lawrence,

Am I right that the factor 1.1(1.08) has the dimension meter?

Many years ago I had to calculate an anchoring system for Panamx sized ships in the port of Montevideo.

I made a program in QuickBasic to calculate the catenary of the anchor chain in combination with the holding force of the anchor.

The catenary formule takes care of an increasing force along the belt.

If you have QuickBasic and are interested I can send it to you.

If it does not help you, it does not harm you either.

(Dutch verb)

take care

teus ■

Dear Derek,

With:

w=mass of load and belt in kg/m

the dimension equation fits.

Thank you for your patience

Teus ■

Dear sirs,

may bee my new patetented rollers will bee you a big help.

I produce rollers out of cheep RECYCLED FULL PLASTIC. In this case, I can give each roller a conic form, so that the belt will go better around concave curves.

The number of rollers and the different diameters of each roller will give you the best result!

Please send me your Mail-adress and I give you more informations

Best regards

BLAHA, Peter

Rosenstr.5

D-85609 Aschhein (near Munich)

GERMANY foerderschuettgut@arcor.de ■

Without going into the detail, the 1.11 factor corrects for variations in the approach and discharge angles for a concave curve radius. When you derive the catenary conditions, the maximum tension must be derived from the entry slope and its counterpart. It is a simple matter when the entry slope is zero and the follow-on slope is positive. It is a puzzle when both of the two slopes are not zero, you will find a point of maximum that is close to 1.11.

Recall most analytic procedures use the slope intercept. The curve radii are not parsed into small segments, such as in BELTSTAT, which allow investigation of the maximum and minimum points within the curves. This is often at or near the minimum belt tension in the curve, at its intercept, definitely not at the maximum tension point.

A worn belt must be treated as a worn belt. With the strong propensity to use heavier belt covers, a highly worn belt can lose 30% or more of the original belt weight making this argument mote.

Dear Mr. Blaha,

The idler barrel cone idea is not good. Think about what you do to the surface speed along the idler surface. Bad for belt and idler plastic surface wear. ■

Teus,

Since you have mentioned mooring in Montevideo; do you ever use Max Irvines "Cable Structures" in your filament calculations? I've found it very thorough & fascinating, especially the treatment of shock wave development in barrage balloon moorings. If you need an electronic version... ■

Dear Zlatni,

Your idea of segmenting the conveyor into 6 or so individual sections, is a common and proper practice, unless you chose to integrate the details across the curve length or spiral the radii geometry.

Our normal criteria varies with geometry. If the conveyor is upward sloping between start and finish of a selected concave radius, the last segment would likely have the highest tension. I am sure you can work out all other geometry and tension scenarios for undulating conveyor geometries.

Given this specific case (also answering your last paragraph), the lift and high tension criteria would be seen as this last segment. The last segment has a number of operating criteria: empty and full belt on the last segment, winter and summer temperatures, new and worn belt, variations in rolling resistance over time, with high tension leading into or just before the last segment. The belt should be analyzed with new and worn conditions as you note. If you have the BELTSTAT Professional version, this can be accounted for in the "Project File" group where you can enter both new and worn belt conditions, summer and winter, variations in material loading patterns, various rolling resistance patterns, etc.

The reason for empty analysis (only the segment under consideration) is to predict potential belt "lift-off" when the belt is loaded that maximizes the tension in each segment to be evaluated. In many cases, a certain amount of belt "lift-off" is allowed, especially near the end of the belts life. For example, no yard tripper conveyor would function with the "no-lift-off" criteria. Prudent design criteria allows for good judgement knowing what performance will follow.

BELTSTAT provides the lift-off dimensions in the last column of the special curve analysis summary page for all conditions evaluated. ■