iTopSpin

Please login or register.

Login with username, password and session length
Advanced search  

News:

Author Topic: The slipping unbalanced top: a riddle and an experiment  (Read 10000 times)

Iacopo

  • Immortal Member
  • *********
  • Posts: 1712
    • Spin tops by Iacopo Simonelli, YouTube channel
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #30 on: July 05, 2020, 11:24:22 AM »

Thanks a lot Iacopo. That must have been lots of work. It seems that you have definitely established that it's a resonance effect.

I thought about it, and it seems to me that if it was spinning at the same time as vibrating, and at the same frequency, the disk center (where the rod attaches) should go around a circle two times per each turn of the wheel (like a figure 8 but folded in half) but I'm not seeing it in the slow-mo video  :-\

Thank you for your input, I would have not thought to whirling by myself.
I learned more than expected from this little experiement.

Maybe I found something other:
Maybe the lack of vibration is not an issue because the rotation itself could be the vibration.
 
Depending on how I start the vibration, I can make the rod to oscillate back and forth, but also I can make it to oscillate making an ellpise, or even a circle, instead of making a back and forth motion.  So maybe rotation and vibration are not so different things.
I tried measuring the frequencies of the rod oscillating back and forth and of the same rod oscillating in circular motion;
The frequency doesn't change, is the same.

But, at this point, I have to admit that Jeremy was right.
If the constrained rotation of an unbalanced mass can produce whirling, the unbalanced top can whirl.

The constraint, (the rod, in the umbalanced disk, trying to make the disk to rotate about its simmetry axis, instead of about the CM), in the case of the spinning top, is the tip: 
if the CM is at the same height of the tip, (a spindulum), and the top doesn't slip, the CM has no freedom at all to move horizontally where it wants and is constrained to simply spin about the tip. This would be the equivalent of the stiff rod situation in the disk. 
This makes the applied force to have an effect in its same direction. 
The heavy side of the wheel with a stiff rod moves outwards, centrifugal force.
The heavy side of a spindulum sinks down, gravity.

If the constraint is weak, (soft rod in the disk, CM far from the tip in the top), and the speed high enough, the effect of the direction of the force becomes shifted by 180 degrees;  the heavy side goes towards the rotational axis, both in the top and in the disk, and not outwards, as expected for centrifugal force to behave.


It seems that there are overlapping concepts in the literature of whirling and in that of a mass wanting to spin about its CM, the second maybe could be in some way considered a case of whirling.
« Last Edit: July 05, 2020, 02:55:39 PM by Iacopo »
Logged

ta0

  • Administrator
  • Olympus member
  • *****
  • Posts: 14235
    • www.ta0.com
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #31 on: July 05, 2020, 12:11:42 PM »

Depending on how I start the vibration, I can make the rod to oscillate back and forth, but also I can make it to oscillate making an ellpise, or even a circle, instead of making a back and forth motion.  So maybe rotation and vibration are not so different things.
I tried measuring the frequencies of the rod oscillating back and forth and of the same rod oscillating in circular motion;
The frequency doesn't change, is the same.
A circular motion can be considered the superposition of two linear oscillations at 90 degrees to each other (of the same amplitude and frequency and at 90 degrees phase). So any symmetric pendulum will oscillate in a circular motion with the same period that it oscillates in a plane. It can also oscillate in an elliptical motion (if the amplitudes are different or the phase difference is not 90) but the frequency won't change.

I think we should limit the use of the term "whirl" to the case where there is flexibility or elasticity in the structure and resonances become important. But I have not read the literature on whirl so I'm not sure if they limit themselves to that case.
Logged

Iacopo

  • Immortal Member
  • *********
  • Posts: 1712
    • Spin tops by Iacopo Simonelli, YouTube channel
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #32 on: July 05, 2020, 03:18:20 PM »

A circular motion can be considered the superposition of two linear oscillations at 90 degrees to each other (of the same amplitude and frequency and at 90 degrees phase). So any symmetric pendulum will oscillate in a circular motion with the same period that it oscillates in a plane. It can also oscillate in an elliptical motion (if the amplitudes are different or the phase difference is not 90) but the frequency won't change.

This is also an interesting piece of information, which is helping me for some further reasoning, thank you.
Logged

ta0

  • Administrator
  • Olympus member
  • *****
  • Posts: 14235
    • www.ta0.com
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #33 on: July 06, 2020, 08:51:40 PM »

The unbalanced case looks very complicated near resonance.

I suspect Jeremy is just enjoying watching us whirl our brains trying to figure out this.  ;D
Logged

Jeremy McCreary

  • ITSA
  • Demigod member
  • **********
  • Posts: 3781
    • MOCpages
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #34 on: July 06, 2020, 11:56:10 PM »

I suspect Jeremy is just enjoying watching us whirl our brains trying to figure out this.  ;D

It is kinda fun. :D :P >:D

I'll have some things to add once the self-discovery subsides.
Logged
Art is how we decorate space, music is how we decorate time ... and with spinning tops, we decorate both.
—after Jean-Michel Basquiat, 1960-1988

Everything in the world is strange and marvelous to well-open eyes.
—Jose Ortega y Gasset, 1883-1955

ta0

  • Administrator
  • Olympus member
  • *****
  • Posts: 14235
    • www.ta0.com
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #35 on: July 07, 2020, 12:52:40 PM »

It is kinda fun. :D :P >:D
I'll have some things to add once the self-discovery subsides.
Self-discovery is fun.  ;)

The "pendulum" circular oscillations of the bar are not rotations: a face painted on the disk would remain oriented always in the same direction.
When you add the rotation due to the lathe you get a complex curve for each point on the disk (that is not the center). If it's rotating close to the vibrating frequency, the superposed movements describe a curve that is biased to one side (a cardioid type). I can see that an unbalancing mass attached to the disk will pull the center of rotation to one side. I suspect that below resonance, the pendulum circular motion is in the same direction as the rotation and above it's in the opposite direction. The shift of the center of rotation must be due to the change in the path when the direction of resonance switches.

I will try to graph the curves tonight.
Logged

Iacopo

  • Immortal Member
  • *********
  • Posts: 1712
    • Spin tops by Iacopo Simonelli, YouTube channel
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #36 on: July 07, 2020, 12:53:34 PM »

The unbalanced case looks very complicated near resonance.

I suspect Jeremy is just enjoying watching us whirl our brains trying to figure out this.  ;D

I too was thinking to what it happens at the transition speed.  I would need more time for thinking and experimenting.

Jeremy, what things you would add ?  You might be helpful.
Logged

Iacopo

  • Immortal Member
  • *********
  • Posts: 1712
    • Spin tops by Iacopo Simonelli, YouTube channel
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #37 on: July 07, 2020, 03:20:08 PM »

When you add the rotation due to the lathe you get a complex curve for each point on the disk (that is not the center).

I could see this complex motion when I made the experiment. 
It seems like the superposition of two wobbles, which should be the vibration of the rod, and the rotation due to the lathe.
If the frequency of the two wobbles is not very different, intermittent wobble appears:
alternate phases of wobble and absence of wobble.

The complex motion appears after a disturbance, like an acceleration or a deceleration of the lathe engine, or when I turn it on, or if I kick the rod while it is spinning.

If I let the rotation undisturbed, after maybe 10-30 seconds, the motion settles in a way that only the rotation about the chuck axis remains, having the speed of the lathe.  The motion with the resonance frequency disappears completely, and each point of the wheel and of the rod ends making a simple circular trajectory, as it can be seen in the videos I posted here.  This stabilization happens both above and below the resonance frequency.
Logged

ta0

  • Administrator
  • Olympus member
  • *****
  • Posts: 14235
    • www.ta0.com
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #38 on: July 08, 2020, 12:39:48 AM »

If I let the rotation undisturbed, after maybe 10-30 seconds, the motion settles in a way that only the rotation about the chuck axis remains, having the speed of the lathe.  The motion with the resonance frequency disappears completely, and each point of the wheel and of the rod ends making a simple circular trajectory, as it can be seen in the videos I posted here.  This stabilization happens both above and below the resonance frequency.
Only at the resonance frequency, or very close, will the lathe rotation couple energy to the resonant mode, so you would expect the oscillations to dissipate above and below. The unbalance might keep the spinning eccentric far from it, but the switch that you see may still be produced at resonance, where the oscillation builds up.

These are graphs at resonance of the movement described by a point on a balanced disk.
On the first ones, the oscillation amplitude is of the same order as the distance of the point to the center of the disk (oscillation/distance = 1/1.3 and 0.6/1.3)

 

The green is the circle of the center with just circular oscillation. The blue is the trajectory of the point if it's oscillating in the same direction as the lathe rotation. The black if its on the opposite direction.
Small relative oscillation (0.18/1.3, same point on the disk):



Note that the black curve is actually a circle. This is true for any oscillation amplitudes.
The center of the black circle is the disk center, so if it was oscillating in the opposite direction of the lathe spin, the disk would just rotate in place but displaced from the center of the lathe.
A point on the disk close enough to the center, for an oscillation in the same direction of the spin, it will rotate at double the frequency (0.6/0.1):





I need to think more about it  :-\

« Last Edit: July 08, 2020, 01:13:45 AM by ta0 »
Logged

ta0

  • Administrator
  • Olympus member
  • *****
  • Posts: 14235
    • www.ta0.com
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #39 on: July 08, 2020, 09:20:18 AM »

I tried changing the frequency above and below resonance. As expected, now the curves don't close after one cycle and start to shift, against the spin for lower frequencies and in the same direction for higher frequencies.
I think I got to a dead end here . . .  :(

Here is a link to the graphs I created on Desmos.com. There are sliders you can play with (w = frequency ratio to resonance, R = radius of oscillation, d = distance to the center of disk, t = angle in degrees)
https://www.desmos.com/calculator/pl42tjyqgs
« Last Edit: July 08, 2020, 02:36:07 PM by ta0 »
Logged

Jeremy McCreary

  • ITSA
  • Demigod member
  • **********
  • Posts: 3781
    • MOCpages
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #40 on: July 08, 2020, 02:03:44 PM »

Sorry, I've been distracted by moving my life into the basement bedroom for COVID quarantine. If I do have COVID, it's mild so far. Test results tomorrow.

Preparing a more detailed post regarding how the whirl we see in Iacopo's last test rig applies to spinning tops with only gyroscopic contol of the motions of their "heads" ( free ends). Meanwhile, find links to some free online PDFs with good introductions to engineering whirl below. All focus on whirl due to static unbalance. Strongly recommend Swanson's Figures 7 and 9.

To get the connection to tops, you have to think of them as overhung (not center-hung) rotors with one "foot bearing" at the tip-ground contact or tip-string contact, as in a merry-go-round with a fixed-tip top. You won't find many bearings like these in real machines, but they're still bearings. The foot bearing in a top welcomes spin, tilt, precession, and (with large ball tips) pure roll while discouraging (with varying success) all other relative motions.

Examples of "overhung" rotors include Iacopo's last test rig, most fans, empty lathe chucks, and grinding wheels. A top being turned in a lathe is overhung when supported only by the chuck and "center-hung" when also supported at the other end by the  spindle. The bearings involved are those of those of the chuck and spindle. Again, center-hung rotors are not directly analogous to freely spinning tops, but whirl in overhung rotors differs only in detail.

Importantly, only the rigid modes of whirl apply to tops, as they involve no bending. With the top rotor+shaft much stiffer than its foot bearing, all of the whirl in rigid modes is then accommodated at the foot bearing and the top's gyroscopically constrained head.

I think I see both cylindrical and conical rigid whirl in my unbalanced LEGO test tops. In my more flexible tops,  pretty sure I also get bending modes with large unbalances at high speeds.

Note that in industrial overhung rotors with much more restrictive bearings, the gyroscopic effects are secondary, serving mainly to shift resonant frequencies. In tops, they're primary, but nothing about that precludes whirl.



Swanson, E., et al., 2005, A Practical Review of Rotating Machinery Critical Speeds and Modes

Nelson, F., 2007, Rotor Dynamics without equations

Freese, T.D., and Grazier, P.E., 2004, Balance this!

If you read only one of these, make it Swanson. For something more mathematical, and with discussions of rotating machines closer to spinning tops, try...

Nelson, H.D., and Talbert, P.B., 2003, Rotordynamic considerations (chapter 10 of unknown book)
« Last Edit: July 08, 2020, 05:34:26 PM by Jeremy McCreary »
Logged

Jeremy McCreary

  • ITSA
  • Demigod member
  • **********
  • Posts: 3781
    • MOCpages
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #41 on: July 08, 2020, 02:33:05 PM »

I had assumed that I could always select the axes so the point on the disk, the disk center and the center of the lathe were aligned at some point in time. I now realize that is not the case, so I added a new angle slider s, that takes care of this. For the oscillations in the same direction of the spin you get some new possible curves, but no new insight to explain the experimental results. Here are the graphs with the new slider: https://www.desmos.com/calculator/of4ftqmoz0

Wow, that graphing site is my 11th wildest dream!

Not sure how your graph applies to Iacopo's last test rig, but I had a lot of fun with the sliders. Amazingly responsive.
Logged

ta0

  • Administrator
  • Olympus member
  • *****
  • Posts: 14235
    • www.ta0.com
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #42 on: July 08, 2020, 02:55:01 PM »

Sorry, I've been distracted by moving my life into the basement bedroom for COVID quarantine. If I do have COVID, it's mild so far. Test results tomorrow.
Wow, I'm sorry. I hope it's not covid. If it is, I wish you a very mild case.

I had assumed that I could always select the axes so the point on the disk, the disk center and the center of the lathe were aligned at some point in time. I now realize that is not the case, so I added a new angle slider s, that takes care of this. For the oscillations in the same direction of the spin you get some new possible curves, but no new insight to explain the experimental results. Here are the graphs with the new slider: https://www.desmos.com/calculator/of4ftqmoz0

Wow, that graphing site is my 11th wildest dream!

Not sure how your graph applies to Iacopo's last test rig, but I had a lot of fun with the sliders. Amazingly responsive.
I only discovered it yesterday. I had used other online graphing utilities before but this one is pretty good. It only took me a few minutes to learn how it works and as you say it's a lot of fun. The best thing is that I can share it easily (and probably embed it, but I haven't tried it).
By the way, I made an error when I added the s slider. This is the correct version: https://www.desmos.com/calculator/5y9jyt7ejj
Logged

Iacopo

  • Immortal Member
  • *********
  • Posts: 1712
    • Spin tops by Iacopo Simonelli, YouTube channel
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #43 on: July 08, 2020, 04:45:24 PM »


I thought a lot in these days and I will write various things in the next days.
Also I am eager to read what you find, I see some things but not everything.
The understanding of whirling can open an interesting perspective on the dynamics of imbalance wobble, and something more too I think.
I need time.  Tomorrow I will be not at home. I will post again on friday probably.
« Last Edit: July 08, 2020, 05:05:20 PM by Iacopo »
Logged

Jeremy McCreary

  • ITSA
  • Demigod member
  • **********
  • Posts: 3781
    • MOCpages
Re: The slipping unbalanced top: a riddle and an experiment
« Reply #44 on: July 08, 2020, 06:00:03 PM »

The understanding of whirling can open an interesting perspective on the dynamics of imbalance wobble, and something more too I think.

Agree. In tops, as with other rotary machines, you have a running battle for control of behavior -- with gravity, air and tip resistances, inertial forces due to unbalance, and gyroscopic hindrances all in the fray. Trying to take in all of these coupled influences at once makes my head hurt. Badly. And mentally separating their contributions to observed top behavior is just as mind-boggling.

Ed Witten once said that humans may not be smart enough to take string theory to completion. And this from the father of string theory. Not sure this human's even smart enough to grasp -- I mean really grasp, at gut level -- the full spectrum of real top behavior.

Unbalance wobble keeps reminding me that I have to think beyond the gyroscopic in tops. But only in physically compaible ways. And therein lies my biggest stumbling block.
« Last Edit: July 08, 2020, 08:48:52 PM by Jeremy McCreary »
Logged
Pages: « 1 2 3 4 5 6 7 »   Go Up