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[Jeremy McCreary]

Thanks for the photos and data. Very clever construction!

So your rotor has 4 main components, not counting the screws. And each has a simple shape with a well-known AMI formula. So you calculated an AMI for each component separately and then added them up to get a total AMI of 3.7e-3 kg/m² about the spin axis. Correct?

If so, agree, your total AMI should be pretty accurate.

[Iacopo]

Ortwin is good at pointing out possibilities and I'm going to test his suggestions and some of my own on eddy current.

Even after having seen your top disassambled I continue to think that probably you shouldn't have significative magnetic drag.
But I will wait for the results of your tests.

[Jeremy McCreary]

Since we're running out of explanations, I'll ask again...

Bill: Any chance your deweighting magnet could be affecting the digital scale under your test top?  The two were at closest approach for the suspect 80 g run.

[ortwin]

Since we're running out of explanations,....

?
Are we really?As I understand it, there are as well more vacuum tests as well as more eddy current tests still in the pipeline! I don't think we need to do further speculating until those tests were performed.
In fact there is another part of the eddy current test I did not mention explicitly up to now.
What I did propose was this:...
do the experiment again with the full weight of the top, but no magnet attached the top and no outside magnet near by. 
Then do the experiment one more time with still no magnet attached to the top, but this time the outside magnet approximately at the spot where you had it when you did the 80 g run. The difference you see in these two runs will be due to the force of the braking eddy currents.
   Additionally you should do the same experiment again, this time with the magnet in the stem of the top but take only the magnet out of the "weight adjustment apparatus" while it is in the 80 g position. The difference to the "no magnet" case is a further contribution by Mr. E. Current.

[Bill Wells]

Bill: Any chance your deweighting magnet could be affecting the digital scale under your test top?  The two were at closest approach for the suspect 80 g run.

Excellent question. I just went to the shop to test. I put a non-ferrous 32g (brass) object on the scale. Using a strong magnet I measured the height at which it began to affect the scale. Yes the magnet does affect the scale, beginning at a height of 65mm. Since the de-weighting magnet is at least twice that height, I don't think it is a problem. But I will consider it when conducting my next test.

[Bill Wells]

Correct?.

Yes, you describe exactly how I calculate an AMI of 3.7e-3 kg/m² about the spin axis.

[Bill Wells]

As I understand it, there are as well more vacuum tests as well as more eddy current tests still in the pipeline!

Ortwin, yes more tests upcoming. Including your suggested test.

[Iacopo]

I plotted RPM vs. weight for several trial runs on my 1370g top, then calculated average tip friction for each.

Weight, g      Average tip friction, millionths N-m
1200            269
1000            242
600             198
80               190

Waiting for the test results, I put here a few data, from my tops:

Weight, g      Tip friction, milionths N-m
656              13 - 18
104              0.7 - 1.3

If the top is unbalanced, the tip friction can increase significantly at high speed, but this happens because the tip is dragged in circular motion along the spinning surface, rubbing against it. While the top spins, it can be seen that the tip "vibrates".  But at low speed, the tip tends to settle in a spot of the spinning surface, and at that point the tip friction decreases, becoming almost normal. 

The air drag of the top of Bill, I very roughly calculated, could be 1000 millionths N-m, or more, at 1800 RPM.
 

[Bill Wells]

If the top is unbalanced, the tip friction can increase significantly at high speed, but this happens because the tip is dragged in circular motion along the spinning surface

Yes, my thoughts are the same. The top wants to spin around its center of mass (barycenter). The tip then draws circles around the barycenter.
Since my test flywheel is now disassembled, I re-balancing it. As an added feature to the current topic, I will post photos of the balancing process.

[Jeremy McCreary]

Soon I'll be sharing an engineering model with some application to tip resistance in spinning tops. For now, I used it to estimate the frictional braking torque Q_F acting on Bill's top with magnetic deweigthing in a vacuum.

Without going into great detail, the model assumes only simple dry sliding friction at the tip -- no air or rolling resistance, no damage, no viscous lube. Accordingly, Q_F is independent of speed but varies with the weight W on the contact in a slightly nonlinear way:

Q_F = -A W ^4/3,

where A is a positive factor depending only on the materials and radii of curvature in contact. For a series of experiments like Bill's, A would be constant.

This equation says that Q_F doesn't just double with a doubling of W — it increases by a factor of 2.52!

Below is a CORRECTED graph of braking torque vs. weight. (Sorry, original had a data input error at 2nd blue point from right). The blue curve follows Bill's measurements, and the red curve, the theoretical Q_F from the model. At the 2 higher highest weight, agreement is within 20% -- not bad considering that I had to use generic values for the material properties involved.



At the 2 3 lower weights on the left, Q_F behaves as you might imagine, while the measured torques stay unexpectedly high. Guess we're all wondering if some resisting process other than simple friction jumped in here?

The model passed a few cursory tests in the journal article but seems to be on solid theoretical ground — provided that the assumption of simple friction acting alone is a good one.

[Jeremy McCreary]

If the top is unbalanced, the tip friction can increase significantly at high speed, but this happens because the tip is dragged in circular motion along the spinning surface, rubbing against it. While the top spins, it can be seen that the tip "vibrates".  But at low speed, the tip tends to settle in a spot of the spinning surface, and at that point the tip friction decreases, becoming almost normal.

Exactly what I see with many different kinds of LEGO tops. Mine generally put a spinning ABS plastic ball (radius 1.6-17 mm) on dry flat polished stone or convex concave glass. So if anything gets damaged, it's the ball. And I see surprisingly little wear.

In high-CM tops with larger ball tips, you eventually end up with pure rolling around the vertical through the CM with no drilling or milling. Bill's test top isn't far from that category. But I gather that it slept pretty quietly during data collection. So that dynamic doesn't relly apply.

[Bill Wells]

The air drag of the top of Bill, I very roughly calculated, could be 1000 millionths N-m, or more, at 1800 RPM.
 

Iacopo, yes my calculations agree with your estimate.
Attached are charts from tests run last week with my 1.37kg top:

[Iacopo]

We know that this in the Bill's top is not a tip friction but a total braking torque, which includes a mysterious drag, which maybe could be approximately 189 millionths N-m.  If the force of this mysterious drag is constant at the changing of weight, the real data of the tip friction could be:
                                                            Expected
Weight                             Tip friction     tip friction
1200         269 - 189 =          80                41
1000         242 - 189 =          53                30
600           198 - 189 =           9                 14
80             190 - 189 =           1                  1

The expected tip friction is calculated on the data of my tops.

[Iacopo]

Iacopo, yes my calculations agree with your estimate.

Thank you Bill, it is nice to know it.

[Jeremy McCreary]

We know that this in the Bill's top is not a tip friction but a total braking torque, which includes a mysterious drag, which maybe could be approximately 189 millionths N-m.  If the force of this mysterious drag is constant at the changing of weight...

Subtracting a constant torque from Bill's earlier values just shifts his curve upward toward yours (green) — from the blue to the red position below.



But that doesn't address the shape difference. We see that your curve and his are all nonlinear with weight. But his curve is much more curved than yours. And that indicates a significantly different torque-weight relationship.