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[Aerobie]

What about a solid, tapered, knurled extension of something even less dense than aluminum -- say, Delrin or ABS or titanium alloy or even wood? Guessing that this top has a high-enough axial moment of inertia to benefit from a stem taper with a starting diameter of ~8 mm below and a final diameter of 3-4 mm above. In my experience, such a taper should cover an axial length of ~32 mm for best results in single-twirl play.

Thin wall aluminum is lighter than the materials above, which must be solid, except for titanium, which is about 50% denser than aluminum.  My present aluminum tubes are pretty soft.  I've ordered some hardened aluminum tubing.  And some titanium tubing, carbon fiber, and even ceramic (alumina).  That should keep me busy for a while.

And I'm also experimenting with lift-off stems.  Or, if not lift-off, still detachable for pocket carry.

Best,

Alan

[Jeremy McCreary]

One thing to keep in mind with plastic pieces is that all thermoplastics have huge coefficients of thermal expansion. 

Thanks, Alan! Didn't know that, but it could have something to do with why so many axles come bent. Axles presumably come out the mold warm to hot and then drop onto a rather disordered pile of axles in a bin below. Lots of opportunities for sagging and uneven cooling there.

Hmmm, wonder if the high thermal expansivity could be used in straightening somehow?

One way to check for straightness of a shaft it to chuck it in an electric drill or Dremel and run it.  You'll see bend - especially with magnification.

Yes, I was doing the manual eye-ball version of that in the photo, but adding magnification could help a lot. Low finger speeds generally work best for me, but different bends seem to become apparent at different speeds. Hence, I have to sweep the speed up and down in both directions with fine control with each and every axle.

[Jeremy McCreary]

Everything is new, the pump, and the chamber. The ultimate pressure indicated in the plate of the pump is 0.3 Pascal, (0.003 millibar). It would be excellent but I don't know if this is true.   

Learned something interesting today. For a top the size of your Nr.26 at 18°C, 0.3 Pa happens to mark the (rather fuzzy) upper pressure limit of a "molecular free flow" (MFF) regime in which viscosity has no meaning. Scary, I know, but there's a silver lining.

The good news: We've never had a reliable way to calculate aerodynamic braking torque (ABT) in tops at room pressure, where air molecules exchange momentum with each other vastly more often than they do with any solid surfaces involved. (That's fundamentally why air can normally be treated as a viscous fluid.) But we do have a simple and reliable way to calculate ABT in the MFF regime, where air molecules effectively exchange momentum only with the top.

In fact, the MFF ABT calculation is predictive enough to underpin one of the mainstays of modern high-vacuum technology -- the spinning rotor manometer. In this regime, ABT is strictly proportional to the current angular speed, and the proportionality constant is easily calculated from widely available data. If ABT were the only braking torque, MFF spin decay curves would then be exactly and reliably exponential.

This fact might open up some valuable experimental opportunities for you -- provided your apparatus can reach MFF pressures.

The bad news: Below ~23 Pa, a top like Nr.26 enters a "transitional" flow regime where neither MFF nor viscous treatments like the von Karman swirling flow model apply.

[Iacopo]

0.3 Pa happens to mark the (rather fuzzy) upper pressure limit of a "molecular free flow" (MFF) regime in which viscosity has no meaning.
Below ~23 Pa, a top like Nr.26 enters a "transitional" flow regime...

I will not be able to measure fractions of Pa.  Even with the new gauge I should receive in January, there could be measurement errors of maybe 25 Pa, maybe more.

Do you think this could be a problem ?  Isn't air drag torque practically irrelevant, compared to tip friction torque, both at 0.3 Pa, and, let's say, 30 Pa, whatever the flow regime ?

[Aerobie]

Balancing again.

I think Iacopo posted something along these lines about a year ago.

I have a 31mm, 41g top, spinning on a 6mm ceramic ball.  A small fraction of my tops go through a speed of large wobble, then smooth somewhat.  This top does that, with max wobble at about 550 RPM and topple just under 330 RPM.  (Most of my tops just gradually wobble prior to topple, without this intermediate peak wobble).

I observed the reflected laser beam in the manner taught by Quark.  The laser test is supposed to indicate the angle on the wheel which needs more weight.  This angle suddenly shifts 90 degrees clockwise as the declining speed passes through the speed of peak wobble.

Help.  Iacopo.

Best regards,

Alan

[Jeremy McCreary]

Isn't air drag torque practically irrelevant, compared to tip friction torque, both at 0.3 Pa, and, let's say, 30 Pa, whatever the flow regime ?

I'd be happy to go along with that if the red curve labeled "Tip friction" in your last graph were perfectly flat. But it clearly slopes down to the right, and we need to know why.

If I understand this red curve correctly, it really plots total braking torque (TBT) vs. speed at your actual ultimate pressure P_U, whatever that may be. If so, the TBT at P_U still includes a contribution varying directly with speed. Could be nothing more than "wet" (lubricated) friction, but we're not yet in a position to rule out aerodynamic drag.

I recommend repeating the experiment "dry" -- i.e., without lubrication of any kind. If the dry red curve comes out flat, you'll have your answer: Any aerodynamic braking torque (ABT) remaining at P_U must be very small compared to the observed TBT. But if the dry red curve still slopes down to the right, the remaining ABT can't be ignored. The outcome could vary from top to top.

This strategy rests on 3 very reasonable assumptions with lots of experimental support in related settings:
1. Aerodynamic drag varies directly with speed, regardless of flow regime.
2. Wet friction can also vary directly with speed.
3. Dry friction does not vary with speed.

[Iacopo]

I recommend repeating the experiment "dry"

Thank you, Jeremy.  I will do this, and see what it happens.
You understood the red curve correctly, it is about the TBT at the ultimate pressure.

[Iacopo]

A small fraction of my tops go through a speed of large wobble, then smooth somewhat.  This top does that, with max wobble at about 550 RPM and topple just under 330 RPM.   ...intermediate peak wobble.

An intermediate peak wobble, based on my experience, is not due to unbalance, but to weared contact points.
With a new ball tip, the defect should disappear.

This angle suddenly shifts 90 degrees clockwise as the declining speed passes through the speed of peak wobble.

This is something interesting, I have an idea..
If possible, could you post a picture of this top, (a side view) ?

[Aerobie]

They are 1.24" diameter bronze, about 40-50g, with top groove or not and flat bottom or shallow cone.  I have three like this.  The flat bottom one looks like the recent pic I posted of 1.5" and 1.75" tops together on a mirror with greenish frame.  This is also the one I did the described laser work with.  But the other two also have intermediate wobble and may do the same thing.

All  three 1.24" tops are machined from an ugly old rod of bronze.  I'm suspicious that this piece has non-uniform density.  I may try the same design with a rod of brass.

One bit of clarification is that the shift occurs over a range of about 20 RPM.  It's pretty quick, but not bistable.  Mid point on the shift is probably the RPM of maximum wobble.

12/23 Update:  I just discovered that the ball tip is .0035" off center.  It's pocket is at the end of a 0.94" drilling which began at the top of the stem.  I had presumed that the drill remained centered, guided by it's own body like rifle bores.  But it wandered .0035" off center, which results in .007" peak-to-peak eccentricity!!  Yoiks!  I'll fix that today.

Centered ball within about .0001 to .0002" and intermediate wobble is gone.

But on a slightly larger (1.5" diameter, also 50g) top I tried a 2.6" long carbon fiber stem.  Despite truing the stem, this top has a huge intermediate wobble around 420 RPM.  Shortening the stem to 1.5" totally eliminated the intermediate wobble.


Alan

[Iacopo]

I'm suspicious that this piece has non-uniform density. 

One bit of clarification is that the shift occurs over a range of about 20 RPM.  It's pretty quick, but not bistable.  Mid point on the shift is probably the RPM of maximum wobble.
But it wandered .0035" off center,

Centered ball within about .0001 to .0002" and intermediate wobble is gone.

long carbon fiber stem.  Despite truing the stem, this top has a huge intermediate wobble around 420 RPM.  Shortening the stem to 1.5" totally eliminated the intermediate wobble.

I thought for some time to all these your observations, but I am confused.

Normally, wobbling due to unbalance becomes more and more intense while the top slows down, and it reaches the peak of intensity when the top topples down.
This is the common situation, with my tops.
It doesn't matter the cause of the unbalance, whether the tip is off centered, or whether the distribution of weight is asymmetric.
There is not an intermediate peak wobble.
I didn't observe differences in this behaviour related to the lenght of the stem.

If something different happens, it is because there is a superposition of another movement, nutation or maybe precession, that makes things more complicated. 
A few times I observed in my tops an intermediate peak wobble:
this peak wobbling was not due to unbalance, but to the top starting to nutate (nutation) spontaneously at a certain speed.   The nutation, mixed with the unbalance, caused the temporary increase of intensity of the wobbling.
Later during the spin, nutation disappeared, as spontaneously as it started.
This spontaneous nutation is triggered by a large contact point, (it can be a weared spiked tip, or maybe a very large ball tip, or a ball tip with even minimal wear, because the contact point in ball tips enlarges very rapidly with wear).
Lack of lubricant makes the nutation to happen with stronger intensity and for a longer time.

I am not sure, but still I think that the intermediate peak wobble you see could be due to nutation:
it is difficult to say from a distance, but you can recognize nutation because it has a different speed from spin speed.
An easy way to check this, is with the tachometer.  Measure spin speed as you do usually.
Then direct the tachometer at the upper part of the stem.  Hold a piece of white paper behind the stem. The stem wobbling will intercept the light reflected from the white paper at intervals, and will let you know the speed of the wobbling.

If spin speed and wobbling speed are the same, this wobbling is due to unbalance.
If spin speed is different from wobbling speed, this wobbling is due to nutation.
If wobbling speed is twice the spin speed, and you pointed the tachometer at the center of the movements of the stem, this wobbling is unbalance, and the wobbling speed is twice because the tachometer reads two light interceptions for one round of the stem, one time when the stem goes to the right and another time when it comes back to the left.  I point the tachometer a bit sideways, so I have one light interception for each round of the stem.

Precession is slow so it is easily recognizable. But at the very end of the spin, precession, if present, becomes fast, and could contribute to confuse ideas.

All the times I had an intermediate peak wobbling, this was due to nutation.
I never had an intermediate peak wobbling due to unbalance alone
If you are seeing something different, it is something I still don't understand.     

[Aerobie]

Thank you Iacopo.  I hadn't thought of aiming the tach at the top of the stem.  I like that idea.  I'll have to restore some long stems to do it.

I've seen confluence of nutation and vibration.  One behavior is a periodic "twitch" when they momentarily sync.

I've tried to use your paintbrush on light (50g) tops with problems.  The lightest contact causes the stem to "grab" the wet brush and tilt towards it.  Have you successfully used that method with such a light top?

One thing of interest is that the intermediate wobble speed is repeatable, which tends to rule out nutation.

Happy Christmas

Alan

[ta0]

But on a slightly larger (1.5" diameter, also 50g) top I tried a 2.6" long carbon fiber stem.  Despite truing the stem, this top has a huge intermediate wobble around 420 RPM.  Shortening the stem to 1.5" totally eliminated the intermediate wobble.

Sounds like some sort of "resonance". The top is probably too rigid for this to be due to some elastic deformation of the top. But perhaps there is coupling between spin and wobble (nutation? as Iacopo suggests) due to an imbalance and the coupling depends on frequency. It would be interesting to change the stem length in little steps and see if the spin rate of maximum wobble changes accordingly.

[Aerobie]

For years, I've found a spreadsheet convenient for recording spins.  It's easy to add a column which instantly provides useful info.  Below, I'll list some of my columns:

Twirl energy:  Iacopo does this correctly by measuring the inertia of each top, but I haven't measured the rotational inertia as he does, so my lazy formula for "relative" twirl energy is:

E=KiloRPM^2 x kilograms x Diameter^2     Diameter is inches.

He measured the inertia of the 3" top I sent him, which provided an opportunity for comparison. 
My lazy E came out to be 1.57 x his measured joules. 

Merit:  This evolved from the start of this thread and settled at:
   Merit = Seconds / (RPM^0.63 x Diameter^.5 x kilograms^.5)    diameter is millimeters

   My best twirlers have merit in the range of 6 to 8
   I use merit to answer the question,
   "How does this top compare to my others, allowing for twirl speed and top dimensions?"

Average decay per minute = (twirl RPM / topple RPM)^(1/duration in minutes)
   Example 1.085 is my best 2.25", 143 gram twirler
                 1.125 is typical of small 50 gram twirlers

As Jermemy posted, this can predict duration of spin.
Duration (minutes) = Ln(twirl RPM / topple RPM) / Ln(Average decay per minute)

You can use this to predict minutes remaining by using present RPM instead of twirl RPM

Happy Christmas

Alan

[Jeremy McCreary]

As Jermemy posted, this can predict duration of spin.
Duration (minutes) = Ln(twirl RPM / topple RPM) / Ln(Average decay per minute)
You can use this to predict minutes remaining by using present RPM instead of twirl RPM

I think you're referring to my post at http://www.ta0.com/forum/index.php/topic,5161.msg55049.html#msg55049. How are you calculating "average decay per minute"?

[Jeremy McCreary]

I've tried to use your paintbrush on light (50g) tops with problems.  The lightest contact causes the stem to "grab" the wet brush and tilt towards it.  Have you successfully used that method with such a light top?

I've had good luck with a slack chalk line -- even with LEGO tops much lighter than that.