I've been working on this project for a few months now and I am still nowhere near done, since I still have some parts on the way but I thought I would share what I have come up with my research and how it is going, and hopefully I can post an update afterwards.
Well, what is a ball mill?
A ball mill is a type of machine used in grinding media into very fine powders for applications like dressing processes, paints, pyrotechnics, and ceramics and it's typically cylindrical and rotates around a horizontal axis, partially filled with grinding media (often balls made of steel, ceramic, or rubber) and looks something like this on the industrial scale:
How ball mills actually work, is the actual steel/rubber/ceramic balls inside the drum spin with the drum, causing them to go along the wall of the drum, gaining some kinetic energy, which they then transfer to the particles when they drop back down to the bottom of the drum, in a constant cycle, so they are constantly smacking against each other, and crushing the material in between the impact through the constant collisions and attrition between the balls.
This way of working leads us to questions like, what is the optimal rpm of a ball mill, or the optimal ratio between the drums diameter and length.
To start off, the optimal rpm of the ball mill has to do with the gravitational force on the balls themselves and the centrifugal force from the actual spinning drum. For example, at higher speeds, the balls are sort of stuck to the wall, so aren't very good at moving around and colliding with each other. At slower speeds however, the balls tend to not move much from their position at the bottom of the drum, so there needs to be a some sort of point in between these two extremes where the balls momentarily stick to the wall of the drum and as they climb the wall, gravity prevails, allowing them to cascade down and impacting with each other. Of course, this is dependent on the diameter of the drum itself, so the formula to calculate this critical speed is :
Where Nc is the critical speed measured in rpm and D is the diameter in meters of the drum.
However, optimal speed and optimal rpm are not the same, optimal rpm is about 65 - 75% of the optimal speed.
The other factor to be considered, The drum diameter ratio to the drum length, has two different sides. For somebody who is looking for a higher impact, which is good for coarse grinding, the recommended ratio of the drum diameter to the drum length is 1 : 1.15 respectively. However, if you are looking for more attrition which means a finer grind, a ratio of 1 : 2 ranging to 1 : 3 is perfect.
There are many types of ball mills that differ from what I have been talking about, for example planetary ball mills which are small jars that are very high energy and rotate on their own axis, ideal for really fine powders and look something like this:
Other types include vibratory ball mills and stirred ball mills, which I haven't really looked into.
Another thing to note, is that ball mills can have different types of drive systems, which is the mechanism by which a motor transfers power from itself to the moving parts of a machine. The types include Direct drive, Belt drive, Gear drive and chain drive.
For direct drive, the motor is hooked up to the drum using a shaft coupling usually and it is a much simpler set up in general, needing less parts and factors to consider, not having to consider pulley ratios or gear ratios for example, but it requires a low speed high torque motor to run it, which may be more expensive in some cases.
For belt drive, the motor drives a pulley, which then drives a belt connected to the shaft of the drum (it could be possible to connect it to the actual body of the drum however I am not completely sure) and is a great system for people who would like to play around with the pulley ratios, but it is also generally cheap and is relatively easy to build. A problem with this however is the belts can wear or stretch.
For gear drive, there's a gearbox that connects the motor and the drum and turns them, and is more efficient when transferring torque than the other options and allows for precise control while being long-lasting. However, the set up is of course more complex and more expensive as well.
Then, you have chain drive which is like belt drive and gear drive had a child, which uses sprockets and a chain to turn the drum. It could be used since it is stronger than belts but it is more complex to pull off.
Without further ado, let's go oer my own experience.
I started off with some design ideas, as I had decided to utilize a direct drive system, I made a sketch or two
I then purchased a motor from Aliexpress rated for 12V and 108RPM, and grabbed some wood from the DT department at my school for the frame.
Then I ordered some castor wheels my drum could spin on, and a shaft coupling to connect the motor's shaft to a bolt I had screwed into the drum.
As my drum, I got a cylindrical container I had lying around. for the actual motor stand,it was just a piece of wood that I screwed into the frame.
I had my friend press-fit a ball bearing for me into the whole where the motor shaft would go through. I also ordered some steel balls to grind the media. A problem I encountered was that the shaft coupling I had ordered was too small for the shafts I was using so I had to drill it out to fit them. In my case, my drum's diameter is approximately 10cm so in my case, using the equation, my optimal RPM (according to the formula) is 157-183 RPM, but this is purely theoretical, since this doesn't tend to work in reality and so the actual optimal rpm would be around 60-90.
This is a video of it all set up and working (but definitely not optimal speeds which is why I am getting a motor speed controller soon and ill 3d print a case for it):
In the end, I made countless mistakes, like making the motor stand at a very bad height, and having zip tied the motor down, letting the drum move around like that probably due to the bad placement of the wheels but also the drum not being an even cylinder throughout its length, which let it wobble around, and also not having the right rpm setting. However I have 3d printed a new motor stand (just a block) and I am going to try figure out a way to have the motor be stable. Hopefully I will revisit the project, since I have learnt a lot from it, in terms of designing, and also the mechanics of how these great machines work.
Thank you for reading.