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[spincakes]

Ortwin, I've gone through the balancing methods you mentioned on the forum and with those came up with a very expensive but probably very efficient method of balancing the tops; an industrial laser distance sensor (that can measure micrometers at 100mm distance) coupled with a stroboscope that flashes every time the measured wobble reaches the high point. You'd have to mark the top somehow to find at which side the stroboscope is flashing, but this way you'd get a quantified magnitude and a place to correct this magnitude.

The laser distance sensors cost about €1200,- though.

After this I came across a suggestion by yourself:

I started not by suspending a panel like Bill did, I placed 3 (12 mm) steel balls between the base that can be leveled and the actual base plate with the domed sapphire. Once I get usable results with the method I will make a video where this part should become clear.

I feel I'm missing some context of this statement, but got me to think that putting a light base plate on small light balls, so it could move freely, and attaching a fast accelerometer (instead of a heavier phone) to that could make a 'wobble detector' that would purely measure tip wobble when spinning a top on it. You'd still need the stroboscope to flash at the top every rotation, to show where to change the balance, but it would save a whole lot of money compared to the laser sensor. Ideally the surface would have a lot of resistance... I hope it would be sensitive enough, but I could definitely give a prototype a try.

@Jeremy, do you know the inertia, RPM, and spindown curves of those tops you tested with that method? I'm curious at the power lost during a spin, and how it compared to the small 35mm top shapes I tested with. I had trouble using a similar method, copied from a Simonelli video, as I had to go up to 9000RPM to reach significant air resistance losses on these tiny tops, at which the wobble in the bearings did cause larger losses than the air resistance I tried to measure.

[spincakes]

Perhaps using a concave surface would increase the amount of wobble translated from the top tip to the surface it's spinning on...

Using this calculator I found that a 0.1mm amplitude oscillating motion at 1200RPM / 20hz would produce a maximum acceleration of 0.16g at the tip. If 10% of that transfers to the base plate somehow, 0.016g... that might not be enough to reliably measure. Hmmmm.

[ortwin]

..., but got me to think that putting a light base plate on small light balls, so it could move freely, and attaching a fast accelerometer (instead of a heavier phone) to that could make a 'wobble detector' that would purely measure tip wobble when spinning a top on it. You'd still need the stroboscope to flash at the top every rotation, to show where to change the balance, but it would save a whole lot of money compared to the laser sensor. Ideally the surface would have a lot of resistance... I hope it would be sensitive enough, but I could definitely give a prototype a try....

Yes, definitely something along those lines! From my first experiments I got the impression that even a heavy phone might work. I found the largest problem is the availability of (or rather the lack thereof)  an app that can be configured to the needs of spin top measurements: sensitivity range, integration time, storage of results,.....
I do not think a strobe would be needed in a simple version: In principle two grub screws are enough to give it perfect balance. After a first measurement of the "tip wobble", I would move one of the screws in arbitrary direction and do the next measurement. If the tip wobble increased, I chose the wrong direction to start with, so I go the other direction with the grub screw now. After optimizing the position of the first screw this way, I would do the same with the second screw. It might be necessary to do it over a few times for best results. I think you get the idea.


As I said, I am not so pessimistic about the sensitivity issue. An idea how to increase the sensitivity if needed would be to have the top spinning on a system that has a resonance at a typical top speed (corresponding to a frequency).


The resistance of the surface is definitely a factor. For really long runs I am using concave sapphire lenses. For measurement like the ones you plan, normal paper or even sandpaper could be used - for a test at least.

[spincakes]

How heavy are your tops typically? And do you have an idea how much wobble the tips typically have before balancing? You would have the screws offset 90 degrees?

I planned to just cut some plastic off the 3D prints I'm working towards, that would be a lot easier knowing the place to cut from!

I'm an electronics engineer by trade, doable to get a raw sensor or module and have a microprocessor send the data to a PC over USB, to display or log, filtered to the frequency range of a typical spinning top, with an appropriate sampling rate.

Good point on the resonance and using paper for grip!

Also, what kind of tops do you enjoy?

[Iacopo]

A list of the members most interested in top STEM (science, technology, engineering, math) might help in your searches. Besides myself, look for posts from ta0, Iacopo, ortwin, Bill Wells, and johnm.

I would add Alan Adler, (Aerobie).

Welcome to the Forum, David !

[Jeremy McCreary]

@Jeremy, do you know the inertia, RPM, and spindown curves of those tops you tested with that method? I'm curious at the power lost during a spin, and how it compared to the small 35mm top shapes I tested with. I had trouble using a similar method, copied from a Simonelli video, as I had to go up to 9000RPM to reach significant air resistance losses on these tiny tops, at which the wobble in the bearings did cause larger losses than the air resistance I tried to measure.

A 9,000 RPM terminal speed is fast but not unheard of. I have a handheld electric starter that can take small LEGO finger tops to 8,600 RPM, but that motor is much more powerful than the one in the test rig shown above. The rig could be adapted to that motor, but the rebuild would be a pain.

I've compared many tops with this rig but no numbers for moments of inertia and no measured spin-decay curves to share. The 3D mass distributions in LEGO tops are generally too complex to rely on calculated moments. A trifilar pendulum capable of measuring AMIs and central TMIs is on the to-do list.

Since the test rig's no-load speed is only 1,225 RPM as shown, comparisons in terminal speed drop are probably only meaningful in tops with drops of well over 100 RPM. The two VERY dirty tops in the video had reproducible average terminal speed drops of 305 and 345 RPM, resp. Their structural differences were small but clearly significant aerodynamically.

The rig's 30+ year-old 9V motor (not a gearmotor) is LEGO's fastest but weakest in stalled torque — a meager 0.035 N m at 9V if memory serves. The motor's no-load shaft speed at 9V is ~4,400 RPM. The rig usually gears the motor down 3:1 externally, but that's easily adjusted.

Would be interesting to compare the torque-speed curves of our respective motors.

[ortwin]

How heavy are your tops typically? And do you have an idea how much wobble the tips typically have before balancing? You would have the screws offset 90 degrees?

...

My tops run in the 100 g - 150 g range. But I also have one in the +400 g range.
I would not know how to quantify the wobble.
Offset of the screws is 90 degrees if I use four all together, but only two need to be moved.
Offset of the screws is 120 degrees if I use three alj together, but only two need to be moved.
Actually in one version of my top I have a lot more screws that can be moved around, you know there is static balance but than there is also dynamical (un)balance. Are you aware of that already?

...
I'm an electronics engineer by trade, doable to get a raw sensor or module and have a microprocessor send the data to a PC over USB, to display or log, filtered to the frequency range of a typical spinning top, with an appropriate sampling rate.
....

Drool!.....

....
Also, what kind of tops do you enjoy?

Easy for you to ask! If you scroll up and down a bit the many pages of the topic I linked above you can see some of the things I am interested in. There are tops with different "special effects" and "endurance tops". The "quark top"  is the one that brought me to this forum. As a kid I was playing with the many "tops" I found in a broken alarm-clock.  In one top-phase I build a few Levitrons. Two years ago I first put my hands on "throw tops" - those I spent probably most of my top time with lately.

[Iacopo]

...I suppose a top that looks balanced might not have a perfectly center tip still, and a top that seems to wobble could possibly have a tip that is rotating true? Or do you think these always go hand in hand?...

A sample of the first case could be an unbalanced top with a teflon tip spinning on an oiled glass surface: 
The top is symmetrical, not distorted, but the teflon tip is off centered, this makes the top unbalanced.
When the top spins, the tip slips easily and it is dragged in circular motion, while the top spins true and apparently perfectly balanced, at least at fast and medium speeds. The tip wobbles, the top doesn't.
The same can happen also with other kinds of tips, but only if the speed of the top is high enough to constrain the tip to slip.

A sample of the second case could be a nutating top, (torque free wobble).
Nutation is a fast wobble and may look very much like the wobble due to unbalance, but its nature is totally different and it can happen also in perfectly balanced tops, (tops with an external tip do not nutate so easily anyway).
Even an unbalanced top which is not spinning too fast will look wobbling while the tip is rotating true, but for the only reason that it is not slipping.

Nutation, (torque free wobble), in a couple of my tops:
 

   

[spincakes]

A list of the members most interested in top STEM (science, technology, engineering, math) might help in your searches. Besides myself, look for posts from ta0, Iacopo, ortwin, Bill Wells, and johnm.

I would add Alan Adler, (Aerobie).

Welcome to the Forum, David !

I found his figure of merit thread - valuable information! Thank you

Would be interesting to compare the torque-speed curves of our respective motors.

The motor I used was a miniature drone motor, spinning at 10000RPM per volt, measuring 8.0x19.0mm. See the attached picture. You can see the shapes I used for testing - too small for a method like this I'd conclude.

My tops run in the 100 g - 150 g range. But I also have one in the +400 g range.
Drool!.....

The heavier the easier to measure with this method! The 3D printed tests I'm still planning might be difficult... I'll keep you posted on the progress.

You also helped me find the quark top balancing page, explains some more about the balancing process.

I've read about the couple balance, but I don't fully understand it yet.

A sample of the first case could be an unbalanced top with a teflon tip spinning on an oiled glass surface: 
The top is symmetrical, not distorted, but the teflon tip is off centered, this makes the top unbalanced.
When the top spins, the tip slips easily and it is dragged in circular motion, while the top spins true and apparently perfectly balanced, at least at fast and medium speeds. The tip wobbles, the top doesn't.
The same can happen also with other kinds of tips, but only if the speed of the top is high enough to constrain the tip to slip.

A sample of the second case could be a nutating top, (torque free wobble).
Nutation is a fast wobble and may look very much like the wobble due to unbalance, but its nature is totally different and it can happen also in perfectly balanced tops, (tops with an external tip do not nutate so easily anyway).
Even an unbalanced top which is not spinning too fast will look wobbling while the tip is rotating true, but for the only reason that it is not slipping.

This is very helpful! Reinforces the idea that measuring the wobble at the tip would be the best place to go.

[spincakes]

I found some information about couple balance, great stuff with good strategies that align with my thoughts so far. Hope to get something into practice soon.

[ortwin]

... but got me to think that putting a light base plate on small light balls, so it could move freely, and attaching a fast accelerometer (instead of a heavier phone) to that could make a 'wobble detector' that would purely measure tip wobble when spinning a top on it. You'd still need the stroboscope to flash at the top every rotation, to show where to change the balance, ...

My thinking was not to use strobe for determining the the spot where to place some weight, but to use the signal of an RPM speed meter.
From the accelerometer you would get something similar to a sine as signal in best case.
From the RPM meter you would get a pulse every time the reflector on the rim of the top reflects the laser pointing to it.
Combining the two signals allows to calculate a phase difference  and thereby the place where you need to add weight.
If we would be able to make such a device that is compact, robust and easy to use that would not only be great for endurance tops, but also for balancing of peg tops. I am sure at those festivals like Loon plage, Marines, Miamisburg and others - lots of people would be interested in better balancing of their tops.

[Jeremy McCreary]

@David, if you're looking for an excellent textbook treatment of rigid body dynamics, you might like Jerry Ginsberg's Advanced Engineering Dynamics.

It's my favorite top physics reference. Last I checked several years ago, 2 editions of the book were available free online in PDF in their entirety.

Chapter 10 is a very thorough treatment of the ideal (dissipation-free) heavy symmetric (aka Lagrange) top. (Lagrange tops are the kind we usually use, but we don't get to wish away the dissipation.) His stability analysis and approach to critical speed are the best I've seen. And that part's valid with or without dissipation.

[spincakes]

My thinking was not to use strobe for determining the the spot where to place some weight, but to use the signal of an RPM speed meter.
From the accelerometer you would get something similar to a sine as signal in best case.
From the RPM meter you would get a pulse every time the reflector on the rim of the top reflects the laser pointing to it.
Combining the two signals allows to calculate a phase difference  and thereby the place where you need to add weight.
If we would be able to make such a device that is compact, robust and easy to use that would not only be great for endurance tops, but also for balancing of peg tops. I am sure at those festivals like Loon plage, Marines, Miamisburg and others - lots of people would be interested in better balancing of their tops.

That should also work! I can see what ends up easier to implement.

I spent today 3D printing a little test top and working on an easy way to collect and process RPM data, see the attached images. It weighs 9.9 grams, has an AMI of about 1700grams*mm², meaning I can get about 0.1 joule into it at 3200RPM. It can get it to spin for about 3 minutes. It's also pretty wobbly, and has given me a couple of different results without a clear reason. Curious to see if balancing it will change its behavior tomorrow!

Thanks for the recommendation Jeremy

[ortwin]

...

That should also work! I can see what ends up easier to implement.
...

Actually now I found that in the article you cite, there is a graph that describes exactly what I tried to say with words:







About your printed top: I would say 3 minutes is really good for such a lightweight top!
Maybe you could print a top with a hollow rim the upper side of which is open. To add weight you could fill the rim with tungsten putty. I have never used any, but it has a density of about 10 g per cubic cm I read, it should be available in fishing supply stores.

[spincakes]

I've never heard of tungsten putty, but definitely want some! Might be hard to keep it balanced, unless it's very tightly pressed somewhere, but worth a try.

I've played around with the printed top some more and recorded 4 unlubricated runs, and 2 lubricated runs - with forehead oil, as advised on this forum. 

It's spinning on a steel ball bearing on a makeup mirror, and there's a clear difference between the two. I found a 'power loss vs speed' graph to show most clearly, where the unlubricated graphs move around a lot at the lower section, and the lubricated ones (run 7, run 8 ) are a lot 'tighter'. Less skating around. See the attached images.

In the last minute the lubricated runs have about 30% less losses!

Up to more playing around, going to print some different tops.