Well, here's my first attempt at using FEA (Finite Element Analysis) to try and put some real numbers to axle deflection. You may, or may not agree with how I did this, or the assumptions I made for the initial data. If someone else cares to tackle this project, send me your output data, and I'll be happy to post it if appropriate.

I'd also like to thank my friend and neighbor Mark, who owns the hardware and software used to do this analysis. He's an aero engineer who has fairly extensive experience using FEA software. Without him, this would not have happened.

Here's how I did it:

Kart and driver weigh 325 lbs. 55% of that is 178.75 lbs. I made the assumption that at maximum cornering force, 100% of the rear weight was on the outside tire. According to Steve O'Hara's data aquisition numbers, a kart generates about 2.5 Gs of cornering force. I multiplied 178.75 by 2.5 to get about 447 lbs of sideforce. So... the center of the contact patch is out 8" from the center of the outside axle bearing, and is 5.5" below the axle centerline. That's where the force vectors originate from.

Also... I restrained the axle in X,Y and Z on the outside axle bearing (to simulate an axle collar being outside the bearing), and I restrained the axle in the other bearing in Y and Z. The reason I did this is because my quick and dirty layout in Applied Structure assumed the structure between the axle bearings was rigid. If the axle was restrained in the X axis in both bearings, a tension would be induced between the 2 axle bearings (as the axle is deflected on the outside of the bearings), and that would influence the deflection that we're trying to analyze. I allowed free "roll" in the Y/x and Z/x axis (on both bearings) to simulate self aligning bearings. (sidenote: There aren't really "bearings" in the FEA software.... there are only points of support with parameters on how you restrain the part in the linear and roll axis)

Additionally, I rotated the force vectors 3 degrees (in the X/Y plane) as an approximate estimate of roll (due to chassis and tire deflection). This was a best guess on my part. I'm open to any ideas on this.

Since the force vectors are fairly straightforward (see drawing below), it was a fairly simple task to convert them to straight X/Y forces (using simple trig), with a moment calculated for shifting the force vectors to the end of the axle (or the 8" point, anyways).

Once this was done, Applied Structure did the rest.

Now the output from Applied Structure

The following output graphic is a GIF image that is 853x620 pixels. Applied Structure outputs only in HPGL or PostScript, and as is typical on a PC-based system; Postscript is a bit difficult to work with. Hence, I just did a simple conversion to GIF, without any resizing. You may need to scroll your browser window sideways or vertically to see the entire graphic (depending on what resolution you are running).

Please note: the rendering(s) that are shown represent the axle from the "far side" axle bearing to a point 8" out from the "near side" axle bearing. The point where the straight line intersects the "axle", is where the axle bearings are located. As you can plainly see, the axle deflects up between the bearings, and down outside the bearings.

As you will see in the text in the left window, the total displacement (deflection) at the "worst" point (this would at the "end" of our imaginary axle) is about .042

Rasna/Applied Structure output: 12k GIF, 853x620 pixel

As a final note, please realize that these numbers, (or my analysis procedure) are not necessarily THE answer to how much an axle deflects. Kart width, chassis stiffness, axle wall thickness, cornering forces, axle overhang, etc. etc. can, (and will), have an effect on what is actually happening.