Dampers - The Effects of Delaying Weight Transfer

[CWA]

Guys,

I'm trying to get my head around dampers and the part they play in modifying the "handling" behaviour of a vehicle.

I have been applying a step-steer simulation to what started as a simple 2DOF single-track model (see my initial post for my detail - http://www.fsae.com/forums/showthread.php?11388-Dynamic-Simulation-Step-Steer-Problems ). In keeping with the step-steer theme, I have moved on from linear cornering stiffness coefficients and added some non-linear "tyre data" to include the effects of weight transfer and see how this changes the behaviour of the vehicle (I am yet to draw conclusions from this). My next step is/was to include the effects of dampers into this model. The final step (perhaps my next step, if dampers confuse me too much) would be to add in the effect of tyre relaxation lengths.

Anyway, here is my confusion detailed. I have been told that stiffer dampers (or, a higher damping ratio) improves "response" of the car to steer inputs. I used to believe this without question, but now that I've actually had to think it through, something makes me want to think the contrary.

Let's look at a car with no suspension travel (and let's assume rigid links and tyres), it will have a response similar to what I have already modelled. The front wheels are given an instant steer angle, they assume slip angles and create force, weight transfer will be almost instantaneous, and the cornering capability of each axle almost instantly drops because load immediately shifts from the inside wheel to the outside. The only thing controlling how fast this system settles into steady-state, and governing how fast the lateral acceleration and weight transfer occurs is the yaw inertia of the body, as per the basic 2DOF single-track model.

Compare this with a car with "soft" damping (damping ratio in roll <=0.1) and let's say soft springs to match; lots of wheel travel. The front wheels are given an instant steer angle, but weight transfer from inside wheels to outside does not occur immediately. The lateral force immediately created by the front wheels gives the car yaw acceleration and lateral acceleration, but because of the soft dampers, the body is still rolling, because the springs/dampers haven't gathered enough force to react the roll inertia of the body and pass this onto the wheels as a change in normal load. Perhaps this very transient state may only last for 0.25 seconds, and it may be a very simplistic view of the situation. But for this time duration, it's fair to say that there is a more equal load on the front wheels than in the first car's case. This means, due to the non-linear effects of tyres, that the front axle, when given equal slip angles due to the same steer input being applied, is actually able to give more total force, until the weight transfer is actually seen at the tyres. It may take this fictional 0.25s or more or less to reach this steady-state, but during this time, the extra front axle force is being used to apply more yaw acceleration to this second vehicle than the first vehicle had. Technically, doesn't this make the second vehicle more responsive?

I am aware that the down-sides of such a low damping ratio would give excessive overshoot and oscillation of the body, and this detrimental effect would subjectively be the worse set-up option. And there are of course negative subjective implications of having the driver's head experiencing a lateral acceleration "lag" with excessive body roll to be considered (Harty, 2004). But using the same trend to compare a car critically damped in roll (damping ratio = 1) to a car over-critically damped in roll (damping ratio = 2), wouldn't this actually make the former, less-damped car more responsive?

As with most of my endeavours on this subject, I am probably wrong, and my thought-process is flawed somewhere. If someone could point out the incorrect assumptions or deductions I've made, I'd be very grateful. I look forward to your corrections!

Cheers,

Chris

[Moop]

I have been applying a step-steer simulation to what started as a simple 2DOF single-track model (see my initial post for my detail - http://www.fsae.com/forums/showthread.php?11388-Dynamic-Simulation-Step-Steer-Problems ). In keeping with the step-steer theme, I have moved on from linear cornering stiffness coefficients and added some non-linear "tyre data" to include the effects of weight transfer and see how this changes the behaviour of the vehicle
I'd be careful with using a step steer input for a nonlinear simulation. For a linear range simulation it's fine, but for a nonlinear system the way the system responds depends on the input, so you want to make sure your input is right, or at least in the reasonable ballpark of being right. All the DAQ traces of steer angle I've seen on corner entry are roughly a ramp steer, so I think it makes more sense to use that as an input if your system is nonlinear.


The only thing controlling how fast this system settles into steady-state, and governing how fast the lateral acceleration and weight transfer occurs is the yaw inertia of the body, as per the basic 2DOF single-track model.
Not true. Your tire cornering stiffnesses(or cornering compliances if your car has a suspension/chassis) will determine the natural frequency and damping in your system, which will affect the response time and overshoot. Take the Laplace transform of your 2 DoF bicycle model and you'll see this. The system unfortunately has zeros though which complicate things a bit, but just looking at the characteristic equation, you'll be able to see that linear understeer increases the natural frequency and the product over the sum of the axle weighted cornering stiffnesses(that might be upside down) is related to the damping in the system. Bill Cobb has talked about this a couple of times(not sure where the threads are).


Anyway, here is my confusion detailed. I have been told that stiffer dampers (or, a higher damping ratio) improves "response" of the car to steer inputs. I used to believe this without question, but now that I've actually had to think it through, something makes me want to think the contrary.

Compare this with a car with "soft" damping (damping ratio in roll <=0.1) and let's say soft springs to match; lots of wheel travel. The front wheels are given an instant steer angle, but weight transfer from inside wheels to outside does not occur immediately. The lateral force immediately created by the front wheels gives the car yaw acceleration and lateral acceleration, but because of the soft dampers, the body is still rolling, because the springs/dampers haven't gathered enough force to react the roll inertia of the body and pass this onto the wheels as a change in normal load. Perhaps this very transient state may only last for 0.25 seconds, and it may be a very simplistic view of the situation. But for this time duration, it's fair to say that there is a more equal load on the front wheels than in the first car's case. This means, due to the non-linear effects of tyres, that the front axle, when given equal slip angles due to the same steer input being applied, is actually able to give more total force, until the weight transfer is actually seen at the tyres. It may take this fictional 0.25s or more or less to reach this steady-state, but during this time, the extra front axle force is being used to apply more yaw acceleration to this second vehicle than the first vehicle had. Technically, doesn't this make the second vehicle more responsive?

I am aware that the down-sides of such a low damping ratio would give excessive overshoot and oscillation of the body, and this detrimental effect would subjectively be the worse set-up option. And there are of course negative subjective implications of having the driver's head experiencing a lateral acceleration "lag" with excessive body roll to be considered (Harty, 2004). But using the same trend to compare a car critically damped in roll (damping ratio = 1) to a car over-critically damped in roll (damping ratio = 2), wouldn't this actually make the former, less-damped car more responsive?
The explanation I've always heard is similar to that used for roll stiffness distribution. Some people say that if your roll damping distribution is biased towards the front, more transient load transfer on the front makes your front tires less effcient, and then they say that that makes the car turn in less quickly because of that. You could also argue that it makes the car respond more quickly, since the rear tires would be more efficient and hence better able to damp the car in yaw. Of course, this says nothing about the damping ratio in roll.

An important thing to think about is - what's the definition of the "response" of the car to steering inputs? Is it the rise time or settling time(and of what?)? The two are very different. You could have a set of front tires with a really high cornering stiffness and a set of rear tires with a really low cornering stiffness. You'd produce a very high initial yaw moment from steering and it would take forever for the counter yaw moment on the rear to build up, so the car would have a short rise time, but it would also oscillate for a long time(in open loop) since the rear tires aren't doing as much to damp the car in yaw.

I've done some investigation into the impact of damping on yaw dynamics as a part of work so I don't think I can say too much about it. I did find though that the traditional explanation didn't really hold up at all, at least with the model I was using.


The final step (perhaps my next step, if dampers confuse me too much) would be to add in the effect of tyre relaxation lengths.
Chapter 8 of Tire and Vehicle Dynamics has some examples of the effect of tire relaxation length on the linear step response of a car if you're curious.

[BillCobb]

Just as your car has a load transfer distribution front/rear due to springs, kinematics and body torsional stiffness, it ought to also have a velocity based load transfer distribution due to dampers, strut mounts, etc. That distribution is usually more rearward than the stiffness fraction. Much of such a 'designed' fraction depends on the amount of kinematic steer and camber you want to also admit into the vertical load and steer recipe. These factors greatly affect the vehicle's dynamics because they alter the transient axle sideslip per g function.

Much of this also depends on your roll inertia, roll centers, tire overturning moments and camber-by-roll fractions since they are the simple parameters which define the roll dynamics.

You might be surprised at how low a fraction of critical damping is in the roll mode of most vehicles. Production cars are usually between 0.1 and 0.2 of critical damping. Its a simple thing to measure with a lateral accelerometer and a roll or roll velocity gyro. Use a yaw velocity gyro on its side to get roll velocity response and integrate it in the time or frequency domain. If you can perform a frequency response handling test, you will obtain the steady state roll compliance, the peak to steady state ratio (from which you calculate percent critical) and the roll damped natural frequency. The roll damping level (peak roll) is directly correlated to 'pleasability' in the production engineering world. And in high performance vehicles with high tire stiffnesses, the roll natural frequency value is a big player.

In your simulation, you will probably find only a very small portion of your damper curves are used in roll mode control. Think of it: roll velocity is pretty small compared to wheel impact bumps and bruises found on road straightaways.

Now the relaxation stuff has a more profound reaction to damper force changes. The problem you will have is getting the surface functions of relaxation properties for slip and load change inputs and removals. It is being done but remains very proprietary.

You might think up some clever ways to get some values using a mechanical linkage in your shop, perhaps even using a device attached to the trailer hitch of a weighted truck.

[Z]

Chris,

Firstly, thanks for starting threads a bit more interesting than "Can we change tyre on rim, pls advise urgently!?".
~o0o~

Regarding a car's "responsiveness", it is quite common to hear long discussions at track days about how the new, stiffer springs and dampers on the car make it much more "responsive", but for some reason the lap times are slower! This can be due to the lateral acceleration at the driver's head following the steering movements more quickly (so "more responsive"), while the car bounces around the track because of the stiffer springs/dampers (again feeling "more responsive" to the bumps) but ultimately losing time because wheels often not in contact with the road.

Also, many of the (usually open-wheeler) racecars with "monoshock" suspensions only have these at the front. So no roll-damping at the front (with the monoshock-damper only reacting to axle-heave). The rear wheels have a damper each, so can react to roll. My understanding of this arrangement is that the rear-only-roll-damping increases the rear LLTD during initial turn-in, thus "loosening" the car (ie. more oversteer), thus making it more "responsive". (Mid-corner OS/US balance goes back to whatever LLTD is set by the springs and kinematics.)

So for "responsiveness" your thinking in your first post is correct, IMO. Namely, stiffer dampers reduce grip.
~o0o~

Lastly, you might want to compare step-steers for otherwise similar cars, but with different amounts of pro- or anti-Ackermann. So the "average" step-steer angle of the two cars is the same, but the pro-Ackermann car has greater steer-angle of its inner-wheel, and less of its outer-wheel, while the anti-Ackermann car is the other way around.

I reckon the pro-Ackermann car will be more "responsive" (faster initial yaw acceleration), especially if the LLTD is rear-biased.

Z

[BillCobb]

Much can be learned from measuring the induced roll just due to steering input. The car does not have to be out on the track, just stationary in the garage. A constant amplitude 'chirp' input by a driver with talent is necessary. Machine inputs are more cool. Grease plates or air bearings make the task even easier. As is often the case, you can induce a higher roll fraction from steering than from cornering. That brings all the rear suspension parameters into play.

A frequency response analysis of roll by steer up to about 4 hz (or whatever the driver can do) will show you how bad it is. Then its just a Matlab process:

nfft=pow2(length(steer));
(RollSwaTxy,f)= tfe(steer,roll,nfft,sps); % sps is your scan rate per second
RollSwaGain=abs(RollSwaTxy);
RollSwaPhase=angle(RollSwaTxy);

Plot the gain and phase vs. f(frequency) and put your seatbelt on.

It's that simple, folks...

A possible downside of caster and caster offset settings.

[murpia]

...You could have a set of front tires with a really high cornering stiffness and a set of rear tires with a really low cornering stiffness. You'd produce a very high initial yaw moment from steering and it would take forever for the counter yaw moment on the rear to build up, so the car would have a short rise time, but it would also oscillate for a long time(in open loop) since the rear tires aren't doing as much to damp the car in yaw.
Slightly off-topic I suppose, but I'm interested in this idea.

It occurred to me some time ago that there could be advantages to different tyre diameters front and rear. If we consider the usual 10" vs 13" debate I can see several packaging reasons why 13" fronts and 10" rears might be preferred. But, for even tyre temperature build-up, 10" fronts and 13" rears might work best as the front contact patches 'come around again' faster than the rears (which are heated more by traction). Front-rear cornering stiffness distribution is another thing to add into the analysis, and also relaxation-length distribution front-rear.

To the tyre experts, is there any correlation between rolling diameter and relaxation length?

Perhaps the ideal is 13" rims front and rear with very low profile fronts for smaller rolling diameter, higher cornering stiffness & shorter relaxation length, plus 'balloon' high-profile rears for good traction & launch?

Also, what do the rules say, are you actually allowed radically different tyre types front and rear?

Regards, Ian

[BillCobb]

The correlation is not very good between diameter and relaxation, although for the want of something better, a fraction of circumference (hence diameter is often speculated). Relaxation is a distance traveled phenomenon. Instead, the correlation between section height and aspect, and relaxation is very good . Construction details in the bead and tread to sidewall attachment areas are the prescribing factors.

Do a 'think' experiment on the Mz relaxation process and you will score some points. Its definitely NOT proportional to Fy if the tire is steered (as in Front Tires). And, its different for rear (unsteered) tires.

And bias is usually much better (shorter) than radial construction.

[exFSAE]

Perhaps the ideal is 13" rims front and rear with very low profile fronts for smaller rolling diameter, higher cornering stiffness & shorter relaxation length, plus 'balloon' high-profile rears for good traction & launch?

Cranking up front cornering stiffness and/or dropping relaxation length will just make the car an oversteer machine... slow, sloppy response and junk for slaloms, IMO.

Back to the thoughts on dampers - something to think about is how much roll stiffness FSAE cars tend to have. How much suspension travel do you really have, and how much velocity are you generating in the dampers? Probably not much in either case. I'd guess the proportion of tire normal load resulting from damper velocity in any given maneuver is probably a drop in the bucket compared to the other force elements (springs, bars) - and overall a pretty marginal effect on handling when there are much bigger hitters out there (including the mass distribution and diff!).