Roll Stiffness Evaluation

[Blake Hinsey]

We ended up with some bad ARB calculations, so I have decided to go back and evaluate them myself. However I've run into a few things that trouble me. Perhaps someone can help.

I had a few questions concerning the article about roll stiffness distribution. I have used the RCVD book as well as your article. For these calculations.

After calculating the additional ARB roll stiffness required to achieve the selected roll gradient, it is distributed front and rear by the TLLT% (magic number). However, once I go back through the calculations and double check my total roll stiffness, I arrive at a number that is larger than my desired total roll stiffness.

Per the optimum G article and RCVD...

Roll gradient is given by... (1)

phi/Ay = W*H / (KphiF + KphiR)

The equation for additional roll stiffness required... (2)

KphiA = [ KphiDesired * KphiTire / (KphiTire - KphiDesired) ] - KphiW

After I calculate the additional roll stiffness required (KphiA) and distribute it front and rear via ARB, I now have my required roll stiffnesses required for each anti roll bar (KphiARB-F and KphiARB-R).

However, in order to do the load transfer evaluations, I need to know KphiF and KphiR (the total roll stiffnesses for each end of the car).

Rearranging equation (2), using KphiARB-F / KphiARB-R in place KphiA, solving for KphiDesired should give me the resultant roll stiffness for that end of the car.

After I calculate KphiDesired for each end of the car, the sum of these roll stiffnesses is greater than the initial design by as much as 30%. Resulting in a much smaller roll gradient (stiffer).

If I divide the value of KphiA as first calculated in equation (2) by a factor of two before distributing it front and rear, my resultant total roll stiffness is within a percent or less.


In summary, using the additional roll stiffness that I calculated per RCVD & Optimum G article article, I end up at a total roll stiffness greater than that of the initial target.

Anyone have any experience with this? It seems most of the solutions tell you how much roll stiffness you need, but never re-evaluate the roll gradient.

[exFSAE]

Suggestions...

1. Put RCVD and OptG articles aside for now. Just draw it out yourself.. come up with your own set of equations that make sense. I hate digging through other people's equations and terminology.. partially because I'm lazy! Also makes a difference if you naturally think of things in terms of linear springrates (function vertical displacement at the wheel) or rotational springrate (function of chassis roll angle)

2. Drop the tire component to start with to make things easier.

Remember, on a FSAE car you don't need to be super accurate with this. Aiming for a specific TLLTD will get you in the ballpark.. but there's gonna be heaps of wheel, suspension, and frame compliance that will throw you off. 30 minutes worth of spring/bar tuning on the real car, instead of 3-4 hours of chalkboard work.

For these sort of things that aren't gonna be super precise anyway, I'm all for very fast results rather than "exact" analytical solutions.

[Silente]

Hi Blake,

this is the way i would do it.
Write an excel spreadsheet where you can specify things like spings, roll centers, car mass, front mass distribution, motion ratios etc.

Then calculate all the things your interested in, such LLT, LLTD and also roll gradinet. Doing it, for now live ARB stifness at 0.

Then, you can begin to try to increase ARB stiffnes to catch the LLTD and roll gradient you desire.

If you want, you can already insert in your sheet a real Sway bar calculation, where you specify inside and otuside diameter of your bar and arm length to see which kind of bars you should use.

For example, i prefer to have anything as a linear stiffness, [N/mm]. Only at the end i calculate roll stiffness contributions as Nm/deg.

I know it's not as fast as Optimumg metheod, but at least you understand the steps your are making and the effect of each change on the car.

And anytime in the future you are going to change anything in your setup you will se exactly the effect you're going to have.