Quote:
Originally Posted by fe1rx
Needing a distraction while waiting for my new front springs I decided to investigate the OE anti-roll bars.
My plan is to start out with the OE anti-roll bars because just the spring change will result in a significant increase in roll stiffness. Also, I have no data to support a decision to change the bars. So while waiting for my new front springs to arrive, I decided to collect some data on the OE bars. That means more measuring and more graphs.
Having an actual front bar stiffness measurement allows me to construct and validate a simple mathematical model of the bar. The usefulness of this is that, if it works, will be to allow me to estimate the stiffness of other bars that I may consider but not have the opportunity to measure. The mathematical model is based on these assumptions:
1) The arms of the bar are much stiffer than the torsion section, so all significant deflection in the bar occurs due to twisting of the torsion section (clearly not valid for the rear bar, but looks reasonable for the front bar).
2) The bar is formed from tubular material with minimal material removal at any section, so every section has approximately the same cross sectional area (possible because the bar is hollow).
As a first approximation, the cross sectional area was assumed to equal the cross section of the bar at the pin holes (assuming no hole was drilled), because the lug is formed by fully flattening the tube end.
The critical dimensions of the OE front bar are shown below:
Attachment 1010214
The bar can be simplified for analysis purpose as follows by eliminating the tapered sections.
Attachment 1010215
The stiffness of the bar follows from these assumptions and this geometry and is within 4% of the measured stiffness. By adjusting the assumed constant cross sectional area appropriately the model has been made to match the measured data:
Attachment 1010216
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The reason the calculated vs measured stiffness is within 4%, is just pure luck, thanks to one mistake calulating the value of
J .
I bow to your excellent SAE quality write up, with excellent images to convey your thoughts ... one of the best write-ups I have encountered. But, we need to talk about some swaybar tech. In calculating the twist, you used J = pi r^4/4, but the correct value is pi r^4/2. So you have stiffened the calculated stiffness by a factor of 2. But even so, you were still close to the rate of the bench test, which the Puhn equation is based on. We ran ito this on the Mazdaspeed6 forum, where the measured rate was about 1/2 the calculated rate (you would have the same issue with the proper J used) :
mazdaspeed forum, Phate, sway bar rate calc'n vs measured value Lower on this page is Phate's bench test set-up.
What we found was at the load we tested at (250 lbs on a 414 lb/in bar) we found the bar deflected as a rigid body in the oem ~stiff rubber bushings. Phate measured the bar motion next to the support bushings, and determined the effect at the bar ends. This was about 50% of the measured displacement during the test! This was noted on the top of the next page.
I came up with an imperical correction factor to be applied to the Puhn results to account for oem bushing deflection: Kpuhn/R^ 1.35, based on just one data point.
R= span between bar end holes / span between bushing centers. In our case, R^1.35=2, for 50% of the Puhn stiffness.
Note that urethane bushings are stiffer, but not tested. And, it could be at higher loads the stiffness increases toward the Puhn "no bushing" calc'n. On my old GT6, that I built for SCCA DP + trip dcoe Webers, I built the adjustable rear bar, and made pivot bushings for the front and rear out of split aluminum, grease with never-seeze ... no squeaks, no friction, no deflection.
Finally, you must think of the difference between the Bench Test / Puhn formula, and being in a corner. The Formula reflects a single wheel hit on the road, where the center of the bar is at about 1/2 the bar twist angle. In a corner, the bench test displacement is split between the lever going up on the outer side, and down on the inside by the same amount. This means the center of the bar has no rotation. Bottom line is you multiply the Puhn/bench rate by 2X to get the stable corner rate.
BTW, how I got here? Someone on Phate's Mazdaspeed thread that I was working on, offered a link to this site where actual bench testing was also happening. That's when I saw the "J" error, and noticed the oem bushings being used, like we did.
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