pulley math

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SE18

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background: I bought a homemade mill from a friend and he didn't know the rpm of the original drill press but fortunately there was a table of speeds on the sides for the 5 original pulleys: 3100, 2340, 1720, 1100 and 620.

The pulley diameters for both drivers and driven are 1.75, 2.25, 2.5, 3 and 3.5" on each cone.

Also, I could measure the diameters of all the pulleys, driven and driver pulleys AND I own a 19th edition of Machinery's so armed with all of this data, I began my quest with the ultimate goal of measuring the rpms of my fabricated compound pulley.

So in order to do the math on the compound pulley, I started with finding the drill presse's rpms from the motor shaft.

According to my handbook, the rpms can determined by multiplying the diameter of the driven pulley times the driven speed. That total will then be divided by the driver pull.

So the math works out to 3.5 X 620 / 1.75 +2,170 rpm at motor shaft.

1. Correct?

2. In figuring the diameter for pulleys, my handbook tells me to measure the tops of each pulley. I'm sort of puzzled by that because it would seem to be more accurate to measure the bottom of each pulley trough. The reason I say this is because different pulleys have different trough depths. In any case, I'm not too concerned about this because the discrepancies will be negligent. Just wondering.

DSC05674.JPG
 
The math is really simple; best described with examples.

Lets say you have two sheaves (I prefer to call them sheaves BTW) one is 3 inches diameter, the other is 1 inch diameter. The small one will go 3 times faster than the large one and conversely, the large one will go 1/3 the speed of the small one.

Another example: one is 5" and the other is 2". The small one goes 5/2 the speed of the big one and big one goes 2/5 the speed of the small one.

The sheave that's connected to the motor has no choice but to travel at the same RPM as the motor. So, if an 1800 RPM motor were connected to the 5" sheave, the small one would be going 5/2 x 1800 = 4500 RPM.

As for where you measure the diameter... Technically speaking this is akin to the pitch diameter of a screw. If you're using a drive belt, the typical method is to calculate the median diameter between the high and low point of where the belt makes contact. It's actually a little more complicated than this and it depends on the type of belt etc but, using the average diameter is a darn good approximation.

If the sheaves on both sides are the same design, it makes little difference really where you measure the diameter as long as you're consistent across all the measurements. This is because it's the ratio that is important -not necessarily the actual measurement. For quick calculations, I always read the diameter measured from the top of the belt -only because it's an easy measurement to make with a pair of calipers...


Ray
 
motor rpm times the dia. of first pulley divided by the dia. of the second pulley, times the diameter of the third pulley divided by the dia. of the forth pulley, and so on and on and on. . . . . .


dia. = diameter measured outside is fine. . . . . . . .
 
that's a nice calculator; trouble is, it assume you know the motor rpm in advance. That's actually what I'm trying to do so I can do the rest of the calculations

anyone know if my math is correct or is my reasoning hard to follow

btw, the sheaves (pulleys) are different styles so I'll have to measure top of belt to top of belt as Ray does
thx
 
SE18 said:
that's a nice calculator; trouble is, it assume you know the motor rpm in advance. That's actually what I'm trying to do so I can do the rest of the calculations

anyone know if my math is correct or is my reasoning hard to follow

btw, the sheaves (pulleys) are different styles so I'll have to measure top of belt to top of belt as Ray does
thx
Click to expand...

Since the middle speed is 1720 that was almost certainly the speed of the original motor as the middle pair on a five-level set of cone pulleys would be 1:1. 1725 is also the most common rated full-load speed for single phase induction motors.
 
The motor RPM can only be measured accurately by using instruments designed to directly measure rotational speed.
You cannot get it by just simple mathematical calculations of pulley diameters or sizes since many other unknown factors are involved.
Even the pitch diameters of the pulleys, which are really the sizes that should be used in comparing two pulleys, are not easily measured.

With an unknown true motor RPM speed all other calculations for different sizes of pulleys used are just ball park relative estimations thus cannot be exactly determined.

If you have a Strobotach perhaps you could get the correct rpm measurement easily.
 
I'd love to help you here but, I'm confused about what you're trying to accomplish. Could you re-state your goals/desires?


Ray
 
The sheaves should have the pitch diameter stamped on them. Use these figures for your calculations. Not that a few rpm one way or the other makes all that much difference.
 
Thanks, John, I'll take that rpm as a baseline measure.

Ray, what I hope to accomplish is to measure the added pulley cone speeds. If you look at the photo, there's a pulley by itself that was added by the builder to slow the drill press down so that it can be used for certain milling operations that need a slower speed than the drill press.

Fortunately, the builder plate has the rpm's of cones for the drill press and I can work from there.

It's kind of hard to explain with a typed explanation so sorry if I'm not clear.
 
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