The SAE coordinate system

[BillyShope]

As we analyze a dynamics problem, we occasionally realize that our choice of coordinate system was poor and we are forced to start anew. I doubt if we'll be changing the SAE coordinate system very soon, but I do wish more thought had been devoted to its conception.

It's reasonable to have the origin at the CG, of course. And, I'm certain it was thought equally reasonable to align its axes with the chassis. But, when you consider the dynamics involved...excluding, for the time being, the driver as part of the system...it really makes little sense. The only function of the chassis...apart from being a convenient place to which the wheels can be attached...is to provide the major portion of the inertial force. A more reasonable system would have the XZ plane perpendicular to the axle without steering.

Consider roll "understeer" and roll "oversteer." Since tire loadings are unaffected, these matters do not merit consideration when analyzing the dynamics of the car BY ITSELF. But, by the names which they have been given, they serve to cause a great deal of confusion. If the XZ plane was perpendicular to the rear axle, roll steer would never be mistakenly included in the understeer budget. (Measurement of steer angle would, of course, be more complicated.)

This is not to say roll steer effects are to be ignored, for, when the car-driver system is to be analyzed, they certainly do merit consideration. I just believe it would be better to consider them AFTER the understeer budget has been completed.

Any thoughts?

 

[GregLocock]

Roll steer is included in Bundorf's analysis, why don't you include it?

eg

http://en.wikipedia.org/wiki/Bundorf_analysis

Cheers

Greg Locock

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

 

[cibachrome]

I had to wince a bit at the WIKI entry descriptions and values. The principle cornering compliance terms are the reciprocal weight normalized tire stiffnesses, not "weight transfer" terms. The SAT terms were probably to mean the rigid body self-aligning torque/moment metrics. In terms of values, tires are generally 2.5 to 3.5 deg/g, front aligning torque compliance steer values are .3 to 1.5 deg/g, typical roll steer compliances amount to -.3 to +.6 deg/g. This produces modern cars and trucks with typical front cornering compliance recipes of 3.5 to 6.5 and rear cornering compliances of 1.5 to 4.0 deg/g. The understeers of such vehicles are found to be 1.5 to 4.5 deg/g. This produces acceptable lateral acceleration bandwidths of .8 to 1.3 Hz. i.e. response times of .25 to .45 seconds. The fact is even the Government is involved in handling criteria, from rollover to sine-with-dwell. Anything else in these modern times would simply be unsalable because today's drivers are much more tuned into good vehicle statics and high speed dynamics. BTW: anyone ignoring the force or geometric cornering compliance terms (which is popular in the academic and enthusiast press zones) is never going to have credibility with any manufacturer, from Ferrari to Cherri. A vehicle is very much more than a go-kart on very high pressure tires. Spherical jointed links can have load induced steer. Even your tube framed, carbon fibre, transparent aluminum equipped race cars have managed non-tire cornering compliance.

 

[BillyShope]

Consider a car undergoing Olley's understeer/oversteer test. In other words, it's on a crowned road with the front wheels parallel to the X axis. Further, we'll assume that it's neutral, so the front wheels remain parallel to the X axis and the car goes neither into the ditch nor into the oncoming traffic.

Next, we'll add some roll oversteer. The driver is forced to turn away from the oncoming traffic and, according to Olley's definition, the car is oversteering. But, as far as the tire patches are concerned, nothing has changed. All that's happened is that the chassis has been rotated relative to the car's path and the driver has had to turn the steering wheel to compensate. Since tire loads haven't changed, there is no inherent instability, critical speed, etc. associated with the introduction of roll oversteer.It all comes back to the arbitrary initial definition of the coordinate system. If the X axis is defined as perpendicular to the rear axle and the steer angle changed to maintain its angle relative to the X axis as the axle rotates under the chassis, a more realistic definition of oversteer is obtained.

Again, roll steer is an important consideration, but ONLY when the system under analysis is expanded to include the driver.

 

[cibachrome]

Your presumption is flawed. The "neutral" car still crawls down the road crown because it will continue to sideslip. Addition of front roll oversteer increases the gain of the open loop system regardless of the driver action. Addition of roll oversteer at the rear axle does the same. I'm presuming your car has a reasonable roll degree of freedom. In any case, the system closed loop gain is altered (increased) therefore the tire response are different which the driver will activate to maintain a zero sideslip and zero yaw velocity trim (stay in the lane). Knowledgable readers are aware of the greater effect on transient dynamics from a change in the rear cornering compliance (deg/g basis) versus the same numerical change made in the front. The steady state gain is the same but the XXX is different. Can you tell me what XXX is/are (two elements)?

 

[BillyShope]

All right, I was a bit careless in my wording. Instead of saying "GOES neither into the ditch nor into the oncoming traffic," I should have said "TURNS neither into the ditch nor into the oncoming traffic." The path is a straight line with a neutral car, but, as you put it, the car still "crawls" away from the crown.

With that matter cleared up, it should be obvious that the point I am making is that the straight line path involves the same tire patch loads, whether rear axle roll oversteer is present or not. The roll steer accomplishes nothing more than a rotation of the chassis relative to the path.

 

[cibachrome]

Since roll steer is induced by roll which is itself induced by lateral acceleration (which has yaw velocity and sideslip components), it is manifested as a change in the axle sideslip gain (which Bundorf called Cornering Compliance). Thus roll steer, roll camber, lateral force steer, aligning moment steer, lateral force camber, aligning moment camber, etc, all modify the tire's effective sideslip stiffness at each axle. As a result, all these terms have an effect on the total vehicle understeer, and its natural frequencies and damping levels. With Bundorf's Cornering Compliances having symbology DF and DR, then the understeer is DF-DR and the damping is (DF+DR)/(DF*DR). Your roll steer changes alter the system responses: steady state gain, peak to steady state ratio, and natural frequencies. A Simulink model with some slider controls makes an excellant proof. Note that the vehicle characteristic equation has speed^2 in the denominator. Since the roll characteristic equation has no speed dependence, under certain conditions of tire cornering stiffness (the principle cornering compliance components) and roll moment stiffness, the natural frequencies can overlap or worse, cross-over. This means that your low speed roll under- or over-steer has changed sign. To avoid this quandry, one should avoid the use of roll steer, especially rear roll steer, as much as possible, especially in cars which go VERY fast.

Lastly, the use of understeer, especially rear axle understeer, is primarily concerned with increasing the system bandwidth (shortening response times). The understeer raises the system natural frequency. In so called "Neutral" cars, system respnses are sluggish (1st order) and require exceptionally high cornering stiffness tires to obtain good subjective response quickness. Understeer lets you use more comfortable tires however with more overshoot in the response (which is generally agreed to as being undesireable in excess). Any good simulation will reveal these traits.

 

[BillyShope]

There is obviously a problem in communication. I do not wish to consider, at this point, transient effects. Let me try another tack:

You have two identical neutral cars traveling at a constant speed on the right side (US side) of a crowned road. Car A has a rear axle which remains parallel to the SAE Y axis. Car B has a rear axle which, when viewed in the positive Z direction, is rotated slightly clockwise relative to the axle location in Car A. (Don't worry about how it got there. It's simply fixed in that location.) Using the SAE coordinate system, Car A has a steer angle of zero. Using the same SAE coordinate system, Car B has a steer angle equal to the axle location difference.

Cars A and B will follow the same straight path, angling away from the crown, and the tire loadings will be identical.

That's all I'm saying. Well, I'm also asking why, when this identical condition is caused by rear suspension geometry, it is called roll "oversteer," when, for instance, there is no critical speed involved. I'm also maintaining that, while it might be impractical from a measurements standpoint, a coordinate system with the Y axis parallel to the rear axle would eliminate some of the confusion about roll steer.

 

[cibachrome]

Now I get it. I submit that your static change in the rear axle is not ever technically referred to as "roll oversteer", its called a thrust angle. This effect is present in IRS and beam axles. Note that tire plysteer and plyrat offsets at both ends of the vehicle (but especially the front) can and do induce a thrust angle effect. Those of us with canines recognize the "dog tracking" phenom. The management of tire force & moment offset factors, wheel alignments and drive axle thrust angle are major headaches in this business from a leads and pulls warranty standpoint. Your thrust angle interest is especially well placed in the high horsepower, high traction area, including tractor pulling, Nascar (Nextel Series) and Top Fuel.

 

[BillyShope]

Not ever?? The Millikens refer to it as roll oversteer and addressed this matter...at my urging...in Problem 6 for Chapter 17 in the student workbook which accompanies "Race Car Vehicle Dynamics."

Wait minute! Now, I "get it." You're taking my example Car B and making a real car out of it. I thought I was making it clear that it merely represents the effect of roll steer. I realize there are some oval track constructors who shorten up the wheelbase on one side, ending up with a car that looks like a dog that's chased one too many cars. As for high traction applications, I was involved with a factory dragrace team and this certainly never crossed our minds. We were more interested in asymmetric suspensions (to cancel driveshaft torque effects).

Anyway, it seems we now are talking the same language.

 

[2SlowJoe]

I think you are getting at the difference between what Olley called “primary understeer” and “secondary understeer”. They are both understeer, but they work in different ways.

Primary understeer affects not only the steering wheel angle, but also the slip angles at the tires. It is controlled using things such as:
Weight distribution
Lateral load transfer distribution
Camber
Tire properties

Secondary understeer does not change the slip angles at the tires, but does change the steering wheel position. Examples of things that control secondary understeer are:

Roll Steer
Lateral force compliance steer (LFCS)

Imagine a vehicle going around a constant radius turn at a constant speed with no roll steer and no compliance steer. The force at the front and rear axles is known, and the tires will generate those forces by running at some slip angle.

Now take the exact same vehicle and add a spring in the intermediate shaft. (Effectively adding front LFCS) Go around the same corner at the same speed and what you will find is that the road wheel angles are the same as in the case above, the slip angles are the same as the case above, but the steering wheel needs to be turned significantly further to get the same road wheel angle at the same speed. This feels like understeer to the driver, but it did not change the slip angles or road wheel angles for a steady state turn.

I have some philosophical beliefs about when to add what type of understeer…

-Joe

 

[BillyShope]

Thank you, Joe. I've got the Millikens' book on Olley ("Chassis Design"), but I must confess I haven't read all of it. Didn't realize he addressed this matter.

That "feels like" business is when you start considering the driver as part of the system. Brings to mind the little trick that was played with the '57 Chrysler products. If you'll recall, the torsion bar front suspension was a big deal that year. But, the handling wasn't really as different as the magazine testers made it out to be. The big difference...as far as driver "feeling" is concerned...was at the other end of the car, where the leaf springs had been changed to shorten the length from the housing forward. The increased roll oversteer made the driver "feel like" he was driving a car with far less push.

I'm presuming this is the sort of thing included in your "philosophical beliefs." Hey, I'm not disagreeing! Give the customer what makes him feel good.

 

[2SlowJoe]

Also forgot to mention one other thing:

Primary understeer works in the linear range, and at the limit.

Secondary understeer will not work at the limit. Once you write a check the tires can't cash, roll steer or compliance steer will do nothing.

-Joe