Sciencemadness Discussion Board

Planetary Ball mill gear sizes?

NickBlackDIN - 14-5-2023 at 08:50

Ball mills are bloody expensive, so I'm working on making one I can 3D print.

however, I noticed many papers just give an rpm figure without further context, which means I have to get the gearing the same as professional machines, the paper I'm currently interested in uses a Retsch PM100 (which seems to be a pretty common unit) anyone know the gearing ratio's/measurements? the only size I can find is that of the sun gear (141mm) anyone know the other dimensions?

any other input would be greatly appreciated. (or if you have questions on how I plan to do certain things, feel free to ask)


charley1957 - 14-5-2023 at 09:50

Don’t know how big your mill is going to be but it’s really simple to drive the canister with a belt or rubber strap or band with just the shaft of a motor, giving you lots of speed reduction and not having to create a gearbox. It won’t be as durable as a gearbox but there’s a lot of utility in simplicity.

NickBlackDIN - 14-5-2023 at 11:54

I think you may have been mistaken Charley, this isn't a rock polisher, the gearbox is to increase the simulated G-forces applied to the milling media. (in my build there will be 3 canisters, each attached to one of the planet gears)

this picture I think does a decent job explaining it:

[Edited on 14-5-2023 by NickBlackDIN]

Edit #2:
Looking at some videos, and getting some more information, there isn't actually a sun gear in the traditional sense, looks like a plate with bearings that roll the planet gears against the outer gear (at a ratio of 1:-2)

That basically gives me all the info I need.

[Edited on 15-5-2023 by NickBlackDIN]

Rainwater - 15-5-2023 at 01:44

Brilliant design. I never thought of anything like that. I always used a horizontal canister and relied on gravity/rotational speed to produce the waterfall of sample/media. This makes gravity the limiting factor, as once your sample is exposed to a rotational force of 1G, it will no longer fall. Note sure what a perfect value would be for any given grinding operation(i set mine by ear).

With the planetary gear configuration, your have removed gravity from the equation and replaced it with the gforce generated by the orbital of the planet gears.
What will be of great importance( as its the only parameter you can control) is the ratio between planetary orbit rpm vs planetary rpm. PO and P for short
If the radius of the planet(container) is properly matched to the radius of the planetary gear orbit radius, you will be able to maintain a linear G Force ratio across a wide range of rpm's

Gforce within a circle can be calculated with this equation
1.118x10-4x R x (RPM)² = Gforce
R is in millimeters.

Just guessing but a PO/P ratio between .5~.75 should produce a waterfall effect inside the container.

Sulaiman - 15-5-2023 at 03:02

Nice idea but is it practical?
The rotating assembly will need to spin quite quickly to allow tumbling within the grinding cylinders so the balance of the two cylinders will be important to minimise wear.
I can see the benefit
but is the complexity worth the time saved compared to a typical horizontal arrangement?
For commercial/professional use, time is money, so probably yes,
but for amateur use I guess not.

NickBlackDIN - 15-5-2023 at 05:52

Rainwater: spot on explanation!

I sure hope your guess is correct with the PO/P ratio range, since that is exactly what I'm aiming for myself :p (unless I can get more precise numbers)

Not sure if it's practical or not, it's needed.

I'm using 3 cylinders to make balancing easier. Using very small canisters to decrease wear (less weight being slinged around)

Yes, the complexity is necessary. Not nearly enough force in the rock tumbler arrangement. (The chemicals won't bond properly otherwise, the other option is very high pressure & temperature, which I hate doing, this is safer)

Edit: I should probably mention I'm making Na2S-P2S5 (solid electrolyte for an sodium ion battery)

[Edited on 15-5-2023 by NickBlackDIN]

Rainwater - 15-5-2023 at 17:42

excel calculator
R1 in mm 152.4 R1 RPM 30 R2 in mm 50.8 R2 RPM 45 cylinder orbit force = 15.334488 Gs cylinder rotation force = 11.500866 Gs total g force = 26.835354 ratio 0.75

Attachment: gforce.xlsx (9kB)
This file has been downloaded 81 times

So lets say the containers are 1ft apart and 4in wide.
The orbit at 0.5Hz or 30rpm
And the containers are spinning at 1.33Hz or 45rpm
Now lets sat that the weight of 1 container is 1000 grams total (2.2lbs)
The container will, at its extreme, be experiencing and exerting about 26.8 kilos of force(59lbs).

The media/sample will be experiencing a force thats a function of D2 and rpm.
It will be less that the 15.3 g's listed above.
The equivalent would be about the same as using a griending media that weights 15x what your using now without increasing its volume..
Gonna need some heavy steal and a ballast system, or that thing will shake your building apart

Here is a link i used when i was making different gears, which will require a lot of fine tuning and experimentation
When 3d printing a planetary gears, I find it useful to mark the top of the gears with arrows so you can install them correctly.
Also, post processing in hot salt is a must to maximize plastic strength.
I recommend the Herringbone gears for high torque applications

Edit #2
unless I can get more precise numbers

The term "critical speed" or CS is what you need to google. Its basicly the speed at which the gravitational forced approaches the centrifugal force and the media stops falling. Lots of math, there is a sweet spot at 68% of CS that most manufacturers recommend the mill operates at. Not sure how to calculate it, but it is a function of the equation I quoted above.

[Edited on 16-5-2023 by Rainwater]

[Edited on 16-5-2023 by Rainwater]

NickBlackDIN - 16-5-2023 at 00:12

Thank you very much Rain!

with your help I found this link, which includes the formula I need (all I need to do is change the g constant to whatever G force I'll be running at)

That gear generator is the same one I was planning to use, thank you!

and I appreciate the sample math as well =D

unfortunately I cant do much till Friday. but having this to think about will make work more enjoyable ^.^

Thank you.

charley1957 - 16-5-2023 at 10:01

Okay I get it now. That's a whole different animal. It increases the G force for quicker and/or more efficient milling. Well I hope you can get it worked out. I’m a huge fan of DIY to make something work well without having to spend a lot of money on it. Best of luck, and I’ll follow your posts on it.

Fulmen - 16-5-2023 at 10:53

Very interesting idea. It's comparable to a "ring and puck mill"

alexwoo10 - 5-12-2023 at 00:59

Please send the stl files for this project