# I How to determine a load for belt tensioner

1. May 1, 2017

### tzod

Hello all. I am trying to understand how to calculate the load in a certain arrangement. More specifically, when there is no work being done on the belt, a set of idlers are under equal load. When the main drive pulley at the top is rotating counter clockwise, the belt on the right in the image takes on a load ( the system is lifting an object off the ground) and forces the idler swivel plate to the right. I want to understand how to calculate what force is being exerted against the idler on the right to determine what amount of force would be required to cause the idler swivel plate to remain in the center. I want the swivel to remain in the center so I can add pressure sensors to sense what pressure is being exerted so a controller can make decisions.

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2. May 1, 2017

### Staff: Mentor

You'll be able to work this out pretty quickly if you draw a free body diagram including the tension in the belt, at each pulley. Wherever the belt goes over a pulley (drive/driven pulley or tensioner idler) the belt's tension will provide a force in two directions; the vector sum of these forces must be canceled by the force on the pulley's pivot and mounting plate.

The tension in the belt in each segment will be determined by the work being done on/by the pulleys the ends of the segment. The difference between the tension on one side of the pulley and the the other will give you the torque, and that times the RPM will have to be equal to the work done.

To very good approximation, no work is done on a tensioner idler pulley, so the beltvyension will be the same on both sides of an idler; but because the belt enters and leaves the idler in different direction there is a net force on the idler pivot and mount. The tension entering and leaving a driven or driving pulley will be different so there will be both a net force on the pivot and mount, and also a net torque that's foxing the work.

3. May 2, 2017

### sophiecentaur

There is bound to be a certain amount of vibration which could be responsible for producing peak loads well above any basic 'triangle of forces' calculation.
It's going to be a bit difficult to calculate because the tensioner will be almost certainly in the 'return' section of the belt where the loads would normally be much less than on the drive side (ideally zero?). I could even suggest that you would need to measure it under all conditions if you want to find the maximum force involved. This would be when there is 'overrun', when the driven wheel is overtaking the drive, as when slowing down. The 'worst case' could even be higher than using the known forces on the 'driving section'.
I think this could be really hard to do and it could be better to look up the recommended tensions under well known situations.

4. May 2, 2017

### tzod

Thanks for the input. Using a digital sensor like a load cell etc, the processor can average out and remove peaks, whereas a spring>switch based system may not be able to remove the peaks. I was hoping to find a way to calculate the forces to determine which load sensor methods to look at. It is not easy to test the system at this point so that is why I was looking for the math options. Unfortunately after a lot of searching I can find no hits on how to get forces on an idler based on load, angle, etc.