Re: ShopTalk: shaft flex v.s. frequency

[Dave Tutelman]

At 11:04 PM 12/28/02 -0500, Mark A Patton wrote:

I posted a thought on this a while ago on SpineTalk that questioned if we should really be looking at expansion and compression values of separate shaft walls located 180* from each other. (view this as a plane where we take into account 2 compression values located 180* apart as well as 2 expansion values located 180* apart).

So far so good.

I snipped some conversation from it below. Remember a lot of this is thought and I am looking for insight.

As shafts are hollow, we must presume there is a possibility that each
wall of the shaft could act differently. ...

For a shaft to have equal freqs at 180* to each other, the sum of the
resistance to expansion of Wall A and the resistance to compression of
Wall B must equal the resistance to compression of Wall A and the
resistance to expansion of Wall B.

Lets assign arbitrary some values to aid in this with:

                 Expansion          Compression

Wall A       6                        7
Wall B       3                        4

and 2 other walls at 90* to the original walls
Wall C       5                        6
Wall D       4                        5

Uh oh! Here's the problem!

There is no reason to expect that Wall A will behave differently in compression and tension (what you call "expansion"). Steel changes length exactly the same in compression and tension. Composites behave almost the same; those that have any difference at all are usually a tiny bit stiffer in tension than compression, and not enough to matter unless the spine is HUGE.

So, as Alan said:

* One side of the shaft may be stiffer or more flexible than another side, but it is the same in compression and tension.
* The plane (inside the shaft) of zero compression/tension moves toward the stiffer wall, giving more material (to resist bending) on the more flexible side -- so the net stiffness is the same on either side of that plane. By the way, that is called the "neutral plane" or "neutral axis".

That is why the bend is the same in the 180*-separated directions.

I have looked around on the web for some tutorials to illustrate this. The best I was able to come up with is from another sports-engineering hobby, bicycle design. Check out http://www.princeton.edu/~humcomp/bikes/design/desi_63.htm and the next few slides in the series.

Hope this helps.
DaveT