The problem of shimmy explained

jur wrote:
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.

The bigger issue is that you're using an analogy
(the gyroscope, or the bicycle wheel hanging by
one end of the axle) whose precession/nutation
behavior is quite unlike the actual precession of
the front wheel during speed wobble. Recall that
the front wheel's axle is rigidly fixed to a non-spinning
part, the bicycle, which is not true of the gyroscope,
hanging wheel, or the Earth.

I can't evaluate whether this makes any difference
to your model because the wikipedia entry contains
only analogies and no mathematics.

Mark wrote:
Werehatrack wrote:

On Mon, 17 Jul 2006 16:02:13 -0700, Mark
wrote:


Put your knee against the top tube. It's that simple. Almost forgot
this weekend, and almost went into the trees. Then I remembered, and
the shimmy stopped instantly (I was surprised how fast).


Sometimes, merely loosening the grip and transferring the rider's
weight to the seat will stop it.

Could well be, but it's hard to convince one'sself to try it when the
shimmy has gotten big.

Mark

that's the truth. particularly when it shouldn't be happening in the
first place, and is comparatively easy to design out of a frame.

Tim McNamara wrote:
In article ,
jim beam 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.

| It doesn't happen on xyz bike: Not all bikes have enough
| springyness to provide the necessary feedback for nutation to be
| amplified, which explains why many riders have never experienced
| it. Or they have not reached that critical speed where the
| nutation Q factor is high enough, or where the nutation frequency
| matches the natural frequency of any springy mass.

How does the nutation get "amplified?" What role does the
"springyness" of a bike play in that amplification?
that's a good question, particularly in view of the op's dismissal of
frame stiffness as a factor.

He has since partially recanted in one response to Mark Hickey, noting
that a flexible frame can make matters worse. As of yet, however, jur's
theory doesn't explain all the well-known observed phenomena of shimmy.
for example, speed-dependent onset of shimmy; from his description of
his model thus far, shimmy would occur at all speeds if the steering is
undamped by the rider (e.g. riding no handed).

indeed!


| 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.
correct, unless the spokes are slack, wheel stiffness is completely
unaffected by spoke tension.

In case anybody wonders, the relationship between spoke tension and
lateral stiffness has been measured:

http://www.sheldonbrown.com/rinard/wheel/index.htm

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

which would push the resonant frequency of the system upwards.
a stiffer wheel does indeed push the resonant frequency up. that's
why my experiment with stiffer drive side spokes worked in tuning
shimmy out of shimmy-prone frame.

As I recall, that was with thicker spokes, right?

yes, thicker = stiffer.


Have you done the math for the caster effect?

From jur's response to dvt, he has not yet included this in his theory.

Joe Riel wrote:
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.

maybe we have different understandings of the word "dish"? first, the
non-drive side spacing is not increased by any manufacturer i've ever
seen, presumably because those spokes get too slack and there are
practical limits to that. second, the stiffness is asymmetric, so it's
inherently unstable.

jur Wrote:
See here

http://69.16.211.161/showthread.php?...44#post2776844

Please do not post here, go the the link.You've never posted on -The Aussie Thread - on Bike Forums? Too good for
us?


--
531Aussie

jim beam writes:

Joe Riel wrote:
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.

maybe we have different understandings of the word "dish"? first, the
non-drive side spacing is not increased by any manufacturer i've ever
seen, presumably because those spokes get too slack and there are
practical limits to that. second, the stiffness is asymmetric, so it's
inherently unstable.

Dish is the difference of the distances from the centerplane of the
rim to each of the flanges. It's pretty easy to show that, for a
given flange spacing, the lateral stiffness is at a local minimum when
the dish is zero.

I'll have to compute the effect of moving the nondrive flange on
the required lateral force to make a spoke go slack.


--
Joe Riel

a écrit:

The bigger issue is that you're using an analogy
(the gyroscope, or the bicycle wheel hanging by
one end of the axle) whose precession/nutation
behavior is quite unlike the actual precession of
the front wheel during speed wobble.

This is a naive observation, but I'll throw it in anyway.

Holding a spinning wheel by either axle end, a lateral torque on the axle
causes a tilting of the plane of the wheel perpendicular to the axis of the
applied torque. That's as expected. Attempting to apply torque to the axle
while keeping it in plane requires a torque to be applied at right angles to
the first.

However, the if the axle ends aren't restrained in a plane, they can
describe circles, since sinusoidal motion in one axis produces sinusoidal
motion in the other. That's just a verbal description of precession.

Try it: hold a spinning wheel in a vertical plane, then move the axle ends
in circles so that the axis of the axle describes a cone. You'll quickly hit
the natural precession mode. It's often struck me how similar this feels to
a shimmy.

James Thomson