Need some help!

[Laverne3ca]

It's been close to 50 years since college so I'm not sure where to go with this problem.
I have a grinder that has a 16000 rpm motor, one pulley .875 diameter and one pulley 2.230 diameter. There are 7 driven speeds from 3200 to 46200, how do I calculate the minimum number of pulleys required to get the seven different speeds? At the low end of the range the speeds are rounded to 10 to 25 rpm and at the top end 50 to 100 rpm.

 

[Deleted member 4993]

It's been close to 50 years since college so I'm not sure where to go with this problem.
I have a grinder that has a 16000 rpm motor, one pulley .875 diameter and one pulley 2.230 diameter. There are 7 driven speeds from 3200 to 46200, how do I calculate the minimum number of pulleys required to get the seven different speeds? At the low end of the range the speeds are rounded to 10 to 25 rpm and at the top end 50 to 100 rpm.

You want to reduce speed from 16000 rpm to (as low as) 3200 rpm? 1/5 reduction?

Is this a "practical" problem or "academic" problem? How are you connecting the "driver" and "driven" (- by shaft-pulley-belt-pulley-shaft?)? For a practical problem, I would keep an eye on "shaft diameter" and "power transfer".

 

[Laverne3ca]

This is a practical problem, it's for an existing commercially built tool post grinder(Dumore #57) that is missing most of the pulleys. The drive is by a very thin 3/4 inch wide(19mm) flat belt, there are no issues with the drive, motor or spindle it's driving, once I can calculate the pulley diameters the biggest issue will be balancing them.

 

[Deleted member 4993]

This is a practical problem, it's for an existing commercially built tool post grinder(Dumore #57) that is missing most of the pulleys. The drive is by a very thin 3/4 inch wide(19mm) flat belt, there are no issues with the drive, motor or spindle it's driving, once I can calculate the pulley diameters the biggest issue will be balancing them.

So to reduce speed 1/5 th (16000 \(\displaystyle \to \ \) 3200) you should use a driven pulley with 5 times the diameter of the driver pulley (assuming no slippage).

 

[Laverne3ca]

That's the easy part but there are 7 different discrete speeds required and the manufacturer lists 5 or 6 different pulley combinations to get them all, that's what I'm trying to calculate. The problem is that the pulleys are listed by part number, not diameter.

 

[Deleted member 4993]

That's the easy part but there are 7 different discrete speeds required and the manufacturer lists 5 or 6 different pulley combinations to get them all, that's what I'm trying to calculate. The problem is that the pulleys are listed by part number, not diameter.

In a similar manner, calculate the "desired" speed-ratios and from that diameter ratios. Please give us an exact problem - so that we can talk exactly.

 

[Laverne3ca]

In a similar manner, calculate the "desired" speed-ratios and from that diameter ratios. Please give us an exact problem - so that we can talk exactly.

Ok, here's the exact problem;
The drive motor is 16,000 rpm
The speeds desired are: 42,600, 27,900, 23,400, 12,500, 10,600, 7,000, 5,375, 4,150 and 3,200
There are the following pulleys: .75, 1, 1.2, 2, 3, and 4. Pulley #1 is 0.875 diameter and #3 is 2.233 diameter
The combinations listed on the nameplate are:
motor rpm - drive : driven
42,600 - #1.2 : #4
27,900 - #1 : #2
23,400 - #2 : #3
12,250 - #1.2 : #1
10,600 - #3 : #2
7,000 - #3 : #1.2
5,375 - #3 : #1
4,150 - #3 : #.75
3,200 - #4 : #.75

What is required is the diameters of all of the pulleys given that 16000/(2.233/.875)=6270 instead of 5,375 so #1 and #3 can't be the proper sizes either.

 

[Laverne3ca]

Is there a more appropriate section of the forum to post this?
Correction to the previous post, for the list of speeds, the rpm is the driven speed, the motor speed is fixed at 16,000 rpm.