HP and belt tension requirements for a "no load belt conveyor"

[Life is a bowl of problems]

I'm am designing a belt conveyor that transports thin polybags from where they are cut free from a roll to a packing table. I believe the transport of these practically weightless bags are not significant enough to include in any initial calculation. So the pretension and running tensions for the belts are only required to transport the belt itself at the design speed without slipping at the drive shaft (pulley).

The .042 thick by 4.875" wide by 144" long cotton belts weigh only .131 lbs/sq ft.
The conveyor's top speed is 465 FPM.
The driving shaft is 1.563" in diameter.
The wrap on the driving shaft is about 150 degrees (2.62 Rad) and coefficient of friction is .3.
The only friction comes from the idler rollers that support and tension the belt.

I've attempted to solve for high side belt tension using (T1-wv^2/g)/(T2-wv^/g)=e^(F*alpha) solving for T1 assuming T2 =0 represents the point of slippage. I'm not so sure that that's a correct interpretation.
I get a -.118 result that seems to be a clear indication that I'm on the wrong track.

Can anyone suggest the proper way to determine minimum belt tension just to convey the belt under these conditions?

Thanks,

 

[jlnsol]

Usually the belt pre-tension is listed in the belt suppliers spec sheet (at least for Pu belts with fabric layer(s) inside).
So look at the cotton belt specs for a value like x newtons per mm belt width or similar.
That pretension value is based on experience and will suit most applications to run good.
Please check this and then we can start from there.

 

[robyengIT]

why not to coat the driving pulley with 2-3 mm of "knurling" rubber so just to increase the friction coeff ?

 

[Life is a bowl of problems]

jlnsol, The Belt Manufacturer's specs call for pre-tension of 22 lbs per linear inch(width). There are 14 belts adding up to about 68 inches of total width resulting in 1500 lbs of pretension. I don't believe my 1.563 dia x 80" long drive shaft can sustain these loads. This leads me to believe that these belts in this type of application are tensioned well under their recommended specification. I have limited freedom to increase drive shaft dimension. This design is based on slightly narrower machines. I do have some flexibility to increase drive shaft size but I need to understand the loads to determine how much and then be able to sell it to management.

In response to robengIT, the drive shaft has a knurled surface so the actual friction is higher than .3 but I need to start my analysis somewhere and build on it as necessary.

Thank you both for your response.

 

[jlnsol]

This case is similar to what I experienced more than once! The lower the pretension the better it is for the construction and rollers/bearings. The value of 22lbs/inch (width) is a safe factor for the supplier which will work in many applications. However the belt supplier is not building the conveyor;-)
For Pu belts with fabric layers inside I have good experience to run at 1/3 or even 1/6 of the suppliers pretension.
So that would be between 500 or 250 lbs in your case.
How is your roller supported? Only on two bearings?

 

[Life is a bowl of problems]

Narrower machine had 2 bearings. For the wider machine with the longer drive shaft, I split the shaft and added a third bearing in the center but I don't like the arrangement I used. I used a roll pin to connect the left and right halves of the drivesahft and fear that the joint will fatigue if there is any misalignment and there mostly will be. That's another issue to resolve. I had very little room to fit a bearing there especially when allowing for thermal expansion. Self aligning bearing was too wide which is another concern and the unknown loads make it difficult to determine if the bearing is adequately spec-ed. So I'm tryng to go back to basics to determine the expected loads.

 

[Compositepro]

I do not understand your analysis. It all depends on how much the the belts stretch and you do not even have belt stiffness as one of your factors.

 

[Life is a bowl of problems]

Compositepro,
The belt specs are 1% stretch at 22 lbs/linear inch. I don't believe I need that tension and in fact I believe it to be way over what is requied for this application As as a result the bearings, shafting, tensioners ect are not and can not be designed to operate under that level of tension. There exists slightly narrower machines with similar construction that at are operating fine.

These belts are not transfering power nor conveying any significant load which would require the higher tension and also require beefer mechanics to handle the higher loads. I believe that I only need enough tension to prevent the unloaded belt from slipping. The only loads it will experience is its own weight and some roller friction. The question is how to estimate what that might be.

I hope that adds some clarity.

 

[jlnsol]

based upon F=1500lbs to stretch 1% and a roller to roller distance L(length) = 144" the beltpart stiffness is 1500 lbs/1.44" or 1041 lbs/inch or 182 N/mm'
I suggest to check the deflection of the roller first at 1 promille stretch which means 2 times a pretension force of 150lbs per beltpart or 300 lbs total equally distributed at roller length.
If roller deflection is acceptable, then calculate the required angle of wrap to overcome all frictions (conveyor bed, idler rollers etc) and find how much safety is left in relation to the angle of wrap (150degr).
Is that too small, then increase the pre-tension to 2 promille for instance.

 

[Compositepro]

You need to look at this problem in terns of strain rather than tension or force. Belts vary in length and machines parts deflect. If your belts were steel, keeping all of them under the same tension would be very difficult or impossible using your design approach. You would need tensioners on each belt to compensate for machine deflections and belt variations. But you do not need steel belts, or even cotton ones. Use an unreinforced urethane belt, or similar, and your design problem becomes trivial. You can put 5% stretch in the belt with little tension and all the belts will always be tight and carry your poly bags, with no further analysis. Cotton belts may work very well in your application. I use steel versus rubber only as an example of how you should be thinking about your problem.

You are getting confused by doing very detailed calculations without understanding the fundamentals of the problem. Friction is almost not even a factor here.