How many balls for the mill?

[DonCopal]

Hi there, I've got a 2L ballmill and I usually make around 100g of BP at once.

So, if I use lead balls, how many do you suggest me to put in there? I can also choose between 12.1mm and 15.1mm diameter (15/32th" or 19/32th").

The weights are 10.4g and 20g per ball.

 

Best Regards

Edited January 15, 2015 by DonCopal

[BurritoBandito]

What are the dimensions of your jar, and RPMs for your mill? This is going to determine the media size you need.

[Arthur]

In reality this depends on the power of the mill and the friction on the surfaces of the drum and roller. If you have a big motor then half fill the jar with media that is about 1/8 of the drum bore. Then the optimum load is the amount of powder that just covers the balls.

 

HOWEVER if you are using a rock tumbler then it may not turn this much lead and you will have to take balls out til you have some balls in there AND it turns without stalling the motor or the drum.

[Col]

From a litre point of view, approx 512 x 12mm balls will fit into 1L of space. If the mill isnt powerful enough to turn it you need a bigger motor, no sense dropping the media charge to accomodate a weak motor. The other option is to use a smaller jar with less media..that way the efficiency doesnt suffer

Edited January 15, 2015 by Col

[Arthur]

I'm aware that most mills in the UK seem to be small rock tumblers used with much less than the optimum half full charge of media. Whether it should happen... but it does. I also know a 205 litre drum used as a mill with a three phase motor and soft start controller

[BurritoBandito]

I was looking at it from this perspective...

Optimal speed = 265.45 / sqrt(Jar ID - Media Diameter) * .65

So, the optimum media diameter = (160000 * Jar ID * RPM^2 - 4763346289) / (160000 * RPM^2)

Then to determine how many pieces of media will be needed you'd just divide the jars volume by the volume of a single piece of the media, then divide by 2 (half fill the jar). I don't know if my explanation makes sense, or is overly convoluted, but that was my thought process. Of course it does not take into account the motors ability to turn the jar once filled.

[Col]

Thing is spheres dont fit together like cubes The 50% charge is the media volume + the space inbetween the individual pieces of media.

The way i look at mills is if you`ve got to use one (which we do) its best make it as efficient as possible so it doesnt have to run any longer than necessary to get the job done From that standpoint, a large mill with a 50% charge will do a better job than a small mill with a 50% charge. Mills with less than 50% will have to run a lot longer and they still wont do as good a job as the other two

Edited January 16, 2015 by Col

[BurritoBandito]

Damn, I hate making myself look like a fool, but I'm sooo good at it.

[DonCopal]

Hi, I forgot to mention that I have a selfmade ballmill with a motor that should be strong enough for at most 4kg of media, I think. My speed is nearly exactly 60 RPM.

The bulk density of both diameter balls is 7kg per liter. So, a half way filled jar would have 7kg. But I thought a 1/4 filled jar would already fit for lead balls?

[FlaMtnBkr]

How did you get that 512 12mm balls will fit into a liter space? Out of curiosity.

 

From my bass ackward math I come up with closer to 700.

 

512 would give a packing density that takes up less than 50% of the space which seems a bit low. Just curious.

[Col]

high tech 1 litre pyrex measuring jug

457 fills a 100 cd spindle lid this full

 

 

My small mill jars use 10mm od x 10mm long (bead shaped) alumina, which runs at 830 per litre. They`re quite a bit lighter at 2.5kg/L

Edited January 16, 2015 by Col

[DonCopal]

Well, the seller writes that the bulk density of his 12.1mm balls is around 7kg/l.

[Mumbles]

Sounds like you need to purchase 7kg then.

 

Another thing I've been meaning to mention. You should probably revaluate the amount of BP you're planning to mill. 100g seems far too low. A jar of that size should hold a charge of 4-500g approximately. Undercharging a mill with BP will lead to unnecessary wear on the media, and there is some concern of increased likelihood of accidents since there isn't sufficient BP isn't there to cushion the media from one another. I'm not sure about the accident thing, but the increased wear is a real phenomenon.

[Col]

7kg sounds about right, you`ll probably find its a bit less but not much (250g)

+1 to mumbles comment. I run 100g bp in a 0.5L jar with alumina, with willow charcoal the finished bp is 150ml by volume so its slightly more than 25% after milling. Paulownia and balsa bp would likely need less than 100g to finish at the same 150ml.

[stix]

Theoretically...

 

(15/32th") = 11.9mm and (19/32th") = 15mm

If they are Lead (density of 11.36g/cubic cm)

That would be 10g and 20g per ball respectively.

 

Anyway, that's not too important and pretty close but what I have worked out doesn't make sense (wouldn't be the first time).

 

I've done some calculations given: "The theoretical average packing density of same sized spheres in a cylinder is approx. 70% of total volume", I came up with this:

 

791 balls (11.9mm diam) are required to fill 1 litre.

395 balls (15.0mm diam) are required to fill 1 litre. (almost exactly double the volume of the smaller ones, and half the amount which makes complete sense)

 

Strangely though, if they are Lead Balls, that would equate to 7.9kg/l ??? I'll have to re-look at this tomorrow.

 

The simplest method is what Col did - what size is the round media in that pic Col?

 

Of course I've overcomplicated things as usual, what mumbles said: "Sounds like you need to purchase 7kg then" is all that's required, and no need to really know how many balls, as they would normally be sold by weight, in this case weight per volume which makes it very easy.

 

However, I would like to know as I'd like to now include it in my ball mill calculator that I've been working on, which when finalised I'll post if anyone is interested.

 

It would be useful, if anyone has the time, to measure 1 litre of their ball media - preferably in a cylinder like Col did, and count them, giving the diameter and weight of 1 ball and post the results here.

 

I used the formula to test on my ball mill. 20mm media: Calculated 166 balls, measured 155 balls - not too bad??? That 70% of volume is never going to be correct, apparently there isn't an exact formula. I imagine the smaller the media, the more accurate the result.

 

Cheers.

 

Oh, then I saw this:

 

From a litre point of view, approx 512 x 12mm balls will fit into 1L of space....

 

That's it, I'm going to bed.

Edited January 17, 2015 by stix

[Col]

They`re 12mm, i cast just under 40kg of lead using two fishing weight moulds...8 balls per mould!

[DonCopal]

Stix, please remember that they are HARDENED lead balls, that means they also contain antimony which makes them lighter.

[BurritoBandito]

"The theoretical average packing density of same sized spheres in a cylinder is approx. 70% of total volume"

The figure I found was 63.4% packing density for randomly packed spheres, and 74% for optimally packed ones. So maybe you could multiply the volume of the jar by .634 and then divide by the volume of the media. Thought about that last night, but didn't want to be wrong twice in one thread. I haven't worked out the math with actual values yet, so I don't know how accurate it would be, if at all.

[FlaMtnBkr]

I believe that the bigger the sphere the better it packs in a known orientation, and the smaller it is the more random they pack until it becomes almost impossible to predict the packing density. The spheres tend to sit in a particular orientation but there will almost always be the random ones that don't behave which throws things off. The smaller the diameter, the more they don't sit right plus the more pieces total so an increase in the ones that don't sit right even if it was a constant percentage of the total. Hope that makes sense.

 

So you can probably get a good approximation based on volume. But you should get an exact number based on weight.

[Arthur]

There is no easy way to guess the number of spheres in a cylinder as all depends on how well a size fills the circle of the base. Easiest method is trial and error, count the balls in your mill jar.

[Mumbles]

I've always used 65% packing density, but we're all guesstimating here really. For 12.1mm is 700 balls, for 15.1mm it's 360 balls, both weighing around 7.4kg based on pure lead. Ballpark accuracy is the only thing that really matters. You're got going to affect your efficiency by only filling the jar 45% full.

[Col]

Being close probably matters more if your buying media and having it shipped, if casting your own, just keep going til you have enough or you run out of lead

[stix]

Ok thanks - I've now plugged in 65% for the average packing density as suggested.

 

They`re 12mm, i cast just under 40kg of lead using two fishing weight moulds...8 balls per mould!

 

That still works out to approx. 717 balls - it mustn't be pure lead then?

 

 

Stix, please remember that they are HARDENED lead balls, that means they also contain antimony which makes them lighter.

 

That would account for the difference, as I now have 7.4kg/l for pure lead.

 

 

"The theoretical average packing density of same sized spheres in a cylinder is approx. 70% of total volume"
The figure I found was 63.4% packing density for randomly packed spheres, and 74% for optimally packed ones. So maybe you could multiply the volume of the jar by .634 and then divide by the volume of the media. Thought about that last night, but didn't want to be wrong twice in one thread. I haven't worked out the math with actual values yet, so I don't know how accurate it would be, if at all.

 

I'm now using .65 as the multiplier. Since joining this forum, I've been wrong more times than I care to admit. I think this is good though, so long as I'm learning. Well, that's my positive spin on it.

 

 

I believe that the bigger the sphere the better it packs in a known orientation, and the smaller it is the more random they pack until it becomes almost impossible to predict the packing density. The spheres tend to sit in a particular orientation but there will almost always be the random ones that don't behave which throws things off. The smaller the diameter, the more they don't sit right plus the more pieces total so an increase in the ones that don't sit right even if it was a constant percentage of the total. Hope that makes sense.

So you can probably get a good approximation based on volume. But you should get an exact number based on weight.

 

I thought the opposite, as in more opportunity to pack in tighter when smaller, difficult when bigger. Although now that I think about it, the smaller balls means a less accurate count on 'how many' but the percentage of error would be less. Maybe.

 

 

There is no easy way to guess the number of spheres in a cylinder as all depends on how well a size fills the circle of the base. Easiest method is trial and error, count the balls in your mill jar.

 

I thought about this - true, definitely would make a big difference. If your circle base was an unfortunate match for your media it could be a big waste of space. Perhaps this is the main reason why theoretical and measured can be so different.?

 

Yep, trial and error is all well and good if you actually have the media at hand - I'm looking at this from the point of determining before hand what media size, and approximately how much of it to buy.

 

 

I've always used 65% packing density, but we're all guesstimating here really. For 12.1mm is 700 balls, for 15.1mm it's 360 balls, both weighing around 7.4kg based on pure lead. Ballpark accuracy is the only thing that really matters. You're got going to affect your efficiency by only filling the jar 45% full.

 

I'm now using 65%. My calculations now match yours exactly - which is good because at least I'm confident that my math is correct. With my own ball mill, I'm now out by one ball. As you pointed out Ballpark accuracy is good enough anyway.

 

My .5ltr ball mill runs too high rpms and the media is too large for it - which I haven't sorted out yet, which is probably more important for efficiency than being out by a few percent when filling.

 

 

Being close probably matters more if your buying media and having it shipped, if casting your own, just keep going til you have enough or you run out of lead

 

Yeah Col, that was the point, that is determining beforehand prior to shipping. I have a few kilo's of linotype metal that I'm still yet to cast. It's not high on my list of priorities and I seem to get sidetracked all the time, like on this thread

 

------

 

I do want to finish the project I started which is a "stand alone" ball mill designer application for those wanting to build their own. It has a simple to use interface which allows easy "what if's". I'll post it on the apc forum, since this is where I got most of the info from. Therefore I want it to be accurate as possible to avoid any undue criticism (as apposed to the due kind).

 

I will first post it in it's raw form (beta), and ask for critique, ideas and improvements. It will only deal with spherical ball media and I probably won't bother to go further as this aspect (ie. how much media required) was an afterthought from originally reading this thread.

 

It would however be handy to have a list of various common ball media materials and densities - doesn't have to be entirely accurate at this point.

 

Cheers.

Edited January 18, 2015 by stix