Centrifugal Accelerator-Kinematics Problem

[roamer]

OK here is my nutty design problem. I want to make a centrifugal nut cracker to crack hazelnuts. The basic design premise is very simple when the nuts are thrown perpendicular to a surface at a desired speed the shells split very nicely into two pieces. Anyways I want to make a centrifugal accelerator that throws/ejects the nuts onto a hard surface. The basic design is a rotating disk with two radially mounted blades. The nuts fall in the center of the disk and are accelerated outward until they are ejected with some velocity V that has both a radial and tangential component (see attached picture). I desire to make the nuts come out with as much radial velocity as possible and as little tangential component as possible. To do this I need to derive the equations for the nuts velocity. I am for now not considering frictional forces or any forces and just trying to get the kinematic relationship.
The way I have the blades mounted the tangential velocity is simply v_t=R*W. Where R=radius and W=rotational speed. The radial velocity is where I am stuck. I know centrifugal acceleration is a_r=W^2*R. The problem is that the this acceleration varies with respect to radial position. So the nuts experience a greater and greater acceleration force as they travel along the blade. It is just like being on a merry go round where as you travel to the outside a larger and larger force is pulling out. Anyways I don't know how to treat this equation I guess it could be written as a second order diff. eq like d^2r/dt^2=W^2*R, which if this is the right equation I don't know how to solve, any ideas?

 

[Danger]

Personally, I believe that you're way over-thinking this. I'd go with trial and error. To reduce/stabilize the tangental speed, I recommend firing them into a chute or wall that's curved back away from the direction of rotation so they're guided with minimal deceleration into the target at a right-angle. That will also simplify the collection process, since you can simply have a drop cup under the target. If you have a little fan blowing across the drop area, you could also maybe blow the shells away into a separate container. I don't think that any formulae are necessary; just crank the sucker up until they break.

 

[roamer]

Danger,
Thanks for the suggestion, you might be right about over complicating, I am normally all for trial and error. The problem is I can only afford to have one rotor laser cut out (it needs to be balanced to spin at 1800rpm) so i need to know the size I want. If I fired them into a chute like you would suggest I would have to retain them with some wall and the would probably break at impact on the wall unless I could drop them in at just the right spot.
All I am after is what the radial velocity is from centrifugal acceleration. If that equation is right maybe I should post it in a math forum.
What I think is that the radial velocity is dependent on W^2 and the tangential speed is a fnc of W*R. So if I wanted to minimize tangential speed and maximize radial speed I should make a small disk and spin it fast right??

 

[roamer]

Danger,
I've attached another crappy pic. Is that your idea??

 

[Danger]

Not quite, but almost. Give me a while; I'll fire up a sketch. Sorry I can't help with the formulae at all; I know nuthin' about math.

 

[Danger]

Well, I've got the sketch all done up, but for some reason Image Shack won't upload it. I've been in contact with them for a couple of hours trying to get it sorted out, but it looks like nothing will be resolved tonight. Please don't progress with your laser machining until I have a chance to get the illustration and explanation posted, because I think that I can save you a lot of money. I might be wrong about that, but it's probably worth your while to wait a day or so. Sorry about the delay.

 

[Danger]

Okay, it wasn't Image Shack's fault. The file was corrupted, but I don't know how or why. The whole thing has been giving me absolute fits since I finished drawing it. Nothing more that I can do until I get home from work in 6 hours or so.

 

[Danger]

Okay, I finally got the damned thing working. Turned out that my Photoshop is outputting corrupted files. Once I downshifted from Illustrator 10 to 6 and resaved it as a jpeg, it worked.

http://img241.imageshack.us/img241/3843/nutcrackeryz7.jpg

Unfortunately, it's now 3:40 in the morning and I have to get up for work in 4 hours. The explanation will have to wait until then.

 

[FredGarvin]

What is the purpose of wanting to minimize the tangential component?

 

[Danger]

Fred: If I understand the term 'tangental component' properly, it would be to maximize the impact force when the nut hits the target. A 'glancing blow' wastes a lot of that in angular acceleration. Also, it would make it easier to catch the things.

Roamer: My thought here is that you could use a good sturdy, flexible material such as 60mil PET (pop-bottle plastic) for your impellers. If they're cut longer than the radius of the container, they'll automatically bend into the sort of curvature shown in the sketch. That will give a total seal against the wall, so prematurely fractured nuts can't jam it up. In addition, if the opening is slightly taller than the blades, there'll be a 'whiplash' effect as the blades spring outward into the gap, which will impart even higher speed to the nuts. That would increase the noise level, but it's going to be loud anyhow.
Unless you made a typo and meant 18,000rpm, there's no need to balance it even if you do use metal. Regular household fans turn at 1750rpm, and they'll keep running even if you cut one of the blades off (not recommended; it pounds the hell out of the bearings).
If you do want to stick with your original metal idea and higher speed, you could still save a chunk of change by finding a screwed up turbocharger and use the compressor side for your device.

 

[roamer]

Fred I wanted to minimize the tangential component for the exact reasons Danger cited. However this issue isn't even critical in Danger's design.

Danger your idea looks really good. I appreciate you posting your thoughts on it. I am thinking if that the fan blades will wear out rather quickly with an interference fit, but they would be rather cheap to replace.
Any other input you have would be great. I'm going to go start looking some PET!

 

[Danger]

You're more than welcome, roamer. I just love messing about with stuff like this. The PET was just an off-hand example, and it's quite cheap. What might be even better, and more 'self-lubricating', is the stuff that they make those spatulas out of that you have to use with Teflon frying pans to avoid scratching the surface. I'll have a go at finding out what it is.

edit: Having given it some thought, I believe that it's a form of nylon.

 

[Danger]

Hi again;
A couple more thoughts on the subject. Plastic impellers should be jam-proof even without a total seal because they'll flex around an obstruction. I still like the interference fit because of the whiplash, though.
Also, if the housing is made out of a similar material, it should be a lot quieter. The target, of course, should be metal to eliminate the shock absorption that plastic would provide.
I'll probaby have a few more quicky posts like this once in a while. When I go into 'brainstorming' mode, I tend to just spew stuff out as it arises, and worry about analyzing it later.