Slope of 100% anti-squat line

[BillyShope]

When calculating percent anti-squat for a RWD beam axle car, the 100% line is commonly assumed to have a slope equal to the CG height divided by the wheelbase. Some time ago, I realized that the line must pass slightly below the rear tire patch IF the weight of the rear axle assembly is taken into consideration, but I considered this as merely a displacement and not a change in slope. As I was explaining all this to a non-engineer, I suddenly realized that the line must still pass through a point, on a vertical line through the front tire patch, at a height equal to the CG height. The slope, then, MUST change. Specifically, the ratio of CG height to wheelbase must be multiplied by the ratio of total weight to a value equal to the total weight less the rear axle assembly weight.

I'd be interested in knowing if the anti-squat, as calculated by the different software packages, changes with changes of rear axle assembly weight input.

 

[cibachrome]

"Dynamic Modelling and Simulation of Front-Wheel-Drive Drag Cars", Knauff, Michael D., Law, E. Harry.
Society of Automotive Engineers, SAE-2005-01-0421

 

[NormPeterson]

Would it be of any advantage to work with a composite CG made up of the unsprung mass and its CG height and the front unsprung mass and its CG height (which usually is different) instead of the total vehicle mass CG height? That will normally give a slightly greater slope than using the total mass CG (at least in most cases and textbook diagrams) but lets you work from the contact patch, which might be easier to visualize than a point below grade. Might even help track what happens as the nose rises a little better (a closely related question that came up on protouring.com has had me pondering this lately).

I can see where a heavier rear axle will "bleed off" more of any given horizontal accelerating force (taken at rear axle height) without affecting the torque reaction at that same point, so the relationship between the reactions at the chassis side of the SVSA would change slightly. Less net forward force combined with the same perpendicular force opposing the torque does sound like a larger anti-squat value.


Norm

 

[BillyShope]

Yes, Norm, I am working with "a composite CG made up of the unsprung mass and its CG height and the front unsprung mass and its CG height." (I'm sure you meant that first "unsprung" to be "sprung.") There's no reason to separate out the front suspension in this analysis.

I'm certain noone will disagree about the change in slope when rear axle assembly weight is considered, but I'm still curious as to whether this is recognized by the analysis software commonly used.

 

[GregLocock]

I'll run it tonight or tomorrow.

Since the ADAMS model is a true MBS the behaviour of the model is correct if the model is accurate- but that does not exclude errors in interpretation. For instance I don't know how it measures antisquat - in previous versions it often used hardpoint derived definitions, now it tends to use instantaneous centres and so on, which are more accurate and do not require assumptions about how the mechanism works.

FWIW I don't even bother looking at those numbers, I use the pitch and hip point rise during an acceleration run and a braking run.

Can you point me at a picture of the sort of suspension you are most interested in - I default to 4 near parallel longitudinal links and a watts link, as that is our old production suspension, and is still used on the V8 Supercars. It has the virtue that the geometric method for establishing the IC is entirely straightforward.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[BillyShope]

Couldn't care less about the suspension type, Greg. It's either going to show a change in percent anti-squat with a change in rear axle assembly weight or it's not.

Thanks.

 

[GregLocock]

OK, and the result is .... no change. here's why:

"This request can only be accessed for half or quarter vehicle suspension models. Also, the analysis must be run using "kinematic analysis" since the routine uses velocity vectors to establish the location of the instant centers."

I think this is basically the same as the difference between geometric roll centres and force based roll centres.

The net longitudinal force into the sprung mass is the same, there is just an additional moment, (additional axle mass)*(acceleration)*SLR, which on a 4 bar live rear axle is just given by slight changes in the axial load on each link.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[BillyShope]

So, you're saying that you have to accept a built-in error in the calculation of percent anti-squat? I would strongly suspect that, if they wanted to, they could make the necessary corrections.

And, I don't understand your comment about the net X force to the sprung mass remaining constant. If the total weight is, say, 3000 pounds and, in one case, the rear axle assembly weighs one pound, but, in another, the rear axle assembly weighs 2999 pounds, the net force to the sprung mass would certainly be different. Or, are you saying that the net force is input into the program? In that case, you'd have to adjust the input value as you change rear axle assembly weight.

 

[GregLocock]

No, I'm only changing the mass of the axle.

The force at the CP goes up, for a given longitudinal acceleration, but the net force to accelerate the unchanged mass of the sprung body remains the same.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[BillyShope]

I apologize for making my request unclear. I wanted to see if the software ignores the weight of the rear axle assembly when calculating percent anti-squat. So, if it's not too much trouble, could you please try it again, but keep the total weight constant as you change rear axle assembly weight?

Again, thank you.

 

[GregLocock]

OK, that'll need new springs.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[BillyShope]

Wait a minute! While the post immediately above describes that which I had anticipated, your first run has already indicated a software problem. With constant acceleration and a total weight that is increasing with increased weight of the rear axle assembly, the horizontal component of the vector pushing on the sprung weight must move downward to balance the increasing inertial moment of the rear axle assembly. In other words, as you increased rear axle assembly weight as you described, the calculated percent anti-squat should have decreased.

 

[GregLocock]

Ah, I think you need to recognise that the definition they are using above is the sort of thing an engineer could do on a drafting table, in the good old days, indeed current CAD packages try to replicate these methods, but they are NOT robust, they do not agree with real measurements.

As usual it comes down to definitions - suppose we were to set the side view arm angles up to give 100% antisquat, then we would have to change the angles as the axle weight increases.





Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[BillyShope]

Yes, as a septegenarian, I go back to "the good old days." And, I would certainly be upset if an expensive suspension analysis program couldn't even calculate something as basic as percent anti-squat.

What you said:

"As usual it comes down to definitions - suppose we were to set the side view arm angles up to give 100% antisquat, then we would have to change the angles as the axle weight increases."

is, of course, what I'm getting at and, since a software correction is so simple, I can't understand why it hasn't been incorporated.

(I'll take this opportunity to correct a statement in my first post:
"Specifically, the ratio of CG height to wheelbase must be multiplied by the ratio of total weight to a value equal to the total weight less the rear axle assembly weight."

This will get you a bit closer...since the tire radius, as an approximation of the CG height of the rear axle assembly, is close to the CG height of the remainder of the car..., but it is not quite true.

I've found it most convenient to simply add an amount...equal to the tire radius times the ratio of the rear axle assembly weight to the weight of the remainder of the car...to the pertinent vertical dimensions. In other words, I'm moving the rear tire patch down in order to treat the rear axle assembly weight as zero and the total weight as being equal to the weight of the car less the weight of the rear axle assembly. It is then necessary, of course, to subtract that addition from, for instance, the calculated height of the instant center.)

 

[GregLocock]

The first step in introducing a new procedure (MBS modelling) is to prove equivalence to the old procedure (manual drafting). Which is what that calculation does. If I am designing a suspensions antisquat properties I don't rely on that antisquat calculation to give me a flat ride, I use actual measures of pitch and displacement. This accounts for many second order effects that the instantaneous centre approach ignores. In other words, the IC method is superceded.

Even so your proposal, in my opinion, is not a simple mod to make robustly - it assumes that you know what the unsprung mass is.

An MBS program does not really understand 'unsprung mass' as such, all it sees is a matrix of inertias and forces and so on. Unsprung mass is an abstraction made by human beings - for instance a live rear axle has a different unsprung mass in a roll event compared with a ride event, a pure IRS does not. That is physically absurd, masses don't change depending on road surfaces, or connectivity between sides of the car.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[BillyShope]

Yes, I understand what you're saying and I can understand why you might choose not to consider the calculated percent anti-squat, but, whether it "understands" it or not, you were evidently able to input a different weight for the rear axle assembly and the program then spit out what it purported to be the percent anti-squat, which value now appears to be in error. And, that is what would upset me. If it can't be calculated properly, it shouldn't be included in the output.

If this was calculated according to the matrix of inertias and forces which you mention, the value would have changed with your change in input. But, when it comes to this particular calculation, they evidently revert back to the "old procedure," and slap a 100% anti-squat line through the rear tire patch. And, that is just what I suspected might happen.

 

[GregLocock]

Because they were specifically trying to duplicate the manual method. If they had come up with a different number then people would say : silly software, can't be trusted.

As an example I see this very specifically on scrub radius - I have two suspensions that have a positive scrub radius in reality (ie toe out with a rearward force at the CP) , but if you draw them up on the CAD then they have a negative scrub radius.






Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[BillyShope]

Yes, you're probably correct. I've yet to see a text with the inclusion of a comment that would explain that the illustrated 100% anti-squat line assumes that the weight of the rear axle assembly is negligible compared to the total weight.