Air Cylinder connected to a Lever that drives a Pulley for Applying Belt Tension

[Jeremy Sawatzky]

TL;DR Summary

I need to apply 4500lbs of force to a belt using an air cylinder and a lever Assembly. How do I calculate the required air cylinder size?

Hi, I am looking for some guidance on how to approach this calculation. I have an air cylinder operating a lever assembly that then applies pressure to a pulley of which a belt is wrapped around. I need the belt to have about 4500 lbs of tension. How do I work backwards to figure the required power of the air cylinder?

In the first image, the belt will be totally slack so effectively I am only overcoming the friction of the pivot points and the sleeve guides that support the pulley assembly. I have prior experience with this assembly and know the friction to be negligible and not important to the initial movement of this assembly. However I am sure that it plays a part later on.

In the second image, the air cylinder is fully extended putting the full tension on the belt. The belt is returning 4500lbs of force. The belt tension increases rapidly towards the end of the air cylinder stroke as it barely stretches at all. I would hazard a guess that 99% of the work is done in the last 3" of the air cylinder stroke.

Thanks!

 

[Baluncore]

The distance moved by the roller is decided by the length of the 2.25” crank.
That will not decide the belt tension unless the belt is precalibrated. How elastic is the belt ?

 

[Jeremy Sawatzky]

The belt is very strong and will stretch maybe 3/8" I have a rough idea of how tight I need the belt to be. The final belt tightness is set by another screw adjustment further down the line. I just need to figure if the belt tension increases from 0-4500lbs in about 0.5" of travel, how large of an air cylinder will I need.

 

[jrmichler]

Question: 4500 lbs total force on the belt pulley, or 4500 lbs belt tension = 9000 lbs total force?

This problem requires more than one simple calculation. With the setup in your sketch, the air cylinder force at peak belt tension approaches zero as the angle between the 2.25" link and the connecting rod approaches 180 degrees. The peak air cylinder force occurs when the belt is at partial tension. Be aware that, since the peak cylinder force occurs before the belt is fully tight, the cylinder will jump forward and slam to a stop. An air cylinder with built in cushions is recommended.

Assumption: The belt tension is set by the screw adjustment with the angle between the 2.25" link and connecting rod exactly 180 degrees. Then you can calculate the link angles when the belt starts to tighten, and for a series of steps from there to fully tight. Calculate the cylinder force at each step. Plot the results. The peak cylinder force determines the size of the air cylinder.

The easiest way to do these calculations is to start with single line diagrams. Each link is a single line, with a small circle for the pivots. The first diagram is the point of initial contact with the belt, the last diagram with the air cylinder fully extended. Then do 4 or 5 more diagrams at equal intervals in between. These diagrams are the blue, yellow, and red lines in your sketch with some added information. The fully extended diagram will show the 4500 lb force, the initial contact diagram will show zero force, and the intermediate diagrams will show force calculated using linear interpolation.

Do that, post the diagrams, come back, and we will coach you through the next steps.

 

[Jeremy Sawatzky]

I should have replied back, I followed these steps, the machine operated beautifully. If I remember right, I think I used a 2.25" diameter cylinder.