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[spincakes]

Ortwin has inspired me to work on an accelerometer top balancing setup. We talked about it for a bit in this thread: https://www.ta0.com/forum/index.php/topic,7178.0.html, but it is time for its own place!

I've made a little setup with a hard cardboard box on ball bearings (weighing 36.9 grams), with a small IMU module in it, to spin a top in. The module is not great, and not fast, but seems good enough for some basic vibration data! I haven't done any processing yet, only a low pass filter to filter out some noise.

In the attachments you'll find a picture of the setup, and three graphs. One of a full spin (which doesn't last long on the cardboard), and two of zoomed in data showing the resolution at 1600RPM and at 800RPM.

Next up would be a way to identity the place to add / remove weight, which includes processing the data to get the angle, and (the easiest method I'll go for first) at a certain angle flashing a strobe onto the top to show the orientation it's imbalanced in. I hope to get a module with a higher sampling rate later, to improve the resolution on showing this angle. Also not sure yet how to determine the height for the weight to be changed at yet, but I can start at the center of gravity.

One question I have for the experienced people here, is it safe to assume a properly balanced top will show no vibration with this method? Or is it not that simple?

I'd love to discuss the various aspects of this, and will keep you posted

[spincakes]

First problem: The amplitude is heavily dependent on how close the top is to the module. I think I'll have to find a way to have the module right below the top, perhaps finding a small (grippy) concave plexiglass mirror or lens

[spincakes]

I have been able to work on the math; calculating phase, the vector length, and RPM based on the recorded data. I'll try to work on the mechanical setup soon!

[Jeremy McCreary]

Way over my head, but a very exciting project! Looking forward to seeing your progress.

Thanks to LEGO precision molding and dimensional stability, I seldom have to worry about balance when all parts are symmetrically arrayed and fully seated. And Iacopo's clearly perfected the effective but laborious paintbrush method.

But an affordable, user-friendly version of the device you have in mind would be a fabulous contribution to topmakers and serious top users alike!

A top with perfect dynamic balance can still wobble from a slight tip misalignment. (Probably my biggest source of wobble.) Would be great just to know when that's the real problem — and even better to know exactly how to fix the tip in advance.

[ortwin]

First problem: The amplitude is heavily dependent on how close the top is to the module. I think I'll have to find a way to have the module right below the top, perhaps finding a small (grippy) concave plexiglass mirror or lens

I am thinking of a concave glass lens for this purpose. To make it "grippy" one could sand blast it to become like frosted glass. Maybe you are one of those poor people that don't have a sand blaster in the garage, but you could use sandpaper instead, or some tool with a grinding tip.

[Iacopo]

First problem: The amplitude is heavily dependent on how close the top is to the module. I think I'll have to find a way to have the module right below the top, perhaps finding a small (grippy) concave plexiglass mirror or lens

I am thinking of a concave glass lens for this purpose. To make it "grippy" one could sand blast it to become like frosted glass. Maybe you are one of those poor people that don't have a sand blaster in the garage, but you could use sandpaper instead, or some tool with a grinding tip.

I agree, a concave glass lens would work.  There is no need to make it grippy, you can even use some lubricant if you want. The top doesn't slip so easily, (unless badly unbalanced), just don't spin it too fast.

[spincakes]

I have a prototype! Still with the cardboard box, so the amplitude measurements vary +-25% depending on position, but it's quite workable for balancing.

Here's a video - the heavier side always points left.



These tops are only 10 grams, at a certain point I just won't have any data left to balance with. A more sensitive accelerometer or better mechanical setup might help for this, but with heavier tops (which are more fun anyway) this shouldn't be a problem.

Attached is an image of the what the data looks like on the PC.

I haven't yet found any concave lenses that have a flat bottom (for the ball bearings). I'd like plastic, lighter is better for measurement sensitivity. I'll keep looking. I'd love to make a proper setup for this.

[ortwin]

Great! I looks as if you are going to have something very useful very soon!!


https://astromedia.de/Opti-Media-Linse-OM1a


This is a cheap (€ 1.60) acrylic lens that I found. No idea if it is available at your place. Maybe you can find a suitable lens if you take an old camera tele apart?

For tests you could get a cheap top like this.


Edit: To what spin times can you bring this one if you balance it properly? 10 minutes?

[Jeremy McCreary]

You can also get inexpensive concave and biconcave lenses of optical quality from Edmund Scientific. Among other things, the optical part insures that, unlike those in cosmetic mirrors, the glass surfaces have reasonably uniform curvatures.

High surface curvatures (short focal lengths) strongly promote precession over sleep and definitely reduce spin times — at least in LEGO tops, which have hemispherical tips of proprietary ABS plastic with radii of curvature ranging from 1.6 to 17 mm.

I recommend starting with focal lenths of 2,000 mm or more. Doesn't take much curvature to keep a sleep-prone top centered.

[Iacopo]

Also not sure yet how to determine the height for the weight to be changed at yet, but I can start at the center of gravity.

When you add weight to a side of the top, at the height of the center of gravity, you are shifting the vertical principal axis of inertia, maintaining it parallel to its previous position.  You shift it without tilting it.
If you add weight to a side of the top, above or below the center of gravity, you are shifting and tilting the vertical principal axis of inertia.

I had to think for a while if there is a difference by detecting the unbalance at the tip or at the stem, and I found that there is a difference in fact:

with your system, you are detecting the direction towards which you have to shift the vertical principal axis of inertia, for to make it pass through the tip.  When the vertical principal axis of inertia passes through the tip, the top is balanced;  the tip doesn't vibrate anymore, the spin times are increased, and the topple speed reduced.

But there is a third element, the top symmetry axis, which we would like to be superposed and coincident to the vertical principal axis of inertia, otherwise the top might look wobbling even if it is balanced.

Your system gives the informations for to align the vertical principal axis of inertia to the tip, but not those necessary for to align the vertical principal axis of inertia to the symmetry axis of the top. 
Depending on how much finicky you are about it, this probably will be not a big problem anyway, you correct the unbalance just by adding, (or removing), weight at the height of the center of gravity and the result usually will be fine.
 
But if you have to balance a top which has the two axes tilted towards each other, you can't know in which direction the tilting of the vertical principal axis of inertia has to be corrected. In this sense, it would be better to detect the unbalance at the stem, because this allows to gather the informations for to align all the three elements and to make the top to be balanced, and, also, to look balanced.     

 
 

[ortwin]

Yes Iacopo, we have to consider and think about those issues.
Do you think by using the stem instead of the tip we can achieve both: a balanced top and a balanced look? Probably not exactly.
At the moment I consider the balance at the tip more important as the visual balance. Of course it is desirable to have both.
If we have reached perfect balance as indicated by the tip but still wobble is visible in the stem, we would have to tilt or even move the stem sideways to get rid of that. And only if the stem is nearly weightless we would not alter the balance by that, otherwise we would need to do some more balancing with the tip method and so on until everything converges.


The other extreme we explored to some extend  in the offset top topic.
It would be cool to have such an circular shaped offset top where the tip is positioned such that the top is perfectly balanced, but the stem is located in optical  symmetry axes. It may be hard to start well by that stem, maybe starting such a top by methods used for stemless tops would work better.

[spincakes]

This is a cheap (€ 1.60) acrylic lens that I found. No idea if it is available at your place. Maybe you can find a suitable lens if you take an old camera tele apart?

These are better than the ones I found so far! And they ship here - ordered some of the larger ones.

Those are some good points Iacopo. I think visual balance also decreases air resistance, which is still one of the more significant losses.

I did find out that shining a flashlight on the top, next to the stroboscope, allows me to visually identify the side the top 'leans' towards in the spin. The flashlight painting a picture of the 'fuzzy' rotating image, with one sharper image from the stroboscope, where the sharper image leans to one side and the orientation of the top is visible by the marker used for the laser tachometer. Hope that makes sense.

I am encountering some less than ideal things with the setup, where different tops (weight, grippiness) have different phase shifts between the top and the base (and thus sensor), making that the heavier side doesn't always point the exact same way when the strobe flashes when the sensor crosses its 0° point. This means I'll have to do a few test runs, really weighing a top to one side, and seeing where that side points, before figuring out where the heavy point will be for that particular top.

The resolution is also a bit limited, with the sensor outputting data at 1000Hz, spinning at 1800RPM gives me 33 samples per rotation, making the 'heavy side' jumps around by about 11° between flashes.
Workable, but getting a faster sensor would be preferable.

[Iacopo]

Do you think by using the stem instead of the tip we can achieve both: a balanced top and a balanced look?

Yes, of course !
I am doing this for years.
 
The trick is that, by using the stem as the reference, depending on how the top is spun, the top will exhibit predominantly the static unbalance, (if present), or the couple unbalance, (if present), so that the two unbalances can be fixed separately, and the result is that the top in the end will be balanced and will look balanced.
It is impossible to do the same analyzing only the vibration of the tip because with this method the position of the symmetry axis is ignored.

...otherwise we would need to do some more balancing with the tip method and so on until everything converges.

I believe that, for to make everything to converge, the tip method has to be complemented by a method where the position of the symmetry axis is observed.

[ortwin]

Do you think by using the stem instead of the tip we can achieve both: a balanced top and a balanced look?

Yes, of course !
I am doing this for years.
 
The trick is that, by using the stem as the reference, depending on how the top is spun, the top will exhibit predominantly the static unbalance, (if present), or the couple unbalance, (if present), so that the two unbalances can be fixed separately, and the result is that the top in the end will be balanced and will look balanced.
...

Hm, more questions: how can you spin the top to exhibit predominantly one of the two unbalances (static or couple)?
In my last post here, I was of the impression that with the tip method one can in principle correct the static as well as the couple unbalance but not the visual unbalance.  You seem to say that you correct the static and the couple balance independently and therefore the  visual unbalance disappears as well? I can't fully see that, I'll think a bit more on it, but maybe Iacopo, you can see already a point that I misunderstood.

[Iacopo]

I am encountering some less than ideal things with the setup, where different tops (weight, grippiness) have different phase shifts between the top and the base (and thus sensor), making that the heavier side doesn't always point the exact same way when the strobe flashes when the sensor crosses its 0° point.

One possible cause, (I don't know if this is your case), are the different proportions of the tops.
If the axial moment of inertia, (AMI), is sufficiently larger than the transverse moment of inertia at the tip, (TMI_tip), the unbalanced top spins staying tilted towards its heavy side. If the TMI_tip is larger than the AMI instead, the top spins staying tilted towards the light side. Tops with or near to the intermediate proportions have the most complex behaviour, staying tilted towards the heavy side at high speed and towards the light side at slow speed, changing gradually the direction of the tilting from 0° to 180°, during the spin down, which makes them the most confusing and difficult to balance.