PDA

View Full Version : Rpm of a pulley on wood lathe---forgot formulae



ACACIA
18th February 2017, 06:09 AM
Hello again --

Have found a electric motor -one HP ----To replace ---old lathe motor(burnt)
Unusua request ------please

cananyone --

help me calculate -----the following RPM?

OK ---Electric motor ---shaft ---has RPM of 2770 --ok ?

MOUNTEDN THAT 19 MM DIAM shaft----

IS a 3 INCH----DIAMETER V PULLEY---

ALL I WANT -----T KNOW ---WHAT IS THE RPM --of that 3 ( THREE INCH) DIAM PULLEY--

THATS ALL ---(It drives a bigger--17 inch--diam pulley via V belt---on the lathe shaft====) but thats irrelevant)

obviously --the 3 inch pully------will spin faster --than the shaft--its mounted on
BUT I forgot the formula---(Engineering websites---forums --22---all failed this SIMPLE Question


(Ratio is not required)
just RPM ----of the 3 inch pulley ---
many thanks ACACIA

-

----

NCArcher
18th February 2017, 06:32 AM
3" Pulley is rotating at the same speed as the shaft. 2770 rpm.
The suface speed of the pulley is 870 inches per second or 22.1m per second

Blocklayer
18th February 2017, 08:16 AM
For a 3" pulley rotating at 2770 RPM I get ~435 in/sec surface speed (2175.6 ft/min)
Here's a calculator to make working it out easier Pulley Calculator. RPM, Belt Length, Speed, Animated Diagrams (http://www.blocklayer.com/pulley-belteng.aspx)

NeilS
18th February 2017, 11:23 AM
3" Pulley is rotating at the same speed as the shaft. 2770 rpm.


No more, no less, rpm.



Stay sharp!

Neil

Lappa
18th February 2017, 12:52 PM
Pulley speed as above (2770). I get surface speed as 435 inches/sec.

if 3" pulley is 2770 RPM, 17" pulley will be approx 488 rpm

Oldgreybeard
18th February 2017, 03:26 PM
The simple math is:
The speed at which the shaft rotates is constant and is not effected by the size of the pulley. What can change is the circumference of the pulley and thus the distance that the belt travels with each revolution of the shaft.

Circumference of of 3" pulley is pi * diameter = 3 * 3.1416 = 9.425"
Circumference of of 17" pulley is pi * diameter = 17 * 3.1416 = 53.41"


Therefore the 3" pulley must rotate 53.41 / 9.425 times or 5.667 times for the 17* pulley to rotate once.

If the small pulley is rotating at 2770 revolutions per minute, the 17 " pulley will rotate 2770 / 5.667 times per minute or 488.8 rpm.

or more simple the driving rpm (2770) divided by the ratio of the large pulley to the small pulley (17:3 = 5.667) giving 2770 / 5.667 = 488.8 rpm as above

Hope this helps
Bob

ACACIA
18th February 2017, 06:01 PM
Thanks

ACACIA
18th February 2017, 06:11 PM
My point is ---that you missed--

a dot on the outer circmference of 3 inch pulley has to travel 9 . 426 inches
verse the dot on the Shaft circumference ---only travels 62 84 MILLIMETRES!--

surely the V belt --driven by the 3 inch OUTER circumference ---of that pulley --

is travelling FASTER than the shaf t /pulley inner circumference----- Velocity???? am iRIGHT??

Tying typing is extremely difficult ------something wrong --leteres do not appear---

anyhow ---
many thanks --appreciate ---

ACACIA

ACACIA
18th February 2017, 06:28 PM
By the way --discovered RED CEDAR as Australians call it

Indian / s e Asian MAHOGANY--

fabulous grain ---light ---gunstocks & lamps look good --easy to turn--imported here circa 1900

see fotos--
Saw Wbsite in Austrlia --woocarver----creates masterpieces fromthis wood --

regards Accacia

NCArcher
18th February 2017, 06:29 PM
For a 3" pulley rotating at 2770 RPM I get ~435 in/sec surface speed (2175.6 ft/min)



Pulley speed as above (2770). I get surface speed as 435 inches/sec.



Not sure how i got double, but it was early:doh:

Big A
18th February 2017, 07:49 PM
NC - from the Bandsaw forum, I thought you were good at maths!
Alister.

Oldgreybeard
18th February 2017, 10:07 PM
a dot on the outer circmference of 3 inch pulley has to travel 9 . 426 inches
verse the dot on the Shaft circumference ---only travels 62 84 MILLIMETRES!--

ACACIA

I think you are confusing RPM with the belt speed. Irrespective of the size of a pulley attached to the spindle the pulley will always rotate the same number of turns in any given time. If you count the number of times the 'dot' on the outer circumference completes a 360 degree turn it will always be the same number of times as the RPM of the motor shaft, irrespective of the daimeter of the pulley.




surely the V belt --driven by the 3 inch OUTER circumference ---of that pulley --

is travelling FASTER than the shaf t /pulley inner circumference----- Velocity???? am iRIGHT??

ACACIA

In your original post you asked how to calculate the RPM, but this is not the same as the belt speed or to use your term 'velocity"

You are correct in assuming that the belt speed will increase with the increase in the diameter of the pulley and that increase is proportional to the change in the diameter of the pulley.

In post #3, Blocklayer gave you a link to a calculator which will define all these relationships. Can I ask you to try it and enter the sizes of your pulleys and the RPM of your motor (2770 rpm I think you said). You will then get the belt speed for different pulley combinations and how it affects the final RPM of the larger pulley.

If you still have difficulty in understanding the results, give me some specific examples and I will try to help you.

Regards

Bob

powderpost
18th February 2017, 10:53 PM
Put simply, multiply the revolutions of the motor by the diameter of the driving pulley, then divideby the diameter of the driven pulley will give you the rpm required, and bob's you uncle.

Jim

NCArcher
18th February 2017, 11:44 PM
NC - from the Bandsaw forum, I thought you were good at maths!
Alister.
I used to be. But that was a week ago.

ACACIA
19th February 2017, 12:37 AM
Thanks Block layer ----

I have tried that calculator ----

BUT --- it asks for RPM of BOTH drive& driven pulleys---

I do not know RPM of 3 inch plley---
and how do I know what RPM driven pully is ?-

Anyhw the rratio is easy ---not required ---4 : 1 for a 3 inch / 12 inch pair of pulleys

What I am confused bout is the V BLT must run much faster ---than 2770 shaft speed

HOW can the perimeter SPEED---- of a 3 inch pulley----be 2770 RPM --AS WELL ?? ( as the 19mm motor shaft speed )?

Take an old 33 1/3 RPM vinyl record ----outer track rotates much faster than the centre---ok ?

Chopper blade TIPS- travel close--but not exceeds--- to mach one ----- YET the centre drive shaft is MUCH- slower--for reduction torque(former air force grease monkey )
see my problem?---LARGER DRVE PULLEY --SAY 8 INCHES ---- BELT THEN ACCELERATES THEBIGGER TOP PULley
EVEN FASTER ----SO FINAL DRIVEN PULLEY---SPEEDS UP =====RATIO ALTERSRASTICALLY!
Apologies ---typing is a nightmare-------something wrong --internet in Africa is !!!

QC Inspector
19th February 2017, 02:49 AM
I think you are looking for the surface speed of the 3" pulley and are confused between the rotational speed and the surface speed.

The outside distance of any circle (pulley circumference) is Pi x diameter. I'll use 3.14 for Pi because I can't remember it to infinite decimal places. ;)

So the diameter of your shaft, 19mm x Pi = 2.349", the circumferance (I converted it to imperial .748" to match the rest of the numbers). That is the distance the point on the shaft travels for 1 revolution. Multiply that by 2770 rpm and your shaft point travelled 6506.23" or 542.19'. So the shaft point surface speed is 542.19 FPM (feet per minute).

The pulley diameter of 3" x Pi = 9.42" (the outside of your vinyl record), multiplied by 2770 rpm = 26,093.4" or 2174.45'. A shaft point surface speed of 2174.45 FPM.

Now if you look at Blocklayer's calculator it shows you a belt speed of 2175.6 FPM which is more accurate than my rounded off but close enough calculations. You only need to put in 1 pulley speed to get results not both. So the point speed of the 3" pulley and the belt speed are the same thing. 2175.6 feet per minute.

I hope that helps and doesn't frustrate you more.

Disclamer. I ain't no mathemutician and I am trying to help by using the terms ACACIA is using.

Oldgreybeard
19th February 2017, 09:07 AM
Thanks Block layer ----

I have tried that calculator ----

BUT --- it asks for RPM of BOTH drive& driven pulleys---

I do not know RPM of 3 inch plley---
and how do I know what RPM driven pully is ?-

!
You are confusing the RPM which is the number of rotations of the pulley. This does not change it is always the same number as the RPM at the shaft of the pulley.The RPM is the number of revolutions that a dot on the circumference (outer diameter) of the drive pulley makes in 1 minute - that is the RPM of the motor (2770 in the case of your motor). It is not a measure of the speed at which the dot is travelling. The speed will change as the distance between the centre of the shaft and the radius of the pulley changes, but the number of revolutions is always the same as the RPM at the shaft.

OK, the calculator asks you to enter the RPM of either of the 2 pulleys - not both. When you enter the RPM for the small pulley and press the CALCULATE button, it will display the RPM of the large pulley. At the same time it will display the ratio of the two pulleys and the belt speed.


To work out the belt speed for yourself, the first thing you have to do is to calculate the circumference of either pulley.To do this, measure the diameter of the pulley and multiply it by pi (3.1416). This is the distance a point on the belt would travel if you turned the shaft one full rotation. So for a 3" pulley , the circumference or distance the belt would travel in 1 full rotation is 3 multiplied by 3.1416 = 9.425 inches.

We normally talk of the belt speed in terms of the distance travelled in 1 second or 1 minute. So if the pulley rotated 10 times in 1 second, the distance travelled by a point on the belt would be the circumference (9.425") X 10 = 94.25" and we would express that as 94.25"/sec.

Applying that logic to your motor and pulley we have:

Diameter of pulley = 3"
Circumference of pulley = 3 x 3.1416 = 9.425" ( distance a point on the belt would travel if the pulley was turned for 1 complete rotation)
RPM of motor = revolutions per minute of the shaft = 2770
Distance that a point on the belt would travel in 1 minute = 9.425" x 2770 revolutions = 26,107.25" or 2,175.6 feet

This gives a belt speed of 2,175.6 ft/minute or dividing by 60 to convert to ft/second = 36.26 ft/sec.

I know that I am repeating what others have said but I hope it will helps you to understand.

Bob

Chief Tiff
19th February 2017, 11:06 PM
Hi Acacia,

The brains here have done the hard maths; but maybe I can put the numbers in a different way?

The 3 inch pulley has a rotational (round and round) speed of 2770 revolutions per minute.

At any point on outer edge of this pulley there is a VELOCITY of 2175.6 feet per minute.

Because the belt is being driven by the outer edge of the pulley it also HAS THE SAME VELOCITY of 2175.6 feet per minute.

The belt is driving a larger 17 inch pulley. Because the belt is driving the pulley at a velocity 2175.6 feet per minute, then any point on the outer edge of the large pulley also has the SAME VELOCITY.
However, because the pulley is a larger diameter it has to run at a slower rotational speed to achieve the same velocity of 2175.6 feet per minute at it's outer edge. The rotational speed of the large pulley is 488.8 revolutions per minute to achieve this.

I think the bit you need to understand is that all three parts are travelling at the same velocity WHERE THEY ARE TOUCHING. The fact that there is a belt between the pulleys is actually irrelevant; it could be a chain, or the two pulleys could be rubbing together, they could be two gears or even two cogs with a third cog between them; it doesn't matter. Because they are touching and driving each other the rotational speeds of each pulley shaft are directly linked at a fixed ratio; this ratio is the larger pulley size divided by the smaller pulley size. 17 divided by 3 which equals 5.667 Now if you divide your 3" pulley shaft rotational speed of 2770 rpm by this number you get 488.8 rpm; this is the rotational speed of the 17" pulley. The velocity of any point on any pulley or any point of the belt or cog or whatever is exactly the same in a mechanism like this.

I hope this helps!

ACACIA
19th February 2017, 11:08 PM
Many many THANKS ----Oldgreybeard ---and all the others ---

finally --its sunkito my thick skull ---reallyappreciate ---l your hard work /research

U arespot on -----was onfusing prmeter velocity --(outer pulley SPEED )---wth RPM -

OK its firmly locked in memory --

I wenyt back to that alculator -----typed in

2nch small pulley ----11 inch newly turned eucalypt wood pulley--

distance between puleys apprx --

got 5.5 :1 ratio ---

BIG PULLY RPM isnow 503 RPM muh safer for giant acacia & leadwood (combretum) logs --tatweigh20 kg aveage

50 m long --10nch damter -----these logs spun way too fast ----NOW I have safe speed ====

still Keef Rowley says---SLOWEST speed -below 750 PM----

my lathe is bush DIY ----really primitive --butworks well

thanks again ---ACACIA ( Apologies for typing --iernet gone mad !

Chief Tiff
19th February 2017, 11:55 PM
We'd love to see a picture of your "bush lathe", it's amazing what people can build to suit their resources or preferences.

I visited Kenya back in the 1990's and went to a craft workers cooperative; I was amazed to see the fantastic quality of work being produced on the most basic lathes imaginable. The lathe frame sat on the ground, the wood was being turned back and forth by a hand held belt and the chisel was held in the craftsman's feet; yet these guys could knock out matching spindlework like pairs of candlesticks without profile templates in only a few minutes each.

ACACIA
21st February 2017, 01:16 AM
Yes ---here in East & Central Africa ----bicycles are used to power lathes --very very primitive affairs
Two giant truck axle taper roller bearings ---jammed in the fork of two roughly parallel trees --2-3 metres apart ---SUPPORT a hardwood shaft /mandrell----onwhich wood pulleys of arying diameters are mounted
--all rather wobbly /off center --- chuck made from ebony flange---!--
Had a foto -back in the 60 ,s
One power dude cycles ---(Zambian villager)
another turns monster bowls/lamps /barstool legs----with a ground bastard file---

from Mpinga (ebony) logs----and many species like Pterocarpus Angolensis--Pericopsis etc--(Teak with gorgeous grain )
sweat & hard work ------produced some astonishing products -----no trouble with Pulley ratios

That's where I got the idea of Wooden DIY pulleys---!---
will post a foto of my bush cast iron / heath robinson 1920 pillow block frame---all diy /scrapyard

can only dream of a Myford fancy headstock 4jaw beauty----tailstock that has mortise taper inserts etc

one day -------
see ya ACACIA

powderpost
21st February 2017, 10:08 AM
Hi Acacia,

The brains here have done the hard maths; but maybe I can put the numbers in a different way?

The 3 inch pulley has a rotational (round and round) speed of 2770 revolutions per minute.

At any point on outer edge of this pulley there is a VELOCITY of 2175.6 feet per minute.

Because the belt is being driven by the outer edge of the pulley it also HAS THE SAME VELOCITY of 2175.6 feet per minute.

The belt is driving a larger 17 inch pulley. Because the belt is driving the pulley at a velocity 2175.6 feet per minute, then any point on the outer edge of the large pulley also has the SAME VELOCITY.
However, because the pulley is a larger diameter it has to run at a slower rotational speed to achieve the same velocity of 2175.6 feet per minute at it's outer edge. The rotational speed of the large pulley is 488.8 revolutions per minute to achieve this.

I think the bit you need to understand is that all three parts are travelling at the same velocity WHERE THEY ARE TOUCHING. The fact that there is a belt between the pulleys is actually irrelevant; it could be a chain, or the two pulleys could be rubbing together, they could be two gears or even two cogs with a third cog between them; it doesn't matter. Because they are touching and driving each other the rotational speeds of each pulley shaft are directly linked at a fixed ratio; this ratio is the larger pulley size divided by the smaller pulley size. 17 divided by 3 which equals 5.667 Now if you divide your 3" pulley shaft rotational speed of 2770 rpm by this number you get 488.8 rpm; this is the rotational speed of the 17" pulley. The velocity of any point on any pulley or any point of the belt or cog or whatever is exactly the same in a mechanism like this.

I hope this helps!

My method, multiply the rpm of the motor by the diameter and divide that by the diameter of the driven pulley. 2770 x 3/ 19 = 437.3 rpm for the lathe. Much simpler and easier to understand.

Jim