The problem of shimmy explained

jim beam writes:

dvt wrote:
Similar comments to above. In addition, how would an equally dished
wheel be less prone to shimmy? I believe it has been discussed on this
newsgroup that dishing *increases* the lateral stiffness of a wheel,

that's not right. increasing dish, [reducing angle of the spokes with
the rim plane] reduces lateral stiffness.

For a given flange spacing, dishing a wheel increases its lateral
stiffness. Note that while half the spokes are reduced in bracing angle,
the other half are increased, and the effect of the larger angle dominates.


--
Joe Riel

On Mon, 17 Jul 2006 21:33:33 -0700, jim beam
wrote:

jur wrote:
jim beam Wrote:
jur wrote:
If I assume for a moment you are familiar with control theory, then
you
would understand the meaning of the phrase that the nutation pole is
dominant in the loop. Basically it means that it dictates the overall
behaviour. Think not of it terms of cause and effect, but of
participants. If spinning wheels did not have the tendency towards
nutation, where would be no shimmy. Exactly as in placing your hands
loosely on the bars. This causes such a massive amount of damping
that
the nutation pole is no longer dominant. It's still there, but has no
dominant effect on behaviour any longer. Undamped, nutation poles
have
to be taken into account.
if they are of a frequency that "feeds" a natural frame/wheel harmonic,
yes. but that's the whole point - a system where there is no harmonic
is a stable system, nutation poles be damned.
Not so. My simplest simulation has only nutation poles and unity gain
feedback, and it is unstable. No other poles. Nix. Nada. Frame flex not
required.

but we're talking manifestation! practical reality is that shimmy can't
propagate from microscopic unless it has the freedom to do so, and a
resonant frame is that freedom.

What caused this "death wobble" shimmy?

http://video.google.com/videoplay?do...2751&q=toolbag

Doesn't seem like there was enough time for an ocillation to develop.

R Brickston Wrote:

What caused this "death wobble" shimmy?

http://tinyurl.com/kxbmg

Doesn't seem like there was enough time for an ocillation to develop.Nice example of death wobble.

Along the lines of my hypothesis, death wobble requires the following:

firm grip on the bars - check.
a sudden steering movement to cause a sideways displacement of body
mass - check. (bike came down with front wheel at an angle)
rider's body gets thrown from side to side, jelly-like, through saddle
padding compliance or body compliance - check.
Clearly the instability grows exponentially in that vid.


--
jur

In article ,
jur wrote:

Tim McNamara Wrote:
No, you've just failed to demonstrate your theory as of yet. I will
enjoy reading your proofs in hopes of learning something new. I'm
looking forward to your discussion with Jobst on this topic, since
both
of you like to adopt the authoritative tone to quell any disagreement.

You are unfortunately making the common error of believing and
defending
your idea before it's been proven. As others have pointed out, we
have
seen dozens of guys turn up in the newsgroup shouting "eureka!" only
to
have reinvented the wheel or to have gotten the wrong end of the stick
entirely. So you will have to forgive us if we adopt a wait-and-see
attitude towards your breakthrough theory. Saviors come and go all
the
time.

You are assuming an awful lot here. If you thought that i haven't
studied all posts here and elsewhere with *close* scrutiny to see if
anyone at all has hit on the explanation, well you're just plain wrong.
Because of my keen interest in this particular subject, I have studied
everything I have come accross which is by now an awful lot.

Not added anthing new? Again, you most certainly have not understood at
all - you are merely exhibiting you own ignorance and inability to grasp
a new concept.

(And I know it is Brandt not Brand, just a typo.)

Are you at any time going to make a positive contribution?

Here's my contribution:

Scrutiny
Scru"ti*ny (?), n. [L. scrutinium, fr. scrutari to search
carefuly, originally, to search even to the rags, fr.
scruta trash, trumpery; perhaps akin to E. shred: cf. AS.
scrudnian to make scrutiny.]

1. Close examination; minute inspection; critical
observation.

--
Michael Press

jur wrote:
Wrote:

Is there a reason that you are calling the oscillation
of the axis of rotation "nutation" rather than "precession"?
This paper discusses the difference between the 2:

http://faculty.ifmo.ru/butikov/Applets/Gyroscope.pdf

Nutation could be called the high frequency behaviour of precession.

Here is another link showing the equations of motion:

http://www.gyroscopes.org/math2.asp

When I watch those videos of shimmy or death-wobble,
I see an oscillation of the axis of rotation of the front
wheel, about its normal un-wobbly position. I don't see
a second-order oscillation about that first oscillation.
Of course, the second order effect could be happening
and just be too small for me to see, but then it would
not be the primary component of speed wobble.

When one does the experiment of hanging a spinning bicycle
wheel by one end of the horizontal axle (a common experiment
in physics labs), a gravitational torque is exerted by the
weight of the wheel about the supported end of the axle,
which causes a slow precession of the system about the
vertical axis:
http://hyperphysics.phy-astr.gsu.edu/HBASE/rotv2.html
If then the axle is given a slight whack, the axle should
oscillate about the first-order precession. This is nutation
and is torque free since (after the initial whack) there is
no torque driving the nutation. This is the example
at the bottom of http://www.gyroscopes.org/math2.asp.

However, it is not the case of the shimmying bicycle wheel.
The wheel axle is supported at both fork ends and the
force at the axle end is the weight of the bike pushing
down. If the bike+rider are perfectly centered over the
wheel, there is no torque about the hub center. However,
if the bike+rider lean slightly, there is a torque, exerted
at the axle ends, which causes the wheel to lean about
the forward/back axis ("roll" in aviation terms). Due to
the steering geometry of bikes, as the wheel undergoes
roll, it also yaws a little.

We're all familiar with this, it's how you turn a bike:
as the rider leans, the gravity force tilts the bike
to one side and exerts a torque on the wheel, which
causes the axis of rotation of the wheel to change
direction.
http://hyperphysics.phy-astr.gsu.edu/hbase/bike.html
This is not torque-free.

In speed wobble, hands on or off, the system enters
an oscillation where some part of the bike+rider tips
from side to side rapidly (at least the head tube and bars),
causing a torque on the axle which rapidly changes the
axis of rotation of the front wheel. I believe it would be
more accurate to call this a torque-driven precession
than a torque-free nutation. Although the frequency
is much faster than we are used to see examples of
precession, there is no absolute rule that precession
is low frequency and nutation is high.

Ben

I wrote:

We're all familiar with this, it's how you turn a bike:
as the rider leans, the gravity force tilts the bike
to one side and exerts a torque on the wheel, which
causes the axis of rotation of the wheel to change
direction.
http://hyperphysics.phy-astr.gsu.edu/hbase/bike.html
This is not torque-free.

Just for clarity, I think that page is oversimplified
because it neglects that the lean is initiated by
countersteering. Countersteering has been discussed
here many times, and an example is shown he
http://ist-socrates.berkeley.edu/~fajans/Teaching/Steering.htm
But in this context of shimmy, the main point is that
leaning a bike exerts a torque on the front wheel
to change the direction of the axis of rotation.

Ben

Ben: I think you mis-understood the concept of torque-free nutation.
"Torque-free" is only some wording someone has introduced to indicate
that a spinning body's spin axis can move without a torque being
exerted. It is not a case that if there is torque, then it can't be
nutation. Rather, a spinning body will not only precess when torqued,
but it will also wobble because a spinning body is an underdamped
second order system. Somone has seen fit to call this
wobbling/oscillation by a separate name, nutation.

"Second order" as used in this context indicates that there is a
double-derivative in the differential equation describing the system.
See the Damping entry in wikipedia.


--
jur

jur wrote:
dvt Wrote:
jur wrote:
'here' (http://en.wikipedia.org/wiki/Speed_wobble) is my explanation
in words.

I think you're going down the wrong path. I haven't read it all, but
here are a few paragraphs from that link that need some attention,
IMO.

I'm not sure what you mean by wrong path. I already have a complete
explanation in mathematical terms which explains everything and takes
properly into account nutation which is dominant. Surely you can't mean
my explanation is wrong after all that?

Surely you aren't assuming I will accept your math without seeing it?

This will clearly be shown once I post the model on the wiki entry.

Here's my attempt to help: quit spending so much time on these fora and
put it towards publishing your math. From what I've seen, you're not
improving your credibility by your participation here.

| The back wheel will usually be flexing the most since 1) it is not
as
| stiff as the other components; 2) it is under rider load, so the
lower
| vertical spokes' tension is reduced, and with a dished wheel the
| non-drive side spokes are under even less tension; and 3) it is
subject
| to a lever action. It requires only a small amount of sideways
flexing
| to account for the head tube movement.

You're saying that the rear wheel stiffness depends on local spoke
tension? I don't agree.

| All these predict that a stiffer wheel, and an equally dished wheel
| will be less prone to shimmy. Double-butted spokes should be more
prone
| to shimmy, and likewise heavier riders will reduce bottom spoke
tension,
| increasing shimmy.

Similar comments to above. In addition, how would an equally dished
wheel be less prone to shimmy? I believe it has been discussed on this
newsgroup that dishing *increases* the lateral stiffness of a wheel,
which would push the resonant frequency of the system upwards.

With stiffness of the
wheel I mean the ability of the axle to _twist_ away from the null, not
to be displaced sideways _along_ the axis. This mode of stiffness is
perhaps different to the lateral one you mean?

Yes, I think you are talking about a different stiffness than I was.
I'll assume that your "stiffness" refers to the axle rotating away from
the perpendicular to the plane of the rim. That's a tough sentence to
read; I hope you can parse it. Anyway, my "stiffness" refers to the axle
translating axially while remaining perpendicular to the plane of the rim.

Neither stiffness will be affected by spoke tension unless the spoke(s)
go slack. You should scratch that from your wiki entry. The effect of
dish on torsional stiffness is not easily determined; I'd need some
proof before I accept your statement as published on the wiki.

Have you done the math for the caster effect?

I have only shown that it is not required for instabilty;

Again, take the time that you're spending on this forum and apply it to
your math. I haven't seen your proof that the caster effect is not
required, so I can't comment.

--
Dave
dvt at psu dot edu

Everyone confesses that exertion which brings out all the powers of body
and mind is the best thing for us; but most people do all they can to
get rid of it, and as a general rule nobody does much more than
circumstances drive them to do. -Harriet Beecher Stowe, abolitionist and
novelist (1811-1896)

jur wrote:
"Second order" as used in this context indicates that there is a
double-derivative in the differential equation describing the system.
See the Damping entry in wikipedia.

By that definition, any resonance is second order.

--
Dave
dvt at psu dot edu

Everyone confesses that exertion which brings out all the powers of body
and mind is the best thing for us; but most people do all they can to
get rid of it, and as a general rule nobody does much more than
circumstances drive them to do. -Harriet Beecher Stowe, abolitionist and
novelist (1811-1896)

In article ,
jur wrote:

jim beam Wrote:

jur wrote:
If I assume for a moment you are familiar with control theory,
then you would understand the meaning of the phrase that the
nutation pole is dominant in the loop. Basically it means that it
dictates the overall behaviour. Think not of it terms of cause
and effect, but of participants. If spinning wheels did not have
the tendency towards nutation, where would be no shimmy. Exactly
as in placing your hands loosely on the bars. This causes such a
massive amount of damping that the nutation pole is no longer
dominant. It's still there, but has no dominant effect on
behaviour any longer. Undamped, nutation poles have to be taken
into account.

if they are of a frequency that "feeds" a natural frame/wheel
harmonic, yes. but that's the whole point - a system where there
is no harmonic is a stable system, nutation poles be damned.

Not so. My simplest simulation has only nutation poles and unity gain
feedback, and it is unstable. No other poles. Nix. Nada. Frame flex
not required.

Then every bike would shimmy all the time when ridden hands-off, and
that just doesn't happen.

You're still making claims without offering proof, giving the appearance
of self-inflicted local excavation. I'm still hoping your idea has
merit, don't blow it this early in the discussion.