NEED SIMULATION INFO

[BillyShope]

I'm retired and am requesting a favor from one of you guys who has access to chassis simulation software. I'd like to know the ratio of right front spring rate to left front spring rate, for a beam axle RWD car, that will provide cancellation of the driveshaft torque. Obviously, many parameters are involved, but I'd like a ballpark figure for an "average" car. Yes, I realize that asymmetric rear suspension links would provide a much better solution, but, if the ratio is reasonable, this would be a quick and dirty solution for the dragracer who either has adjustable coilovers or...as in the Chrysler products...has a torsion bar adjustment. Please keep the sum of the spring rates constant. Thanks in advance.

 

[GregLocock]

I'm struggling with the free body diagram of this, I can't see how to cancel the roll (if that's what you want) due to torque on the back of the gearbox by changing the front spring rates.



Cheers

Greg Locock

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[BillyShope]

Greg, the goal is to equalize rear tire loadings, during launch, to maximize tire traction. If the right front spring has a higher rate than the left front, the LF corner will rise higher than the RF, meaning the RR will be forced down, tending to cancel driveshaft torque effects and equalize rear tire loading.

 

[GregLocock]

Oh OK, I didn't know what you wanted to cancel. Do you want equal rear springs?



Cheers

Greg Locock

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[BillyShope]

Yes, equal rear spring rates. Thanks, Greg.

 

[GregLocock]

Are you expecting a different result from the first couple of chapters in Gillespie?

Cheers

Greg Locock

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[BillyShope]

Don't have Gillespie. Have RCVD (used it as a text when teaching), but it doesn't seem to be of any direct help.

I realize that the reaction torque is distributed, front-to-rear, in proportion to the roll stiffness, so that which I fear is that the required rate ratio would be infinite, since only that would mean zero front roll stiffness. But, the problem is sufficiently "cloudy" that I hope I'm wrong and that a reasonable ratio will be found. Certainly, if the problem is simplified to the point that the fronts are assumed to rise equally (no twisting of the chassis), the ratio can be easily found and is quite reasonable. Intuitively, the idea seems to be a "slam dunk." The sum of the right side loads must remain equal, so, with a high rate spring at the right front, this would mean the majority of the weight transfer would be going to the right rear. But, my intuition has gotten me into trouble so many times in the past that I no longer trust it.

 

[GregLocock]

Hey Billy, as I think you expected there is no general solution. You can tune the corner weights so that at one particular torque the rear wheel weights are equal, but it won't work for all torques.

That's from a 3d model, I'll look at the free body diagram again, just to make sure.

Cheers

Greg Locock

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[BillyShope]

No, I'm not after a static preload. If the front spring RATES are different, the effect will be dynamic and the cancellation...either full or partial...will be equally effective for all values of driveshaft torque. Same situation as with asymmetric trailing links at the rear.

 

[GregLocock]

Yes, that's what I'd thought you wanted, but using my model I couldn't find a solution that did that. It could be a modelling problem as it wasn't the best model I've ever knocked together.



Cheers

Greg Locock

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[BillyShope]

I thought you'd have a "plug and crank" at your place of work. I'll try and model it myself. If you have a personal interest, I'd appreciate your verification of my results. If not, thanks for your interest to this point.

 

[GregLocock]

I do have a plug and go model, but to be honest I've got enough work to do at work, without doing odd jobs on the side!



Cheers

Greg Locock

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[BillyShope]

I understand. I'm retired, so it's a little different. Thanks, anyway.

I should have a solution to post later today.

 

[BillyShope]

I'm pretty certain that, for complete driveshaft torque cancellation, the ratio of RF wheel rate to LF wheel rate should be equal to the ratio of (1 + Z) to (1 - Z) where "Z" is the fraction of the total roll stiffness at the front. So, complete cancellation might be impractical for a "street" car, but, for something like a long wheelbase dragster, it would appear desirable to try some sort of suspension on the LF only.

Certainly, the ease with which the effectiveness of such a scheme can be tested in the shop...using d'Alembert's Principle...should be considered. Simply slipping wheel scales under the front tires and observing the load changes as a horizontal chain is tensioned out the rear is a worthwhile test.

 

[bhart]

Billy,

I recently went through the painstaking process of writing out long hand expression for all of the dynamic load transfer components on my type of racecar. I have a live axle @ the rear w/ a torque tube, and a solid axle up front. I think most drag cars probably have independent front, but adapting my expressions is just as simple as making front spring rates = front wheel rates, and front spring width = front track width. When I do that, in order to get the cancellation that you speak of, I get a somewhat different expression than you:

K_R/L = ratio of RF to LF wheel rate
= N/D
N = %FRS + %RRS*(t_f/2)*(h_cg/L)*(eta/R_L)
D = %RRS*(t_f/2)*(h_cg/L)*(eta/R_L) - %FRS

%FRS = your "Z" value
%RRS = fraction of total roll stiffnes @ the rear
t_f = front track width between contact patch centers
h_cg = CG height from grd.
L = wheel base
eta = torque multiplier between where the driveshaft pivots
on the vehicle and the rear wheels (rear end ratio
usually)
R_L = rear tires loaded radius (assumed = side to side
which is actually true if the tires are loaded
equally)

The %FRS terms come from the engine torque compenent of load transfer, and all that other junk has to do with the fact that asymmetric spring rates @ the front will cause the car to roll whenever it is required to pitch, which will transfer load across through the rear roll stiffness.

My confidence in these expressions is probably 70% as it is easy to make a mistake when doing that much algebra by hand, but it's up for discussion now anyway.

 

[BillyShope]

You're probably correct. I realized, after I had posted, that the axle ratio had been dropped somewhere in the derivation and I couldn't see how that could possibly happen. Yes, the algebraic manipulation can give one a headache. As I indicated, the matter could be settled with a relatively simple test setup, but I'm retired and no longer have the space or even access to wheel scales. I've tried to get local hotrod shops interested, but, when I start talking about pulling backward with a chain while the front wheels are on wheel scales, they quickly conclude I'm just another senile old man.

 

[bhart]

Well, most people wouldn't classify me as old just yet, so in my case, it's just another senile engineer.

 

[85chief]

Billy,
You might try a little trick we use on roundy round cars and use rebound adjustable front shocks and set the LF with MORE rebound than RF. The weight will transfer to the LR more quickly than the RR and you can tune it with the twist of a knob.

Wayne Malmstrom

 

[mloew]

There is no meaningful weight transfer in automobiles unless there is significant roll or pitch angles (or movable ballast, as in the old DTM racecars). I suspect you mean load transfer. How does adjustable damping change the load transfer?

Best regards,

Matthew Ian Loew


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[NormPeterson]

Transitionally, by affecting the velocity-sensitive components of load transfer. No help once you get to steady-state, though.

Norm