# Belt tension to rotational force

This may be an obvious question, but here goes anyhow.

If you have two pulleys (different diameters) with infinitely strong bearings and shafts, does increasing the belt tension have any effect on the torque required to turn the system? I.e. Is a super tight belt is harder to turn than a weakly tensioned belt (assuming no belt slip in either case)?

Ignoring the cost and wear implications of doing this as increasing the tension will obviously wear out your belts and bearings significantly faster.

I've done a force balance, and it seems as though, no, everything balances out. If you increase the tension on a belt you're increasing the force on both sides and the torque on the pulley input seems to be independent of the belt tension. When the system is moving at a constant speed under a constant load, belt tension doesn't seem to factor in (again ignoring the loads on the bearings and shaft)

However from a practical point of view it seems to make intuitive sense that if you crank up the belt tension it'll be harder to turn them. Is my intuition wrong, or is there something I've over looked?

## 3 Answers

Your intuition is correct in "real life", but incorrect within the specific parameters laid out in your question.

In "real life" (where your intuition rightly stems from), the extremely tight belt will put a high radial load on the bearings, and this will introduce friction into the system meaning it takes more torque to turn the pulleys.

In your imaginary perfect system, the extra tension will simply be balanced by higher reaction forces at the bearings, with no effect on the torque/friction, since the bearings are perfect.

• Beauty, it's nice to know I'm not crazy. So then to extend your answer to practicality. Cranking up the tension beyond what's needed to stop the belts from slipping would likely result in failures due to bearing wear, the shaft bending (potentially) and shortening on the belt lifespan as well. I.e. a really really poor way to increase the load. Feb 7, 2018 at 17:46
• Yep - You got it! There are lots of different bearing designs/arrangements that have different pros/cons re: cost, ability to withstand axia/radial loads etc., so if your components are wearing out too fast because you need to increase tension to reduce slipping, then there solutions out there, but, a chain/timing belt might be better still! All depends on the specific application. Feb 7, 2018 at 18:11
• The question originated more from someone asking me "why don't we just jack up the tension on the belts to increase the load, that seems easier than adjusting the input load", and I was having troubles finding a reason/explaining why it was a bad idea lol Feb 7, 2018 at 18:21

The answer depends on whether the belt is flat/toothed or smooth/vee-profile. In the case of the vee belt, increasing the belt tension increases the work it takes to pull the belt out of the pulley groove as the pulley rotates. This increases the amount of work it takes to rotate the two-pulley system and heats up the belt. This effect does not occur if the belt engages the pulley surface with teeth.

• The system i'm working with is a vee-profile belt so this load would apply possibly. How much of an effect does the belt tension have on the overall load. I assumed there would be some additional deformation of the belt that would result in a higher load, but that the effects would be negligible. Would I be off on that assumption? Feb 7, 2018 at 19:23
• Diesel, best thing to do is download a design guide from one of the vee belt manufacturers, they will have recommendations on maximum and minimum values for belt tension, torque load, operating temperature and efficiency losses due to wedging/unwedging action of the belt in the pulley groove. Feb 7, 2018 at 20:38

From reading your answers (provided as comments) to the answers given, the “best solution” to increasing the load capacity is to change to multi-belt pulleys: 2 and up to 8 are used in some situations - belts can provide a “softness “ compared to gears or a shaft.