Another bloody ball mill speed question

[stix]

I've already done some reading first, so my question is more out of confusion than laziness.

 

I'm currently in the process of making a ball mill for small batches of comps (100 grams max.)

The jar I'm considering using is 1/2 litre (500 mil) 8.5cms diam. with 20mm diam. ceramic media.

 

I have all the bits, motor, rollers, bearings etc. I have access to a lathe so I will be making the pulleys (motor & drive shaft) out of delrin or nylon. Therefore I can make them to whatever diameter as needed.

 

I think I'm good to work out the math required, what I'm not sure of is the optimum rpm of the mill jar.

 

I've read 60-90rpm should work well. As a basic test I've loaded the jar third full and rotated it best I could by hand whilst doing a rough timing. Around 90rpm "sounded" ok.

 

Without any practical experience and just looking at it, the ball media "seems" too large for the jar. Not sure, hence this post.

 

I'd really rather use the media I already have, but If nesser, I could buy some 10mm diam. or so brass rod and cut down to pellets.

Or a use a slightly bigger mill jar.

 

Your thoughts and ideas?

 

Cheers, Steve.

Edited November 16, 2014 by stix

[MrB]

The jar I'm considering using is 1/2 litre (500 mil) 8.5cms diam. with 20mm diam. ceramic media.

 

Without any practical experience and just looking at it, the ball media "seems" too large for the jar. Not sure, hence this post.

You are right. Media "should" be half the size, or so. With that size your speed should be around 105rpm according to a nifty little tool someone made me. I would credit them, but i don't remember who it was. They are around here somewhere so they might take credit, in which case i'm going to try and make a note of it.

B!

[Mumbles]

The formula for optimum speed is based on the critical speed, which is the speed that the media will begin to stick to the walls instead of tumbling. Optimum speed is approximately 65% of the critical speed.

 

Critical speed = 265.45/sqrt(Jar ID - Media Diameter)

 

This is in inches, so you will need to convert from metric. Presumably the constant could be modified for metric.

 

Doing the math, it looks like you need around 110 RPM. However, I'm inclined to side with you on the feeling that your media is too large. The general rule of thumb I was taught was no more than 1/8 the jar ID. For this to work for you, the jar ID would need to be at least doubled, which would require a volume 8x as large. I get the impression this is larger than you'd prefer.

 

A somewhat larger diameter jar (10cm or so) would work pretty well with the 10mm media you describe.

[Col]

You could shorten the jar to reduce the amount of media required, but 10-12mm would do a better job. I run my 500ml jar (75mm) with 10mm alumina at 100-110rpm, its not as efficient as the big mill but its really useful for milling small batches.

[Bobosan]

Nylon for the pulleys doesn't sound too safe in regards to static buildup. Not sure of delrin electrical characteristics. If possible, go with "off the shelf" metal sheaves and save yourself some work.

Edited November 16, 2014 by Bobosan

[Eagle66]

I think you're pretty much on track with your design. However I would recommend a change in the motor/drive placement.

 

If you extended the drive shaft outside of the bearings, with the pulley attached there, you would be able to isolate the motor more easily.

 

Like this:

 

About the pulleys. I am all for making your own (BTDT I cast the blanks out of Zinc or Aluminum), but the idea of using delrin, nylon, or any other plastic for pulleys in close proximity to reactive compounds gives me the chills just thinking about it. Major static generation issues. Metal pulleys are much safer.

Edited November 16, 2014 by Eagle66

[Col]

A TEFC motor doesnt need to be isolated but the box will help reduce the noise from the mill jar

[psyco_1322]

I'd suggest just making a larger mill jar. You will probably kick yourself down the road for making a mill that will only handle a 100g. It's not like you can't mill 100g in a mill that could handle 400g.

[Col]

I'd suggest just making a larger mill jar. You will probably kick yourself down the road for making a mill that will only handle a 100g. It's not like you can't mill 100g in a mill that could handle 400g.

You`d need a different jar for 100g and likely a speed adjustment/pulley change. If you put 100g in a jar optimised for 400g, you`d get a lot less grinding action.

[stix]

Thanks for all the good practical ideas - Sorry about this long reply, but felt I should respond to all.

 

You are right. Media "should" be half the size, or so. With that size your speed should be around 105rpm according to a nifty little tool someone made me. I would credit them, but i don't remember who it was. They are around here somewhere so they might take credit, in which case i'm going to try and make a note of it.

B!

 

Thanks MrB, seems like my general assumptions were pretty much correct - some work to do.

 

 

The formula for optimum speed is based on the critical speed, which is the speed that the media will begin to stick to the walls instead of tumbling. Optimum speed is approximately 65% of the critical speed.

 

Critical speed = 265.45/sqrt(Jar ID - Media Diameter)

 

This is in inches, so you will need to convert from metric. Presumably the constant could be modified for metric.

 

Doing the math, it looks like you need around 110 RPM. However, I'm inclined to side with you on the feeling that your media is too large. The general rule of thumb I was taught was no more than 1/8 the jar ID. For this to work for you, the jar ID would need to be at least doubled, which would require a volume 8x as large. I get the impression this is larger than you'd prefer.

 

A somewhat larger diameter jar (10cm or so) would work pretty well with the 10mm media you describe.

 

Thanks Mumbles, seems like the larger 10cm jar with the smaller brass media is the likely solution - or at least a reasonable compromise without too much mucking about. I hope!

 

You could shorten the jar to reduce the amount of media required, but 10-12mm would do a better job. I run my 500ml jar (75mm) with 10mm alumina at 100-110rpm, its not as efficient as the big mill but its really useful for milling small batches.

 

Yep! thanks Col, I've often thought about this one as well - ie. A large diameter, but like a 'slice' of the jar. That way you have the rotational benefits without unnecessary volume.

 

 

Nylon for the pulleys doesn't sound too safe in regards to static buildup. Not sure of delrin electrical characteristics. If possible, go with "off the shelf" metal sheaves and save yourself some work.

 

Are you serious? Bloody hell, I didn't think I would have an issue like that! ok, fine - not doubting your ideas but would need to have that confirmed - don't forget that I'm only doing small amounts.

 

I think you're pretty much on track with your design. However I would recommend a change in the motor/drive placement.

 

If you extended the drive shaft outside of the bearings, Closeup of Bearing.JPG with the pulley attached there, you would be able to isolate the motor more easily.

 

Like this: Box Enclosing Jar & Drive.JPG

 

About the pulleys. I am all for making your own (BTDT I cast the blanks out of Zinc or Aluminum), but the idea of using delrin, nylon, or any other plastic for pulleys in close proximity to reactive compounds gives me the chills just thinking about it. Major static generation issues. Metal pulleys are much safer.

 

Ok, fair enough, so that's two people who don't like the idea of using pulleys that 'could' cause static. I guess no big issue and easily changed. The diagram I posted was just a rough mockup and I will review your ideas when I get a bit closer to actual construction. Thanks.

 

A TEFC motor doesnt need to be isolated but the box will help reduce the noise from the mill jar

 

I'll have to make do with my induction motor, but make sure it's well protection and isolated.

 

 

I'd suggest just making a larger mill jar. You will probably kick yourself down the road for making a mill that will only handle a 100g. It's not like you can't mill 100g in a mill that could handle 400g.

 

Thanks, but I only want to make small amounts.

 

----

 

Thanks everyone, a lot to consider.

 

[EDIT] Also have an alternate plan, as in a "shaker/pulveriser'' not a ball mill at all.

 

Cheers.

Edited November 17, 2014 by stix

[stix]

Ok,

 

So I have another Mill Jar candidate - 165 units diam. I've done the math and I think my calcs are correct, but would like some confirmation please.

 

The upshot is that I'm thinking I can do this without any 'step down' pulleys arrangement, ie. direct drive with a rubber uni-joint.

 

What I have is this:

Motor rpm: 1250

Driver Roller circumference: 44 units

Mill Jar circumference: 518 units

 

Given that: (44/518) x 1250 would equal approx. 106rpm...?

 

Also with Mumbles info regarding ideal ball media size: "The general rule of thumb I was taught was no more than 1/8 the jar ID". That would be: (165 units mill jar diam. / 20 units ball media diam.) = 8.25 which is approx. the desired 1/8th!

 

I will also be making the mill jar length shorter, approx. 100 units internal length, therefore I can fill to half-way with my current media and optimise the grinding.

 

If the rpm's are a bit too high, I can always increase the diam. of the mill jar with rubber rings. Overall, I think that this all seems a reasonable prospect?

 

Cheers.

[Col]

Assuming the units are mm, a 165mm id jar with 20mm media has a critical speed of 111rpm and an optimal speed of 72.2rpm. The 1250 rpm motor spec is likely with no load so you may need less increase on the jar diameter to get the revs within range

[stix]

Thanks Col,

 

Wether it be "bee's dicks", "elephants balls" or "millimeters" - it shouldn't matter. I thought "GENERIC UNITS" would give more insight and clarity than be distracted by various other units of measure... obviously I screwed up somewhere! - the main point is rotation speed of the mill jar with regard to ball media size.

 

Can you please expand on what you said "The 1250 rpm motor spec is likely with no load so you may need less increase on the jar diameter to get the revs within range"

 

Sorry, but I don't get it - can you please re-word it?

 

Cheers.

[MrB]

He's just saying that a motor with weight on the rollers slows down.

B!

[stix]

Ah!.. thanks MrB got it now!

 

Col means that "with the added media weight slowing it down, I may not need to adjust the diam. of the jar".

 

Makes sense.

 

Cheers.

[Col]

i just meant that it may not deliver the full 1250rpm under load. Adding a calculated reduction based on the 1250 will result in lower rpm than expected. Dont forget that its the mill jar`s inside diameter thats used for the critical and optimal speed calculations, more of an issue with thick walls.

Edited November 24, 2014 by Col

[Mumbles]

The one place that units come into play is for the critical speed calculation. The units change the constant needed.

[stix]

i just meant that it may not deliver the full 1250rpm under load. Adding a calculated reduction based on the 1250 will result in lower rpm than expected. Dont forget that its the mill jar`s inside diameter thats used for the critical and optimal speed calculations, more of an issue with thick walls.

 

Thanks Col - lower rpm will possibly work in my favour.

 

The one place that units come into play is for the critical speed calculation. The units change the constant needed.

 

Thanks Mumbles - yeah fair enough, the units will change the constant in your calculation as you originally pointed out. I'm using millimeters, so the constant would be 6742.4

 

If I understand this formula correctly: Critical speed = 265.45/sqrt(Jar ID - Media Diameter)

Therefore: Optimum Speed = 6742.4 / Sqrt (165 - 20) x .65

I work out the optimum speed to be 364rpm.

 

This doesn't seem right - I must have something wrong???

Edited November 25, 2014 by stix

[Col]

Optimum Speed = 265.45 / Sqrt (165 - 20) x .65 = 72.2rpm

the formula is geared for metric, you`d need a different constant (ie not 265.45) for imperial

 

lol, strike that, the 265.45 constant is for inches not metric, i use an xl spreadsheet that automatically converts mm into inches and uses the inch conversion for the calculation

 

Optimum Speed = 265.45 / Sqrt (6.496" - 0.787") x .65 = 72.2rpm

Edited November 25, 2014 by Col

[stix]

Ok thanks Col, that would explain something but not everything.

 

Wait for it ... ... I STILL can't work out how you arrived at 72.2 ... I calculate 14.3.!!

 

"Holy Mary, Mother of God in the highest plain, forever and ever amen - why dost thou God mock me? - f*ck, f*ck, f*ck, F*CK!!!!"

(sorry if that offends anyone)

 

Before I started this discussion I reckon I had about 10 functioning brain cells - now I've only 3 left.

One is having a beer, the other is concentrating on food, so I only have one left to solve this.

 

Please bear with me, I'll go through my method of working it out in basic format. Hopefully something is revealed.

 

Starting with: Optimum Speed = 265.45 / Sqrt (165 - 20) x .65 = 72.2rpm

 

Assuming: Critical Speed = 265.45 / Sqrt (165 - 20)

 

(165 - 20) = 145

The square root of 145 = 12.04

265.45 / 12.04 = 22.04

 

Given that "Optimum Speed" in this case is 65% of the critical:

22.04 x .65 = 14.34

 

Stix.

 

[lol even bloody louder - just saw your edit Col ]

Edited November 25, 2014 by stix

[Col]

You want inches not mm

The square root of 6.496"- 0.787" is 2.389

265.45/ 2.389 is 111rpm (critical) * .65 is 72.2rpm (optimum)

[stix]

Hang on... Hang on... I think I just heard a beep from my computer... perhaps someone has posted a reply?

 

Wait... I'll just loosen the noose a bit and get off the chair . . . .

 

---

 

Ok, Many thanks Col, Finally!!!

 

I now get the same answer as you... obviously I "assumed" wrongly and converted the wrong part of the formula to inches. All good now

 

So the final analysis is that my 'direct drive' scenario is pushing it, ie.

I've calculated that I'll have 106rpm, and the critical speed is 111rpm and 65% of that is 72.

Looks like I'll need to have step down pulleys after-all. fine.

 

Whilst pulling my hair out I came across another metric formula:

 

The critical speed (rpm) is given by: nC = 42.29 / Sqrt of D, where D is the internal diameter in metres.

 

This worked out to around 70 (given 65%) but doesn't take the media diam. into account.

 

At the risk of asking another question that I don't understand the answer to, why doesn't the weight of the media come into consideration? Surely ping pong balls and lead of the same diameter have differing actions and results?

 

Don't worry, this is just out of curiosity.

 

Stix.

 

[EDIT] btw. I studied drama at school.

Edited November 25, 2014 by stix

[Bobosan]

At the risk of asking another question that I don't understand the answer to, why doesn't the weight of the media come into consideration? Surely ping pong balls and lead of the same diameter have differing actions and results?

 

Don't worry, this is just out of curiosity.

 

Stix.

 

[EDIT] btw. I studied drama at school.

 

There is mechanical loss of rotation speed due to media weight. So, theoretically, with the ping pong balls you should not observe any speed loss (or very minor) but load with same amount and diameter of lead media and you'll see a greater loss of RPM due to mechanical friction and HP loss in the motor in the form of heat. A reduction belt drive helps to overcome part of these issues.

[Mumbles]

...

 

At the risk of asking another question that I don't understand the answer to, why doesn't the weight of the media come into consideration? Surely ping pong balls and lead of the same diameter have differing actions and results?

 

Don't worry, this is just out of curiosity.

 

Stix.

 

[EDIT] btw. I studied drama at school.

 

Well, there may be an extreme where the mass does come into consideration. In a total vacuum, there would be no difference. I suppose the no mass thing might not be totally acceptable if you have to take air resistance into consideration. With any reasonable mass media this is not an issue.

 

This next part may be wrong, and feel free to point out my errors if it is. It is however my general understanding.

 

The reason that there is no mass included in the equation is that it cancels out in the derivation of the math. Essentially what the above formula is derived from is a balancing of forces. Force is mass times acceleration. When both are balanced, since we're talking about the same ball on both sides, the mass falls out of the equation. You have to balance the downward force of gravity, with the upward rotational force. When the rotational force equals or exceeds that of gravity, you get cetrifugation. The formula is actually for the first centrifugation. IE when one layer of balls will stick to the wall. There are additional formulas for the second, third, etc. if you really care to get into them.

 

We are working with ball mill jar diameters that are not excessively larger than that of the media diameter. If you look into industrial ballmilling literature, you'll see the above formula generally with just the jar diameter and a constant given in feet. Since we're not in that realm, the diameter of the circular path the balls follow is calculated to be jar ID - media OD.

[stix]

 

There is mechanical loss of rotation speed due to media weight. So, theoretically, with the ping pong balls you should not observe any speed loss (or very minor) but load with same amount and diameter of lead media and you'll see a greater loss of RPM due to mechanical friction and HP loss in the motor in the form of heat. A reduction belt drive helps to overcome part of these issues.

 

Thanks, that make sense Bobosan.

 

 

Well, there may be an extreme where the mass does come into consideration. In a total vacuum, there would be no difference. I suppose the no mass thing might not be totally acceptable if you have to take air resistance into consideration. With any reasonable mass media this is not an issue.

 

This next part may be wrong, and feel free to point out my errors if it is. It is however my general understanding.

 

The reason that there is no mass included in the equation is that it cancels out in the derivation of the math. Essentially what the above formula is derived from is a balancing of forces. Force is mass times acceleration. When both are balanced, since we're talking about the same ball on both sides, the mass falls out of the equation. You have to balance the downward force of gravity, with the upward rotational force. When the rotational force equals or exceeds that of gravity, you get cetrifugation. The formula is actually for the first centrifugation. IE when one layer of balls will stick to the wall. There are additional formulas for the second, third, etc. if you really care to get into them.

 

We are working with ball mill jar diameters that are not excessively larger than that of the media diameter. If you look into industrial ballmilling literature, you'll see the above formula generally with just the jar diameter and a constant given in feet. Since we're not in that realm, the diameter of the circular path the balls follow is calculated to be jar ID - media OD.

 

Thanks Mumbles, I agree - when dealing with smaller mill jars the media OD should be included in the formula.

 

As for the rest, I'll take your word for it as I have no desire to look any further into industrial ball milling literature and additional formulas than I already have . I'm now looking forward to actually building the bloody thing!!

 

For the record, I have adjusted this metric formula to include the media OD, and the results are the same as the posted imperial version. It's the formula I'm now using and may be of interest to others.

 

Optimum Speed (rpm) = (42.29 / (Sqrt of (Mill Jar ID - Media OD))) x .65

 

Where Mill Jar ID and Media OD is given in metres and 65% of critical speed is included.

 

Cheers, and thanks everyone for your input.

Edited November 26, 2014 by stix