# In an open belt drive, which angle of wrap should be taken for calculating tension in the belt?

An open belt drive with flat belt has different angle of wrap on the larger and smaller pulley. I have to calculate a tension in the pulley. We generally use the formulae

Here θ is the angle of wrap. Now the angle of wrap is different for larger pulley and smaller pulley in the belt drive. So which angle of wrap should be used in this equation?

TL;DR: use the angle on the driver/driving/primary pulley

It depends on which pulley is giving the motion. On a pulley you have a tight and a slack side.

figure 1: Slack and tight side smlease

On the slack side is $$T_2$$ and on the Tight side is $$T_1$$. The distribution is presented below:

Figure 2: Tension distribution -notice that the rotation is opposite to the image above - (source : tec-science)

So the angle should be taken on the driving(driver) pulley.

Note: the second diagram has a less than optimal configuration. It should be upside down. I.e. the slack side be on the top. The reason is that this improves the angle, and the overall traction of the belt on the pulley.

• Hi. I have read it on the following link that the product of coefficient of friction and angle of wrap should be considered for such cases. Whichever product is less, that angle of wrap should be considered for the tension ratio formulae. Link: engineering108.com/Data/Engineering/Mechanical/… If the coefficient of friction is same for both pulleys, then I think smaller pulley will have less angle of wrap and it should be considered for calculation. Aug 12 '21 at 5:49
• Shigley Mechanical engineering design, at chapter 17-2 Flat- Round-Belt Drives p883-884, describes Firbank's (Mechanics of the Flat Belt Drive) theory. It states that the "angle of contact is made up of the effective arc through which power is transmitted, and the idle arc.". Usually, the driving pulley one, is the smaller one (which is in accordance to your reference). Aug 12 '21 at 13:24
• @AshishMutekar I have rejected your edit because it was not aligned with my original answer. I think the best course of action is to can provide and accept your own answer. Aug 15 '21 at 6:16
• Ok. Thanks for the advice. Aug 27 '21 at 6:17

It depends on the product of angle of wrap (θ) and coefficient of friction (μ) of the corresponding pulley. Whichever product is less that angle of wrap is considered.

In case the coefficient of friction is same for both the pulleys in open-belt drive system, angle of wrap of the smaller pulley is usually considered.

In case of crossed-belt drive system, angle of wrap is same for both smaller as well as larger pulley so the smaller coefficient of friction is considered in the formulae.