can we go deeper on Dyna Beads and balancing?

[gunderwood]

Summary

I've learned a lot from this thread, specifically because it made me curious enough to really investigate the topic. Thanks to the OP for starting it. I've provided references where possible, but as always, there is some interpretation of the information and I'm not infallible, so please feel free to ask questions and challenge the statements.

The theory of "autobalance" isn't new and certainly devices have been designed, built, and sold which utilize this mechanism for achieving dynamic balance. However, they are few and far between in practice and there's several very good reasons for that.

I'm surprised no one has bothered to really look it up...there are plenty of theoretical, analytical, and experimental papers out there on the subject. In fact the first theoretical reference I could find was from 1904 and the first real reference nearly everyone cites is Thearle in 1932. The first patent appears to be from 1916, but one of my references says Thearle showed it couldn't work as he proved that an autobalancer mechanism requires discrete weights and the patent used a liquid; i.e. the liquid in tires to make an autobalancer appears to be BS as far as I can tell (more on this later). I've narrowed it down to three papers as I feel they adequately address the Dynabead physics, but it's important to note that none of them actually address the Dynabead product. However, they convinced me to not use Dynabeads...YMMV.

Let's cut to the chase. IMHO the basic physical theory which Dynabeads uses is sound. The theoretical, analytical, and experimental physics all back up the concept of an autobalancer. The fact that you can do it and that it can work very well is not at all in question. However, if you look deeper it becomes obvious IMHO that their particular implementation is lacking as it appears to violate several key assumptions and worse still, autobalancers have well documented issues which are exactly why engineers (like myself) have not built them into many products. These issues, IMHO, so far invalidate the usefulness of an autobalancer, particularly a suboptimal one like Dynabeads, on a motorcycle.

Please note that I have not totally convinced myself yet that no autobalancer design can work well on a motorcycle, but simply that Dynabeads isn't it.

There are several different ways to build an autobalancer, but they all suffer from increased instability if they aren't spinning supercritical (i.e. until it reaches an RPM which is "fast enough," aka supercritical) and really don't like being perturbed (e.g. bumps, acceleration, turning, certain dampening states, etc.). The problem isn't that autobalancers don't work, it's that they only work well within particular set of parameters and if you violate them they actually make the imbalance much worse. This is exactly why engineers generally only use them in relatively static environments or they make them active balancers (sensors, actuators, etc. to actively change the balance...i.e. not an autobalancer). I also think this is why some people have success and others don't. It's a fragile system and even minor things can upset it.

In my next post I'll present my case, but I wanted to summarize it here because it's a bit long.

 

[gunderwood]

Analysis

Here's the papers I will use (partially because they are free and you can get them too):
http://rsta.royalsocietypublishing.org/content/366/1866/705.full.pdf
http://downloads.hindawi.com/journals/ijrm/2004/783480.pdf
http://74.220.207.117/~horvathl/PASSIVE BALANCING FOR ROTOR SYSTEMS USING PENDULUM BALANCERS.doc

Balance
First, let's first discuss theoretically what we are trying to do with dynamic balance. A dynamic imbalance is where the center of gravity (Cg) isn't around the center of rotation. This is the very similar to what we think of static balance, but the imbalance only shows up when you rotate the wheel/tire. Consider the wheel/tire on your bike, when it's sitting still, there is no dynamic imbalance. There can be a static imbalance and you can fix that pretty easily; we already do this when we manufacture a device. However, if you start spinning that wheel, there will be a dynamic imbalance if the Cg isn't right on the axial. Consider that the tire is sitting on the ground...it has a deflection which means it's mass isn't uniformly distributed anymore. That implies things like the quality of the tires, the lot, air pressure, the road surface, and even your weight all affect the dynamic balance. It should be obvious that a great many things can affect the Cg of your spinning wheel/tire and that's exactly why static balancing can't fix a dynamic imbalance.

An interesting side point is those tire balancing machines. You might ask how we can dynamically balance tires with what amounts to a static weight. We can't, at least not for all RPMs. Basically we cheat and purposefully create a slight static imbalance so as to reduce the dynamic imbalance. The dynamic imbalance is constantly changing though so static weights can only solve the problem at a given RPM. If you spin the wheel slower or faster it will become dynamically imbalanced again. Those balancing machines aren't really finding a single point solution, they are attempting to find the best compromise.

This should be even more obvious with the Hunter RoadForce machines (best commercially available AFAIK). They apply a substantial force on a roller to the tire so that it acts like the tire is rolling along the ground. A tire balanced that way is practically guaranteed to be statically imbalanced! However, it actually creates a better balanced tire because the sidewall stiffness of the tire varies (as does the rim concentricity). E.g. a high spot on the rim (which doesn't have to show up in a static balance!) on a hard part of the sidewall will give a bad ride as the resulting system isn't concentric. The point isn't to get a tire which will spin well on an unloaded axial or has good static balance, it's to get one that is properly dynamically balanced under load. You want the effective Cg to be right on the axial when in use, who cares about a test bed. As a quick side note, when using a tire balancer like the RoadForce you can actually line up the stiff part of the sidewall with a rim depression or vice versa. This usually isn't need if you have good quality rims and tires. Remember, you will never get perfect balance...engineering is the study compromises, so you can get of close enough for practical purposes.

One last thing on balance. All of this isn't to say that static balancing isn't of value. On the contrary, it's very important too, but just not for the reason most people assume. Most people are trying to achieve a dynamic balance with a static solution. As we talked about, you can't do it. However, consider this. Let's say you spend a lot of time statically balancing your rims and checking their concentricity (got to do both!). A rim is a fairly rigid system and as such, if you just spin it up there should be very little to no dynamic imbalance. Think about it. The statically balanced rim has it's Cg over the axial, unless there is a mass shift, which a rigid system like the rim really doesn't have much of, there won't be a dynamic imbalance either. The Cg doesn't magically change because you start spinning it; it changes when mass moves around in the rotating system. Of course the problem is that as the rim gets dirty or you mount something which isn't as rigid (e.g. a tire) or you put it under load (e.g. ride on it since that deflects things like the tire and even the rim a tiny amount) you've just created a dynamic imbalance. Thus, it should be apparent what a good static balance does for you...it gives you a good starting point for a mostly rigid system that doesn't experience too much mass deflection to achieve dynamic balance. That's great because it's easy to do and because it should significantly reduce the amount of dynamic balancing mass you need. As we'll discuss soon, those moving masses which allow for a dynamic balance aren't free of bad side effects; thus minimizing them with a good static balance helps.

Don't forget about concentricity either! You can have a statically and dynamically balanced system which isn't symmetric/concentric. I.e. a perfectly balanced rim which isn't concentric is going to have a very bad ride.

Autobalancers
So to fix this situation we need to figure out a way to move some mass around the rotating system so as to bring the rotating Cg back to the axial and that's what autobalancers do (and active balancers, but that's a different thread). Simply put, they exploit the physics of a rotating system so as to "perfectly" redistribute the mass and achieve dynamic balance. This is how Olsson 2004 describes it:

Another alternative is a mechanism that automatically adjust the balancing state, referred to as autobalancing. The are primarily two applications for this alternative: (1) when extreme accuracy is necessary (disk drives may be an example), and (2) when the state of balance is continuously or intermittently changed. A typical example of this is the centrifuge for a laundry machine, however fans, grinding wheels, and separators also belong to this category.

Sounds great, right? It is, but all isn't rosy.

There are several different theoretical ways to build an autobalancer. The most common is two rings/races each with a ball bearing that can freely move in them (a lubricant is often used as a dampener too).

Such dynamic imbalance has inspired the use of self-compensating, automatic dynamic balancing (ADB) mechanisms for eccentric rotors. 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. Viscous damping in the ball race causes energy dissipation, allowing the balls to come to rest in asymptotically stable steady-state positions.

Let's look at some of the requirements or operating modes of the system to understand when it works well and when it doesn't. Olsson 2004 discusses the basic theory, Horvath/Flowers/Fausz 2005 discusses the theoretical, analytical, and experimental two pendulum balancer and has some good practical application, and finally Green/Champenys/Friswell/Munoz 2011 discusses the possibility of more than two balancing masses. I'll only use the first name/date from here on out.

At least two balls/rings...
You can also build this with two rotating pendulums. One ball/pendulum works too, but unless the mass of the balancer is exactly equal to the mass of the imbalance it will create its own imbalance. You must use at least two to achieve a perfect dynamic balance.

Thus far the rotor has been regarded as a point mass. All real rotors also have an extension and, consequently, a moment of inertia. This also means that they have two or more natural frequencies and dynamic as well as static unbalance. In order to balance such rotors one must have two balancing planes and in order for the auto-balancing to work there must be two balancing rings... It is obvious that a perfect balancing requires two balancing rings. If only one exists, perhaps for some practical reasons, there will be a residual unbalance.

Simple enough, Dynabeads has many balls so they shouldn't have a problem here unless it impossible/impractical for all of those balls to completely counterbalance each other out. More on that later.

"Free" balls

This article deals with the method of free balls. The basic theory includes any number of balls, but is valid only if the balls stay out of contact with each other...

This implies that for a two ball system you must have two independent rings/races for the balls to move in. I think this is because if the balls come into contact with each other they can degrade to a single ball solution under certain parameters and as we already discussed, you need at least two. Of course that means they are offset a bit and that should cause a torque around the z axis (the suspension forks). The masses should be small so it should be much though.

Dynabeads has many balls, but they are not independent of each other. Thus, under certain conditions they could degrade into a single "ball" solution. However, I don't think that is the case. The Dynabeads are small enough and are "captured" by the tire in such a way that I think they partially behave like a liquid would. I.e. the apparent centripetal force is sufficient that it will "flatten" them out and not allow a sufficient clumping like two balls in the same ring. That however brings up the next point.

Fluids as an Autobalancer
Nearly everyone cites Thearle 1932 in their papers, but only Green 2011 makes this note:

In this paper, there is also a discussion on why an ADB consisting of a fluid, in place of solid weights, would not work.

ADB is Automatic Dynamic Balancer. I do not have a copy of Thearle 1932 so I'm left only my rationale. I think the reason for this is because the apparent centripetal force is so great that unless the ADB mass can hold itself together, like a solid weight would, it gets somewhat uniformly distributed ("flattened") around the container (in our case the tire) and don't act as a true counter balance. Thus, solid masses can behave very much like a point mass solution, the liquid can't.

Dynabeads are small enough that I think they also behave partially like a liquid and partially like a solid mass solution. The liquid properties are good because it should allow them to avoid the two or more dependent masses degrading to a single mass solution (see Free Balls above), but that comes at the expense of the somewhat uniform distribution of the beads (aka liquid like), which results in most of them not acting as an autobalancer. A detailed analysis of these mechanisms should be possible, but I'm generally satisfied that the beads are a reasonable compromise at steady-state. They partially behave like an autobalancer, but require much more mass to achieve the required redistribution of the Cg than a solid mass solution would. That additional mass, above and beyond what an ideal/true autobalancer requires, has all the problems of adding un-sprung/rotational mass to your motorcycle.

I suspect that the size/material of the beads was a compromise between these two properties (or it should have been). This also implies that the liquid in tires as an autobalancer is nonsense.

Concentricity
Dynabeads takes it on the chin here...

Again we note that the ring will rotate with its center stationary, and the rest of the rotor has to adjust its motion to this. This confirms the result as obtained for the eccentric ring: the only way for the balls to be at rest is when the ring is running concentrically. This means that there is no guarantee that the rotor as a whole will run smoother, even if the balancing in itself has been successful... Deviations from a perfect ring geometry will greatly aggravate the possibility to balance. In particular, an ellipticity can cause severe residual unbalance.

Ouch. Since the tire is the dynabeads "ring" it can't be concentric...the fact is that the tire is loaded and thus deflected and not round (remember it's one reason why we have the whole dynamic balance problem in the first place). Even if the balancing sort of works, it can't become stable as the ring is eccentric! Thus, we have a perpetually unstable system, which while it may provide some level of autobalancing, it will never come close to an optimal autobalancer.
I would guess this tendency is exacerbated by bikes like cruisers which use a bias ply tire and less so by those that use a radial. The bias ply should exhibit more non-concentricity as it conforms/flattens to the road more than a radial does. I'd bet this is why wide tires are an issue more so than narrow.

Autobalancer Mass
Since at least two solid masses are required for the autobalancer to work properly, each mass should be approximately half of the total dynamic mass imbalance. Any more mass than that and you amplify the negative stability problems (which we haven't covered yet) and get even more of the usual issues with adding more rotational/un-sprung mass. If the two masses are very close to the dynamic imbalance they will take a position approximately 180 degrees from it. If they are too little they will be exactly at 180 degrees, but won't move the Cg enough to totally cancel the dynamic imbalance. If they are more than is needed they will separate and take a position between 90 and 180 degrees from the imbalance. If they are less than 90 degrees from the dynamic imbalance they will be unstable and the whole system will suffer. If this isn't quite clear take a look at Horvath 2005 as they have some good pictures you can use to increase your understanding.

The problem is this, how much dynamic imbalance do you have? I certainly don't know and its going to vary widely from bike to bike, wheel to wheel, and tire to tire. Don't forget that you actually have to add more mass than the ideal autobalancer would because some of the Dynabead mass will behave like a fluid. This is probably the biggest practical issues of implementing a Dynabead solution. I'm sure through testing you could come up with some rules of thumb, but IMHO it's a hack at best.

Supercriticality
Basically a real rotor has at least two natural frequencies and until you spin the rotor fast enough the physics involved with an autobalancer actually make the vibrations (whirl) worse, not better. In an ideal autobalancer where the balancer mass is equal to the imbalance it will be twice as bad as the autobalancer mass will "align" with the imbalance. Now that's just the rough sketch of it as in reality it won't perfectly align since the system is highly unstable in this region (if you are accelerating to get to supercritical rotation). All you need to understand is that until you spin it fast enough (aka supercritical), a system with an autobalancer will be unstable and will amplify the dynamic imbalance, not make it better.

For subcritical operating speeds, the steady-state phase delay of the displacement related to the exciting force is less than 90O. In this case, the stable pendulum position will be between 0O and 90O as measured from the horizontal axis (as shown in figure 11.a) which exacerbates the mass imbalance of the system.

Dynabeads has the same problem although the fluid mechanism of it may actually help a bit on a steady-state sub-critical rotation as a portion of its bead mass won't act like an autobalancer. However, its worse when you consider the non-stead-state system...Dynabeads should behave worse than an ideal autobalancer.
This could explain why many GS riders think it makes their bike worse, they probably ride sub-critical and Dynabeads do make it worse.

Stability and Perturbations
This is, IMHO, the absolute worst thing for Dynabeads and all autobalancers on a motorcycle. I think this is exactly why your BMW doesn't come with autobalancers from the factory. It's not that they couldn't, it's really that we probably shouldn't. Factor in that Dynabeads is a sub-optimal autobalancer in many ways which exacerbates all of the issues with autobalancers (except a minor one which I noted above) and I'm convinced not to use them. Again, YMMV.

Simply put, autobalancers have bad transition states when not in steady-state and everything you do on a motorcycle, besides cruising at a constant highway speed, perturbs them considerably. The faster you go, the less susceptible an ideal autobalancer becomes and the longer it takes to settle back to steady-state. Worse still is that based on the above analysis I don't think Dynabeads can achieve state-state stability.

Only recently have fully nonlinear analyses of the autobalancer been undertaken. Based on a Lagrangian description of the equations of motion, steady-state bifurcation studies were carried out by Chung & Ro (1999) and by Adolfsson (2001), who identified regions in parameter space where stable rotating states, whether balanced or not, are possible. By moving to a rotating frame, Green et al. (2006a) carried out a detailed nonlinear investigation in the case of two balls, by computing both isolated branches of periodic solutions and those emanating from Hopf bifurcations of the equilibrium states. Significant regions of bistability were found between these steady and periodic states, chaotic states and states in which the balls rotate at a different angular frequency than the rotor. Furthermore, perturbations were shown to result in a large growth in the vibration before subsequent transient decay. This prompted the study by Green et al. (2006b), where the authors used the concept of pseudospectra to analyse this sensitivity to perturbation. It was found there that while the completely balanced state becomes increasingly stable for high rotation frequencies, it also becomes increasingly sensitive to perturbation, with an increasingly larger transient response before settling to the steady state.

This explains why the sport bike guys generally hate them, they are constantly perturbing the system and experiencing it's very negative effects. At high speeds the transient becomes very severe. Accelerate, turn or brake and the portion of the Dynabead mass that's acting as an autobalancer is working against you. That's not my opinion, that's a know. Exactly how and how bad depends on a lot of factors.

My Two Cents
Now that I have a better understanding of the mechanisms involved, I don't plan on using them. I don't think they are needed given quality rims, quality tires, and a good static balancer...or better still a good RoadForce balance. Don't keep the tires properly inflated, use poor quality tires or just get a bad lot, etc. and you can end up needing an autobalancer for your motorcycle, but those things are best mitigated through other methods IMHO.
Enjoy.

 

[Mike_Philippens]

Now that I have a better understanding of the mechanisms involved, I don't plan on using them. I don't think they are needed given quality rims, quality tires, and a good static balancer...or better still a good RoadForce balance.

I was asking myself the same thing: what is the problem these things try to solve? It seems that the Dynabeads sell in the US, and are next to unknown in Europe. Just a handfull of people know about them and just a couple of them use them over here.
I never had any problem with tyre vibration or whatever that would be solved with Dynabeads. I had a slight vibration in my front wheel, which was worn and cupped after 20.000km and up for a change. The vibration was very slight and only noticable when entering a slow corner. If you paid attention, because I let my mechanic ride the bike and he didn't notice it.

That's why I'm constantly asking myself - whenever I bump into the Dynabeads time and again - what is the problem that they're trying to solve? My conclusion: there is no problem. I don't see the point in investing money in something that should cure something that's not bothering me.

 

[gunderwood]

I was asking myself the same thing: what is the problem these things try to solve? It seems that the Dynabeads sell in the US, and are next to unknown in Europe. Just a handfull of people know about them and just a couple of them use them over here.
I never had any problem with tyre vibration or whatever that would be solved with Dynabeads. I had a slight vibration in my front wheel, which was worn and cupped after 20.000km and up for a change. The vibration was very slight and only noticable when entering a slow corner. If you paid attention, because I let my mechanic ride the bike and he didn't notice it.

That's why I'm constantly asking myself - whenever I bump into the Dynabeads time and again - what is the problem that they're trying to solve? My conclusion: there is no problem. I don't see the point in investing money in something that should cure something that's not bothering me.

The problems there, it's dynamic imbalance. I'm satisfied that Dynabeads at steady-state can in fact work...the problem is that they aren't needed IMHO, work sub-optimally which also increases the negative aspects when they are working but you don't want them to.

You hit the nail on the head when you said you never had a problem. Dynamic imbalance is always there and definitely real for our wheels/tires when rotating, but with the right parts and performing other things like static balance well, it should be minimized to that point of being a non-issue. If I came across a dynamic imbalance on my bike I wouldn't be searching for an autobalancer, I'd be trying to figure out why the dynamic imbalance is so bad in the first place. Odds are it's cheap tires or a bad lot.

 

[gunderwood]

Consider this...

The whole point of a suspension is to keep the tire in contact with the road so that you have maximum traction; ride quality is a distance second IMHO. Imbalance resists this and causes a loss of traction. Where do you need maximum traction the most? When you're cruising down the highway at steady-state speeds or when you are accelerating, braking or turning? Emergency maneuvers?

As I sort of stated in the analysis post, IMHO that's why autobalancers aren't commonly found and don't come from the factory. They provide the best balance when you least need it and absolutely make things worse when you need every last bit of balance (which in our case is maximum traction).

That being said, perhaps an active-balancer could have some benefits, but I doubt it considering the added rotational weight and un-sprung mass. It seems not only easier, but better, finding ways to avoid dynamic imbalance (Cg shifting due to rotational forces) when possible, than to seek out an autobalancer on a motorcycle.

 

[wzellwzell@yahoo.com]

I use Rosary Beads in all my tires

If I did this, I would be struck by lightning for sure.

 

[Mike_Philippens]

You hit the nail on the head when you said you never had a problem. Dynamic imbalance is always there and definitely real for our wheels/tires when rotating, but with the right parts and performing other things like static balance well, it should be minimized to that point of being a non-issue.

It may be there, but - as you said - with the right components, it's next to a non-issue and/or we're used to it.

But I still find it amazing that this looks like a big thing in the US and in Europe it's virtually unknown. If I'd ask around at the biggest biking forum in Holland, I'd get a response from the technically minded folks. They follow everything and are bound to have heard from it, but the average rider wouldn't have.

 

[N0ZR]

Why dynabeads?

So far I haven't read the reasons for the high interest in Dynabeads. May I venture a guess that it's because they can be sourced locally and installed with no expensive tools and adapters? The need for costly rear wheel adapters to static balance a wheel makes testing Dynabeads (or any plastic BBs for that matter) tempting. My local dealer thought I'd walked in from Mars when I asked him if he had a rear wheel adapter to fit my R1150R so I could balance the wheel. He said he didn't but could "research" it.

I'm gonna give 'em (beads) a try.

 

[dadayama]

They are snake oil like it or not.

I've put 16,000 miles and five states on this snake oil... can't tell you if they work or not... all i can say is there has been no problems with wheel balancing....

And i guess i could have perfectly balanced rims and my two sets of tires have also been perfectly balanced.... or maybe i just don't notice when i cruising down the road at 75 mph or 30 mph that there is an imbalance... all of the above could be true...

oh well...

while all those who argue about snake oil... i'm going riding

Pedro in OKC, OK

 

[Ken F]

Gunderwood, thanks for taking the time to research this and bring your craft into the discussion! It was facinating, and I learned a lot. I really appreciate your efforts!

Ken

 

[jeffd]

I had them put in the last set of tires I had mounted, never used them before. I had the dealer leave the old weights on the rims. Ran that way for a week then removed the old weights. I could not tell the difference in the ride. Just a simple test that worked for me. Next set of tires will be getting the beads.
Jeff

 

[tommcgee]

Summary -- and round and round we go, so to speak

- The beads worked for me.

- The beads didn't work for me.

- The beads clogged my valve stems.

- The beads didn't clog my valve stems.

- The beads are snake oil.

- The beads are magic.

- Here's the scientific sounding bull hooey in favor of the beads.

- Here's the scientific sounding bull hooey opposed to the beads.

 

[MotorradMike]

- The beads worked for me.

- The beads didn't work for me.

- The beads clogged my valve stems.

- The beads didn't clog my valve stems.

- The beads are snake oil.

- The beads are magic.

- Here's the scientific sounding bull hooey in favor of the beads.

- Here's the scientific sounding bull hooey opposed to the beads.

I hear you Tom. I'm tired of it too.
You have to admit though, that gunderwood made a really good effort to analyze the issue and present it from an unbiased Engineering point of view.
I haven't yet understood everything he posted but I haven't given up either.
Thanks gunderwood.

 

[scott.lambert]

That was beautiful gunderwood...

Now, if I could just get your opinion on these motor oils...

 

[beemer01]

Thanks Gunderwood -

Excellent and in-depth analysis.

 

[billy walker]

Many, many views on Dynabeads... pretty high readership for something people can't decide whether they do the job or their on the black magic side of life.

 

[chasmrider]

where would you put dyna beads in a tire with an inner tube?

 

[lmo1131]

where would you put dyna beads in a tire with an inner tube?

Im guessing that it might take a while to get enough of them through that tiny little hole in the valve stem...

 

[junkjohn]

where would you put dyna beads in a tire with an inner tube?

I know were my grandfather would tell me to put them.

 

[lkchris]

Traditional tire balancing is a fairly labor intensive process--that means it's expensive.

If General Motors/Ford/Chrysler/Toyota/BMW/Mercedes/VW/Porsche/etc. could save some production expense by throwing in a few beads, they'd do it, don't you think?

They'd do it if it worked, that is.