Formula for belt tension

[Gokhan]

It looks this formula is almost impossible to find on the Internet. I am posting it here in case someone needs it to estimate belt tension without using a tension gauge. The idea is to apply perpendicular pressure on the belt midway between two pulleys and measure the deflection. Your index finger applies about 10 lb of pressure when you push with it but you should first "calibrate" your index finger using some kind of weight scale to see how 10 lb feels like. The formula is:

(Deflection of belt) = (0.25)*(span length of belt between the two pulleys where the force is applied)*(perpendicular force applied on belt midway between the two pulleys)/(belt tension)

Force applied on belt will be roughly 10 lb when you push with your index finger but "calibrate" your index finger first. You should measure the deflection accurately by placing a ruler adjacent to the belt. Measure the span length between the tangent points -- between the centers of the two pulleys when viewed perpendicular to the belt with ruler held parallel to the belt.

Note that the special case of 160 lb of belt tension and 10 lb of perpendicular force applied on belt gives (Deflection of belt) = (span length of belt between the two pulleys where the force is applied)/64. This special case is all over the Internet but I wanted to provide the far more useful general formula here.

 

[Bluestream]

Great info...

I just make them tight as a bow string and as long as they don't squeal call it a day

 

[Kuato]

Calibrate finger and calculate? Although I appreciate the math, that's hardly necessary when all the calibration you need is the deflection in the first place!

 

[Gokhan]

Originally Posted By: Kuato
Calibrate finger and calculate? Although I appreciate the math, that's hardly necessary when all the calibration you need is the deflection in the first place!

I am not sure what you mean. As you can see in the formula, deflection is a function of both the finger pressure and belt tension. Deflection will increase when you press harder. That's why I said, use a weight scale to get an idea of how much pressure your index finger is capable of. It should be about 10 lb but it obviously depends on the person and how much he/she presses.

 

[Kuato]

Originally Posted By: Gokhan
Originally Posted By: Kuato
Calibrate finger and calculate? Although I appreciate the math, that's hardly necessary when all the calibration you need is the deflection in the first place!

I am not sure what you mean. As you can see in the formula, deflection is a function of both the finger pressure and belt tension. Deflection will increase when you press harder. That's why I said, use a weight scale to get an idea of how much pressure your index finger is capable of. It should be about 10 lb but it obviously depends on the person and how much he/she presses.

First off, I don't mean to be a jerk but I just don't get the reason for this.

Of course the belt will deflect further with more pressure. You're a smart guy, but in this case you are being too smart.

What I mean is that there is absolutely no need to get a scale, measure how much pressure your finger can exert, and calculate the deflection based on that pressure modified for the distance of the run in order to do the job. Simply measuring the deflection while adjusting is sufficient; if your finger strength isn't enough to do the job, then get some fat fingered big guy to do it while you tighten the idler pulley.

UNLESS the manufacturer recommends a certain pressure to properly tighten the belt (and I don't know of any that do) you are simply wasting your time.

 

[Gokhan]

Originally Posted By: Kuato
Originally Posted By: Gokhan
Originally Posted By: Kuato
Calibrate finger and calculate? Although I appreciate the math, that's hardly necessary when all the calibration you need is the deflection in the first place!

I am not sure what you mean. As you can see in the formula, deflection is a function of both the finger pressure and belt tension. Deflection will increase when you press harder. That's why I said, use a weight scale to get an idea of how much pressure your index finger is capable of. It should be about 10 lb but it obviously depends on the person and how much he/she presses.

First off, I don't mean to be a jerk but I just don't get the reason for this.

Of course the belt will deflect further with more pressure. You're a smart guy, but in this case you are being too smart.

What I mean is that there is absolutely no need to get a scale, measure how much pressure your finger can exert, and calculate the deflection based on that pressure modified for the distance of the run in order to do the job. Simply measuring the deflection while adjusting is sufficient; if your finger strength isn't enough to do the job, then get some fat fingered big guy to do it while you tighten the idler pulley.

UNLESS the manufacturer recommends a certain pressure to properly tighten the belt (and I don't know of any that do) you are simply wasting your time.

I figured out the part you don't understand.

The part you don't understand is that for a given belt tension, belt deflection is directly proportional to the vertical force applied. So, if the belt deflects 1/4 inch when you push with 10 lb of force, it will deflect 1/8 inch when you push with 5 lb, and it will deflect 1/2 inch when you push with 20 lb. So, unless you can judge the vertical force on the belt accurately, the belt deflection alone is useless in determining the belt tension.

All manufactures either specify the belt tension -- such as 160 lb -- or belt deflection and vertical force -- such as 1/4 in at 10 lb. If they don't specify the vertical force when they specify the deflection, that's only because they specified a certain gauge with a known force (such as 10 lb) and therefore the vertical force is specified implicitly through the specification of a certain gauge.

I hope it's clear this time.

 

[doitmyself]

Gokhan, I understand your point. If one has the patience, the video below shows the "by the book" method of adjusting belts to maximize performance. Kuato is sharing his time tested "by feel" methodology which all mechanics in the real world use. This type of stuff applies to bearing adjustment also.

What one doesn't consider is that when bearings go bad in a non tensioner belt set up, is it because the belts were too tight? While everyone accepts that their "by feel" method doesn't result in immediate failure, we can only guess if there are long term negative effects.

For those with engineering, geek-type brains, this stuff is interesting.

It's not unlike torque wrench use. Those that don't understand all the background principles of torque assume use of a high quality tool automatically results in correct results. It's good, IMO, to understand the principles even when doing the "by feel" method.

 

[Gokhan]

Originally Posted By: doitmyself
If one has the patience, the video below shows the "by the book" method of adjusting belts to maximize performance. Kuato is sharing his time tested "by feel" methodology which all mechanics in the real world use.

Thanks for the video, which is for a particular gauge and particular belt manufacturer. However, you still need their tables to calculate the tension from the gauge reading. My formula, on the other hand, is very simple and entirely general -- you can use it for any belt.

Of course, using your index finger as a force gauge is not very accurate. That's why I suggested that you use a weight scale to "calibrate" your index finger first. Alternatively, if you can find a force gauge or some kind of inverted spring scale, use it instead of your index finger.

I don't know about all mechanics using the "feel method." There is no way in the world that the tension will be correct even within a factor of two just by feeling the belt. You should measure it with a professional gauge or if you can't, use my method and formula to get a good approximation, which could have better than 20% accuracy if you are careful. The only error results from estimating the force your index finger is applying and measuring the deflection with a ruler. The formula is 100% accurate otherwise.

I agree that setting the belt tension incorrectly could reduce the belt and bearing life and it could also result in poor performance for the belt-driven accessory.

Physics of my formula is fairly simple. It uses the net-force-equals-zero equation for static equilibrium (statics). All the formula is saying is that the deflection is directly proportional to the span length and vertical force and inversely proportional to the belt tension. There comes the proportionality constant of 0.25 (1/4) in front that multiplies the variables when you do the actual calculation to derive the formula.

 

[Lubener]

I go with half inch deflection in the middle of the longest span. This does not apply to timing belts.Not rocket science. Anyway, I would rather be "slightly" loose than too tight.

 

[Gokhan]

Originally Posted By: Lubener
I go with half inch deflection in the middle of the longest span. This does not apply to timing belts.Not rocket science. Anyway, I would rather be "slightly" loose than too tight.

Try to understand what I've explained in this thread. Belt deflection alone is meaningless in determining belt tension without knowing how much force you are applying when you are pushing on the belt.

 

[Silverado12]

The tension is pretty much 10lbs with 1/2" deflection, or about what your index finger is able to push comfortably. Don't overthink this.

 

[Yah-Tah-Hey]

The one thing I did like about the 66 Dodge Dart I owned was the set up for tensioning the AC belt.The compressor mounting bracket had a 1/2" square hole so that a a beam type torque wrench could be used for setting belt tension.I never could pull the correct tension and tighten the bracket at the same time, but ti was a very accurate way to tension the belt with the aid of a helper.

 

[Gokhan]

Originally Posted By: Silverado12
The tension is pretty much 10lbs with 1/2" deflection, or about what your index finger is able to push comfortably. Don't overthink this.

Overthinking? Where did you even come up with these two numbers?

Those two numbers (10 lb vertical force and 1/2 inch deflection) result in 55 lb of tension for my alternator belt. OEM spec for new alternator belt is 160 lb and used alternator belt is 130 lb. So, those two numbers are off 66% for the new belt and 58% for the used belt.

Deflection depends on the span length between the two pulleys. You can't just assume it will be 1/2 inch deflection for any belt. If the span length is half, deflection will be half.

You should try to understand how tension and deflection are related to span length and vertical force. Read above. It's really simple.

 

[tom slick]

I use a Gates Krikit on automotive belts and the pencil style on industrial belts. In my experience, guesstimated belt tension is always lower than the spec.

 

[Lubener]

Originally Posted By: Gokhan
Originally Posted By: Lubener
I go with half inch deflection in the middle of the longest span. This does not apply to timing belts.Not rocket science. Anyway, I would rather be "slightly" loose than too tight.

Try to understand what I've explained in this thread. Belt deflection alone is meaningless in determining belt tension without knowing how much force you are applying when you are pushing on the belt.


Good thing I am not paying you by the hour. If you know what you are doing, you should already know that "force".

 

[Garak]

Originally Posted By: Gokhan
Try to understand what I've explained in this thread. Belt deflection alone is meaningless in determining belt tension without knowing how much force you are applying when you are pushing on the belt.

Agreed. On an "average" automotive application, deflection is a pretty good measure. But, to really illustrate your point, take a look at belts in industrial settings, where some belts have a very small circumference, and others are extremely long. Compare the tension in those.

 

[Gokhan]

Originally Posted By: Lubener
If you know what you are doing, you should already know that "force".

Even if you know the vertical force exactly, you still need to know the deflection spec. OEMs will often specify only the belt tension without specifying the deflection at a vertical force. You need my formula to calculate what the deflection will be for a given tension, span length, and vertical force. 0.50 inch deflection doesn't work for any belt, as span lengths vary. For example for my alternator belt, correct deflection is 0.21 inch (used belt) or 0.17 inch (new belt). These numbers result in 130 lb (used belt) or 160 lb (new belt) tension for 11.0 inch span length and 10 lb vertical force.

 

[SubLGT]

Originally Posted by Kuato
...UNLESS the manufacturer recommends a certain pressure to properly tighten the belt (and I don't know of any that do) you are simply wasting your time.


For my Subaru, the factory service manual specifies a pressure of 22lb be applied to the belt, to measure deflection. It also specifies where on the belt to do the deflection test.

 

[Yah-Tah-Hey]

My Toyota shop manual specifies belt deflection for belts using a tool made for measuring belt deflection. Using that tool is next to impossible on my Camry V6. I have never had such a tool and no belt change ever resulted in a bearing failure due to too tight a belt. For the polly belts, if I can turn the belt through about ninety degrees of rotation at mid span, the belt tension is adequate.