What is the total force on a round form without using air cylinders?

[paul11273]

If this is in the wrong section, please let me know. I will gladly re-post to the correct area.

Here is a real problem we face at work, and I would like some help quantifying it.

We have a round form, whose diameter is adjustable. Air cylinders are used to expand or contract the overall diameter of the form as needed.

This form receives several wraps of a product. The form rotates, and the wraps of product get wound around the form. Kind of like a garden hose carrier. The product translates along the cylindrical length of the form as the form rotates, so a single wrapped layer is applied to the form.

While the product is being wrapped around the form, there is about 1.25 kg of force (tension) on the band. If the force is too high, we experience "crush" of the form. Basically, the air cylinders are overcome by the compression, and they begin to allow the form to shrink in diameter. This is the problem we face. "Crush" is not desirable.

Here is the question:
How can I quantify the total compressive force against these cylinders?
I am able to know the number of wraps of product, and the linear tension of the product as it is applied to the form. I have been toying with the idea of simply multiplying the kg of force by the number of wraps, but that doesn't seem quite right.

Of course, it would be better if we didn't use air cylinders to begin with, but this is what we have, and we need to make it work. At least once we understand the total force we are dealing with, then we can begin to tackle the problem a little better.

Any help on this would be greatly appreciated.

Thanks.

Paul

 

[paul11273]

Quick diagram

Here is a quick diagram to help you visualize what I have described.

 

[AlephZero]

This is similar to the stress in a pressurized cylinder http://en.wikipedia.org/wiki/Cylinder_stress except you know the "stress" and want to find the pressure, not the other way round.

Consider one segment of the form and the section of wrap that covers it. You have the tension of the wrap acting on its two edges, directed along the tangents to the circular shape. You also have the force in the air cylinder acting outwards. Just resolve the wrap forces in the direction of the air cylinder. If there are n segments, each one covers an angle of 360/n degrees, so the wrap tensions are angled "inwards" by 180/n degrees at each end.

(As a sanity check, it should be obvious that if there were just 2 segments, the force in each air cylinder would balance twice the wrap tension (twice because there are two sides to the segment). If there are more segments, the force on each air cylinder will be less.

 

[nvn]

paul11273: It looks like each adjustable pneumatic actuator spans across the entire diameter of the cylindrical form, correct? It looks like there are three adjustable actuators at approximately one x-station location inside the cylindrical form. We might need to know the width of the product band. And we might need to know the length of the cylindrical form supported by each set of three adjustable pneumatic actuators; or in other words, we might need to know the length of the cylindrical form, and the x-axis coordinate (location) of each set of three adjustable actuators, measured from the beginning (x = 0 mm) of the cylindrical form. (The x-axis is the longitudinal axis of the cylindrical form.)

 

[paul11273]

nvn: Thanks for the reply. The way I drew the diagram is a bit misleading in that respect. I just wanted to represent the different sections. It is not literally built the way I drew it. There are actually about 16 separate sections that make up this form, and they are connected to the air cylinders via some mechanics. Not directly coupled to the forms outer plates. I tried to simplify this in the drawing, and ended up misleading you. I am sorry about that.
My main concern is calculating the total "crushing" force the band applies to the form. From that we can define the force each actuator + it's mechanics needs to be able to resist.
I hope that helps clarify.

 

[nvn]

paul11273: Let's say each pair of opposite sectors of the cylindrical form is supported by one adjustable actuator that spans across the entire diameter of the cylindrical form, similar to your diagram, which is a good schematic representation. Let n1 be the number of adjustable actuators. Therefore, n1 = one half of the number of sectors. Therefore, we have,

F1 = 2*F2*(L/b)*sin[(90 deg)/n1],​

where n1 = number of diametrical adjustable actuators = 8, F2 = tensile force in product band = 12.26 N, b = width of product band, L = axial (x-direction) length of cylindrical form per set of eight adjustable actuators, and F1 = compressive force in each adjustable actuator.

For example, if there are eight diametrical adjustable actuators supporting each 1104 mm of axial length of the cylindrical form, and the product band width is 95.5 mm, then we have L = 1104 mm, b = 95.5 mm, and n1 = 8. Therefore, we have, F1 = 2*F2*(L/b)*sin[(90 deg)/n1] = 2(12.26 N)[(1104 mm)/(95.5 mm)]*sin[(90 deg)/8] = 55.30 N.