Question about arb calculations

[koollama]

While attempting to determine required stiffness for our car's arbs, I used the formulas found in optimum g notebook. The part where it stops making sense to me is where the book sets forth a formula that is inversely proportional to the roll stiffness of the car due solely to springs, and then calls this value the "Desired Roll Rate". If you continue to follow their steps (which I tried my best to understand), you come up with a value of units (Nm/degree roll) which ends up being proportional to our input spring rate (since the rest of the variables are decided). This is referred to in the book as NEEDED anti roll bar rate. According to these formulas, if we have softer springs we will need ARBs that apply less Nm/degree roll to achieve the same roll per degree. That doesn't make sense to me. Any help appreciated, cheers!

[koollama]

While attempting to determine required stiffness for our car's arbs, I used the formulas found in optimum g notebook. The part where it stops making sense to me is where the book sets forth a formula that is inversely proportional to the roll stiffness of the car due solely to springs, and then calls this value the "Desired Roll Rate". If you continue to follow their steps (which I tried my best to understand), you come up with a value of units (Nm/degree roll) which ends up being proportional to our input spring rate (since the rest of the variables are decided). This is referred to in the book as NEEDED anti roll bar rate. According to these formulas, if we have softer springs we will need ARBs that apply less Nm/degree roll to achieve the same roll per degree. That doesn't make sense to me. Any help appreciated, cheers!

[koollama]

Just to be clear, I have vehicle race dynamics and I will probably have to re-do the calculations with that book as a reference, but I'm not sure if I have time, so I'd rather see if someone could provide some insight as far as what to do with this "needed arb rate".

[Sormaz]

roll per degree hmmmmmmm

[Silente]

IMHO the esiest way to do your work is to create a spread sheet (or something similar) where all te contribution to roll stiffness are in.

You will have to know your motion ratios and tracks as well. You can start doing this calculation setting the arb stiffness at 0.

Then, you can add stiffness to you ARB untill you reach your targeted roll stiffness. If you want, you can also use excel target functions to do it.

This method is not as direct as Optimum g one, but it can help you to better understand how each stiffness contributes to the overall roll stiffness of the car.

[Goost]

Not sure what part of the optimumG book you're referring to - I couldn't find the error you say you had if you tell me what page or chapter I'll look into it. Anyway, the simnplest way to look at it I think would be this (note - you can figure out intermediate units and conversions on each step yourself):

1) Determine Desired Roll Gradient (deg./g) based on wanted suspension travel at the wheel (or damper, include MR of course) and weight transfer during a maximum condition (lateral usually). (Note: you have to make up some numbers here for % front anti-roll to calculate weight transfer, this is an iterative game, ha)
2) Desired Ride Rates = weight transferred/allowable travel (this is a spring rate effective at the wheel, or a Wheel Rate) give you K_ride_front K_ride_rear (lb/in)
3) note: for tuning the front/rear - ride frequency is easily calculated directly from these and the vehicle weight (front and rear) to find omega_F and omega_R (hz)
4) Desired Roll Rates := K_f (or K_r) = K_ride*Track^2/2 (ft*lbs/rad)
5) Now our actual Roll Gradient will need to be (W*CGheight)/(K_f+K_r) (deg/g)
hold onto this for a minute.
6) Actual Wheel Center Rates := K_w = Tire Spring and suspension spring in series. Include Motion Ratio! (lb/in)
7) So now we have a desired roll rate from (4) which will not quite be achieved by the tire/springs alone (K_w). to find ARB roll rate needed:
K_needed = (K_desired*t^2/2)/(kt*t^2/2-K_desired)-K_w*t^2/2 (ftlbs/deg)
So that's what the ARB must provide. Of course if the Wheel Center Rate is too high then this number will be negative.
8) see what the new weight transfers are and check through it all again.

Just a note - none of the calculations above showed a conversion from inches to feet. Should help anyone who is already annoyed that I didn't use SI unitshttp://fsae.com/groupee_common/emoticons/icon_smile.gif
I can't claim any of this - it's just what I recall from chapter 16 RCVD.

hope it helps.