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Rear axle sideslip stiffness
3

Rear axle sideslip stiffness

Rear axle sideslip stiffness

(OP)
Hello,
how is defined "rear axle sideslip stiffness"?
how does this value affect handling and performance?

Thank you for explanation,

RE: Rear axle sideslip stiffness

In the linear range it is part of your understeer budget. It 's the gradient of the curve of rear axle slip angle vs latacc. Strongly related to your understeer gradient and yaw delay time. Less is good. I don't ever remember having a development engineer complaining about too little rear sideslip. Sadly I'm tone deaf when it comes to subjectively evaluating cars for steering feel, I can't tell you what it feels like.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Rear axle sideslip stiffness

Well said.
My feeling of going off the road:
Oversteer: 1961 Corvair with brand new rear tires that haven't been worn in yet on a spiral curve off-ramp. In the rain.
Understeer: 240Z in slow, near-full-lock turn. Also in the rain.
Of course it's the rain's fault, and not my driving.

RE: Rear axle sideslip stiffness

The "rear axle sideslip stiffness" is the generic term for the Rear Cornering Compliance. It is the summation of tire Fz, Fy, Mx and Mz slip and camber effects, rear roll steer and camber, and all sorts of the compliances associated with the rear suspension (which can include multiple axles). It describes this action over the full range of lateral acceleration up to the limit of control. There is a corresponding "front axle sideslip stiffness" named: Front Cornering Compliance, which describes the very same characteristics at the front of a vehicle. Appropriate ISO tests measure Understeer (K) as the derivative of [(steering wheel angle/overall steering ratio)] minus the Ackermann Gradient by lateral acceleration. Then, by means of several techniques including a precision sideslip angle sensor, the sideslip at the rear axle is determined, producing the Rear Cornering Compliance (DR). Adding the Understeer (K) function to the Rear Cornering Compliance (DR) function produces the Front Cornering Compliance (DF). DF = DR + K .

Simple or complex analysis makes it obvious that the lower the DR value is, the lower (better and subjectively more favorable) the lateral acceleration, yaw velocity and body sideslip angle response times are. Think of it in frequency response terms as lower DR produces higher bandwidth. So, DF - DR is the Understeer, while DF + DR is proportional to the damping in the 3 modes (actually Ay response is a combination of yaw velocity and body sideslip states, so its really only 2 modes. Increasing K usually means adding overshoot and longer settling times to vehicle response in order to produce improved response times. But the obvious way to improve the lateral dynamics is to have as low a DR as you can tolerate. This usually means tires with high cornering stiffness. However there is a big price to pay for the ride quality, rolling resistance and the cost of tires in order to get a low DR. This includes very low lateral force suspension compliance etc. meaning hard suspension bushings, oversized tires, cost of replacement tires and other packaging dilemmas. Many vehicles now have much larger rear tires or simply wider wheel rims than fronts if they think they need a 50/50 or more rearward weight distribution. (Think F1, Luxo Rides, big trucks, etc).

A practical handling teaching tool is to make a carpet plot of DF, DR and Ay Response time for any architecture with lines also for constant understeer. DR lines have a steep descent.

Tests (road and simulated) (as in constant radius, step) easily show the DF, DR, and K functions as results to document a vehicle. They help dissolve the lore about whether vehicles are "Oversteer" or "Neutral" since trendy journalistic mouth-breathers are almost always WRONG. Yet, nobody has the data to dispel the myths. Makes for good bird cage lining, though.

BTW: I measured these properties of my outboard Bass Boat (a fish & ski model) using VBOX equipment on a local inland lake. I studied the response for a 3 blade, 4 blade and 5 bladed propeller. The only real challenge was estimating the 'wheelbase' of the hull (to remove the Ackermann effect).

For a very large sample of production cars and light duty trucks, DR ranges from about 1.5 deg/g to 4.0 deg/g (values taken at 0.15 g), with K ranging from 1.0 to 5.0 deg/g. These numbers cover 1 passenger to GVW payloads. For all this you will find Ay response times from about 0.28 sec to 0.50 seconds. These are computed from the 50% steer input to 90% of final response at the 0.30 g's level of a step test sequence.

Short response times from high understeer feel squirelly. From a low DR, feel wonderful!

RE: Rear axle sideslip stiffness

Excellent stuff. In a typical project with the tires already defined the things we mess about with are roll steer (powerful but unsettling on rough roads), compliance steer (which can feel mushy), tire pressures, and toe in. I'd also have a play with RCH and rear sta bar. I'm not really a fan of rear sta bars, in particular. It's always tempting to increase the rim widths.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Rear axle sideslip stiffness

(OP)
Thank you very much,

i understand corret that is possible to compensate insufficient Rear axle slipangle stiffness with:
a) use widder rear rims with same tires dimension?
b) toe steer in favour toe-in under lateral load?

and
a)"stiffer" rear axle slipangle is ALWAYS better for performance
b)some front versus rear ratio is recommended ?
( as Cibachrome recently said : the front cornering compliance reduction to 1.2 would need a corresponding rear cornering compliance change from 2.0 to, lets say 1.0 to keep the car slightly understeering)
(this in fact represents some "transitient understeer presumptions" ???)

(of course my interest are mainly race cars)

RE: Rear axle sideslip stiffness

Racing cars deserve special attention to their cornering compliance recipes because:

They tend to go very fast during straightaway segments. And, they consume a lot of their design elements during competition. By this I mean their weight distribution changes as fuel load goes away, their tires lose tread as a function of use and the tire pressures go to new values. Even a limited slip differential can lose capability from wear.

Since their yawrate due to steering is speed dependent and roll is generally not, it is not unusual for yawrate peak frequency to cross over the roll frequency at some higher speed. If roll steer is present, it's sign will change after the crossover and go from desireable to undesireable effects. Early Corvettes and Camaros had this trait. It was addressed by very high damping settings which killed the ride quality and really did not address the root cause.

Since race 'tires' sometimes still have some camber force capability, roll camber and roll caster (camber by steer) are often used but not really effective in a solid rear axle configuration.

Weight distribution is a major player but now you have to choose when you want to get up on the wheel because its a 'knife edged' factor. Good then bad or bad then good.

In ALL cases, getting the rear suspension correct has the highest value for any application. Then you have a steering system to treat and/or bandage up and a rimforce/tierod load to address and its effects on vehicle control.

Funny how you mention tires on, then suspension is adjusted. I was a fan of finding the tire to make the suspension work. BTW, a rear bar often is used to fix a compliance problem rather than change a roll trait. And in a race car, roll is not one of those 'features' you want to entertain.

RE: Rear axle sideslip stiffness

And in case you wondering, sideslip is kind of important for 'racecars' because the sideslip component of lateral acceleration is very large at high speeds The yaw velocity component is large at low speeds. The speed where this all changes is called the tangent speed. Since sideslip is positive at low speed (let's not debate the signs of all this crap for now), and negative at high speed, there is a magic speed where it is zero. A basic characteristic of low speed sideslip is rear wheels INSIDE the turn path. That's why Grandma knocks down the mailbox when she turns into the driveway. Likewise, at high speed, the body sideslip is negative (positioning the rear wheels outside the turn path. So, the objective of any good race engineer is to get the tangent speed as high as possible in order to get the best (lowest) rear cornering compliance as possible at the max limit of control. Now you don't need a $20K sideslip sensor to help you with this if you are on a limited budget. All you care about is what is the speed at which your sideslip is ZERO. And that situation puts your inside front wheels on the same radius of a path as the rear wheels.

So, when watching or crewing, or driving on a race track, when you see the rear wheels on the line or off the line, you can immediately tell the state of the car. Off the line and outside the turn path (not the racing line) means you are 'tight' (as in understeering state. On the line means the car has about the right balance. You seldom see rear wheel inside the line (oversteering) unless "the driver is better than the car" as we say. So, the goal of any competent team would be to give the car enough understeer to produce acceptable transient response and to keep the rate of change of understeer as small as possible. Many times you hear a driver complain about 'loose' when the sideslip is close to zero. This is usually because the net tire aligning torque peak occurs before the net lateral force peak occurs and the rate of change of steering moment goes to zero or negative. They loose the feel of the turning potential and call it oversteer. The cheap fix is to add enough caster to move the peak Mz effect on the tierods to be coincident with the Fy peak. However this tends to load up the steering system with higher force which creates additional understeer. And that lowers the car's max lat capability. So there you now have the whole enchilada.

RE: Rear axle sideslip stiffness

(OP)
Thanks Cibachrome,
so we want (by all means) maximize rear slipangle stiffness,
BUT
only Up to value when front axle can handle understeer
yes?

RE: Rear axle sideslip stiffness

But it's easy to make the front cornering compliance greater than the rear to have an understeering control situation. Adding compliance (deflection steer or camber) is the way that would be accomplished. Removing a compliance term is very hard. Sometimes this leads to durability concerns because fatigue and fracture are now in the realm of the forcing frequencies. Doing this mechanically involves a time response, damping and settling time quandary.

"Nothing beats a GREAT set of tires".

RE: Rear axle sideslip stiffness

(OP)
"it's easy to make the front cornering compliance greater than the rear"

ok, but vice versa?

in fact really not want to get again more rear toe-in (or wider rear tires) before make the front cornering compliance more?

RE: Rear axle sideslip stiffness

Having trouble following this

Quote:

So, when watching or crewing, or driving on a race track, when you see the rear wheels on the line or off the line, you can immediately tell the state of the car. Off the line and outside the turn path (not the racing line) means you are 'tight' (as in understeering state. On the line means the car has about the right balance. You seldom see rear wheel inside the line (oversteering) unless "the driver is better than the car" as we say.
So I'm wondering what it is I might be missing.


Norm

RE: Rear axle sideslip stiffness

Sierra: If all there was for DR was tire cornering stiffness [CAR, in N/deg] with an infinitely stiff rear suspension and the rear axle weight [ WR ] is specified, then, the required tire cornering stiffness per wheel would be CAR == 9.8*WR/2/DR.

For WR=1000 kg, CAR = ( 1633.3, 2450, 4900, 9800 ) N/deg per tire for DRs of 3, 2, 1, and 0.5 deg/g.
I'm not sure how much you know of tire properties but getting a DR lower than 1.0 takes a remarkable tire construction recipe. Since you mentioned toe changes (roll steer, compliance steer, etc), you must realize that tires just don't listen to steer/slip changes very well as they near peak force levels, so these proposed changes don't do very much for you as a racer. Camber maybe (to minimize Mx).

Norm: Watch cars on the yellow inside pavement line during practice near a constant radius corner. Front and rear inside tires both on this line at the same time in a steady state cornering situation identifies the Tangent Speed. Since sideslip (Beta) per g is zero at this speed, then DR has just a geometric component = 9.8*57.3*b/U^2, where b is distance from total CG to the rear axle and U is the tangent speed in m/sec. It's also the speed where the difference in phase angle between yaw velocity and lateral acceleration are equal. If you are a New School Controls Type (as I am) and can use Big Science to figure it out .

Once in a while (as in a Blue Moon i.e. twice a year), you may observe a car on a track with a light spot appearing under the car near the rear axle. This means they are using a hidden Datron sideslip sensor to measure the rear cornering compliance or just the Tangent speed. Sometimes they forget to turn it off. (Oops).

RE: Rear axle sideslip stiffness

(OP)
and only extra static toe adding?
for example if front axle capability was build up, but rear axle improvement already is not possible ??

RE: Rear axle sideslip stiffness

Front static toe changes (in or out) can improve front grip (reduce understeer) but these settings (including Ackermann steer functions) have other detrimental effects. Same for rear (which could reduce rear cornering compliance by making the pair of tires work better together, but look at how much steer it would take, what mechanism in the rear could do the job, what would it accomplish at max lat and what other penalties do you pay (straight line, aero, tire wear, etc.).

And this requires accurate, specific and appropriate tire test data to determine the proper settings and function values. Changing brands of tires or constructions, wheels and even pressures means you start all over. Otherwise settle for rear or mid-pack positions and enjoy the smell of burned racing fuel !

RE: Rear axle sideslip stiffness

ciba - what I'm having difficulty with is how the condition where the rear tires are tracking outside the line (and the fronts are on it) can be defined as understeer, or when the rear wheels are inside the line that that's oversteer.


On delayed edit . . . unless it's the rear axle's (wheels' & tires') own understeer or oversteer that's meant.


Norm

RE: Rear axle sideslip stiffness

I have the same difficulty. In my understanding, if the rear wheels are tracking outside the path of the front wheels, it's an indication of how much rear slip angle is there compared to the trajectory of the car (and it's quite apparent to me that this situation would be more prevalent at higher speed), but it's unconnected with how much slip angle the front tires have at the same time.

RE: Rear axle sideslip stiffness

"Oversteer: 1961 Corvair with brand new rear tires that haven't been worn in yet on a spiral curve off-ramp. In the rain."

Yeah, I was trying to figure out how oversteer on that old Corvair was supposed to put the tail inside the front wheels. Huh? I should have spun out inwards?

RE: Rear axle sideslip stiffness

What I'm considering in the edit to my previous post is that rear axle oversteer means it's effectively steering too much, and as a result runs inside. That's not the same as perception of understeer or oversteer of the car as a whole.


Norm

RE: Rear axle sideslip stiffness

Well, (as I understood Sierra's line of questions), he has a RWD racing car. So, what is the condition and influence of the rear axle's countersteering mechanism when under full power in a turn ? And what would it be ideally (and why)? And what would a be a clever way be to help this situation ?

RE: Rear axle sideslip stiffness

(OP)
Thank You Cibachrome,
although I have AWD Car 34/66 % F/R torque distribution, i think not depends, because lateral acceleration effects pays more or less for all cars (if main load is lateral)

what is specific case when front toe-out decrease understeer?

RE: Rear axle sideslip stiffness

Watching the neighbor kid riding his skateboard and watching his trucks steer/countersteer with roll. He distributes his weight for or aft on the board, depending on his desired feel for the turn. He could install front and rear trucks with different pivot axis angles for over/understeer. Although his wheels are not powered, is this what you mean?

RE: Rear axle sideslip stiffness

What I was suggesting is the use of driveline torque to 1) apply a controlling yaw moment to the car by means of difference in side to side tire mu (on 1 series I'm familiar with that's lefts turns only). The inside tires have about 2.4 mu and the outsides have 1.4 mu. So, under a driver controlled amount of power, a rear induced yaw moment can be applied. Now recall what the aim of most rear steer algorithms for a 4WS vehicle are: Zero sideslip. 2) Additionally, a clever mechanism in the back end can also be used to induce actual rear axle steer (Tractive Force Steer. EXR would be the symbolic name for it from a K&C test. In fact, some clever teams have produced variants of this to the point where engine rotation direction has been sneaky peeky hidden under the hood to gain the best use of this phenom. Same deal though: a throttle steer effect is created with the goal of producing the zero sideslip motion (front and rear tires on the path at a tangent speed that is very high).

So here is the technical dilemma for the propeller heads: Since the rear induced yaw moment is driver controlled in both scenarios, is it counted as part of the vehicles Understeer/Oversteer recipe ? For a true 4WS vehicle it is not (just like a front steer angle is not counted as part of the slip angle family). In both cases, the contribution is NOT side-force induced (as prescribed by conventional vehicle dynamics theory, terminology and practice).

And Bugger: Yeah, that's sort of what I mean except he is using a roll steer effect to get the job done.

RE: Rear axle sideslip stiffness

(OP)
I've been thinking about it for a while, and I think more or less I understand
Thank you Cibachrome,

How front toe-out can reduce understeer?

RE: Rear axle sideslip stiffness

What car and what brand and size of front tires ? Very tire dependent. I'm guessing here, but it may be related to the amount of tire reserve (Load rating vs. actual wheel loads). If you had some tire data, there is a cool way to get the value, but put on your seat-belt, it can often be more than 1 --> 2 degrees (per wheel). This produces the sum of the peak Ay forces for an inside and outside tire at some slip angle (hence some Ay level). Depends on a few other determinants and could really ruin your day if it goes too far. For some production cars, it can be toe-in. Change tire size and pressure then you have to recalculate. Makes for a great student exercise related to "What should my Ackermann function be ?". Then all the negative effects come forward: air drag in the straights, rolling resistance, tire wear, difficulty going straight, single wheel bumps, turn in, transient response, etc. Like I said, if you overdo it and not change the rear settings, a heap of hurt can result.

If you have a serious amount of understeer, fix the rear first. Maybe I should dig up an example (typical FSAE question, BTW).

RE: Rear axle sideslip stiffness

(OP)
"If you have a serious amount of understeer, fix the rear first??"
Dig up an example!! smile

RE: Rear axle sideslip stiffness

OK, so make up a table as an array of Front Cornering Compliance (DF), Rear Cornering Compliance (DR) plus Lateral Response Time and Yaw Velocity Overshoot as key metrics for your issues. Since understeer (K) is simply the scalar difference between DR and DR, you can talk it all you want but your crew chief will have to guess which end of the car is THE problem if all you can say is that "Its understeering".

so:

DF DR K T_Ay and R_po is your score card. T_Ay is Ay response time (time to reach 90% of steady state) and R_po is the yaw velocity overshoot during a quasi step steer input. Wheelbase is typical of a mid-sized car with a slight forward weight distribution. The model is linear, which is best to educate the masses.

DF DR K T_Ay R_po
3 2 1 .27 4.2
6 3 3 .30 18.1
4 3 1 .38 5.9
4 2 2 .24 8.7
3 3 0 .50 0
2 2 0 .33 0

So if you have a heavy understeering car (6,3), response time is good but the overshoot is NFG. So, you 'fix' the front by tightening it up (4,3) and the overshoot backs down but the response times (think bandwidth) are horrible (think fully loaded P/U truck. So now you 'fix' the rear down to 2 (tires, wheels, air pressure, compliance, axle weight) and drop the front to 4 and you have a maybe decent car (the 8% overshoot may take getting use to).

If all you can do is play instead of design, then all your magazine buddies will call for that famous 'NEUTRAL' car (K=0.0), Yes the overshoot is zero, but the response times are worse than a fully loaded armor plated hearse (which may be convenient for you at a track). Sure, getting the neutral steer really low front (and rear) cornering compliance car could be a player for you but there's no forgiveness by the car as your tires go on vacation, fuel tank is filled and some damage occurs to your aero package.

Meanwhile, the steering gain of you car is so high that you are going to need a really high steer ratio gear to be a player. When diving into the pits at a low speed, make sure you can handle the huge amount of steer angles required to park the thing (get a chest friendly steering wheel knob).

Also (as you mentioned), just kick up the front static toe to +2 degrees in your BMW to experience that low front cornering compliance at a large Ay level. See attached graph from a PFG simulation. Yep, you fixed it all right. But it's transient response and steering gain makes for a lot bigger wish list. And make sure you have LOTS of tires on hand because I can smell the burning Dunlops from here. (Conti's would still be my preferred skin's).

Enjoy.

RE: Rear axle sideslip stiffness

(OP)
Thank you for explanation,

and what you meant:
A rear bar often is used to fix a compliance problem rather than change a roll trait. And in a race car, roll is not one of those 'features' you want to entertain. ?

RE: Rear axle sideslip stiffness

(OP)
How can ARB affect compliance?
Is bar attached with link direct to upright and due to roll create force for adding toe change?
What are benefits? before "classic" roll steer or compliance steer?
Is independent on wheel travel and lateral load but dependent on pure roll?

RE: Rear axle sideslip stiffness

Using the ARB to create toe in roll is not my favorite thing. Your torque idea is good if it mounts to the spindle, the way I think of it is to angle the droplink so that it pushes whatever arm it is attached to, on the bush compliances. It reduces the efficiency of your ARB, and means that your roll steer is now affected by ARB diameter and changes in the bushes.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

RE: Rear axle sideslip stiffness

(OP)
Thank You Greg

Radek

RE: Rear axle sideslip stiffness

Quote (sierra)

A rear bar often is used to fix a compliance problem rather than change a roll trait. And in a race car, roll is not one of those 'features' you want to entertain. ?
Cornering compliance, probably. A rear sta-bar is likely to change LLTD faster than it changes the amount of roll.


Norm

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