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understanding cornering compliance

understanding cornering compliance

understanding cornering compliance

As part of my ongoing efforts to understand vehicle directional control, I've been trying to gain an understanding of cornering compliance. It's not going well.

My limited understanding of the concept is that many factors are included, such as roll steer, camber effects, aligning moments (more about that later), but could be simplistically characterized as the rate of change of vehicle sideslip.
I'd appreciate any input from those who know more than I (ie., everyone).

One aspect that confuses me: I read (some time ago now) that understeer effects on the front axle add to the cornering compliance, while understeer effects on the rear axle subtract from the cornering stiffness. I have to admit I'm accustomed to considering understeer/oversteer as  properties that compare one end of the car to the other.
This begins to get into control systems stuff, I think...I have read that understeer, rear axle understeer in particular, shortens vehicle response time (raises the system natural frequency).

I apologize for the length of this post, and my sincere appreciation to anyone who replies.


RE: understanding cornering compliance

Stop thinking about whether a given axle "understeers". Instead think about toe-in or toe-out, bump-steer, roll-steer, etc.

Tire slippage will always send whichever end of the car you are talking about, outwards towards the outside of the corner. Toe-in or toe-out in response to bump or roll could go either way. Compliance in the bushings etc could go either way.

The only way you can get an "understeer" action from a rear axle is if the axle has severe toe-in in response to suspension compression or compliance of the outside wheel, to the extent that it is greater than the tire slippage. Given that any more than very slight toe in or toe out with bump or roll or compliance is generally regarded as "bad", the magnitude of this is such that the only way it's going to happen is with designed-in 4-wheel steering systems. I presume that's not what you are talking about.

RE: understanding cornering compliance


At least one manufacture had the audacity to call pronounced rear end bump steer "passive 4 wheel steer". It drove like a pig on bumpy and undulating roads, especially with mid corner bumps.

I also would have called changes in tyre slip angle due to different front to rear tyre load changes or camber changes under steer or over steer as well. I, maybe incorrectly, call it under steer if you have to increase steering input to maintain a line, or over steer if you have to decrease steering input to maintain a line, no matter what the actual cause. For instance changing anti roll bar relative stiffness between front and rear can alter what I call under steer/over steer characteristics without changing toe at the rear. Certainly toe at the front changes with steering input changes that are required. Now I have confused myself I think.

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RE: understanding cornering compliance

Patprimmer- I think you might be, in a way, confusing over/understeer definition. Your definition would be in terms of whole vehicle (balance), but when considering either front or rear 'axle' I think the definition would be less intuitive, because it would work the opposite way when applied to rear wheels (when driving forward)... E.g. I would think that introducing, say compliance, understeer on rear wheels would lead to decrease of vehicle's understeer characteristic (or increasing vehicle oversteer).

RE: understanding cornering compliance

Read the wiki article on Bundorf Analysis, I'm fairly sure it is right, if not helpful (grins).

When you do an understeer axle analysis you include the weight and tire effect on that axle, so in fact the contributions of each axle are of similar magnitude, typically.

Note that the above is mostly concerned with linear range understeer.

Your comment about delay time (yaw delay) reflects the usual situation, but I have certainly worked on cars where the relationship was reversed. This is mostly a tire issue.

Milliken's discussion in RCVD is good, as is Bundorf's original SAE paper, which I think is probably available on the web for free. Gillespie also presents it in his book Fundamentals of VD, which you can read on google books.

Limit handling is more complex. The same ideas apply, but everything is non linear.


Greg Locock

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RE: understanding cornering compliance

Thanks guys, much appreciated.
It was suggested to me by someone a LOT smarter than myself that, if we assume the front axle is 'fixed', a change could take place in the rear axle (compliance steer, etc), that could contribute to understeer.
I think I need to read the original Bundorf paper, and RCVD/Olley (primary/secondary understeer).

Thanks again to all.

RE: understanding cornering compliance

Absolutely, yes you could set a car up that way. It would probably be extremely unpleasant to drive, but yes, you could derive all your vehicle level understeer from rear compliance.


Greg Locock

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RE: understanding cornering compliance

Its actually quite simple. The cornering compliances are the net front and rear axle sideslip gradients (derivatives) at any level of steady state lateral acceleration. Units are degrees per g. The degrees are the reference steer angle corrections and the g' are g-whizz.

There are usually 11 recognized cornering compliance terms:

Tire stiffness normalized by weight (front and rear)
Lateral force steer and camber (front and rear)
Aligning moment steer and camber (front and rear)
Overturning moment steer and camber (front and rear)
roll steer and camber (you guessed it)
rigid body aligning moment (the sum of all the tire self aligning moments acting on the vehicle).

There rest is just sign convention: for all computations, for either axle, an effect which reduces the axle sideslip angle gradient magnitude is positive, and an effect which increases the axle sideslip gradient magnitude is negative. We call positive effects understeering and negative effects oversteering.  In most everyday vehicles, net front axle effects are understeering and net rear axle effects are oversteering. No question that by far the most significant factors are the tire effects, followed by front aligning moment steer (steering system compliance) and roll steer front and rear. The symbology of the cornering compliances are to use DF for the front cornering compliance and DR for the rear.  In general conversations, though, we usually just refer to the scalar values of DF and DR.  In those terms then, DF-DR (DF minus DR) is the vehicle's net understeer while DF + DR is an indicator of the vehicle's transient response time, and (DF+DR)/(DF*DR) is a measure of the syste damping factor.  Given a simple but elegant s-plane transfer function analysis of a 2 DOF handling model, quite a bit is revealed:  Good cars have cornering compliances that universally have similar recipes and values. The neutral steer car has sluggish transient response, an oversteering vehicle is not unstable in open loop control unless (you figure it out), rear axle cornering compliance changes have much greater influence on transient response than front effects, you can't fix one cornering complience deficiency with another, and that NOTHING beats a good set of tires.

In the realm of real cars, typical DF is in the range 3.5 to 6.5, DR is in the range of 1.75 to 3.5, If you only knew the stacking, then you could determine that typical understeer is in the 1.5 to 4.0 range for 0 to .4 g normal driving.  After that things can get mixed up pretty fast, depending on what nonlinear effects are taking place (tires rolling off, steering systems hardening up, roll bars mashing on tires, etc.

From all of this, you should conclude that discussing vehicle road performance in terms of understeer is ridiculous. Why?  Because a car with a DF of 5 and a DR of 2 has an understeer of 3 degrees per g.  So does an inter city bus with a DF of 10 and a DR of 7.  Are you car dynamics the same as a bus? I wouldn't think so.

Ther classic driver responses can be explained, too: You tighten up the rear and it plows (yeeah baby), you tighten up the front and its loose (naturally). Besides, these changes have dramatic influences on the damping and settling times, too,

Using good tire test machine data and a good K&C machine, all of these factors can be assimilated into simulation programs which can predict DF and DR net values very closely. Its not until engine power and a few other factors (limited slip diffs) kick in that the simple models drift off.

But it all fits.  Best part of this is that a optimization program given the freedom to select weight distribution and cornering compliances for a typical highway speed of operation, will always arrive at the DF and DR values of some pretty respectable production vehicles.  And it won't be a neutral steer car (Df = Dr). (and the weight distribution won't be 50/50).

Howzzat ?

RE: understanding cornering compliance

Thanks ciba(wac)chrome....I was hoping you'd contribute and I appreciate it.


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