Mavic introduces wheel with compression spokes

Luns Tee wrote:
In article ,
Luns Tee wrote:
I believe that the latter happens, and that lateral stiffness
of the rim restrains the radially loaded section against this deflection.
In the radially affected region, the rim isn't allowed to deflect
laterally as much as it needs to to keep the ~2:1 tension ratio it
started with - the lateral force from the rim causes the left side
spokes to lose more tension, and the right side spokes less, than if
the rim were laterally flexible. The spokes outside the radially load
affected zone are what support the rim to provide this force, and they
get pushed the opposite way: with the left side spokes there
experiencing an increase in tension, and the right side spokes
decreasing.

The question of magnitudes is still open, but this is
where I think an FEA could be very valuable. I'm looking into whether
I can drum up access to FEA software, or better yet, someone familiar
with using it.

I managed to find an FE model of a bicycle wheel in MATLAB
written by Eric Soroos about 12 years ago. Interestingly, it had popped
up in a discussion here as the last post in a thread, where Jim
Papodopoulos was saying pretty much the same things as I did in my
previous post. The code for solving the FE is credited to G. Miller, and
is used as part of a structural mechanics course at U. Washington - I
will guess that Eric's wheel model was connected to a class he was
taking there at the time, and not purely in response to discussions in
RBT.

I've taken Eric's model, and modified it slightly. His was
for a 3-cross wheel, but I've made it radial so as not to confuse things
with effects from lacing. I also reduced the dish somewhat - the
original model had flanges at 2.5" and 0.5" away from the rim plane -
I've made the spacings 2" and 1". I haven't verified the numbers for
bending moment of the rim, but the numbers used are given as being for
an MA-40 rim, with 32 2.0mm steel spokes.

The effect at the very bottom of the wheel are as I expected:
the reduction in spoke tension from wheel loading is not in the 2:1
ratio of the wheel dish. The ratio is closer to 4:3. This means that
under pure radial loading of the wheel, the left side spokes do go slack
before the right side.

As has been mentioned, having thinner left side spokes would
help this. Halving their sectional area to match the 2:1 dish would
eliminate lateral effects from radial loading and increase by about
30% the vertical load needed to make left spokes go slack.

-Luns

when you're ready, can you post a link? it would be good to check it out.

-snip-
Luns Tee wrote:
I've made the spacings 2" and 1". I haven't verified the numbers for
bending moment of the rim, but the numbers used are given as being for
an MA-40 rim, with 32 2.0mm steel spokes.
-snip-

" two inches"
" one inch"
" 2.0mm"

As an aside, wouldn't it make sense to use either all inches or all CGS?
Do you commonly work in inches? Just curious.

--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

In article ,
A Muzi wrote:
-snip-
Luns Tee wrote:
I've made the spacings 2" and 1". I haven't verified the numbers for
bending moment of the rim, but the numbers used are given as being for
an MA-40 rim, with 32 2.0mm steel spokes.
-snip-

" two inches"
" one inch"
" 2.0mm"

As an aside, wouldn't it make sense to use either all inches or all CGS?
Do you commonly work in inches? Just curious.

I generally dislike using inch measures, and avoid them whenever
I can. However the wheel model as I received it implemented everything
in inches, and I wasn't about to re-work all the dimensions in it to
SI for the hell of it. I see no more harm in referring to the spokes
as 2.0mm than referring to people's height using feet or distances of
miles - while it's a different unit for the same dimension, it's also
a different scale, between which the ratios aren't necessarily useful.
I think people identify with 2.0mm as a spoke diameter better than
0.078740".

I'll give all the dimensions in furlongs next time.

-Luns

-snip-
Luns Tee wrote:
I've made the spacings 2" and 1". I haven't verified the numbers for
bending moment of the rim, but the numbers used are given as being for
an MA-40 rim, with 32 2.0mm steel spokes.
-snip-

A Muzi wrote:
" two inches"
" one inch"
" 2.0mm"
As an aside, wouldn't it make sense to use either all inches or all CGS?
Do you commonly work in inches? Just curious.

Luns Tee wrote:
I generally dislike using inch measures, and avoid them whenever
I can. However the wheel model as I received it implemented everything
in inches, and I wasn't about to re-work all the dimensions in it to
SI for the hell of it. I see no more harm in referring to the spokes
as 2.0mm than referring to people's height using feet or distances of
miles - while it's a different unit for the same dimension, it's also
a different scale, between which the ratios aren't necessarily useful.
I think people identify with 2.0mm as a spoke diameter better than
0.078740".
I'll give all the dimensions in furlongs next time.


I wasn't carping, I just see inches so infrequently it caught my eye.
--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971

In article ,
Luns Tee wrote:
Consider a related experiment: moving the weight vertically
by a small distance, restraining it against lateral motion, and see
what happens. The lengths of the two lines will change by that
distance times the cosines of their angles to vertical. Assuming the
same spring constant for both lines, the change in tensions will also
be proportional to the cosines. The lateral component of these tension
changes is just the sine of the lines' angles times the tension changes.

For the angles present in a wheel, the cosines are effectively
1, while the sines are on the order of 2:1. The lateral component of
the change in force from the two sides does not balance, being at about
this 2:1 ratio. The difference is supported by whatever lateral
restraint held the motion vertical. Without that restraint, the
vertex moves laterally.

It occurs to me that the same reasnong applies to purely lateral
loads. The lengths (hence tensions) now change with the sines relative
to vertical, while the vertical components of the tensions change with
the cosines. A purely lateral motion of the rim results in an
imbalance of vertical forces. If this imbalance isn't restrained - and
the imbalance is of the same sin*cos as before - then there must be a
vertical motion associated with the lateral load, just as we have a
horizontal motion resulting from vertical loads.

-Luns

jim beam writes:

Luns Tee wrote:

I managed to find an FE model of a bicycle wheel in MATLAB
written by Eric Soroos about 12 years ago. ...

when you're ready, can you post a link? it would be good to check it out.

Adding the Matlab model would be useful. Or just email it to me.
I have Matlab.

--
Joe Riel

On Saturday, June 30, 2007 at 6:45:23 PM UTC-7, JoeRiel wrote:
jim beam writes:

Luns Tee wrote:

I managed to find an FE model of a bicycle wheel in MATLAB
written by Eric Soroos about 12 years ago. ...

when you're ready, can you post a link? it would be good to check it out.

Adding the Matlab model would be useful. Or just email it to me.
I have Matlab.

I don't see in Google groups' archives what would have been my original reply to this - perhaps it never made it out - but I'll try here to replenish the breadcrumb trail, and walk it a little further.

Eric's model was easily found with a google search back in the day, but no longer being online, is harder to find now. The matlab model that I started from was at

http://www2.ce.washington.edu/~soroos/matlab/index.html

While Eric's UW account this long since expired, thankfully it can be retrieved from the wayback machine.

In the end, I did two things with Eric's model. The first was to verify the effects of having thinner NDS spokes as I'd previously discussed here with Joe Riel. I won't repeat that discussion except to say that the FEA confirmed the hand analysis. I will add though, informed by this analysis, all the rear wheels I've built or helped build, since then have DT revolution or Sapim Laser spokes on the left side, and Sapim Strong spokes on their right (the equivalent DT Alpine being NLA).

The other thing I did at the time was to look into the effects of prestress in the structure. Eric's FEA model, as with Jobst's, ignored the effect of spoke tension beyond assuming that pretensioning allows compression. When a spoke is carrying significant tension, moving the spoke's endpoints such the direction of the spoke changes, will change the forces at the endpoint not just axially along the spoke, but also laterally from the change in pull angle. The same applies to compression in the rim.

In essence, the previous FEA's assume that a weight hanging on a string sees a vertical stiffness provided by the string, but zero resistance to lateral displacements. I'd essentially modified Eric's model to account for the pretension of the string, making it into a proper model of a pendulum.

Accounting for prestress gives a model that captures buckling of the rim, but I found two things that puzzled me which I'd wanted to dig into further before reporting anything but life got in the way and that digging never happened. IIRC, the first thing I found was that spoke tensions needed to elastically buckle an MA-2 would have been something like 5-10x normal spoke tension. I was hoping to find something happening closer to typical tensions to fit into Jobst's notion of what a rim can bear, but it didn't quite seem to fit.

The other odd thing that I remember was that the mode for buckling at this tension appeared to not be the usual taco (n=2) shape, but was a trilobular (n=3) mode instead (three cycles instead of two of going to the left, to the right, and back again).

My work sat there in limbo, with my primary doubt being in the numbers I was using for the second moments of the rim. I believe these numbers were from Eric's model, in turn originally from Jobst, but I had nothing further to verify them against.

That's where things stood until last night, when I stumbled across work done by Matthew Ford for his PhD at NWU. I haven't yet given his thesis a proper reading, but he does show figures of the different buckling modes, including both the taco, and the trilobular mode I'd observed. He also seems to describe the same phenomenon of going straight to the n=3 mode, and discusses why only n=2 ever shows up in practice.

There's more to Matthew's work most of which I won't try to summarize except to let his thesis speak for itself, but he did also provide an excellent website of his FEA wheel model. You can play with spoke pattern, hub geometry, rim stiffnesses (including several rim models based on actual measurement) and loading, and the page will generate plots of spoke tension, rim deformation, and other results.

Play with it at:

https://bicyclewheel.info/wheel-simulator/


-Luns