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# Conveyor - Catenary Like Curve

## Conveyor - Catenary Like Curve

(OP)
Here is the problem:

I have a gravity belt thickener (belt conveyor used to dewater sludge) that has the first portion of belt horizontal.  The second section is inclined at roughly 30 degrees above horzontal.  It is one continuous belt driven from the top of the inclined section.  The transition between the two sections has a small radius of curvature.  The belt tension under load tends to lift the belt off its bed and cause operational problems (sludge spillage).

A set of rollers above the conveyor belt has been added to keep the belt from lifting.  They do prevent lifting, but cause additional problems as they plow through the sludge.

It is desired to re-design the transition area between the flat and inclined conveyor sections to prevent belt lifting under load.  If belt tension and weight were constant along the length, then the ideal shape of this transition region would be a catenary curve like that of a cable hanging under its own weight.  However, belt tension is not constant, but increases along the belt in the direction of travel in proportion to the supporting force normal to the belt.

What is the easiest way to determine the proper shape of the transition curve?  Can this problem be solved in any way other than a computer finite difference model of the belt?  I'm hoping that the proper shape can be closely approximated by a circular arc or parabola.  I'd also like to be able to verify any computer results via simplified manual calculations.  Any help or additional insights are appreciated.

### RE: Conveyor - Catenary Like Curve

Sounds like an interesting problem, especially with a variable conveyor loading. I can't answer your question but I have some thoughts on your current process. I have built incline conveyors which transition from the horizontal to a 45° incline by using a belt with profiles at the edges of the conveying surface of the belt, at the transition run the belt under narrow idler rollers relieved for the belt profile. I did not have any rollers at points other than the edges of the belt. In order to keep the product out of the roller I used fixed rubber skirt boards which rubbed the belt on the inside of the profiles and thus didn't have product in the area of the rollers. Is your conveyor bed flat? If flat, how do you keep the sludge from running off of the belt? Can you tranistion to a troughed belt at the incline? Another thought is a paddle wheel, either slave-driven or separately driven to match belt speed, located above the belt at the transition. The paddles could be intermittent across the width to allow drainage from the inclined section

### RE: Conveyor - Catenary Like Curve

Try contact Goodyear - conveyor section. I once got a comprehensive manual on conveyor design from them for free. They should be able to provide you with a lot of advice as well.

### RE: Conveyor - Catenary Like Curve

Perhaps you could calculate and plot the "unsupported" catenary curves assuming the entire belt is under its local minimum and maximum tensions.  If the difference between the two curves is small enough, you could build to the nominal and/or provide roller adjustment in the field.

### RE: Conveyor - Catenary Like Curve

Measure the drive power and calculate the operating drive belt tension.  kW(power) = kN (Belt tension force)* m/s ( belt velocity).

Clamp the loaded belt at the tail end and using a hydralic cylinder and clamp at the head drive end, tension the belt to the maximum operating tension. Measure the belt lift and readjust any support rollers to suit the tensioned belt.

Starting tensions may need to be reviewed.

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