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Belt speed formula (?)
- Thread starter RUJOCO
- Start date
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- Mar 4, 2005
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- 417
I went looking, and found this. The forum search kicked up threads about belts but nothing useful.
http://www.eriebearings.com/solutions/helpful-formulas/beltspeed/
http://www.eriebearings.com/solutions/helpful-formulas/beltspeed/
I wrote all of this up one at Don Fogg's forum, so I'm just going to re-post the same info here...It took a while to write. The first part is how to figure out RPMs if you're using step pulleys. The second part gives you SFPM based on the calculated RPM...
Ok...so, here's the math for figuring out your RPM at the drive wheel:
For starters, you need to know the circumference of each pulley. Go back to geometry class for this:
C = Pi * d
Where C is your circumference, and d is the pulley diameter. We'll just use 3.14 for Pi since I'm lazy. So:
C = 3.14 * 3 = 9.42" for your 3" pulley
C = 3.14 * 4 = 12.56" for your 4" pulley
C = 3.14 * 5 = 15.7" for your 5" pulley
Now, to figure out the RPM with your various pulley pairs, you need the RPM, and the circumferences of the two pulleys being connected by the belt. Then, a little more math gives us some answers. There's a couple ways to do this. One with ratios, and one with some goofy math that I tend to do because my brain is a little sideways from the rest of you...
Using Ratios:
You need to figure out the ratio of the drive pulley to the driven pulley (the one attached to the motor is the drive, and the other is the driven). So the pairings you'll have with this setup are:
drive -> driven
------------------
3" -> 5"
4" -> 4"
5" -> 3"
To calculate the ratio, divide the driven diameter by the drive diameter.
5 / 3 = 1.666 = 1.666:1
4 / 4 = 1 = 1:1
3 / 5 = 0.6 = 0.6:1
So, for each 1 revolution of your drive pulley (the right side of the ratio) at the 5" drive, you get 1.666 revolutions on the 3" driven pulley.
Now, add RPM into the mix to get the grinder driveshaft RPM:
d = m * r
Where d is driveshaft RPM (what we're solving for), m is motor RPM, and r is the drive ratio from above. So:
d = 1760 * 1.666 (for the 5" drive, 3" driven scenario)
d = 2932.16 RPM
Now, to calculate how much belt you're moving in SFPM (Surface Feet Per Minute) you need to know this driveshaft RPM, and the circumference of your belt drive pulley. I'll assume a 4" pulley from Rob @ Beaumont for these calculations. So, if we look back up above, we can see that the circumference of a 4" pulley is 12.56". So, we know that for each revolution of the belt drive pulley, we're moving the belt 12.56". Time for more math to figure out the SFPM at a given RPM (we'll stick with the 5"->3" setup for this one).
SFPM = (RPM * IPR) / 12
Where SFPM is Surface Feet Per Minute, RPM is the figured driveshaft RPM from above, and IPR is Inches Per Revolution of your belt drive pulley. So:
SFPM = (2932.16 * 12.56) / 12
SFPM = (36827.93) / 12
SFPM = 3068.9942
So just about 3,069 feet of belt pass over your platen every 60 seconds you have the grinder running at your highest speed.
Just as a point of reference, a mile is 5280 feet, so it would take a little less than 2 minutes for a mile of belt to pass under your blade as you grind...
Hope that helps!
-d
Ok...so, here's the math for figuring out your RPM at the drive wheel:
For starters, you need to know the circumference of each pulley. Go back to geometry class for this:
C = Pi * d
Where C is your circumference, and d is the pulley diameter. We'll just use 3.14 for Pi since I'm lazy. So:
C = 3.14 * 3 = 9.42" for your 3" pulley
C = 3.14 * 4 = 12.56" for your 4" pulley
C = 3.14 * 5 = 15.7" for your 5" pulley
Now, to figure out the RPM with your various pulley pairs, you need the RPM, and the circumferences of the two pulleys being connected by the belt. Then, a little more math gives us some answers. There's a couple ways to do this. One with ratios, and one with some goofy math that I tend to do because my brain is a little sideways from the rest of you...
Using Ratios:
You need to figure out the ratio of the drive pulley to the driven pulley (the one attached to the motor is the drive, and the other is the driven). So the pairings you'll have with this setup are:
drive -> driven
------------------
3" -> 5"
4" -> 4"
5" -> 3"
To calculate the ratio, divide the driven diameter by the drive diameter.
5 / 3 = 1.666 = 1.666:1
4 / 4 = 1 = 1:1
3 / 5 = 0.6 = 0.6:1
So, for each 1 revolution of your drive pulley (the right side of the ratio) at the 5" drive, you get 1.666 revolutions on the 3" driven pulley.
Now, add RPM into the mix to get the grinder driveshaft RPM:
d = m * r
Where d is driveshaft RPM (what we're solving for), m is motor RPM, and r is the drive ratio from above. So:
d = 1760 * 1.666 (for the 5" drive, 3" driven scenario)
d = 2932.16 RPM
Now, to calculate how much belt you're moving in SFPM (Surface Feet Per Minute) you need to know this driveshaft RPM, and the circumference of your belt drive pulley. I'll assume a 4" pulley from Rob @ Beaumont for these calculations. So, if we look back up above, we can see that the circumference of a 4" pulley is 12.56". So, we know that for each revolution of the belt drive pulley, we're moving the belt 12.56". Time for more math to figure out the SFPM at a given RPM (we'll stick with the 5"->3" setup for this one).
SFPM = (RPM * IPR) / 12
Where SFPM is Surface Feet Per Minute, RPM is the figured driveshaft RPM from above, and IPR is Inches Per Revolution of your belt drive pulley. So:
SFPM = (2932.16 * 12.56) / 12
SFPM = (36827.93) / 12
SFPM = 3068.9942
So just about 3,069 feet of belt pass over your platen every 60 seconds you have the grinder running at your highest speed.
Just as a point of reference, a mile is 5280 feet, so it would take a little less than 2 minutes for a mile of belt to pass under your blade as you grind...
Hope that helps!
-d
You have to make things so complicated. All of our belt grinders are 2 yard belt grinders - so a mile is actually 1760 yards - unless you live in Canada where things really get screwed up. What we really want to know is how much hand sanding = 1 minute of belt sanding. Don't forget coefficient of friction and God help us all if Stacy sees this.
Rob!
- Joined
- Jul 27, 2003
- Messages
- 5,663
Tell you what, I just got a batterey powered, rather portable, hand held laser tachometer on the auction site. It shoots a little laser dot on whatever you want. You stick on a piece of reflective tape and it gives you an LED rpm reading.
You could put a piece of tape on the belt and it would tell you RPMs and multiply by 6 feet for SFM.
Or stick it on the pulley itself and multiply by diameter of the pulley.
Shoot what ever you want and figure accordingly.
http://cgi.ebay.com/ebaymotors/New-...318QQhashZitem350079669166QQitemZ350079669166
You could put a piece of tape on the belt and it would tell you RPMs and multiply by 6 feet for SFM.
Or stick it on the pulley itself and multiply by diameter of the pulley.
Shoot what ever you want and figure accordingly.
http://cgi.ebay.com/ebaymotors/New-...318QQhashZitem350079669166QQitemZ350079669166
Well that's no fun Karl! I had just finished twisting their brains all sideways and you didn't even let them stew on it overnight
-d
- Joined
- Aug 1, 2000
- Messages
- 863
Right on Deker!!
I simplify things a bit more and take a few liberties in rounding numbers.
For me, everything is based on a 4" drive wheel...which just happens to be about 1 foot in circumference. This makes it easy to figure belt speed...for every revolution of a 4" drive wheel...the belt moves 1 foot.
1000rpms =1000fpm...and so on.
pretty easy so far....
Now, if you use a 3" drive wheel instead of a 4" drive wheel...(3 to 4 )..then your belt speed is slower from the smaller wheel.....it's actually 3/4 the speed of the std 4" wheel
So a 3" wheel spinning at 1000rpm, the belt speed becomes 3/4 of 1000...= 750fpm.
If you use a bigger drive wheel..the belt moves quicker... comparing a 6" to 4" at 1000rpm......the speed is 6/4 of 1000 which = 1500 fpm.
Even if you don't use a 4" drive wheel...keep it in mind to simplify your shop math. I love Pie!! YUM!...but in this case Pie is not a tasty snack that brings ants into the shop to clean up the crumbs...."Pie" is special math thing involved with circles...it's actually spelled Pi and it is roughly the number 3.
The 4" drive wheel X Pi is 4" x 3 = 12".....= 1 foot.
There you go, a 4" drive wheel moves the belt 1 foot per turn. Store this fact in your memory and use it to figure the belt speed for any wheel size. All you do is compare the wheel in question to a 4" wheel.
...or, just post your question here on BF...and we'll be glad to chime in. It's hard to imagine how we managed before Blade Forums...? hee hee!
Have fun with your projects.
-Rob
I simplify things a bit more and take a few liberties in rounding numbers.
For me, everything is based on a 4" drive wheel...which just happens to be about 1 foot in circumference. This makes it easy to figure belt speed...for every revolution of a 4" drive wheel...the belt moves 1 foot.
1000rpms =1000fpm...and so on.
pretty easy so far....
Now, if you use a 3" drive wheel instead of a 4" drive wheel...(3 to 4 )..then your belt speed is slower from the smaller wheel.....it's actually 3/4 the speed of the std 4" wheel
So a 3" wheel spinning at 1000rpm, the belt speed becomes 3/4 of 1000...= 750fpm.
If you use a bigger drive wheel..the belt moves quicker... comparing a 6" to 4" at 1000rpm......the speed is 6/4 of 1000 which = 1500 fpm.
Even if you don't use a 4" drive wheel...keep it in mind to simplify your shop math. I love Pie!! YUM!...but in this case Pie is not a tasty snack that brings ants into the shop to clean up the crumbs...."Pie" is special math thing involved with circles...it's actually spelled Pi and it is roughly the number 3.
The 4" drive wheel X Pi is 4" x 3 = 12".....= 1 foot.
There you go, a 4" drive wheel moves the belt 1 foot per turn. Store this fact in your memory and use it to figure the belt speed for any wheel size. All you do is compare the wheel in question to a 4" wheel.
...or, just post your question here on BF...and we'll be glad to chime in. It's hard to imagine how we managed before Blade Forums...? hee hee!
Have fun with your projects.
-Rob
When I first saw you posting on this thread Rob, I figured I must've gotten something wrong...I was about to check my math!
Then I read this...Did you grow up in Indiana or something?
Oh, wait, that would be have been "Pi is exactly 4!", or 3.2, or.... (If you don't get the reference, and care at all, look here to see what I'm rambling about...-d
Stacy E. Apelt - Bladesmith
ilmarinen - MODERATOR
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I think anyone who does that much math for fun has holes in his head. But, with deker, that is redundant.
Just for fun
and since you asked for it)
Hand sanding is done at about .00006 kilometers per second
Your average belt grinder runs about .02 kilometers per second.
If you are standing in Ecuador you are moving at .5 kilometers per second....as the earth spins around its axis.
If you look up from there ,you will notice that you are also moving at 30 kilometers per second as you circle the sun.
If you look at the stars you will notice that you are rotating through the Milky Way Galaxy at 220 kilometers per second.
And if you look at the cosmic horizon, you will notice that our galaxy is moving through the universe at 390 kilometers per sec, as the universe expands ( this is called peculiar velocity...one of my favorite technical names).
So.... The pulley ratio on your grinder is relatively not changing things much at all, on a cosmic scale.
Stacy
Just for fun
and since you asked for it)Hand sanding is done at about .00006 kilometers per second
Your average belt grinder runs about .02 kilometers per second.
If you are standing in Ecuador you are moving at .5 kilometers per second....as the earth spins around its axis.
If you look up from there ,you will notice that you are also moving at 30 kilometers per second as you circle the sun.
If you look at the stars you will notice that you are rotating through the Milky Way Galaxy at 220 kilometers per second.
And if you look at the cosmic horizon, you will notice that our galaxy is moving through the universe at 390 kilometers per sec, as the universe expands ( this is called peculiar velocity...one of my favorite technical names).
So.... The pulley ratio on your grinder is relatively not changing things much at all, on a cosmic scale.
Stacy
Last edited:
I didn't do it for fun...trust me, math and I don't get along so well. I did it to help folks who weren't as bored as I was on that given day
-d
TekSec
Böse Messer
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I think anyone who does that much math for fun has holes in his head. But, with deker, that is redundant.
Just for fun
Hand sanding is done at about .00006 kilometers per second
Your average belt grinder runs about .02 kilometers per second.
If you are standing in Ecuador you are moving at .5 kilometers per second....as the earth spins around its axis.
If you look up from there ,you will notice that you are also moving at 30 kilometers per second as you circle the sun.
If you look at the stars you will notice that you are rotating through the Milky Way Galaxy at 220 kilometers per second.
And if you look at the cosmic horizon, you will notice that our galaxy is moving through the universe at 390 kilometers per sec, as the universe expands ( this is called peculiar velocity...one of my favorite technical names).
So.... The pulley ratio on your grinder is relatively not changing things much at all, on a cosmic scale.
Stacy
Wow, so if I run in the opposite direction of the earth's rotation while hand sanding, then it would be done almost instantly!!!! :thumbup: Oh, wait a minute, my mom always said don't run with scissors and knives...dang, guess that's out.
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Now you got me doing math. Based on the information that was given by Mr. Apelt.
All of this assumes though, that the galaxy, our sun, our planet, and our hands are all moving in the same direction. For parts of the year, we are going around the sun in the opposite direction that our sun is moving and also in the opposite direction that our galaxy is moving.
But, does it really matter much? We knifemakers are fast. I just can't understand why we sometimes have back orders that we can't seem to get caught up on. We should be able to make knives at light speed, shouldn't we?
- The speed at which we are moving when we hand sand a knife is 2.7234712 (e+10), feet per second.
- or, 5,158,089.156 miles per second which is more than 27 times the speed of light, which is 186,282.397 miles per second.
- Considering that it takes about 8 minutes for light to travel from the sun to earth, this means that we can sand a distance from the earth to the sun in 16.92 seconds. No wonder my fingers hurt so badly and I don't have any fingerprints left.
All of this assumes though, that the galaxy, our sun, our planet, and our hands are all moving in the same direction. For parts of the year, we are going around the sun in the opposite direction that our sun is moving and also in the opposite direction that our galaxy is moving.
But, does it really matter much? We knifemakers are fast. I just can't understand why we sometimes have back orders that we can't seem to get caught up on. We should be able to make knives at light speed, shouldn't we?
Last edited:
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So if your south of the Equator are your swirl marks going in the other directions?
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HOLY CRAP! how about a CHART! please????
Stacy E. Apelt - Bladesmith
ilmarinen - MODERATOR
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Scott
You appear to have made the velocities multiplicative. They are additive.
The sum is 640.52 Km/s. The speed of light is 299,792.458 Km/s
If you are on an airplane traveling at 500 Km/s, and you sprint down the aisle at 20Km/s, you are not going 10,000 Km/s. You are only going 520 Km/s.
You are correct in noting that at any one time, all the parameters are not linear. The layman's translation of that is," Sometimes the stars line up, and sometimes they don't."
Stacy
You appear to have made the velocities multiplicative. They are additive.
The sum is 640.52 Km/s. The speed of light is 299,792.458 Km/s
If you are on an airplane traveling at 500 Km/s, and you sprint down the aisle at 20Km/s, you are not going 10,000 Km/s. You are only going 520 Km/s.
You are correct in noting that at any one time, all the parameters are not linear. The layman's translation of that is," Sometimes the stars line up, and sometimes they don't."
Stacy