# Cannot find any scientific validation of product Dyna Beads for tire balancing

frascati
Cannot find any scientific validation of product "Dyna Beads" for tire balancing.

I'm intrigued by the difficulty in locating any reputable scientific analysis of this method.

http://www.innovativebalancing.com/index.php
There are dozens of additional manufacturers/vendors.

Is there any sound science behind adding loose plastic beads to the periphery of a rotating mass in order to achieve balance?

I cannot find a single instance of rigorous scientific analysis of the efficacy of such methods. It may be that I'm not familiar enough with physics terminology to be using the right key words.

Motorcycling and automotive forums have been aflame with anecdotal skirmishes over these products for many years now with, evidently, no reputable scientific agency, gov't or independent safety research facility, automotive, motorcycle, aeronautic, motorsports manufacturer, university, or other stepping forward to attempt any conclusive analysis of this method. It would seem to be a fairly important safety and performance issue. Again, I'm pretty astonished.

Is it just possible that from a purely scientific standpoint the idea is so patently absurd that no reputable physicist would even bother with analysis?

Otherwise, could anyone kindly point to papers or studies pertaining to such methods of dynamic balancing/stabilizing, particularly as they might either confirm or discredit the method?

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frascati

Can anyone at the very least tell me if this is a valid "physics" question?

xxChrisxx

Sounds to me like they are a rotational analogue to a tuned mass damper. They just damp the vibrations rather than eliminating the source/balance issue.

Homework Helper
Gold Member

Should be easy for a tyre fitter to test them. Just find an out of balance wheel put it on the balancer. See what the balancer says.

Homework Helper

Should be easy for a tyre fitter to test them. Just find an out of balance wheel put it on the balancer. See what the balancer says.

The big problem with that is that you are measuring whether the beads work on a tire balance machine, not in real life. FWIW you would probably measure that they do work on the balance machine, but that doesn't prove much IMO.

If you consider a rigid circular unbalanced wheel, not in contact with the ground, with the axle mounted on equal stiffness springs horizontally and vertically (i.e. a wheel on a balance machine, not on a car), the mass of the wheel and the stiffness of the springs have a natural vibration frequency. If you spin the wheel at a speed below that frequency, it will rotate so it moves with "heavy side out" (i.e.the heavy side is furthest from the point near the axle that doesn't vibrate) and the amplitude of the unbalance force will increase as the RPM increases. When the RPM equals the spring-and-mass vibration frequency, the ampllitude of the out of balance motion will be a maximum. If you increase the speed above this point, the amplitude reduces and the wheel mow moves with the light side out. That may not seem intuitive, but it's a straightforward deduction from the equations of motion, and easy to confirm by experiment. One way to understand it is that a very hgih RPMs, the inertia of the wheel means the "easiest" thing for it to do is rotate about its own center of mass, not about the axle position).

In the "light side out" situation, the beads would tend to move to add mass to the light side, and therefore improve the balance. At low RPM in the "heavy side out" situation they would make the balance worse, not better.

Google found a website with diagrams showing the beads working like that (though it didn't say anything about running faster than the critiical RPM).

But IMO none of the above applies to wheels on a vehicle, because the motion of the wheel is constrained by its contact with the road, and the tire is flexible. The car suspension has a flexible spring in the vertical direction, but there isn't an equal spring acting horizontally (i.e. in the front-to-back direction relative to the car).

If there is an explanation why these work in real life, I think it is going to be quite a lot more complicated than the above model. It isn't at all obvious to me why the beads should move to where they need to be, and then stay there. What the coriolis/gyro forces do when cornering (and on a bike, when the wheel is not vertical) is another complication.

I suspect the bottom line is that apart from high performance cars, wheel balancing isn't very important anyway. After all, you don't need to keep rebalancing the wheels regularly as you wear away several millimeters of rubber from the tires. But (at least in the UK) every tire fitting shop automatically does "free wheel balancing" as standard when they fit tires, so most customers never get to find out if it matters or not.

Homework Helper
Gold Member

I've seen videos of how they are meant to work on youtube but they only appear to demo balance in one plane. When my tyres were balanced earlier this week they needed two sets of weights, one on the inner and one on the outer rim. I don't see how the beads can do this.

frascati

Does any one else share my curiosity about the near non-existence of rigorous scientific testing of this method? I've heard anecdotal reference to washing machine and helicopter rotor applications of some form of this balancing, but still cannot find real data on it.

Heck, even bringing the question to a board such as this, which invites a very wide discussion, from the elemental to the most esoteric physics topics, still only elicits hunches for the most part. Thank you by the way. But it's not what I'm looking for.
The reason why I brought the question here was that this topic seems, judging from most comment in motorsports forums, more akin to matters of philosophy than pure physics. That just mystifies me. Because it's clearly , really unequivocally, not a matter of anything but physics. There ought to be far, far, far, less mere faith than what exists on something as fundamentally physically testable and verifiable as balancing a rotating mass with beads. Is it more complicated than sending a rover to mars?

There are far less apparently applicable matters of physics that attract the attention and rigorous study, and presentation of papers, from industrial and academic researchers. It's not a mars rover, but indeed here is a method of physically balancing a rotating mass, being applied to tires ranging from scooters, through motorcycles and automobiles and fleet transport vehicles (semis), all the way to aeronautics.... and almost no verifiable hard data/study seems to exist.

And yeah, so what if I'm a little OCD? That's not really the point here is it:)

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Homework Helper

Does any one else share my curiosity about the near non-existence of rigorous scientific testing of this method?
There is already a cheap and simple way to balance wheels accurately enough for most purposes. You will find it in pretty much every tire fitting shop in the developed world. If you need higher accuracy, there are machines that will give orders of magnitude more accurate balancing.

It's easy to think of reasons why the bead idea won't work very well. Some of them have been given in this thread. The test equipment to do an experiment (e.g. high speed X-ray measurements to see what happens ito the beads nside a real tire) already exists. But I don't suppose the people who sell this stuff are interested in spending a lot of money to show their system might be no better than snake oil.

Based on the engieering I do in real life, my reaction to this idea is basically "why bother". I certainly couldn't justify spending say $10,000 to investigate it properly, because at best it gives no obvious benefit over a couple of$1 balance weights that can be selected and fitted correctly in five minutes.

frascati

Someone on another forum offered this link and asked me to refute it (assuming no carnival, behind the curtain, sleight of hand is going on in the video). I cannot. The tire spinning at "perfect balance" according to the narrator still leaves a bit to be desired by my eye, but the compensation it provides against the severe condition of the mass of magnet is certainly noteworthy.

Can someone finally provide either solid evidence of "snake-oil" in the physics of this (beyond "i'm a physics phd and i just kind of doubt that works)

Is this as paper as legit as it appears?
http://rsta.royalsocietypublishing.org/content/366/1866/705.full

If it, according to this paper, has been known and investigated since the (previous now) turn of the century, then why is it apparently unknown at this forum, and virtually ignored by any legitimate motorsports enterprise (goodyear, ford, honda, bridgestone, dunlap, et al)?

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Homework Helper

Is this as paper as legit as it appears?
http://rsta.royalsocietypublishing.org/content/366/1866/705.full

If it, according to this paper, has been known and investigated since the (previous now) turn of the century, then why is it apparently unknown at this forum, and virtually ignored by any legitimate motorsports enterprise (goodyear, ford, honda, bridgestone, dunlap, et al)?

It looks legit to me, and it's saying pretty much what I said in my earlier post, for example
The principal idea behind the ADB is that the balancing balls are subjected to a driving force caused by an apparent centripetal force acting from the offset centre of mass to each ball. When the speed of rotation is below the first resonance, this driving force pushes the balls towards the imbalance, thus moving the centre of mass away from the centre of rotation. However, when the speed of rotation is greater than the first resonance, the driving force pushes the balls to the opposite side of the rotor than the imbalance, thus moving the centre of mass towards the centre of rotation.

There is a huge diffeerence between the sort of systems investigated in the paper and its referneces, and just putting some balls in a tire and hoping for the best. That's the basic difference between doing physics or engineering and selling snake oil IMO.

mrspeedybob
it gives no obvious benefit over a couple of $1 balance weights that can be selected and fitted correctly in five minutes. The benefits are... That it is self adjuting. A blob of mud stuck to the inside of your wheel no longer causes vibration. It eliminates the need for expensive tire balancing equipment. It eliminates any question about the calibration of said equipment. If it actually works or not I do not know but it would be very simple to test. There are vibration analizer machines designed to measure vibration in a car while driving. Simply install 1 imbalanced wheel on a car, drive it and measure the vibration. Install the beads and measure the vibration again. Remove the beads and balance the wheel with a balancer, then measure the vibration again. If anyone would like to send me some of these beads I have access to the equipment necessary and would be happy to perform this experiment and post the results. HowlerMonkey That "technology" depends entirely on not having runout in the tire or rim. From my 30 years experience with tires, there is no such thing as "zero runout" in a tire/wheel assembly. This is why dealerships use "roadforce matching" though it sometimes requires moving an "off round" tire to an "off round" rim and proper indexing to work. Or you can buy a new 20 inch wheel after every pothole you hit. Science Advisor Homework Helper The benefits are... That it is self adjuting. A blob of mud stuck to the inside of your wheel no longer causes vibration. It eliminates the need for expensive tire balancing equipment. It eliminates any question about the calibration of said equipment. I would suggest the real benefit is that you can sell somebody 50 cents worth of beads for 50 dollars. Occulus I joined this forum just to respond to your query! Im a Rotating Equipment Engineer with an ISO Category 4 Vibration Analysis certification based in Australia. I have just bought some beads to test in my tyres. I had a hunch on how these worked but I only recenly found an article on the natural frequencies of tyres which convinced me my theory may be correct. AlephZero was on the right path. Initially, rotating assemblies spin around their center of geometry. They then pass through their first of many critical speeds depending on the mode shapes for the tyre. The critical speeds (resonance) amplifies the vibration at that frequency. Once passed the first critical speed, the rotating assembly spins around its center of mass and not center of geometry. The frequency of the critical speed is based on the mass and stiffness of the tyre. Changing your tyre pressure can influence where the critical speed is and so can adding the beads which add mass. Below the first critical speed, the high spot and the heavy spot are in phase. That is, the heavy spot of the tyre lines up with the high spot of the tyre caused by the unbalance. At the critical speed, the high spot lags the heavy spot by 90 degrees and above the first critical speed the high spot lags the heavy spot by 180deg. The balancing beads only rotate freely inside the tyre until the centrifugal force is great enough to hold them on up against the tyre as is rotates. If the tyre was perfectly round, they would distribute evenly around the inside of the tyre. If there is a high spot on the tyre, the beads will run into this spot because they are getting pulled outward. Below the first critical, the high spot lines up with the heavy spot and you end up with more mass (beads) at the location of the heavy spot which makes the unbalance worse. Once you pass the first critical speed of the tyre, the high spot lags the heavy spot by 180deg. The beads run into the high spot which is now 180deg from the heavy spot and the tyre is balanced. I just found a study on the natural frequencies of tyres (PM me and I am happy to pass on the link. These typically range from 80-100Hz. I ran some numbers through excel and this relates to a speed of 50-75Km/h. So the tyre does in fact pass through its first critical during operation and should be balanced by the beads once it does. Im actually going to test the beads so I will let you know how they go. billy_joule DizzyDino Here is my "wild guess"... Where the heaviest point of an out-of-balance tire meets the road, after changing direction to a flat plain, it must again return to follow the rotation of the rest of the tire due to kinetic forces. As this point leaves the road, it's inertia causes the tire to change shape, I would imagine somewhat "EGG-like" and it being the 'pointy end' and the near opposite side of the tire being the more rounded end. Beads flow to the outermost points available to them provided by their inertia or AKA "centrifugal force" and limited only by friction against the inside of the tire. These two outermost points created by the unbalanced tire as it increases in rpm are the natural favored location as they are further from the center but beads are ejected from them with the continuous pounding of force of the tire meeting the road and changing direction. Where the beads are not ejected from, they provide a counter balance and find a temporary home until the forces (rpm) supplied are depleted to a point gravity overcomes the process. I imagine if one could freeze-frame the moment of balance, once an adequate rpm has been reached, one would find the outermost points of the egg-shaped tire (while unbalanced) have accumulated the least amount of beads and thus balancing the tire. To me, this is fascinating as there are several variables of contributing force in play but I should add a disclaimer... I am not qualified in anyway to provide technical data or any possible way to prove this and have a very limited education, but to me, this seems to make sense. Nevertheless, I would love to understand how, if I am incorrect. Hopefully I explained it as well as I imagine it. ;) DizzyDino The tire spinning at "perfect balance" according to the narrator still leaves a bit to be desired by my eye, but the compensation it provides against the severe condition of the mass of magnet is certainly noteworthy. My eye too rather disagreed with the narrator. Perhaps mounting the balancing mechanism on the rim leaves the tire, further from the center axle, without compensation? D.Gray3 That video was interesting. As others have stated, below the required rpm, the beads made the balance worse. Is there a top end rpm for the harmony where the tire would come back out of balance? It would be nice to see some sort of treadmill incorporated into the demonstration to simulate the road. Regardless of what hocus pocus is at work here, the tire seemed effectively balanced at speed. The cost of those beads, though! hammockking Get yourselves some non biodegradable airsoft bbs (see below). For$20, you'll have some left over. I have two terribly cupped tires, inserted the right amount of bbs into my tires, and still had a death wobble. Then, I started to remove the balancing weights that were originally and horrifically glued in there. They wrapped more than half way around one of my tires trying to compensate for my cupping. It began getting better. The first day out, when getting up to speed, you could almost feel the tires finding their beads.

So, I went hip deep and removed all the weights. Worked like a charm almost immediately. Took a 1500 mile road trip a few weeks later through all types of terrain without a problem. Have aired down and back with never a concern. You will need to scale out the appropriate amount of weight that you will need. The defining difference between using the bbs instead of the overly priced beads is that they are two big to fit in through your air valve. You will need to break the bead to get em in. I took mine to a tire shop that charged me $5 per tire to do this. Total of$40 including bbs and haven't had to balance my cupped tires for almost 10K miles. I'm ok with that.

Note: I have 285/75r16 on a 3 ton truck. On my road trip the cupped tires were on the rear, but have since moved to, and been in the front for just under 5k miles. I only sense a slight vibration SOMEtimes between 55-65 since they've been put up front. Again, only sometimes and very light. They helped me immeasurably, especially with the cupping, and found it worth spreading the wealth.

Finally getting some new rubber and already have my new $20 worth of airsoft bbs standing by. Spray some silicone lubricant on them to make sure they keep rolling. For reference, I used these: https://www.amazon.com/gp/product/B0048970A2/?tag=pfamazon01-20 See how many ounces your tires need here: http://checkeredflagtirebalancebeads.com/tire-charts/ Last edited by a moderator: TrevorLane Ummm sorry but I must strongly disagree. #1. The tire charts are ounces by weight NOT volume.....So, because the Airsoft bb's are made of a light plastic, 8 weight ounces of airsoft bb's compared to 8oz of high desity ceramic beads would be a huge difference and take up about 5 times more volume (or more) in the tire. I am speaking of the ceramic beads, such as DynaBeads or Checkered Flag Tires carries. #2. You can hear them at slow speeds in town where the ceramic beads you dont. #3. Black top gets around 170 degrees in the summer around the southwest and the Airsoft bb's being a light plastic get soft and will mis-shapen. Now instead of rolling in the tire they will be egg shaped plastic junk bouncing around. Dont cheese out and go with plastic. I don't know about DynaBeads but Checkered Flag Tires has a smokin price on ebay.$33 can take care of 33-35 inch tires.....I know because I bought some for my 35's and all is good. Here is the link - http://www.ebay.com/itm/Tire-Balanc...ash=item2eca75eb43:g:0uAAAOSwKfVXI7Mg&vxp=mtr

Sorry Hammockking.... but the tire chart ( at http://checkeredflagtirebalancebeads.com ) calls for 8oz per tire on your 285/75R16 and for an extra $13 you would have the good stuff in your tires instead of plastic junk. The ceramic beads are re-usable too. MTCW Last edited: TrevorLane In addition here is some info I found as to why they work. "Take a baton, it has a heavy and light end. place it on a finger. When it is balanced the light end is farther from your finger and the heavy end is closer. That demonstrates the center of Rotational balance, not the physical center of the baton. The beads will travel to the greatest distance from the Rotational balance center which will then move the center of rotational balance closer to the center of rotation. The beads acting as a fluid will continue to adjust as long as a rotational force greater than their individual mass is present. That is a simple explanation of how it works. Someone said their memory of physics say it won't work, After some Googling I came across the physics formula that explains why it does work: Think about it like this: x = \alpha \cos \frac{s}{\alpha} \ ; y=\alpha \sin\frac{s}{\alpha} \ . Then: x^2+y^2 = \alpha^2 \ , which can be recognized as a circular path around the origin with radius α. The position s = 0 corresponds to [α, 0], or 3 o'clock. To use the above formalism the derivatives are needed: y'(s) = \cos \frac{s}{\alpha}\ ; \ x'(s) = -\sin \frac{s}{\alpha} \ y''(s) = -\frac{1}{\alpha}\sin\frac{s}{\alpha} \ ; \ x''(s) = -\frac{1}{\alpha}\cos \frac{s}{\alpha} \ . With these results one can verify that: x'(s)^2 + y'(s)^2 = 1 \ ; \frac{1}{\rho} = y''(s)x'(s)-y''(s)x''(s) = \frac{1}{\alpha}\ . The unit vectors also can be found: \mathbf{u}_t(s) = \left[-\sin\frac{s}{\alpha},\ \cos\frac{s}{\alpha} \right]\ ; \mathbf{u}_n(s) = \left[\cos\frac{s}{\alpha},\ \sin\frac{s}{\alpha} \right] \ , which serve to show that s = 0 is located at position [ρ, 0] and s = ρπ/2 at [0, ρ], which agrees with the original expressions for x and y. In other words, s is measured counterclockwise around the circle from 3 o'clock. Also, the derivatives of these vectors can be found: \frac{d}{ds}\mathbf{u}_t(s) = -\frac{1}{\alpha} \left[\cos\frac{s}{\alpha},\ \sin\frac{s}{\alpha} \right]\ = -\frac{1}{\alpha}\mathbf{u}_n(s) \ ; \ \frac{d}{ds}\mathbf{u}_n(s) = \frac{1}{\alpha} \left[-\sin\frac{s}{\alpha},\ \cos\frac{s}{\alpha} \right] = \frac{1}{\alpha}\mathbf{u}_t(s) \ . To obtain velocity and acceleration, a time-dependence for s is necessary. For counterclockwise motion at variable speed v(t): s(t) = \int_0^t \ dt' \ v(t') \ , where v(t) is the speed and t is time, and s(t=0) = 0. Then: \mathbf{v} = v(t)\mathbf{u}_t(s) \ , \mathbf{a} = \frac{dv}{dt}\mathbf{u}_t(s)+v\frac{d}{dt}\mathbf{ u}_t(s) = \frac{dv}{dt}\mathbf{u}_t(s)-v\frac{1}{\alpha}\mathbf{u}_n(s)\frac{ds}{dt} =\frac{dv}{dt}\mathbf{u}_t(s)-\frac{v^2}{\alpha}\mathbf{u}_n(s), where it already is established that α = ρ. This acceleration is the standard result for non-uniform circular motion." Here is the link where I found it http://www.hotrodders.com/forum/does-really-work-tire-balancing-beads-176273-3.html Scroll down towards the bottom of the page. Thanks hammockking Ummm sorry but I must strongly disagree. #1. The tire charts are ounces by weight NOT volume.....So, because the Airsoft bb's are made of a light plastic, 8 weight ounces of airsoft bb's compared to 8oz of high desity ceramic beads would be a huge difference and take up about 5 times more volume (or more) in the tire. I am speaking of the ceramic beads, such as DynaBeads or Checkered Flag Tires carries. #2. You can hear them at slow speeds in town where the ceramic beads you dont. #3. Black top gets around 170 degrees in the summer around the southwest and the Airsoft bb's being a light plastic get soft and will mis-shapen. Now instead of rolling in the tire they will be egg shaped plastic junk bouncing around. Dont cheese out and go with plastic. I don't know about DynaBeads but Checkered Flag Tires has a smokin price on ebay.$33 can take care of 33-35 inch tires.....I know because I bought some for my 35's and all is good. Here is the link - http://www.ebay.com/itm/Tire-Balanc...ash=item2eca75eb43:g:0uAAAOSwKfVXI7Mg&vxp=mtr

Sorry Hammockking.... but the tire chart ( at http://checkeredflagtirebalancebeads.com ) calls for 8oz per tire on your 285/75R16 and for an extra \$13 you would have the good stuff in your tires instead of plastic junk. The ceramic beads are re-usable too.

MTCW

In the vague yet applicable words of donald rumsfeld: "there are unknown unknowns." Thanks for adding to my experience and knowledge on this topic. As for the posited question about adding beads to your tires, I can vouch from first hand experience that it will provide a better ride. As for there being more bbs in the tire to compensate for the weight difference per bead .. I don't see where that would be a problem. Seems, if anything, that it would provide a potentially better distribution of weight to aid in balancing.

I went with 10oz because of how bad my tires were and it def helped. From what i'd read, overkill wouldn't negatively impact the ride or performance and it hasn't in my case. But, the argument of ceramic vs. plastic seems a justifiable one to me. Do the ceramic ones not break down with time? Have you had them in for a while?
my concern with ceramic:
That can be a testament for how durable they are against the extended, slow pounding of high miles.

The airsoft bbs should hold up for a significant amount of time despite the fact that they are plastic. Most of your car is. Just need to make sure you are buying high grade. I too live in the SW and my road trip was through several deserts .. yet to notice a deterioration in handling or signs of clumping. Will examine soon when changing tires and will advise which one I choose depending on what I find.

As for reusing the beads .. nah. Throw it in with the cost of new tires. Happy to say life isn't that difficult. The dynabeads don't seem financially reasonable like the airsoft/ ebay ceramic approach.

Thanks again

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TrevorLane
The Ceramics do last as long as your tire and can be re-used. As for cost...you are looking at the most expensive one out there (DynaBeads). If you look on ebay you will find MUCH lower priced ceramic beads that make more sense. And for a little bit more I would rather go ceramic than PLASTIC.

Over the decades folks have tried "less than desirable" things inside tires to help balance them and all though some work just fine it does not mean people should actually put them in the tires.
For example - golf balls, beach sand, steel balls, lead balls, plastic air gun balls.....I guess it just boils down to each persons idea of what is acceptable.

"To Each Their Own"

For me....ceramic, not anything else.

Thanks

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jasontaylor7
I wasn't smart enough to understand any of the various explanations, so I wrote my own, which I am posting here upon doing a google search to see where people are discussing the question. I posted the answer here: https://www.quora.com/How-do-tire-wheel-balancing-beads-work/answer/Jason-Taylor-16

I will attempt a lame copy and paste and in case my Answer is ever censored or otherwise inaccessible:

Tire balancing beads are beads which are placed inside of tires. Allegedly, they self-balance tires such that there is no need to have any balancing weights.
How or even if they work has always been a mystery. There are hundreds of posts on the internet in which people speculate how they might operate.
I think I can guess how they should be working. To understand my explanation, it important to recognize that if everything regarding the wheel were super strong, there would not be any shimmy, since the axle, wheel, and tire would not bend and could handle any stress given to it from a small unbalanced weight.

In real life, metals bend, and of course the wheel assembly is usually attached to a suspension specifically designed to allow motion.
At low speeds, the situation should look like this:

The arrow represents the force given to the wheel by the extra unbalanced weight. One can see it should cause a low-speed vibration to the assembly.
However, one should also recognize that the vibration should also put stresses into the axle if it is disturbed, such that at higher speeds one may have this arrangement:

Here the axle is bending upwards, and the axis of rotation changes away from the tire center, which itself rotates around the axis of rotation.
What is interesting is that the part of the tire that is furthest from the axis of rotation is no longer where the extra unbalanced weight is. Rather, it is opposite of it. Therefore, beads placed inside of the tire will accumulate there instead of where they would accumulate at low speeds once the centrifugal acceleration exceeds gravity.
Disclaimer: this mode is speculation on my part. Consider if slack in bearings was high. Then, perhaps other modes of oscillation might be dominant.
A motorcycle wheel is different since there is no axle like this. However, the frame’s fork might also resonate opposite to the wheel heavy spot at higher speeds. The speeds at which this would occur would probably be different than the speeds of the same wheel assembly on a car. There is also the so-called death wobble to consider regarding a positive-feedback steering oscillation. In the linked video, the oscillating supportive structure would include the entire machine, motor, and holding frame. In some cases it should be the perpendicular moment of inertia of this supportive structure relative to that of the wheel that determines the frequency/speed at which the beads would help more than hurt shimmies.
“Dr. Jason! Dr. Jason! I have a question!
“Once the beads move to the light side of the tire, won’t the oscillation stop, causing the beads to go back to some other area such that the tire starts to shimmy again?”
Well, the re-positioning of the beads should reduce shimmy amplitude, but it would not bring it to zero. The amplitude of oscillation can be infinitesimal. Thus, the forces pulling the beads back to the heavy side would decrease as the beads drifted off, which would in turn increase the force to pull them back to the light side of the tire. So, effectively, the beads should be stationary as long as the tire is maintained at speed. Their equilibrium positioning would be such that there’s no shimmy. This is excluding dynamic balancing effects (inside vs. outside asymmetries), which I have not considered here, the existence of which is a sufficient reason to not use beads.
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Gold Member
The question of do they work has been answered, by millions of washing machines that have and are being balanced using the same principle. If you go to: https://en.wikipedia.org/wiki/Washing_machine and look under the "modern washers" section you will find the following statement: "Some manufacturers have taken steps to reduce vibration emanating from their washers, by means of reducing or controlling motor speeds, using hydraulic suspensions instead of spring suspensions, and having freely moving steel balls contained inside a ring mounted on both the front and back sides of the drum in order to counter the weight of the clothes and reduce vibration." (i.e for front loading machines, which seem to be the focus of this article)

As for their use on automobile tires, back in the early 1960's the sports car group at my university experimented with this method; but, rather than place the beads inside of the tires we made rings of plastic tubing the correct diameter to fit and be secured inside the wheel rim; and, filled those with light oil inside the tube with the balls to provide some damping of the balls movements. We found that it worked very well, but did cause a bit more vibration as the car passed through the critical speed as discussed above.

berkeman and jedishrfu
Mentor
This thread reminds me of the Click and Clack car story of water in the tire that would be frozen in the morning and cause the tire to be unbalanced.

The motorist took the car to the mechanic who could find nothing wrong after doing an afternoon inspection and the ice had melted back to water and evenly coated the tire hence no off balanced effect.

The Cartalk guys presented it as a weekly puzzler.