# Total force on a round form

by paul11273
Tags: force, form
 P: 156 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
 P: 156 Here is a quick diagram to help you visualize what I have described. Attached Thumbnails
 Engineering Sci Advisor Thanks P: 6,031 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.