[keebler303]

would a plumb bob not be a simpler solution? if you know the exact center of your bottom plate and top plate, might be easier to read than a bubble?

Its a little more difficult to do that once the balls are in place. Every time you move it, it will have to be releveled. Not such a minor task if you use a plumb bob in the center.

Matt

[widgitmaster]

On many a post here on the Zone, I have read where someone had made an "Impulse Buy" on eBay or other stores.

Well, while surfing through eBay I noticed a seller that had large chrome steel precision balls. 2.5000 +-.0002" to be exact! Now most people would just keep surfing, but I bought FIVE of them (chair) So for the next few evenings I stepped away from my current projects and started designing a HUGH "Newton's Cradle" using these large balls! It took me a little while to make everything proportionate, and I have to say that I must be totally NUTZ

Oops, I did it again (chair)

This time I found a super precision B&S height gage, and won it
I have used them in the past, and they are fantastically easy and accurate to .0001" Now I can really make this Newton's Cradle accurate!
Widgit

[BobWarfield]

Wow, you stole it!

I bet that seller wishes they had been a little more descriptive.

Congratulations. I've been lusting for one like it a long time, but they're always over $1000.

Good eye, Widgit!

Cheers,

BW

[mactec54]

Yes they are really nice it's amazing what you can get on Ebay

Getting back to your bearings, if you put a spacer in the centre between the bearings to do the preload it will then give you clearence on the outer bearing face/edges Then the outer edges won't
touch the sides of the frame were they are mounted, I know this will be harder to put together, But putting the preload on the outside of the bearing may make the outer edges of the bearings touch the sides of the slots in the frame

[widgitmaster]

Thanks mactec54,

Yes, in my concept drawing they are in contact, but most bearings have about .001" wider inner race. So like I said, I'll have to wait till they arrive to get the exact dimensions and build around them! I may be able to use the same spacers I made for the cheap bearings too!

Widgit

[Mike Everman]

Hi Mike The knife-edge bearing would not be a good choice for this project, What happens is when the ball hits the other balls the force of the impact lift's the pendulum/ball holder off the the seat of the knife-edge & there is not easy way to hold it down on the seat without creating more friction

Yeah, I agree. I was having trouble imagining how shear loads would get into the knife edges, but I see now that the knife edge would only work if the balls had cables, instead of frames, and the end frames' come to an abrupt stop, or more precisely the frame's instantaneous cessation of rotation, with a reactive force occurring at the knife edge. hmmmm
I think there's an advantage then to having these frames that I didn't realize. To create a counter-torque that negates this shear-on-impact at the knife-edge bearings, the impact point needs to be below the radius of gyration of the pendulum, which it is already, but couldn't possibly just happen to be in the right spot. <insert physics math here> ha
I imagine it would mean a mass below the ball to move the radius of gyration close above the ball impact point. So, counter-torque cancels reaction torque. Wonder if it's worth it?

I'm still trying to understand why all the central ball frames need bearings at all.

[BobWarfield]

Hi Mike The knife-edge bearing would not be a good choice for this project, What happens is when the ball hits the other balls the force of the impact lift's the pendulum/ball holder off the the seat of the knife-edge & there is not easy way to hold it down on the seat without creating more friction

Isn't it fascinating, if that were really true, that every other Newton's Cradle I've seen, except this one, suspends the balls by strings, which have no ability to hold them down either. Watching one in operation, there is no obvious tendency for the balls to rise as well.

I intend to try the knife edge concept at some point. I think it will work great.

Cheers,

BW

[widgitmaster]

Just a note to say that I'm going to take a couple days off from this project, let my brain relax and wait for all the neat stuff to arrive!

Then I will start at the bottom and work my way up, testing, fixing and adjusting as I go!


Now, I need one of you guys with a 3D CAD/CAM to write me a g-code program!

The hole in the bottom plate is no longer needed, and I'm not going to buy and mill-up a replacement! So I have the idea of making a 4" dia brass dome that is 5/8" off the base surface. it will have a 4" radius.

I would like to engrave my EAA logo in the center, and some text around the outside! Now I have a BIG CNC router just looking for something to do, but I do not have time to learn a CAD program or how to G-Code by hand!
The background of the logo to me removed, and blackened. With the raised surface polished! Will look stunning!

You can either make me the code, or make the entire plaque! I will gladly pay for it!

If anyone is interested in this task, I can supply dimensions, and text as needed. Contact me via PM

Thanks for all the kind words, useful suggestions, and challenging engineering concepts! (brain food)

Eric

[Mike Everman]

Isn't it fascinating, if that were really true, that every other Newton's Cradle I've seen, except this one, suspends the balls by strings, which have no ability to hold them down either. Watching one in operation, there is no obvious tendency for the balls to rise as well.
I intend to try the knife edge concept at some point. I think it will work great.
Cheers,
BW

Well, I think the interesting difference here is the frames holding the balls. the impact point is substantially below the CG, so will directly try to jump the knife edge on impact. Strings get around this problem by being nearly mass-less, so the impact is extremely near the cg.

[BobWarfield]

Mike, you might be right, but I don't think the aluminum arm weighs enough relative to the ball for that to be the case, and it looks to me like there will be lever arm effects too that are much longer than the CG displacement.

In any event, I will do a test when I get to building mine just so it is different in some way.

Cheers,

BW

[widgitmaster]

Actually, it is a fact that when all the balls are perfect alignment, the balls in the middle are perfectly stationary throughout the entire swing duration! The only time one of the balls will lift is when one is higher and being struck at a lower point!

My initial video was premature, in as much as none of the balls were in line! If x-axis is the view from the side, and y-axis is the view from the end. Then I have been working only on the z-axis! The distance between the upper & lower fulcrum points on the forks is very accurate on 4/5 forks along with the Concentricity of the ball's mounting holes.

The current problem is the location of the pivot holes and bending of the top plate. So when my new bearings arrive, and I remake the top plate, the z-axis should be finished. Next will be the y-axis, which will be aligned by tightening the end play of the upper bearings (preloading), and making the Delrin bushings custom to each fork. Then all that is to be done is to calibrate the leveling procedure, as there is nothing to be done in the x-axis other than lifting the ball to start the cycle!

A v in V pivot will work nicely and maintain z-axis alignment, but there is NO control of the y-axis, and a pivoting v would need some kind of uni-ball stop to keep it in align. Two such stops would create enormous resistance, and diminish overall performance!

And I thought my brain was resting today

http://www.precisionballs.com/measuring_sphericity.htm

[veteq]

Actually, it is a fact that when all the balls are perfect alignment, the balls in the middle are perfectly stationary throughout the entire swing duration! The only time one of the balls will lift is when one is higher and being struck at a lower point!

Think the balls carry that much energy, that the not perfect horizontal force will result in a nice vertical vector, the balls weren`t in line and there was a distance in between the balls that give a extra vertical force. The distance between the balls make it possible to accelerate the ball to the next, insted off immidiatly giving the force to the next.
Now motion is possible off the balls that needs to be stationary.

[widgitmaster]

The bearings arrived today, and they fit snuggly in the upper bearing bores! After measuring them, I know how much to step the sides of the spacers, so they press against the inner race and not the outer race. The other modification will be in the shoulder bolt, as the standard 1/4" shanks fit too sloppy in the bearing's ID! So I will modify a .3125" shank shoulder bolt, so that it fits snuggly in the top plate and the bearing!

When I make the new top plate, I will bore the holes at a 2.5000" spacing, so there will be zero gap between the balls when they are stationary!

[Mike Everman]

Mike, you might be right, but I don't think the aluminum arm weighs enough relative to the ball for that to be the case, and it looks to me like there will be lever arm effects too that are much longer than the CG displacement.

In any event, I will do a test when I get to building mine just so it is different in some way.

Cheers,

BW

Don't underestimate the contribution of the frame's mass, though it seems small, it's not a small effect.
Pendulums are of two types, simple and compound. Simple is purely theoretical, since it implies a mass-less rod, and a point for a bob mass with no moment of inertia, so really all pendulums are compound in the real world.

With this and precision clockwork, the amount it deviates from simple is a measure of how much grief you'll have trying to make it perfect. (Of course "perfect" means different things to different people. ;-) Considering the frame and ball pendulum here, the impact is happening through the ball center, which is not the cg of the pendulum, so the impact will make torque about that cg when it hits, and that torque translated into shear at the top pivot and bending modes of the frame itself. If you look at the right side ball falling left toward its collision, there the frame is also rotating as well as translating. A rotation that will instantly stop on impact and has its own torque contribution. So there would be some good science in apportioning the mass of the frame so that the impact cancels it's own impact derived torque. Either way, it's ideal for the frame to be mass-less, because rotating it back and forth is a direct loss to the energy of the system. The frames being lighter is better no matter what, if the goal is for it to bounce many times.

On another note, I would skip the bushings at the balls or make them press-fit and non-rotating. Any clearance there is going to turn up as damping and make it stop oscillating that much sooner. Or go all the way and make these ball bearings as well, which is closer to the ideal simple pendulum that has no moment of inertia at the bob, but lots of mass. If it was on a free bearing, then height mis-match would show up as rotation of the bob, which you could adjust out.

[widgitmaster]

Mike,
One pivot arm without pins, bearings or bushings weighs 7.8 oz (221.126 g)
One drilled ball now weighs 2 lbs 4.6 oz (1.0376 kg)

When the balls are pinned in place, they do not rotate freely.
Widgit

[Mike Everman]

Beauty.

[BobWarfield]

Mike,
One pivot arm without pins, bearings or bushings weighs 7.8 oz (221.126 g)
One drilled ball now weighs 2 lbs 4.6 oz (1.0376 kg)

When the balls are pinned in place, they do not rotate freely.
Widgit

Well then the CG is only shifted about 1/4" up off the central axis of the ball along the arm.

Mike, do you still think that will wreak havoc on a knife edge?

I've still got to try it. Those balls are heavy. I'm skeptical the pivot will walk around much at all.

Best,

BW

[mactec54]

Bob it's be done before with a knife-edge bearing & it failed badly, The best that we ever had was to use air-bearings, But this was not easy either, The second best was a Ball & socket & every variation you could think of this was tryed, We also built a 24hour clock which had a 20foot long pendulum with a 26lb ball on the end, It is now in a science museum & has been running for a long time It moves around the clock face on the floor (very large clock face) With the movement of the earths rotation

[Mike Everman]

Well then the CG is only shifted about 1/4" up off the central axis of the ball along the arm.

Mike, do you still think that will wreak havoc on a knife edge?

I've still got to try it. Those balls are heavy. I'm skeptical the pivot will walk around much at all.

Best,

BW

Well, without doing a free body diagram, the simplest answer is yes I am still concerned. The pivot will see shear that is 1/49 of what the ball sees at impact (if we assume your 1/4", and that the pivot to ball center is 10"), which is no small amount. Ball bearings are a good fit here, I think.
Ha ha, don't get me wrong, I'd like to make one with knife edges someday. this is a fun one.

[BobWarfield]

Well, without doing a free body diagram, the simplest answer is yes I am still concerned. The pivot will see shear that is 1/49 of what the ball sees at impact (if we assume your 1/4", and that the pivot to ball center is 10"), which is no small amount. Ball bearings are a good fit here, I think.
Ha ha, don't get me wrong, I'd like to make one with knife edges someday. this is a fun one.

I'm going to do it, but you can bet I'll design it with a backup plan in mind. Probably just make 2 knife edge arms and try it.

Cheers,

BW