Ron Ruff said:Quoted message said:Is this the thread? "I fixed a broken spoke!" It ran from Dec. 4 2006
through Jan. 8 2007.
http://groups.google.com/group/rec.bicycles.tech/browse_frm/thread/80...
That was the start I think, but there was a "summary" thread
afterwards that was a little easier to follow.
So I guess it is there, but I can't search for it. I can't search and
find any posts between mid Oct and late Jan.
I still have the text of the summary on my hard disk, so I shall append
it below FWIW and with no intention to spread rumours.
To the OP: the summary of the summary is that your spokes might have
broken because the elbows were at close to yield stress after the build.
But in theory that shouldn't have happened, since you were careful to
stress-relieve. I have no idea why they failed, but it is interesting to
know the details as broken spokes are not so common these days based on
what I read in RBT.
How much weight did you put on the wheels, and did you use a
tensiometer? If so what was the tension? If you can post pictures of the
broken spokes, especially closeups, we will enjoy poring over them. With
any luck someone who actually knows about these things will tell you
something useful.
Finally, the advice of Sapim not to correct the spoke line was mentioned
here before, and considered to lack credibility in the context of other
remarks from the same source saying things like if one spoke breaks you
need to replace them all, and you should never reuse hubs. It sounded
like they were just disclaiming everything.
************************************************************************
A recent thread entitled "I fixed a broken spoke" about various things
including stresses at spoke elbows got so long it starting disappearing
off the ends of people's newsreaders. But since some people are still
interested in it it was suggested I should do a summary.
I'll try to keep it as short I can. No attributions, but most of the
material is originally from either Jobst or jim beam. Any
misrepresentations are unintentional.
Stress and stress relief
------------------------
This is a picture of a spoke sitting in a hole in a hub flange.
sHHHHHH <--- Hub
sssssssssss
sHHHHHH s
s
<-d->s <--- Spoke
s
s
s
RIM
If you pull the spoke along its axis towards the rim either the spoke
bends a bit more at the elbow, or the spoke cuts into the body of the
hub, or a bit of both.
We'll consider the first possibility in isolation first, so assume for
now that the hub hole is not deformable at all (this is pretty much the
case for a steel hub).
In the diagram the perpendicular distance from the spoke to the hub
flange has been labelled <-d->. The longer this distance, the lower the
force required to bend the spoke. The product of F and d is called a
"moment".
As this distance approaches zero, the force required to bend the spoke
absolutely flush with the flange approaches the force that would be
required to stretch a spoke plastically-- a force that's significantly
higher than spoke tension in a finished bicycle wheel.
In other words, to achieve this situation:
sHHHHHH
ssssssss
sHHHHHHs
s
s
s
s
just by pulling on the spoke would take a LOT of force.
Suppose you pull on the spoke with a force that gradually increases from
zero up to about normal tension, corresponding with screwing up the
nipple as you build the wheel. As the spoke bends towards the hub the
distance "d" gets shorter, and it gets harder to bend the spoke. Soon
you reach an equilibrium position in which the applied force holds the
bend where it is, but is unable to make it any tighter.
This applied force will hold the outside of the bend at just about the
yield stress of the material-- after all it's just been yielding (i.e.
bending) and you haven't relaxed the force, so it will be kept at yield.
So the spoke will not be quite flush with the flange, but some distance
"d" from it. How big is "d" exactly? I don't know for sure, I should
work it out, it isn't hard, and it's an important detail.
If you rode away on the bike like that you would expect rapid fatigue at
the spoke elbows since steel, like many materials, doesn't last very
long if it's cycled (repeatedly tensioned and relaxed again) at a high
mean stress.
But if you pull on the spoke a bit harder still and let go of it again,
you can plastically stretch the outside of the elbow a little bit
further, with the result that when you relax that momentary overload,
the outside of the elbow is left at a much lower stress.
This improves the life of the wheel, and is called "mechanical stress
relief".
Hub deformation
---------------
We've all seen the indentations around the exit holes of used hubs, and
we know that hubs are often made of aluminium that is softer than the
stainless steel used for spokes.
So what if the elbow doesn't bend at all, but instead just digs itself
into the hub a bit as it's pulled flush to the flange by normal
tensioning, and perhaps by some overload applied deliberately during the
build?
When you take an old wheel apart, you can often tell which spokes were
"inbound" and which were "outbound" by the different elbow bends, which
implies that the elbows _did_ bend as they were pulled towards the rim.
But the picture is confused because many builders bend the elbows
manually with their thumb or a crank-arm (which takes relatively little
force to do because of the position and direction in which the force is
applied).
We have seen inbound and outbound spokes from one poster, who advocates
against premature elbow-thumbing, that showed a barely perceptible
difference in elbow angle.
Of course if the elbow doesn't bend, or the hub is too soft to support
the force required to hold a bend in the elbow, there's no reason to
believe that the outside of the elbow will remain at yield stress after
spoke tensioning.
Both spoke bending and hub deformation
--------------------------------------
As tension is gradually applied to the spoke, at first it starts to bend
a bit, but as the spoke's exit line approaches parallel to the force
line, the moment becomes too small for it to continue to bend, and the
spoke elbow is held at yield stress.
In this scenario, as the tension is increased further, the pressure on
the inside of the hub starts to deform the exit hole, and the spoke
continues to pull closer to the flange, not by bending but by cutting
into the hub slightly.
This reduces the distance "d" even further, which means that the stress
at the spoke elbow actually reduces, even though the applied force is
still growing slowly as we wind the nipple. The moment Fd gets smaller
because although F is increasing, d is reducing more rapidly. In other
words, as the pivot around which we're twisting the spoke deforms, the
spoke unbends a bit.
We said at the start that to pull the spoke completely flush to the
flange around a non-deformable pivot would take significantly more spoke
tension than we ever get in a bicycle wheel.
So one possibility is that the spoke doesn't end up completely flush.
Another is that hub-hole deformation allows the spoke to pull flush, and
a consequence of this is that the spoke elbow does not remain at yield
after tensioning. There may still be some stress at the elbow though--
how far the bend gets relaxed depends on the extent of each of these
effects.
Spoke Line Correction
---------------------
So far we've been talking about building a wheel by just putting the
spokes in and tightening them up, followed perhaps by some momentary
overload process to relieve bending stress at the elbow.
But many builders push the spokes towards the flange earlier in the
process with their thumbs or old crank arms. If the elbow angle can be
made just right before the spoke is tensioned, then it won't need to
bend during the build, and we can expect the spoke to lie flush to the
flange when we're finished without requiring either hub-hole deformation
or yield stress at the elbow.
But is it possible to get the angle just right? In theory, no, on the
grounds that you cannot bend the spoke further than flush (the flange is
in the way), and that after you bend it it's always going to bounce back
a little bit.
In practice I'm not so sure. If the spoke is still quite loose, it may
not be sitting in quite its final position in the hub hole. If you can
hinge it back a bit before bending it, it seems at least possible that
you should be able to exceed the angle of the flange.
Which is right?
---------------
We can be fairly sure that spoke tension cannot hold the bend at yield
for the small value of "d" implied by flushness, and therefore that if
the spoke really is truly flush when we've finished, the bend is no
longer at yield.
So is the spoke truly flush? How far away does it have to be for it to
be reasonable for normal spoke tension to hold the elbow at yield?
It's hard to say. Small differences in angles and lengths is all it
takes one way or the other. Furthermore the spoke may end up bent into a
kind of question-mark shape just where it exits the flange, meaning it
can lie flat a bit further away, requiring less tension to keep it
there, but making it look flush unless you inspect very carefully around
where it exits the hole. The tighter the radius of the question-mark's
hook, the more tension is required, although the geometry gets much more
complicated at this scale. Do we see hooks? What are their radii? It
would help to have a close look at a few wheels, especially ones that we
knew hadn't undergone manual spoke line correction, but even then it
would be hard to know exactly what to conclude.
A good argument against hub-hole deformation relaxing yield stress at
the elbow (or in any way mitigating the bending of the elbow) is that we
would expect any deformation of the hub to happen sooner rather than
later in the build process. As the wire first starts to sink into the
aluminium, the contact patch is a thin line on the surface of the spoke
which sinks in like a knife blade. But as more of the wire sinks in, the
size of the contact quickly grows, and the amount of compressed
aluminium pushing it back increases. By the time the spoke is getting
near the flange, it's already sunk in enough that the apparently soft
aluminium hub is effectively no longer deformable.
My own conclusion is that theory doesn't tell us for sure whether or not
the spoke elbow is kept at or close to yield by spoke tension. More
evidence is needed. Carl puts it best: "the spokes do whatever they do
regardless of our red herrings".
It also depends on the choice of components used, in particular the
length of the elbow shanks and the orientation of the hub holes, which
varies even between different recent hubs from the same manufacturer as
people have been discussing recently. The situation may be different in
different wheels.
We have good ancedotal evidence that temporarily overloading the spokes
after tensioning produces more durable wheels. We know that this process
would relieve tensile stress at the elbow if it were there, and that
that would improve fatigue life.
On the other hand the temporary overload may have other benefits. It may
be that it helps seat the spokes into the hub, it may just be that
temporarily underloading the spokes (a sideeffect of certain
temporary-overload procedures) takes out windup.
Or it may have no positive benefits at all. The anecdotal evidence it
does something useful is good, but as time goes by the components we buy
from the manufacturers change with quite significant differences in
materials, geometry and importantly surface finish which is known to be
highly significant in fatigue failure.
It's less clear how different processes of stress relieving could do any
harm, although I think mechanisms may have been suggested by which that
is possible. As far as I remember I think we're all pretty much agreed
that the "Mavic Method" is probably beneficial and unlikely to do any
harm.
"Residual stress"
-----------------
The bend stress that may exist at the spoke elbow after tensioning that
I've been describing is sometimes called "residual stress". I believe
this is the term used in Jobst's book _The Bicycle Wheel_.
This seems a reasonable thing to call it on the plain-English grounds
that it's residual (left-over after bending) and it's stress.
But the term has another technical sense to describe stresses inside a
material that remain after plastic bending and spring-back. When you
bend a wire, the material near the skin goes through bigger angle
changes than the stuff nearer the centre. After the wire springs back
(the bend bounces out a bit), you're left with the unyielded interior
pushing elastically against the yielded exterior.
Note that these stresses are compressive on the outside of the bend and
tensile on the inside, so if present in a spoke would actually mitigate
the tensile stress on the outside of the elbow that may remain after
bending.
The spoke-toasting experiment of Carl Fogel indicated that these
residual stresses are relieved at tensions below what you expect in a
normal wheel anyway.
But these are not the same "residual stresses" as the bend stress
remaining at the elbow that we've been talking about. However many of us
didn't realize that that was what we were talking about until quite late
in the day.
Is is correct to use the term "residual stress" for this bend stress
remaining at the elbow? I don't know, but I do know I promised Ed
Pirrero a 500-post flame war on the subject. So, gentlemen, in your own
time, start whenever you're ready.
Residual stress of a similar kind to that remaining after spring-back
may remain in spokes after fabrication, and here we get into the
descriptions of the fabrication process. It would seem that the
spoke-toasting is good evidence that these stresses, if present, are
relieved anyway by normal tensioning, but there are also arguments
people have made against that.
A simple test for presence of residual stress from fabrication is the
chloride test.
