Re: ShopTalk: shaft flex v.s. frequency

[Dave Tutelman]

At 11:56 AM 12/26/02 -0600, John Kaufman wrote:

Dave, thanks for your support!

Might I offer you the same heartfelt thanks.

It's not the FLO that
effects club performance it's the shaft being bent in something other than
it's weakest plane. When a shaft is bent a torque is generated which tries
to
rotate it into the weak plane. I assume the torque is a function of the
differential frequency and the amount of the bending force. I'm guessing at
this because I couldn't find it in a text book. Maybe Dave can help me.

I'm afraid I can't. That's my intuitive feel too, but I don't trust my intuition on things like this. (The equal-bend-both-ways shows the dangers of intuitive thinking here.) Any time I try to calculate anything using either vibration or bending torque, I find that the difference is trivial. The calcs show it taking a lot of spine (maybe 7-10cpm) before any effect could be noticeable. There's no way I can explain people noticing or feeling the effect of a 3cpm spine. But I know at least one anecdotal report of such.

BTW John, I'm with you on the non-utility of aligning very small spines. If a shaft has less than a 3cpm spine, I don't bother. And if it has more than 5cpm, I try to avoid that manufacturer in the future.

One last comment. Dave mentioned my "bowtie" plots. I must confess these
have always confused me. If I plot stiffness in grams per inch vs. angle and
use a polar plot to display the results I get a near perfect circle for
extremely uniform shafts. As the differential frequency gets larger the plot
turns into an oval or  ellipse. I don't understand the "Bowtie". It's a
ellipse with a constriction in the middle. In theory I don't think that
should happen. It think it should always be a pure ellipse. I never went
back and did a detailed study of the data to see why I got the distorted
ellipse. I guess I should generate a polar plot of the weird asymmetrical
1/2" aluminum shaft I mentioned above.

I have an explanation. But I got there the hard way.

First I computed "I" for a few non-circular sections to see if I could come up with a demonstrably non-elliptical pattern. Failed miserably. Did you know that the pattern for a square cross-section is a circle? Not productive for explaining bowties, but I learned or re-learned a lot.

Then I took a good look at your bowtie plot, and understood immediately why it's not an ellipse. You took out the origin and first 320 units of the R-axis; it is linear, but not proportional. That amplifies any difference in R, so the ellipse becomes a bowtie. If you re-plot it on polar coordinates starting at 0, you should get an ellipse.

Cheers!
DaveT