Spoke tension meter

[Luns Tee]

In article <[email protected]>,
<[email protected]> wrote:
>If a spoke elbow is bent on a mandrel, is the idea that the
>inside curve is neutral in terms of stress, while the center
>is stretched into some tension (t) and the outside curve
>into more tension (T)?
>
> _______________/|
> / | |
> T . . . | |
> / t __________| |
> | . 0 m m m \|
> | . |m m m
> | . |m m m = bent on mandrel
> | . | T = more residual tension
> | . | t = less residual tension
> 0 = no residual tension

This can't happen as you've drawn it: a tension can't exist in
isolation without something to pull against. It can either pull
against a matching compression (in which the lines of force for the
tension meet the lines of force of the compression tangentially), or
it can be supported by tension downstream, in the lengths of the spoke
to either side of this bend.
This diagram is plausible only if just the right amount of
tension is applied to the spoke (but not labelled), but there's no
reason whatsoever for this to be the case. The assertion that the neutral
axis as at the spoke to mandrel interface is completely without grounds,
though with an applied tension, it is closer to the mandrel than what
would otherwise be the neutral axis.


>While if a spoke elbow is just bent with no mandrel, then
>the no-stress line is in the center (0), the inside curve
>goes into some compression (c) and the outside curve goes
>into some tension (t)?
>
> _______________/|
> / | |
> t . . . | |
> / 0 __________| |
> | . c \|
> | . |
> | . | no mandrel used
> | . | t = some residual tension
> | . | 0 = no residual tension
> c - some residual compression
>
>If these ASCII diagrams do show where and what kind of
>residual stress occurs, where should these elbows start to
>break--inside or outside of the elbow?

This figure is accurate for the spoke while it's in the machine
creating the bend, with the machine pushing outwards on the inside of
the bend, and inwards at two points on the outside of the bend where it
transitions to straight spoke. This will *not* be the case when those
forces are released - the tension and compression that you've shown
will act to straighten the spoke, and will do so until they encounter
something to prevent further straightening.

As the spoke straightens out, all the material outside the
neutral axis reduces in tension, and material on the inside increases,
with the amount of change proportional to the distance from the neutral
axis. If the original bend is only an elastic bend, then the tension and
compression that are there to begin with are also proportional, and this
straightening happens until there's nothing left (the spoke is
straight).

However, with the spoke bent to yield, the outermost layer of
metal stretches, and/or the innermost (inside the bend, not inside the
thickness of the spoke) layer crushes, so the tension/compression
present at these layers is not proportional, having been relaxed by the
yield. Layers closer to the neutral axis which did not reach yield, are
still proportional.
Now, as the bend relaxes, the outermost layer relaxes to no
tension, and the innermost layer reaches no compression before the
unyielded layers do. The unyielded layers still try to straighten the
spoke, but now the outermost layer goes into compression, and material
inside the bend goes into tension.

So, a spoke as it sits in the box from the maker, actually has
_compression_ on the outside and _tension+ on the inside of the bend!
Then, between these layers, closer to the neutral axis, these reverse
to the tension outside/compression inside that you've drawn. The neutral
axis aside, there's actually two other lines along which there is no
tension or compression and only shear. These lines diverge away from
the central axis and exit the surface of the spoke as the bend
transitions to the straight sections.

-Luns

 

[Luns Tee]

In article <[email protected]>,
Luns Tee <[email protected]> wrote:
>The neutral axis aside, there's actually two other lines along which
>there is no tension or compression and only shear. These lines
>diverge away from the central axis and exit the surface of the spoke
>as the bend transitions to the straight sections.

Actually, I retract the last sentance of this: on further
thought, it's not so clear to me how the lines terminate, the
transition from uniform bend to uniformly straight spoke not being a
simple one. Still, within the unform section of the bend, what I'd
said still holds.

-Luns

 

[jim beam]

Luns Tee wrote:
> In article <[email protected]>,
> <[email protected]> wrote:
>
>>If a spoke elbow is bent on a mandrel, is the idea that the
>>inside curve is neutral in terms of stress, while the center
>>is stretched into some tension (t) and the outside curve
>>into more tension (T)?
>>
>> _______________/|
>> / | |
>> T . . . | |
>> / t __________| |
>>| . 0 m m m \|
>>| . |m m m
>>| . |m m m = bent on mandrel
>>| . | T = more residual tension
>>| . | t = less residual tension
>> 0 = no residual tension
>
>
> This can't happen as you've drawn it: a tension can't exist in
> isolation without something to pull against.

if you mean during deformation, the spoke head is held tight - there is
an impression in it opposite the mandrel marking.

if you mean after deformation, residual stress occurs where yielding is
least, so you'll get more nearer the inside of the elbow [the part that
was held against the neutral plane of the mandrel] than on the outside
where gross yielding occurred.


> It can either pull
> against a matching compression (in which the lines of force for the
> tension meet the lines of force of the compression tangentially), or
> it can be supported by tension downstream, in the lengths of the spoke
> to either side of this bend.
> This diagram is plausible only if just the right amount of
> tension is applied to the spoke (but not labelled), but there's no
> reason whatsoever for this to be the case. The assertion that the neutral
> axis as at the spoke to mandrel interface is completely without grounds,
> though with an applied tension, it is closer to the mandrel than what
> would otherwise be the neutral axis.

it is with applied tension, and the mandrel /is/ the neutral axis. if
you substitute t's for d's, or deformation, in carl's diagram, you get a
better idea of what's going on.

>
>
>
>>While if a spoke elbow is just bent with no mandrel, then
>>the no-stress line is in the center (0), the inside curve
>>goes into some compression (c) and the outside curve goes
>>into some tension (t)?
>>
>> _______________/|
>> / | |
>> t . . . | |
>> / 0 __________| |
>>| . c \|
>>| . |
>>| . | no mandrel used
>>| . | t = some residual tension
>>| . | 0 = no residual tension
>> c - some residual compression
>>
>>If these ASCII diagrams do show where and what kind of
>>residual stress occurs, where should these elbows start to
>>break--inside or outside of the elbow?
>
>
> This figure is accurate for the spoke while it's in the machine
> creating the bend, with the machine pushing outwards on the inside of
> the bend, and inwards at two points on the outside of the bend where it
> transitions to straight spoke. This will *not* be the case when those
> forces are released - the tension and compression that you've shown
> will act to straighten the spoke, and will do so until they encounter
> something to prevent further straightening.

hmm, what can i do to explain the nature of deformation? the material
yields. when it yields, it yields to an equilibrium of tension vs.
force requred for further deformation. when applied force is removed,
it springs back, so there is no stress remaining in the material unless
there is local residual where some regions are in close proximity to
regions that yielded where they themselves were no sufficiently stressed
to do so.

>
> As the spoke straightens out, all the material outside the
> neutral axis reduces in tension, and material on the inside increases,
> with the amount of change proportional to the distance from the neutral
> axis. If the original bend is only an elastic bend, then the tension and
> compression that are there to begin with are also proportional, and this
> straightening happens until there's nothing left (the spoke is
> straight).
>
> However, with the spoke bent to yield, the outermost layer of
> metal stretches, and/or the innermost (inside the bend, not inside the
> thickness of the spoke) layer crushes,

not when the neutral plane is at the mandrel interface - the swhole
material, apart from an infinitely thin layer at the interface itself,
experiences a degree of tension proportional to the radial distance from it.

> so the tension/compression
> present at these layers is not proportional, having been relaxed by the
> yield.

but they're not wholly relaxed by the yield. when you look at a
stress/strain graph, you have the hookes law region, and the
yielding/work hardening region on top of that. when you relax, you
follow a hooks law line back down again - the materil does /not/ yield
to zero.

> Layers closer to the neutral axis which did not reach yield, are
> still proportional.
> Now, as the bend relaxes, the outermost layer relaxes to no
> tension, and the innermost layer reaches no compression before the
> unyielded layers do. The unyielded layers still try to straighten the
> spoke, but now the outermost layer goes into compression, and material
> inside the bend goes into tension.

again, this is assuming an internal neutral plane - which is not the case.

>
> So, a spoke as it sits in the box from the maker, actually has
> _compression_ on the outside and _tension+ on the inside of the bend!

no. see above. and of course, that's using the /gross/ assumption that
the manufacturer is unaware of residual stress mitigation and has not
performed any such operation.

> Then, between these layers, closer to the neutral axis, these reverse
> to the tension outside/compression inside that you've drawn. The neutral
> axis aside, there's actually two other lines along which there is no
> tension or compression and only shear. These lines diverge away from
> the central axis and exit the surface of the spoke as the bend
> transitions to the straight sections.
>
> -Luns
>
another way to think about this is to consider the manufacturer of a
close bound coil spring, an extension spring. ask yourself how it would
be possible to coil the wire so that the coils spring back to touch each
other and hold tight like this:

http://www1.mscdirect.com/CGI/NNSRIT?PARTPG=NNLMK32&PMPXNO=3319304

the answer is to coil under sufficient tension that the neutral plane is
not just on the inside edge of the material, but actualy /outside/ it.
that way, the springback is both on the internal and external surfaces
of the curve, [correctly angled of course,] so it assumes this form.
think about it. if you need convincing, try coiling a piece of wire
around a mandrel and see how close you can bind the spring using just
bending force.

 

[[email protected]]

On Fri, 17 Jun 2005 19:20:34 -0700, jim beam
<[email protected]> wrote:

[snip]

>guess which one [intentionally] leads to yielding in
>modern engines where the head bolt initial torque is 98% of yield???
>you /do/ know intentional yielding is why you can't re-use many modern
>cylinder head bolts, right?

[snip]

Dear Jim,

Can you take a moment to explain this "intentional yielding"
and what sounds like torquing until the cylinder head bolt
is quivering on the edge of stretching?

A quick Google for "intentional yielding" left me staring at
a handful of entries about sex, Mennonites, Chinese fiction,
and Christian neurology:

http://www.google.com/search?as_q="...s_occt=any&as_dt=i&as_sitesearch=&safe=images

Carl Fogel

 

[jim beam]

[email protected] wrote:
> On Fri, 17 Jun 2005 19:20:34 -0700, jim beam
> <[email protected]> wrote:
>
> [snip]
>
>
>>guess which one [intentionally] leads to yielding in
>>modern engines where the head bolt initial torque is 98% of yield???
>>you /do/ know intentional yielding is why you can't re-use many modern
>>cylinder head bolts, right?
>
>
> [snip]
>
> Dear Jim,
>
> Can you take a moment to explain this "intentional yielding"
> and what sounds like torquing until the cylinder head bolt
> is quivering on the edge of stretching?
>
> A quick Google for "intentional yielding" left me staring at
> a handful of entries about sex, Mennonites, Chinese fiction,
> and Christian neurology:
>
> http://www.google.com/search?as_q="...s_occt=any&as_dt=i&as_sitesearch=&safe=images
>
> Carl Fogel

for things like car cylinder heads, especially the light alloy ones on
the euro-style & japanese cars, the consistency of the head bolt torque
is very important for reliability. especially when striving to have a
head gasket that doesn't need to be re-torqued or replaced every few
thousand miles. the way to do this is to have a head bolt torqued at or
close to yield. when the bolt /does/ yield, as it does the first time
the engine reaches operating temperature, the resulting tensile force
applied to the head across every bolt is pretty much identical. bolts
that are not torqued to yield are subject to considerable torque
scatter, especially on any rebuild, so some bolts are much looser than
others, leading eventually to gasket leakage & failure.

 

[[email protected]]

On Fri, 17 Jun 2005 23:36:33 +0000 (UTC),
[email protected] (Luns Tee) wrote:

[snip]

> So, a spoke as it sits in the box from the maker, actually has
>_compression_ on the outside and _tension+ on the inside of the bend!

>Then, between these layers, closer to the neutral axis, these reverse
>to the tension outside/compression inside that you've drawn.

>The neutral
>axis aside, there's actually two other lines along which there is no
>tension or compression and only shear. These lines diverge away from
>the central axis and exit the surface of the spoke as the bend
>transitions to the straight sections.
>
>-Luns

Dear Luns,

Is this roughly what you have in mind?

Compression on the outside elbow curve is matched with
tension underneath, exiting toward the surface.

On the other side of the neutral center, the inside of the
spoke elbow has tension on the surface matched with
compression underneath, exiting again.

_______________/|
/ / ||
/ / ||
c t . . . ||
/ / 0 ____ ||
|_/ . c __\_______||
| . | t \|
| . | | spoke sitting in box
| . \| t = residual tension
| . | 0 = no residual tension
| . | c - residual compression

Sorry about the quality of my etch-a-sketch artwork.

Carl Fogel

 

[Michael Press]

In article <[email protected]>,
[email protected] (Luns Tee) wrote:

> In article <[email protected]>,
> <[email protected]> wrote:
> >If a spoke elbow is bent on a mandrel, is the idea that the
> >inside curve is neutral in terms of stress, while the center
> >is stretched into some tension (t) and the outside curve
> >into more tension (T)?
> >
> > _______________/|
> > / | |
> > T . . . | |
> > / t __________| |
> > | . 0 m m m \|
> > | . |m m m
> > | . |m m m = bent on mandrel
> > | . | T = more residual tension
> > | . | t = less residual tension
> > 0 = no residual tension
>
> This can't happen as you've drawn it: a tension can't exist in
> isolation without something to pull against. It can either pull
> against a matching compression (in which the lines of force for the
> tension meet the lines of force of the compression tangentially), or
> it can be supported by tension downstream, in the lengths of the spoke
> to either side of this bend.
> This diagram is plausible only if just the right amount of
> tension is applied to the spoke (but not labelled), but there's no
> reason whatsoever for this to be the case. The assertion that the neutral
> axis as at the spoke to mandrel interface is completely without grounds,
> though with an applied tension, it is closer to the mandrel than what
> would otherwise be the neutral axis.
>
>
> >While if a spoke elbow is just bent with no mandrel, then
> >the no-stress line is in the center (0), the inside curve
> >goes into some compression (c) and the outside curve goes
> >into some tension (t)?
> >
> > _______________/|
> > / | |
> > t . . . | |
> > / 0 __________| |
> > | . c \|
> > | . |
> > | . | no mandrel used
> > | . | t = some residual tension
> > | . | 0 = no residual tension
> > c - some residual compression
> >
> >If these ASCII diagrams do show where and what kind of
> >residual stress occurs, where should these elbows start to
> >break--inside or outside of the elbow?
>
> This figure is accurate for the spoke while it's in the machine
> creating the bend, with the machine pushing outwards on the inside of
> the bend, and inwards at two points on the outside of the bend where it
> transitions to straight spoke. This will *not* be the case when those
> forces are released - the tension and compression that you've shown
> will act to straighten the spoke, and will do so until they encounter
> something to prevent further straightening.
>
> As the spoke straightens out, all the material outside the
> neutral axis reduces in tension, and material on the inside increases,
> with the amount of change proportional to the distance from the neutral
> axis. If the original bend is only an elastic bend, then the tension and
> compression that are there to begin with are also proportional, and this
> straightening happens until there's nothing left (the spoke is
> straight).
>
> However, with the spoke bent to yield, the outermost layer of
> metal stretches, and/or the innermost (inside the bend, not inside the
> thickness of the spoke) layer crushes, so the tension/compression
> present at these layers is not proportional, having been relaxed by the
> yield. Layers closer to the neutral axis which did not reach yield, are
> still proportional.
> Now, as the bend relaxes, the outermost layer relaxes to no
> tension, and the innermost layer reaches no compression before the
> unyielded layers do. The unyielded layers still try to straighten the
> spoke, but now the outermost layer goes into compression, and material
> inside the bend goes into tension.
>
> So, a spoke as it sits in the box from the maker, actually has
> _compression_ on the outside and _tension+ on the inside of the bend!
> Then, between these layers, closer to the neutral axis, these reverse
> to the tension outside/compression inside that you've drawn. The neutral
> axis aside, there's actually two other lines along which there is no
> tension or compression and only shear. These lines diverge away from
> the central axis and exit the surface of the spoke as the bend
> transitions to the straight sections.
>
> -Luns

Kowabunga, Batman! You put that very well indeed. Upon reading it
the first time I could see exactly what is going on. Congratulate
yourself for the most excellent discourse.

May we have this in the FAQ?

--
Michael Press

 

[Luns Tee]

In article <[email protected]>,
<[email protected]> wrote:
>Compression on the outside elbow curve is matched with
>tension underneath, exiting toward the surface.
>
>On the other side of the neutral center, the inside of the
>spoke elbow has tension on the surface matched with
>compression underneath, exiting again.

Close, but the notion of matching isn't as strong as your
statement - the compression and tension outside the neutral axis
don't necessarily match, and ditto with the stresses inside the
neutral axis (but these mismatches will match). The first moment
(stress times the distance from the neutral axis the stress is at) for
everything outside the neutral axis does sum up to match the sum for
everything inside the neutral axis, but these sums aren't necessarily
zero.

I should also mention, the compression on the outside of
the bend and the tension on the inside of the bend are not necessarily
symmetric. Compressive yield and tensile yield aren't symmetric, and any
tension applied to the spoke during bending will also add a bias
(essentially shifting the neutral axis more to the inside of the bend).


> _______________/|
> / / ||
> / / ||
> c t . . . ||
> / / 0 ____ ||
> |_/ . c __\_______||
> | . | t \|
> | . | | spoke sitting in box
> | . \| t = residual tension
> | . | 0 = no residual tension
> | . | c - residual compression
>
>Sorry about the quality of my etch-a-sketch artwork.

Excellent etch-a-sketch! The internal tension line should
extend somewhat farther so it terminates roughly opposite the internal
compression line, but otherwise, this is an accurate picture.

-Luns

 

[jim beam]

[email protected] wrote:
> On Fri, 17 Jun 2005 23:36:33 +0000 (UTC),
> [email protected] (Luns Tee) wrote:
>
> [snip]
>
>
>> So, a spoke as it sits in the box from the maker, actually has
>>_compression_ on the outside and _tension+ on the inside of the bend!
>
>
>>Then, between these layers, closer to the neutral axis, these reverse
>>to the tension outside/compression inside that you've drawn.
>
>
>>The neutral
>>axis aside, there's actually two other lines along which there is no
>>tension or compression and only shear. These lines diverge away from
>>the central axis and exit the surface of the spoke as the bend
>>transitions to the straight sections.
>>
>>-Luns
>
>
> Dear Luns,
>
> Is this roughly what you have in mind?
>
> Compression on the outside elbow curve is matched with
> tension underneath, exiting toward the surface.
>
> On the other side of the neutral center, the inside of the
> spoke elbow has tension on the surface matched with
> compression underneath, exiting again.
>
> _______________/|
> / / ||
> / / ||
> c t . . . ||
> / / 0 ____ ||
> |_/ . c __\_______||
> | . | t \|
> | . | | spoke sitting in box
> | . \| t = residual tension
> | . | 0 = no residual tension
> | . | c - residual compression
>
> Sorry about the quality of my etch-a-sketch artwork.
>
> Carl Fogel

but that still shows the neutral plane inside the spoke. that's not the
case we see with mandrel bent spokes. your first diagram had the right
idea.

 

[jim beam]

Luns Tee wrote:
> In article <[email protected]>,
> <[email protected]> wrote:
>
>>Compression on the outside elbow curve is matched with
>>tension underneath, exiting toward the surface.
>>
>>On the other side of the neutral center, the inside of the
>>spoke elbow has tension on the surface matched with
>>compression underneath, exiting again.
>
>
> Close, but the notion of matching isn't as strong as your
> statement - the compression and tension outside the neutral axis
> don't necessarily match, and ditto with the stresses inside the
> neutral axis (but these mismatches will match). The first moment
> (stress times the distance from the neutral axis the stress is at) for
> everything outside the neutral axis does sum up to match the sum for
> everything inside the neutral axis, but these sums aren't necessarily
> zero.
>
> I should also mention, the compression on the outside of
> the bend and the tension on the inside of the bend are not necessarily
> symmetric. Compressive yield and tensile yield aren't symmetric, and any
> tension applied to the spoke during bending will also add a bias
> (essentially shifting the neutral axis more to the inside of the bend).

we're getting there... that's right, and if you apply sufficient
tension, the "bias" of the neutral plane is outside the spoke entirely.
spokes are tensioned so that the neutral plane is the surface of the
mandrel.

>
>
>
>> _______________/|
>> / / ||
>> / / ||
>> c t . . . ||
>> / / 0 ____ ||
>>|_/ . c __\_______||
>>| . | t \|
>>| . | | spoke sitting in box
>>| . \| t = residual tension
>>| . | 0 = no residual tension
>>| . | c - residual compression
>>
>>Sorry about the quality of my etch-a-sketch artwork.
>
>
> Excellent etch-a-sketch! The internal tension line should
> extend somewhat farther so it terminates roughly opposite the internal
> compression line, but otherwise, this is an accurate picture.
>
> -Luns

 

[[email protected]]

On Sat, 18 Jun 2005 06:56:49 -0700, jim beam
<[email protected]> wrote:

>[email protected] wrote:
>> On Fri, 17 Jun 2005 23:36:33 +0000 (UTC),
>> [email protected] (Luns Tee) wrote:
>>
>> [snip]
>>
>>
>>> So, a spoke as it sits in the box from the maker, actually has
>>>_compression_ on the outside and _tension+ on the inside of the bend!
>>
>>
>>>Then, between these layers, closer to the neutral axis, these reverse
>>>to the tension outside/compression inside that you've drawn.
>>
>>
>>>The neutral
>>>axis aside, there's actually two other lines along which there is no
>>>tension or compression and only shear. These lines diverge away from
>>>the central axis and exit the surface of the spoke as the bend
>>>transitions to the straight sections.
>>>
>>>-Luns
>>
>>
>> Dear Luns,
>>
>> Is this roughly what you have in mind?
>>
>> Compression on the outside elbow curve is matched with
>> tension underneath, exiting toward the surface.
>>
>> On the other side of the neutral center, the inside of the
>> spoke elbow has tension on the surface matched with
>> compression underneath, exiting again.
>>
>> _______________/|
>> / / ||
>> / / ||
>> c t . . . ||
>> / / 0 ____ ||
>> |_/ . c __\_______||
>> | . | t \|
>> | . | | spoke sitting in box
>> | . \| t = residual tension
>> | . | 0 = no residual tension
>> | . | c - residual compression
>>
>> Sorry about the quality of my etch-a-sketch artwork.
>>
>> Carl Fogel
>
>but that still shows the neutral plane inside the spoke. that's not the
>case we see with mandrel bent spokes. your first diagram had the right
>idea.

Dear Jim,

Here's a rough version of what Luns thinks is getting close
to the residual stresses in a spoke after forming:

_______________/|
/ / ||
/ / ||
c t . . . ||
/ / 0 ____ ||
|_/ . c __\_______||
| . | t \|
| . | | spoke after forming
| . \| t = residual tension
| . | 0 = no residual tension
| . | c - residual compression

Are there two kinds of spokes, those bent with and without a
mandrel?

If so, is the sketch above roughly what you expect with a
spoke bent without a mandrel?

And is this anywhere near what you expect from a spoke bent
on a mandrel? (Sorry if I've got the compression and tension
on the wrong side or in the wrong order.)

_______________/|
/ / \ \ ||
/ / / / ||
c c / / ||
/ / / / ||
| / t t _________||
| / / / 0 \|
|/ / / | spoke after forming
| _/ / | t = residual tension
| / | 0 = no residual tension
|__/ | c - residual compression

I'm not arguing with your or Luns, just trying to get an
idea of what's supposed to be going on in the elbow.

If anyone has a link to a 3-D computer graphic of a spoke
elbow, it would be nice, since my etch-a-sketch doesn't show
the sides.

Looking at my curved finger from the side doesn't seem to
help. The outer bend appears to be in tension (skin taut),
and the inner bend appears to be in compression (skin
wrinkled).

Since this seems to the opposite of what you're both saying,
I conclude that yielding articulated fingers may not be the
same as a stainless steel wire. (Some of us reach
conclusions more slowly than others.)

Carl Fogel

 

[jim beam]

[email protected] wrote:
> On Sat, 18 Jun 2005 06:56:49 -0700, jim beam
> <[email protected]> wrote:
>
>
>>[email protected] wrote:
>>
>>>On Fri, 17 Jun 2005 23:36:33 +0000 (UTC),
>>>[email protected] (Luns Tee) wrote:
>>>
>>>[snip]
>>>
>>>
>>>
>>>> So, a spoke as it sits in the box from the maker, actually has
>>>>_compression_ on the outside and _tension+ on the inside of the bend!
>>>
>>>
>>>>Then, between these layers, closer to the neutral axis, these reverse
>>>>to the tension outside/compression inside that you've drawn.
>>>
>>>
>>>>The neutral
>>>>axis aside, there's actually two other lines along which there is no
>>>>tension or compression and only shear. These lines diverge away from
>>>>the central axis and exit the surface of the spoke as the bend
>>>>transitions to the straight sections.
>>>>
>>>>-Luns
>>>
>>>
>>>Dear Luns,
>>>
>>>Is this roughly what you have in mind?
>>>
>>>Compression on the outside elbow curve is matched with
>>>tension underneath, exiting toward the surface.
>>>
>>>On the other side of the neutral center, the inside of the
>>>spoke elbow has tension on the surface matched with
>>>compression underneath, exiting again.
>>>
>>> _______________/|
>>> / / ||
>>> / / ||
>>> c t . . . ||
>>> / / 0 ____ ||
>>> |_/ . c __\_______||
>>> | . | t \|
>>> | . | | spoke sitting in box
>>> | . \| t = residual tension
>>> | . | 0 = no residual tension
>>> | . | c - residual compression
>>>
>>>Sorry about the quality of my etch-a-sketch artwork.
>>>
>>>Carl Fogel
>>
>>but that still shows the neutral plane inside the spoke. that's not the
>>case we see with mandrel bent spokes. your first diagram had the right
>>idea.
>
>
> Dear Jim,
>
> Here's a rough version of what Luns thinks is getting close
> to the residual stresses in a spoke after forming:
>
> _______________/|
> / / ||
> / / ||
> c t . . . ||
> / / 0 ____ ||
> |_/ . c __\_______||
> | . | t \|
> | . | | spoke after forming
> | . \| t = residual tension
> | . | 0 = no residual tension
> | . | c - residual compression
>
> Are there two kinds of spokes, those bent with and without a
> mandrel?
>
> If so, is the sketch above roughly what you expect with a
> spoke bent without a mandrel?
>
> And is this anywhere near what you expect from a spoke bent
> on a mandrel? (Sorry if I've got the compression and tension
> on the wrong side or in the wrong order.)
>
> _______________/|
> / / \ \ ||
> / / / / ||
> c c / / ||
> / / / / ||
> | / t t _________||
> | / / / 0 \|
> |/ / / | spoke after forming
> | _/ / | t = residual tension
> | / | 0 = no residual tension
> |__/ | c - residual compression
>
> I'm not arguing with your or Luns, just trying to get an
> idea of what's supposed to be going on in the elbow.

that's much closer.

>
> If anyone has a link to a 3-D computer graphic of a spoke
> elbow, it would be nice, since my etch-a-sketch doesn't show
> the sides.
>
> Looking at my curved finger from the side doesn't seem to
> help. The outer bend appears to be in tension (skin taut),
> and the inner bend appears to be in compression (skin
> wrinkled).
>
> Since this seems to the opposite of what you're both saying,
> I conclude that yielding articulated fingers may not be the
> same as a stainless steel wire. (Some of us reach
> conclusions more slowly than others.)
>
> Carl Fogel

 

[Luns Tee]

In article <[email protected]>,
<[email protected]> wrote:
> / / \ \ ||
> / / / / ||
> c c / / ||
> / / / / ||
> | / t t _________||
> | / / / 0 \|
> |/ / / | spoke after forming
> | _/ / | t = residual tension
> | / | 0 = no residual tension
> |__/ | c - residual compression
>

This isn't possible. Draw a line diagonally through the elbow -
if there's compression on the top and tension on the bottom, these
stresses will push the bend to be even more acute than what it is. Where
you have the 0 will be put into compression by the tension.

-Luns

 

[Luns Tee]

In article <[email protected]>,
jim beam <[email protected]> wrote:
>> the bend and the tension on the inside of the bend are not necessarily
>> symmetric. Compressive yield and tensile yield aren't symmetric, and any
>> tension applied to the spoke during bending will also add a bias
>> (essentially shifting the neutral axis more to the inside of the bend).
>
>we're getting there... that's right, and if you apply sufficient
>tension, the "bias" of the neutral plane is outside the spoke entirely.
> spokes are tensioned so that the neutral plane is the surface of the
>mandrel.

There is absolutely no reason for the neutral axis to be at the
inner surface at the spoke. While it is possible to apply just the right
tension to do so, there is absolutely no reason to do it, and the
neutral axis doesn't stay there after the tension is released in
removing the spoke from the forming machine, either.

-Luns

 

[Luns Tee]

In article <[email protected]>,
<[email protected]> wrote:
>Looking at my curved finger from the side doesn't seem to
>help. The outer bend appears to be in tension (skin taut),
>and the inner bend appears to be in compression (skin
>wrinkled).

Your finger has muscles in it to cause the bend while the skin
you're observing is trying feebly to resist it. This is the opposite of
a spoke which has no muscles inside of it, only a central core that
wants to return to straight like your skin is doing. The spoke remains
bent only by virtue of the yielded material on the outside and inside of
the bend.
Imagine your finger had its muscles on the outside instead of
your skin.

-Luns

 

[jim beam]

Luns Tee wrote:
> In article <[email protected]>,
> jim beam <[email protected]> wrote:
>
>>>the bend and the tension on the inside of the bend are not necessarily
>>>symmetric. Compressive yield and tensile yield aren't symmetric, and any
>>>tension applied to the spoke during bending will also add a bias
>>>(essentially shifting the neutral axis more to the inside of the bend).
>>
>>we're getting there... that's right, and if you apply sufficient
>>tension, the "bias" of the neutral plane is outside the spoke entirely.
>> spokes are tensioned so that the neutral plane is the surface of the
>>mandrel.
>
>
> There is absolutely no reason for the neutral axis to be at the
> inner surface at the spoke. While it is possible to apply just the right
> tension to do so, there is absolutely no reason to do it,

there is. depending on the lie of the spoke and the build of the wheel,
you can have a bending moment where it's tensile on the inside of the
elbow. in that situation, [and assuming of course that the manufacturer
doesn't address residual stress], to have a residual tensile stress on
the inside of the elbow, as would be the case with an internal neutral
plane, is undesirable.

> and the
> neutral axis doesn't stay there after the tension is released in
> removing the spoke from the forming machine, either.

that's true, but what goes on in the deformation process is what matters.

>
> -Luns

 

[jim beam]

Luns Tee wrote:
> In article <[email protected]>,
> <[email protected]> wrote:
>
>> / / \ \ ||
>> / / / / ||
>> c c / / ||
>> / / / / ||
>>| / t t _________||
>>| / / / 0 \|
>>|/ / / | spoke after forming
>>| _/ / | t = residual tension
>>| / | 0 = no residual tension
>>|__/ | c - residual compression
>>
>
>
> This isn't possible. Draw a line diagonally through the elbow -
> if there's compression on the top and tension on the bottom, these
> stresses will push the bend to be even more acute than what it is. Where
> you have the 0 will be put into compression by the tension.
>
> -Luns
>
>
correct, and that's desirable, per my other post.

 

[Luns Tee]

In article <[email protected]>,
jim beam <[email protected]> wrote:
>Luns Tee wrote:
>> There is absolutely no reason for the neutral axis to be at the
>> inner surface at the spoke. While it is possible to apply just the right
>> tension to do so, there is absolutely no reason to do it,
>
>there is. depending on the lie of the spoke and the build of the wheel,
>you can have a bending moment where it's tensile on the inside of the
>elbow. in that situation, [and assuming of course that the manufacturer
>doesn't address residual stress], to have a residual tensile stress on
>the inside of the elbow, as would be the case with an internal neutral
>plane, is undesirable.

No, there isn't. If your goal is to eliminate the residual
tension at the inside of the bend, then the applied tension only needs
to be enough to prevent compressive yield during the forming. There is
no need to make the net stress there precisely zero, nor is there any
easy way to do so.

-Luns

 

[jim beam]

Luns Tee wrote:
> In article <[email protected]>,
> jim beam <[email protected]> wrote:
>
>>Luns Tee wrote:
>>
>>> There is absolutely no reason for the neutral axis to be at the
>>>inner surface at the spoke. While it is possible to apply just the right
>>>tension to do so, there is absolutely no reason to do it,
>>
>>there is. depending on the lie of the spoke and the build of the wheel,
>>you can have a bending moment where it's tensile on the inside of the
>>elbow. in that situation, [and assuming of course that the manufacturer
>>doesn't address residual stress], to have a residual tensile stress on
>>the inside of the elbow, as would be the case with an internal neutral
>>plane, is undesirable.
>
>
> No, there isn't. If your goal is to eliminate the residual
> tension at the inside of the bend, then the applied tension only needs
> to be enough to prevent compressive yield during the forming.

isn't this what we've been discussing? this is what use of the mandrel
does.

> There is
> no need to make the net stress there precisely zero, nor is there any
> easy way to do so.

the net for the spoke is always zero - it's local residual stress that's
hard to get to zero. but you /can/ get it down to an acceptible level
with a 1-2% additional yield.

>
> -Luns

 

[Luns Tee]

In article <[email protected]>,
jim beam <[email protected]> wrote:
>> No, there isn't. If your goal is to eliminate the residual
>> tension at the inside of the bend, then the applied tension only needs
>> to be enough to prevent compressive yield during the forming.
>
>isn't this what we've been discussing? this is what use of the mandrel
>does.

No, what we're discussing is your claim that the inner surface
of the spoke is a neutral axis. It is not. For it to be neutral, the
compressive stress there from bending must be exactly balanced by an
externally applied tension. To prevent the material from yielding
requres only enough tension to keep the net compression from reaching
yield: it can be anywhere in the elastic region, and not necessarily
the zero that you claim. There is no mechanism to make it zero, nor
is there any need for one.

Besides which, use of a mandrel (and the term is being used
very loosely in this discussion but I'll play along) does nothing to
make the inner spoke surface a neutral axis. For wire being wrapped
around a mandrel like a coil spring, this can happen only if tension is
being controlled precisely enough to precisely match the (untensioned)
wire feed rate to the surface speed of where the wire is being wound
onto. The hammer forming process used by DT looks absolutely nothing
like this. The length of wire involved - only a few mm spanning a
quarter of a turn - is so short that any concept of wire feed rate is
essentially impossible to control.

>> There is
>> no need to make the net stress there precisely zero, nor is there any
>> easy way to do so.
>
>the net for the spoke is always zero - it's local residual stress that's
>hard to get to zero. but you /can/ get it down to an acceptible level
>with a 1-2% additional yield.

Quit your squirming. You change your tune every time I point
out how something in what you've said is impossible. This has nothing to
do with net stress across the spoke, this is about the net effect of
all applied forces at the inner surface of the spoke where you seem to
believe a neutral axis exists. Besides, what you point out here also
contradicts your claim of the neutral axis being at the surface: zero
tensile/compressive stress (definition of neutral axis) at the
surface, and tension through the whole spoke outside of that, is not a
net of zero across the spoke.

-Luns