Crowning of Pulley Wheels 1

[corrosionman]

Small wheels are "crowned" to a radius which keeps the belt central. Wide conveyor belt drums can also be crowned but the same effect is also achieved by machining so the central 33% is parallel with the outer regions tapered to have a trapezoidal profile.
I believe it will not work if the profile simply goes to a central apex.
Please does anyone know if it is acceptable to achieve this crowning by a series of step changes in diameter rather than a slope.
(Our conveyor drum is 48 inches wide and 18 inches dia at centre and crowning reduces the dia at the ends to 17.5 inches and we wish to achieve the change in three equal steps.)
All comments much appreciated
Corrosionman

 

[Ron]

Stepping will likely cause inordinate belt wear.

 

[zekeman]

You are correct. Trapezoidal will not work, but stepping might work with sufficient steps except for the wear problem Ron points out. If the speeds and tensions are low, then maybe wear won't be an issue.
But I'm curious as to why you can't use conventional crowning.

 

[corrosionman]

Zekeman and Ron
My Client is a large Mining Company with very many Conveyor belts and the drums are rubber covered half inch thick to limit wear and reduce belt slip. To Crown a steel drum before it is rubber covered is expensive. To crown the rubber is much less costly. However instead of conventionally crowning the rubber in a big lathe it is easier to build up a step profile by wrapping the drum with 2 mm thick rubber - - more layers in the center, less at the ends etc etc. The rubber is then steam cured in a heated autoclave. The Client is already using drums crowned such as we are proposing to do ourselves but I am curious to know if they really work.My Engineering Directory says steel drums of this size need only 2 mm of crowning but we are asked to do a minimum of 6 mm. I still not yet figured out how crowning works (or is supposed to work)
Regards CM

 

[MintJulep]

The Mint Julep explanation of crowned pulleys (may not be correct):

For any contact patch between the pulley and the belt the friction forces can be resolved into a radial-tangential component and an axial component.

Consider two contact patches symmetrically opposed about the high-point of the roller crown.

When the belt is tracking straight the resultant friction forces on those contact patches are equal and opposite axially and balance each other out.

If some perturbation upsets the tracking one contact patch will move uphill and one downhill.

The strip of belt that is moving uphill will increase its tension, and as a result the friction forces at the contact patch will increase.

The strip of belt that is moving downhill will decrese its tension and friction forces.

Now the forces are unbalanced, and they are unbalanced in a way that tends to drive the belt back towards a centered position.

This of course occurs for every pair of symmetrically opposed contact patches.

 

[GregLocock]

Tire manufacturers know all about squishing layers of rubber into a smooth profile.

On the other hand I wonder how long a rubber step would exist, perhaps the belt would machine it smooth.





Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[zekeman]

Quote"The Mint Julep explanation of crowned pulleys (may not be correct):

For any contact patch between the pulley and the belt the friction forces can be resolved into a radial-tangential component and an axial component.

Consider two contact patches symmetrically opposed about the high-point of the roller crown.

When the belt is tracking straight the resultant friction forces on those contact patches are equal and opposite axially and balance each other out.

If some perturbation upsets the tracking one contact patch will move uphill and one downhill.

The strip of belt that is moving uphill will increase its tension, and as a result the friction forces at the contact patch will increase.

The strip of belt that is moving downhill will decrese its tension and friction forces.

Now the forces are unbalanced, and they are unbalanced in a way that tends to drive the belt back towards a centered position.

This of course occurs for every pair of symmetrically opposed contact patches
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You may be right about the strip pair concept but crowning can also be explained without assuming a tension change in the strip pairs you suggest but the fact that as the belt tends to move axially, say to the right , the angular contact on the left strip(s) increases and the right strip(s) angle decreases so the axial force component on the left increases at the same time the right one decreases, thus pushing the belt to the left for automatic correction. I'm not sure as to the roles of the two mechanisms or if it a combination of the two.

 

[zekeman]

Correction, my bad.
I just realized I made the opposite case of that which I claimed.
Without a change of tension, crowning would cause instability.
So it would appear that there are two different axial force mechanisms at play on the strip pairs, one due tension increase that is self correcting as Mintjulip says and the one from increased angle which is desstabilizing.
Accordingly, the stability rests on the tension increase being the stronger of the two.

 

[Compositepro]

I've studied web tracking mechanics for many years because many processes I'm involved in require it. The explanation for how crowned pulleys work can be found in physics textbooks from the 1920's when the technique was more commonly used.

Once a belt contacts the roller surface, the the point of contact follows the path of the roller surface. This is a circle that is at 90 degrees to the axis of rotation. The crown works by distorting the shape of the belt as it approaches the roller. A belt centered on a crowned roller is stretched more in the center than the edges. When it tracks off-center one side is stretched more than the other and the belt is no longer straight but curved. The belt tension tries to keep the belt in contact with the roller surface. Thus the belt that is approaching contact with the roller moves slightly towards center.

For a crowned roller to work the belt must have certain elastic properties and shear stiffness, adequate tension, and friction (to prevent slip). If load on a conveyor belt is not even it can cause tracking problems. I'm certainly not a conveyor belt expert, but I would have doubts about the degree of tracking control that crowning provides for such a wide belt. Systems that shift the roller side to side while shifting the axle angle slightly are not very complicated and provide very accurate control.

 

[Ron]

To get a good idea of how this works on a small scale, get a belt sander and play with the tension adjustment. You can see the belt ride up and down the crown.

 

[corrosionman]

Gents Thanks for your inputs - - we finally "crowned" the rollers by building up the 6 mm thick rubber covering using several layers of rubber each 2 mm thick. A narrow strip in the centre was applied first, then a strip a bit wider for second layer, and so on. Successive layers smoothed out the steps - - the final job looked OK and, more important, it worked very well keeping the belt central .Thought you'd like to know.
Thanks again
Corrosionman.

 

[racookpe1978]

OK, but add this question - from somebody who normally passes stuff through a simple, round pipe.

If the crown raises the inside of the belt - and I see the reason why stretching a suitably tight belt on a crown forces the belt to the center of a radiused pulley - why doeosn't the load fall off easier?

Wouldn't the overall belt have to be "V" shaped?

 

[NomLaser]

You aren't stretching the belt to the point of elastic deformation. The belt reforms back to its original shape between the pulleys and there are usually support pieces between the rollers that the belt rides on so it doesn't droop too far when there is an object on the belt. Stainless steel or a zinc plated steel work pretty good in this application.