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Pully Math

2412 Views 8 Replies 5 Participants Last post by  maninthesea
Thought I would post this question in the electrical area as Electricians would probably do more pully size figuring than anyone else.

So Here are the givens. I have a compressor that wants to run at 1300RPM and I have a 5HP 3phase motor that runs at 1750RPM(184T frame)

The compressor has a fan integrated pully that can not be changed. I measured it at approximatly 17.5"

First question.
Where do you measure pully diameter from? I asume its not the outside of the pully as the belt fits down in the grove a bit. I am guessing it should be from the outside of the belt when the belt is in the groves. (Basicly measure outside of pully and subtract depth of belt recess x 2.

Second question
What size pully do I want on the motor? Here is what my calculations came out with

Circumfrence = Pie x R = 3.14159 x 17.5"
Distance traveled by the belt per min at 1300RPM = Circumfrence x RPM
Leaving all the #s in the calculator I get 71,471" per min

Drive pully has to move the belt the same distance at 1750RPM so
Drive pully circumfrence = 71,741"/1750RPM = 40.84"
Diameter = 40.84" / 3.14159 = 13

This makes sense to me.

Third question
Planning on using gravity to tension the belt by mounting the motor on a plate that pivots on the pump side of the motor. I am looking for a rule of thumb that I can use to estimate what I need for belt tension.(The last time I made one up like this was on a 20HP motor and the belts were too loose(pivot point too close to the centerline of the motor) I ended up anchoring the motor down with a heavy spring as I did not have room on the frame/plate to move it out any further.

4th question.
recomendations on sourcing sheeve and bushing. Last time I used grainger and not only do I hear they are not best price they screwed it up twice. (I do have two extra Browning 1 3/8" B bushings free to someone who wants them) I am thinking of looking at McMaster Car. Any other suggestions?

Bonus question
Also planning on using a 12" pully so compressor runs a little slower(lasts longer) Also our power is ****ty so slower compressor speed should = less load on the motor and that may keep from overloading the motor when volts are not right. Or do you think dropping to 12.5" should be fine?

Cheers Jim
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Use this to figure your pulleys.

I believe that pulleys are not specifically measured from either inside or outside, but from the pitch diameter which is where the design of the belt is. Here's some more information on it.

I'm not sure if you have a typo there, but you said

Second question
What size pully do I want on the motor? Here is what my calculations came out with

Circumfrence = Pie x R = 3.14159 x 17.5"
and I'm guessing you meant Pi x D, not R. That would make a huge difference if that's the formula you used.

and I'm just being a spelling Nazi, but it's just Pi. I'm a geometry geek.
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I agree, i have also found that RPM may vary with belt wear and if the pulleys have different pitchs. When i worked for the local garnet mine i saw this all the time when working on my own equipment there. The "scalpers" had an adjustable pulley on the motor and a fixed pulley on the fiber drive. The performance of the machine would change from week to week depending on belt wear and the wear on the fiber drive. This equipment was absolete but still performed well if you understood how to work on it and proper maintenance. After i left the company shut down these peices of equipment as no one else knew how to work on it. All the older guys that i learned from either retired or died.
Thanks framerman
Yes I cant spell worth crap. I really was looking for the pi key!. Also yes I was thinking diameter and but wrote radius. Did the math correctly as proved by both the online calculators. Thanks again for the educational link. I will cut an "A" belt tommorrow to use for measuring.

now I gotta find best sorce for bushings and sheeves.

Cheers jim
You inverted your answer

Motor rpm/comp rpm = dia comp/dia motor

dia comp is the unknown, so multiply everything by dia motor

[(17.5")* (1750rpm/1300rpm)] = 23.55"
You inverted your answer

Motor rpm/comp rpm = dia comp/dia motor

dia comp is the unknown, so multiply everything by dia motor

[(17.5")* (1750rpm/1300rpm)] = 23.55"
Logicaly that size does not make sense to me. If I have a larger pully on the motor than the compressor then the compressor will run faster than the motor. Most of the compressors I work on have around 18" or more pully on the compressor and 6" or so on the 3500rpm motor. None of the compressors exceed 1800rpm and most are around 11-1300.

As I look at the formula you put up I think you may have inverted when you sovled so here it is as I solved it one step at a time.

Sm/Sc = Dc/Dm or (Dm * Sm)/Sc =Dc or Dm/Sc = Dc/Sm or

Dm = Sc*Dc/Sm

Definatly faster easier math than what I originaly did but still come out with
1300Rpm * 17.5"/ 1750RPM


Again thanks now I know I can just use ratio's to determine pully diameter. Also learned how to read the diameter of the pully. Now I just need to remember it next time I need it.
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You are right, Maninthe sea, I got lost reading the scenerio, and started thinking that the fixed sheave was on the motor, and not the compressor

You might want to check this place out. I've bought pulleys, belts, chains, sprockets, collars, hydraulics, etc for a number of my contraptions there. If you go to the help section there, it's loaded with all kinds of calculators that you might find helpfull. I bought a pulley, & a set of belts for my 10 hp 21" powermatic planer that were great in quality, & price. They have a great selection, & most is in stock.
Click on the pulley calculator, & plug in numbers.

Yep, it's 13". At that size a single belt would be more than plenty to cary the torque, & have less hp loss in the belt. I have a 5hp two stage (175psi 19cfm) Speedair compressor that uses about the same size pulley on the pump, & about a 6" pulley on the motor equipped with a single belt. I bought it used, & it still has the original belt with never a belt adjustment or squeel. It run all day every day at my shop. The low rpm setup is great for pump life, & noise reduction.
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Thanks Railman
Will check into that site. This is a 3500psi about 8cfm. Used for divers breathing air. Originaly came with an 8HP brigs and stratton diesel. US Army Issue.

Now my next task is brushing the math cobwebs out of my head to see if I can work out how long of a swing arm I need on the motor mounting plate to provide the needed belt tension. I am worried that its a force vector problem. I was pretty good at those 20 years or so ago.

Sometimes I think about how it would be kind of nice to go back to the old school and show a math or science class some of the real world aplications I have used boring math and science principles on.
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