Damping Rates and the Nature of High Speed Input

[MCoach]

I've done quite a bit of reading on dampers and their theoretical and practical applications but I seem to have run into a similar problem that I have with certain features of tires; certain areas just don't readily seem to be covered in a technical enough nature and typically ends up with me reading F1 technical with some post by Jersey Tom (you crazy old bat) telling everyone they're wrong about their F1 speculation. I regularly refer to "The Damper Handbook" by John Dixon and "Vehicle and Tire Dynamics" but Hans Pajecka but can't seem to find much information about the effects of regressive and (specifically) digressive damper rates (not necessarily installation motion ratios) on the unsprung mass with respect to specifically tire force variation and ride.

To get past what I do know, low speed rates are effective for body oscillations and high speed rates are effective for wheel oscillations. Bi-linear rates are most common for circuit cars and highly progressive rates are most common for off-road vehicles to keep them from bottoming out over continuous bumpy areas and ruts. However, digressive rates seems sporadic in it's use and mention with some high level information from Penske and some rally sources. My intuition leads me to think that the normal bi-linear rates are too high of a damping rate to keep grip on the track due to small bumps and variations and so they reduce the high speed range to improve road following. Never mind that there are quite a few features on a high performance vehicle that operate outside of a linear range including the tires themselves so this only seems to make sense to me of for digressive or regressive rates to be used.

If there anyone who may be able to enlighten me to other reasons they may be used, I'm open to hearing them. If there are any other books, websites, or people that you can refer me to that'd be appreciated.

For anyone who has felt this may have gone over their head, I'll offer up this source which illustrates the characteristics of what I'm talking back:

http://www.resuspension.com/assets/Regressive%20Valve%20Tech%20Memo%2012.1.pdf

[Pete Marsh]

Very interesting topic, and please let us know if you find anything.

I have some experience with rally, and there they are used to limit the impact from a rock or rut etc. The idea is for the shock to blow off at some high force level, that would otherwise throw the car off line/damage the tyre or suspension, and let the wheel move out of the way.
They also need a quick return to recover the wheel position after the bump (bouncing it off the bump stop), which is in conflict with the high rebound rate required for landing jumps, so the valve has to allow for that too.

What is interesting is regular mono tube dampers will do this a bit if you have the right gas pressure, but of course your low speed bump is then limited and a happy combination is not always possible.

There must be a few Alumni working in the WRC? Maybe they can enlighten us a little?

Pete

[Goost]

I used to always wonder whether bilinear damping was just useful because it is fairly simple to implement mechanically.

The Dixon book, if I remember correctly, references

FUKUSHIMA et al. Optimum Characteristics of Automotive Shock Absorbers under Various Driving Conditions and Road Surfaces. JSAE Review. pp 62-69. March 1983

which seems to suggest there is benefit to relatively high damping at 'moderate' speeds.
It's mostly experimental, but fascinating nonetheless.

They also recognized (perhaps this was the original objective of the paper) that ideal damping is also stroke-length dependent. I can't find the source, but they later solved this by putting some type of swirl-pot in the damper valve which would restrict flow after a certain stroke length had created adequate turbulence.

[MCoach]

Fair point Goost. I figure I'll have to go look through the sources of my sources and try to glean anything from that and various SAE papers.
I'll check out the one you mentioned and get back to this topic on that. Various textbooks seem to claim .1143 (off the top of my head...) is the optimal damping ratio (of critical) for the unsprung mass, so I'll check that out against my current calcs and see where that lands me. Maybe I'll share that if others are willing to for the benefit of the those reading.

[BillCobb]

Dampers ought to be tuned to tire relaxation, especially MZ on the steered axle for maybe not so obvious reasons. Traction (FX) is another one of the MISO control signals that comes to mind...

[Z]

DAMPERS ARE CRUTCHES FOR STUPID SPRINGS.
======================================

MCoach,

My (heretical?) view on this subject is summarised above.

If you have broken or malfunctioning legs, then you generally get around faster with some crutches. Likewise, most cars (racing or production) have very crudely designed "springing", so they go a bit faster when given some crutches, err..., I mean dampers.
~~~o0o~~~

Note two things:

1. Dampers are frictional devices. They always exert their force in the OPPOSITE direction to their motion. So, from Work = Force-Vector (dot.product) Displacement-Vector, the dampers are always doing NEGATIVE work.

So (maybe draw small diagram...) when a wheel hits the uphill side of a bump, the damper increases the Fz load above its normal value, and also increases the rearward Fx force (from the slope of the bump), which then slows the car down. A moment later, on the downhill side of the bump, the damper reduces the Fz load below its normal value, and this time reduces the forward Fx force that would normally speed the car up again.

So dampers cause large variations in the tyre Fz force (= BAD, because can reduce grip), and also suck kinetic energy out of the car's motion via the Fx forces (= MORE BAD, because more fuel must be burnt, etc.).

2. The sole purpose of the damper's frictional behaviour is to suppress (or "damp", or "suck energy out of") oscillations of the car-body in Heave, Pitch, or Roll motions, and also to suppress the four Wheel-Assembly's "tramp" oscillations. The car-body H/P/R oscillations are of its mass vibrating on its various suspension springs. The WA tramp oscillations are of its mass vibrating between its tyre-spring and suspension-spring (which is why I have great difficulty calling the WA an "unsprung" mass).

To repeat, sucking energy out of oscillations is the ONLY PURPOSE of the dampers. If you could prevent these oscillations some other way, then NO NEED FOR DAMPERS!
~~~o0o~~~

Now imagine a vehicle with smarter springing. Say, a fully-computerised-control, active-suspension, car. Or, better yet, some sort of animal with legs, which are controlled by muscles, which are controlled by some sort of clever nervous system. You can find reasonable examples of such (bi-pedal) animals at the local skateboard park, or on the "moguls" at snow-skiing resorts.

Watch these creatures as they traverse a series of bumps. You see that they LIFT their feet (= wheelprints) as they approach the uphill sections of the bumps, reducing both Fz and Fx forces. Then on the downhill sections of the bumps they forcefully PUSH DOWNWARDS with their feet, increasing both Fz and Fx forces. The end result is an approximately constant Fz force (necessary to counteract gravity), and a net FORWARDS Fx force, which counteracts drag, and can actually accelerate the beast forward.

And as far as the problems of "oscillations" are concerned, there are none! There are certainly lots of masses and elastic elements involved, but as soon as a single nasty oscillation starts to rear its ugly head, it is cut off by the nervous system slightly modulating one of the spring-forces (= muscles).

Bottom line here, NO DAMPERS NEEDED, or even wanted. And a good model for suspension design...
~~~o0o~~~

Getting back to your conventionally suspended car and regressive dampers, the Penske link has.

"Synopsis:
The objective of the regressive valve is to produce a compression or rebound damping characteristic that allows increased low or mid-speed damping force for driver feel, while providing more suitable lower levels of high speed damping for bump absorption. ...
...
Summary:
In test after test, the regressive valve has allowed suspension tuners to unlock hidden performance in many different types of racing. By increasing low speed damping support, and dramatically reducing suspension spring rates without loss of driver feel, regressive valve users have boosted driver confidence and increased grip levels..." (My emphasis.)

As I have ranted about at great length elsewhere, conventional suspensions have STUPID SPRINGS. The springs know nought about the H/P/R-modes of the car-body, nor about the Twist-mode of all four wheels, nor about WA tramp. There is very little adjustability of the springs possible, other than broad but crude changes that boil down to "softer or stiffer".

For example, as hinted at by Penske above, stiffening the corner-springs helps control car-body-H/P/R, which is good for "driver feel". But that makes bump absorbancy worse. Conversely, softening the corner-springs is great for bump absorbancy, but makes the car wallow around like a drunken hippo, which is bad for "driver feel". And trying to stiffen the springing only in the Roll-mode, say, by adding stiffer ARBs, also stiffens the Twist-mode, which is again bad for bump absorbancy, and messes with LLTD from any "twist-in-the-road".

So the Penske solution is to add the "regressive damper" crutch. This allows the car to have softer springs all round, which is a fair starting point for bump absorbancy (although "actively lifting" the wheels would be better, as noted above). The problem of the car "wallowing like a drunken hippo" is then partly fixed by adding the relatively stiff "low-speed damping" crutch.

But, as noted, ANY DAMPING IS BAD. So at higher speeds the regressive dampers "blow-off" so that their force is actually LESS THAN whatever it was at the lower H/P/R-control speeds. In a sense, the crutches are temporarily thrown away. Well, just over the bumpy sections of track.

(Interesting is that the regressive-damping curves are quite similar to those of old-style friction-dampers. These have a highish force while stuck in the "static-friction" zone, with this force then reducing to a relatively constant (ie. velocity independent) "sliding-friction" force over bumpy sections of track. However, the slope of the static-friction zone is much steeper than with hydraulic dampers, which is generally bad, especially for the Twist-mode (less of a problem in the other modes...). Anyway, Penske's dampers seem to be a very expensive version of those older dampers. Such is progress...)
~~~o0o~~~

All things considered, in the long term I think you are better off focussing on improving the springing-system, and AIM TO USE MINIMAL DAMPING. At a fundamental level they are counter-productive. And they are plain un-Natural! :)

Z

[NickFavazzo]

Z, the benefit of using dampers even though they increase load variation it the instant relative motion occurs, ie bump, sudden braking etc, is that they reduce load variations after the event.

A low speed underdamped car can be seen to bounce for more time/distance than an appropriately low speed damped motion
A low speed overdamped car can be seen as too stiff, and effectively locking out the suspension in extreme cases.
High speed is a little different as you want would generally want a low rate here to reduce the impact of the force, ie hitting a curb, having the HS rate= LS rate would cause a huge spike in Fz, upsetting not only the car but likely the driver and team…

Using roll as an example, the rate of load transfer across an axle pair (total load trans = const) is determined by the resistance the damper offers and the rate the load is applied, stiff dampers act more closely to inelastic weight transfer= sudden load transfer=tyres don’t like. Soft dampers slow the rate of transfer, as a driver this means the car feels slow to respond to your input. As such finding damping that makes the car+driver fastest is a compromise between the drivers slowest acceptable response (best for grip) and how quickly the tyre can handle having the load change.

To add to all that, you also need to consider how forces feedback into the chassis/other wheels and obviously the changing wheel geometry through the motion.
If you plot tyre Fz against distance travelled I would argue that the correct damping for grip (and as such reducing Fx variation) would have the least area below the curve hence the closer to critical damping it is, the better, so dampers are inherently GOOD!

Point 2 you are suggesting active control systems that keep constant the Fz and Fx values, I believe that this would be unachievable and that rather it would be great for controlling the maximum rate of change of load (which IMO is the real goal here).
Your active system will need a very good control system to work, not saying that it cannot be done but I think developing a system in a 1 vehicle design phase well outside the scope of a FSAE/FS team

Back to Regressive dampers;

My understanding is that regression rates allow modification to the LS/HS “typically linear” portions of the damper curve and this is really good for HS inputs, where at different road speeds but the same geometry bump will have different accelerations/forces as such, as the input forces increase the desired resistance decreases to maintain what the tyre wants (which I am assuming is very non-linear and closer approximated by a curve).
For ride applications it is further smoothing the transmissibility over a much larger (than standard linear damping curves) input range.

MCoach, are you more after information w.r.t road cars and ride smoothness or race track where tyre load variation is of higher importance?

[Kevin Hayward]

As I see it the main issue with hydraulic dampers is that they behave on roughly as a F-v relationship. What we largely want is dampers that behave on a F-f basis (Force vs. Frequency). We only want the dampers acting when their is oscillation (as Z points out) We want to keep the average acceleration of the Wheel Assembly (agree with Z about the unsprung term not being appropriate) to a minimum. Any vertical load variation on the tyre contact patch will make grip worse. Claude's slides mention the fact of losing more on the increase of load, than you gain on the decrease. The actual situation is much worse. The tyres have a delay of generating grip (relaxation) which doubles down on the loss of grip due to load variation.

Generally we see the oscillating frequencies occurring at lower shaft speeds. This means more damping there, less as it speeds up (or slows down). This is a very rough approximation. The regressive dampers go somewhat towards that, but are a crutch. All of this becomes reasonably dependent on the frequency content of the disturbances of the track. A good bumpy track will sort out a lot of the teams when it comes to how well they understand and tune their suspension.

The end result is with our non-frequency dependent dampers we end up chasing setup between tracks constantly. There are some really cool methods to introduce frequency dependance, but not commonly seen in FSAE. I think a good basic rebuildable damper with a team ready to make some reasonable changes (i.e. not just different sized holes and shims) and you could end up with something that works better.

Another area you may want to look into is how the force varies vs acceleration and jerk. We idealise our dampers as having a clear F-v relationship, but the reality is that there is a lot going on in the valve and the oil movement. The oil has a noticeable mass, that makes a difference when its velocity has to suddenly change. Valves do not open and close instantly. There is turbulance in the fluid. There is fluid friction to consider. Expansion for remote accumulator lines (or interconnected hydraulic lines).

I don't think you need to rely solely on specific damper literature. A lot of the more general texts dealing with hydraulics help a lot. In the specific damper texts there are a lot of good papers on active suspension that have a decent analysis of the problems they are trying to solve. Some of the MR damper papers are also good sources. I wouldn't attempt to try and learn anything meaningful about dampers without some expectation of testing, design, as well as research. One of the saddest things about the better off-the-shelf dampers available now is that far fewer teams look at developing their own dampers. (The same is true for diffs.) When we did the first Kinetics system there were a few teams doing their own, including some playing with frequency dependent dampers. The MTB dampers were just that bad that it was a good option. Now the Ohlins (and others) are good enough and the advantage to be gained is not too large.

Obviously the other area to investigate is the dampers affect on transient balance due to changing the roll moment distribution throughout a corner. However a good understanding of vehicle dynamics will get you thinking along the right lines there.

Long story short, don't bother too much with damper specific texts. All they are is oil squirting through little holes that affects the dynamics of a mechanism with springs. Non-compressible fluid dynamics and rigid body dynamics.

My colleague Nando Guzzomi, did some great work for his PhD looking at the fluid flow through hydraulic valves. A good experimental approach. You can read his PhD here:

Investigation of damper valve fluid-structure interaction through the application of experimental visualisation techniques:
http://repository.uwa.edu.au:80/R/-?func=dbin-jump-full&object_id=34041&silo_library=GEN01

It even references Z in the first page of the introduction.

Kev

[mech5496]

Kev,

thanks for the link and thanks everyone for the interesting discussion going on!

[Goost]

The literature on the interaction of vertical (out-of-plane) dynamics and lateral/longitudinal (in-plane) dynamics is rather weak in my experience. It took me the better part of 3 years of FSAE to even have a grasp of relaxation. I saw in a teammate's new OptimumG binder Claude is now teaching some of this - I expect everyone will be well-versed in the topic within a couple years with a larger audience hearing it.

Anyway, for those who are skeptical that dynamic grip matters (due mostly to "if it's important I would have heard of it by now" syndrome) I scratched together some MATLAB code that adds a relaxation length to a quarter car model. Requires tons of assumptions, but it gives you a feel for 'relaxation matters' and quickly shows 'minimizing tire oscillation' isn't quite a good metric for choosing dampers.

Sorry the code is rough, threw this together in an hour or two just now. just change the extension to .m and it should run.

MCoach,
As far as fair sharing goes, I have approximate spring/damping/weights from one of our cars here, enough to get a discussion rolling on what you find?

[Goost]

Trying to make this more accessible than the previous post:

Took the model, changed the input to a force on the sprung mass (weight-transfer-esque).

I made a little GUI that lets you change the damping rate and see the step response of the contact patch oscillation, and the lateral force.

What does this show: there are damping rates that are good at 'keeping the tire in contact' and others that are good at 'keeping the lateral force maximized' and they are not the same. Generally (and this usually holds true for the nonlinear models) the ideal damping for grip is higher than that for ideal contact.

Before trusting this, please make sure you are comfortable with the parameters used, particularly the masses/springs vs vehicle-speed/relaxation-length.

Sorry if this all seems a bit off topic, but I think it's pretty fun and relevant to choosing high speed rates.

~~~
note on running the code:

Lines 78 and 87 control what type of plot (step, impulse, bode, pz, etc.)
though you may have to comment out 80 and 89 if you change them

This (and the previous code) require Control Systems Toolbox.

[Kevin Hayward]

Sorry if this all seems a bit off topic, but I think it's pretty fun and relevant to choosing high speed rates.



Your last two posts are possibly the least "off-topic" posts I have seen recently. Great stuff. Particularly awesome to have a thread about dampers. All the acceleration event, teams management, engine, electronic throttles (and other mechatronic madness), and aero discussions have been depressing. Nothing quite like discussions about good old-fashioned mechanical grip. Used to be the main topic of choice in FSAE, and one I think was maybe understood better by some during periods of much lower grip tyres, and no decent (and affordable) off-the-shelf dampers.

One word of caution for readers here is not to make too many decisions based on quarter car models. You car's grip will be heavily influenced by roll and pitch motions. A simple extension to what Goost has presented in his code is to have a look at the quarter car model as well as a half model showing roll, and another half model showing pitch. Make sure you can use the results of the second to improve your accel sims. Use testing data to help with your inputs.

The simple state-space models with linear dampers are a decent first pass to gain a little understanding, but I wouldn't run with them for long. Bi-linear is the next step, but I prefer going straight to a simple lookup table for non-linear dampers based off test results. Going further reasonably simple but good hydraulic models are not too hard to implement that can help you start too look at things like the effects of hysteresis.

On top of all of this you need to be able to keep a good overall picture of the car. If you spend a long time fiddling and optimising a car with 4 independent corners, with four dampers, two anti-roll bars etc. then that is what you will have on your car. Quick modelling is cheap. When you start with linear models just run through the process of thinking about interconnected systems, beams, struts and so-on. Think about roll and pitch springs with corner dampers, and corner springs with roll and pitch dampers (and any other possibility). Whatever you do don't make too many hard and fast decisions on either an inaccurate model, or simply because you didn't consider all the relevant concepts.

If you are in a team doing serious development on dampers please post something here. It is nice for everyone to know the work being done, and you can get a lot from good feedback. In my experience sharing knowledge has never led to a competitive disadvantage.

Back in 2003 (US comp) I was pretty astounded by the work one team was doing with frequency dependent dampers. Unfortunately I can't remember the team, but I would love to know whether they kept going. Any ideas on who this was and where it ended up?

Also I am still not aware of anyone that has done a rotary damper for FSAE yet. UWA had torsion bars at one point (the natural progression for kinetics). Torsion bars and rotary dampers go a long way to solving a few packaging and shaft friction problems. Anyone done or doing a rotary damper?

Kev

[MCoach]

I haven't been back to my calcs yet to see where I'm at, as I'm doing the whole 10hr work day thing right now and with my "spare time" working on my thesis, making up the other waking 10hrs of the day...ugh. I will try to get back to everyone by this weekend, but wow am I impressed with replies so far. I have been reading along, just unable to put together a few minutes to reply comprehensively.

Bill, I want to address the bit on the relaxation length, lateral or longitudinal relaxation length?
I understand that relaxation length is related to the gain to maximum x and y generated force...and high speed damping needs to be tuned to this parameter, but I haven't yet had that lightbulb moment to tie it all together. If you could expand a little on this that would be helpful.

Goost, thanks for the simulation input, I'll be digging up my info for the next post as well to share. Currently for me high speed damper rates have been subjective and by focusing on increasing yaw gain on the car (stiffen up everything). Also, I agree on the difference between optimal contact and maximum lateral grip, as I dug up some info on road car dampers where it's apparently normal to be digressive/regressive. It goes completely into that better ride, softer springs bit, but that way of doing it is not ideal for grip.

I'm trying to get ahold of a Kaz re-valve kit this year (basically the same cost to have Kaz revalve them) to do some development work. I've finally got our car to a point where it can be quite a bit faster through iteration than redesign this year so I'm trying to be more meticulous on the details of everything.

Z, I think damping for a system is beneficial. Too much overshoot on a dynamic system can be bad (so can too little). Ideally active suspension is the way to go, and if it were the way I wanted to go, then fortunately I am working for the right company. However, I have neither the time nor the budget to scrap together a hydraulic (or any other) control circuit for this application. Trust me, I have considered it. :)

[Claude Rouelle]

Although not directly related to the question I am throwing a perspective which I think is important in damper setting calculations.

Most of the students follow the text book calculations of the choice of damper ratio (percentage of critical damping) based on the studies mainly made for passenger cars compromise between ride, comfort and response.

These are mostly based on the critical damping calculation of 2*sqrt of (K*M) where K is the wheel rate and M the suspended mass per corner. There are more sophisticated and useful calculations with take the non-suspended masses and the tire stiffness into account but we won’t go there in this post.

However that is just for vertical damping. What about roll and pitch?

In heave, you have the mass “against“ the spring while in roll you have the suspended mass inertia against the springs and the ARBs (and do not forget to use the parallel axis theorem to calculate the suspended mass inertia around its roll axis, not its CG)

In some case like a recent, light FSAE mono-cylinder without wings you will see that with front and rear suspended mass frequency of around 3 Hz, the roll frequency can easily be around 15 Hz. And when heave damping ratio is about 0.7 it could be as low as 0.3 in roll.

Often when you have a good damping ratio in heave it will be too low in roll. And when you have a good damping ratio in roll (and maybe in pitch) it will be over-damped in heave.

There have been very competitive FS/ FSAE cars recently with damping ratio way, way, way above 1. I don't think is not only because most of FSAE / FS tracks are not really bumpy and we do not really care about comfort

Also another aspect of damping tuning (especially in bump) is that it has a considerable effect on the tire temperature. Some people say that “bump is for the tire, rebound is for the driver”. If you have a cold track and hard rubber with difficulties to get tire temperature and you have a very sensitive driver who does not need to “bind the car in rebound to feel it”, I would not be surprised that a given speed of 25 mm/sec for example you will have 3 or even 5 times more bump than rebound.

There are scientific ways to calculate what the ideal damping should be but it requires the knowledge of
- a good trustable and relevant tire transient and thermal model
- the prolife of the track with every single bumps
- all the car inputs especially the K&C because the wheel rate is not necessarily the one you think it is

At that does not even take into account the drivers’ driving style.

So at the end, unless you have all this information and you have time for intellectual mas… gymnastic, make some good basic calculations and go testing (ideally, at least once, with a professional driver).

And do not be afraid to test the car damping outside the text book boundaries.

[mmalinowski]

Mcoach, I’m posting an output page (attached) form my steady state transmissibility simulation code created for a two degree of freedom quarter car model excited by a sinusoidal road input (road input(t)=Y*sin(w*t)). All model parameters here are linear and based on common FSAE values obtained from my team’s 2014 vehicle.


Remember that the steady state response of a sinusoidally excited 2-nd order system will also be sinusoidal with a phase angle “lag” between the input and output (suspend a water bottle on a rubber band and move your hand up and down in a sinusoidal fashion and observe the vertical displacement of the bottle. If you have never done this before, I highly recommend it! Observe the point at which your hand moves up, while the inertia of the bottle pulls it down.).


Transmissibility is the ratio of the steady state amplitudes for any defined system output and the corresponding system input. In the case of my quarter car model, I was interested in simulating the following transmissibilities as functions of the road forcing frequency (“w” variable in the road input(t) function defined in the first paragraph): unsprung mass transmissibility (Xu/Y), sprung mass transmissibility (Xs/Y), and the unsprung mass-road relative displacement transmissibility (Z/Y=(Xu-Y)/Y). Here is a solidworks sketch of the model with the coordinates described (attached).


Take a look at all of the plotted transmissibillities for each suspended mass damping ratio (zeta). There is a significant reduction of all transmissibilities at high forcing frequencies occurring with each 0.2 reduction step in zeta value. This simplified simulation suggests that the “softer” we make the damper, the less we will disturb both the driver and tire at high forcing frequencies. It would seem to me that this effect would be further amplified by a digressive damper curve such as the ones presented in the Penske document which you referenced.

There is something which did puzzle me in that document though…..

In the first presented Force vs. Relative Velocity curve, the slope of the graph becomes negative past the point of digressive “blow off” in the compression area of the graph. Does that mean that the resulting damper force (Fdamper=c*relative speed) is actually helping the damper compress? Is the damper still dissipating energy from the system at this point?


---------------------------------------------------------------------------


Goost, I agree with your statement regarding literature on the interaction and coupling of vertical and lateral/longitudinal dynamics being limited. Or maybe undergraduate students are just afraid of Mr. Pacejka’s Tire and Vehicle Dynamics book… Nevertheless, I had a hard time finding easily understandable information on the topics of tire relaxation lengths and transient tire model time constants. Your posts got my “gears turning” (thank you) and caused me to have to do some homework…


I came across a paper (from the SAE Technical Paper Series) titled “Lateral Stiffness, Cornering Stiffness and Relaxation Length of the Pneumatic Tire” written in 1990 by Jeff S. Loeb, Dennis A. Guenther, Hung-Hsu Fred Chen, and John R. Ellis. A 1-st order, transient, tire lateral force model is developed in the above specified paper with a slip angle unit step response time constant equal to the tire cornering stiffness (C) divided by the product of the longitudinal tire contact patch velocity (U) and tire lateral stiffness (K) (tau=C/(U*K)). This model is only valid for the linear region of tire behavior.


You mention that “there are damping rates that are good at 'keeping the tire in contact' and others that are good at 'keeping the lateral force maximized' and they are not the same.” I began to try to understand and analyze your statement after having read the previously mentioned paper. My thoughts were the following:


In order to keep the tire lateral force maximized through time we would want to keep the dynamic tire vertical load variation within a range of Fz values that would yield the lowest time constant for a unit step slip angle input. Keeping the dynamic Fzs within a range that would give the lowest instantaneous cornering stiffness (C), but highest instantaneous tire lateral stiffness (K) for a given tire would allow the Fy to “jump” to its steady state value as soon as possible (maximizing it through time after the disturbance) by always attempting to minimize this slip angle unit step time constant. So if we had lateral and cornering stiffness tire data as a function of Fz, for a given rim and tire construction, (assuming constant velocity, pressure, and temperature) we could find a heave damping ratio which would maximize the lateral force, instead of just prevent the wheel from hoping. Am I even remotely close?


Here is another question for anyone else who has also read this paper in the past… When measuring the tire lateral stiffness, are the effects of the moment (Mx) created by the Fz vector no longer being “in line” with the wheel center considered? The wheel assembly was “squashed” to a pre-specified Fz value, a Fy was applied, and the contact patch lateral deflection was measured. Is the slope of a plot created based on this data truly the lateral stiffness? I have heard of a method for obtaining contact patch lateral deflection data by dividing the measured tire Mx values by the measured Fy values and plotting them vs. Fy, but what happened here??….. My simplified summation of moments about the wheel center states that Fy*Loaded Radius-Fz* contact patch lateral deflection=Mx… Maybe I'm not understanding something fully in the technical paper?


---------------------------------------------------------------------------


Let’s change direction a bit here… Guys, I cannot describe how big my eyes got when I took Claude’s advice and tested the effects of slow speed compression damping on tire temperature. Not only did I find that compression adjustments in the slow speed range greatly affected tire temp over the axle on which I was adjust the dampers, but these adjustments also helped my team in equalizing the tire temperature distribution between the front and rear tires. Coupled with some roll center height and roll axis inclination testing, my team was also able to greatly improve our car’s corner turn in response though these tests.


Regards,

mmalinowski

[DMuusers]

The literature on the interaction of vertical (out-of-plane) dynamics and lateral/longitudinal (in-plane) dynamics is rather weak in my experience. It took me the better part of 3 years of FSAE to even have a grasp of relaxation. I saw in a teammate's new OptimumG binder Claude is now teaching some of this - I expect everyone will be well-versed in the topic within a couple years with a larger audience hearing it.

Anyway, for those who are skeptical that dynamic grip matters (due mostly to "if it's important I would have heard of it by now" syndrome) I scratched together some MATLAB code that adds a relaxation length to a quarter car model. Requires tons of assumptions, but it gives you a feel for 'relaxation matters' and quickly shows 'minimizing tire oscillation' isn't quite a good metric for choosing dampers.

Sorry the code is rough, threw this together in an hour or two just now. just change the extension to .m and it should run.

MCoach,
As far as fair sharing goes, I have approximate spring/damping/weights from one of our cars here, enough to get a discussion rolling on what you find?

Looking at your numbers, I find the tire vertical stiffness quite interesting. I think you've taken the vertical stiffness from your tire from the TTC data, but I wondered if you've ever validated those numbers? I'm asking because for our tires, we tested the vertical stiffness at different vertical velocities with the same vertical force and also at different forces. For us, there's quite a big difference in low velocity tire stiffness compared to high velocity tire stiffness. Also, as the tires heat up, the internal pressure increases which then causes again a significant increase in tire stiffness. So therefore I think tuning damping or spring stiffness purely by calculation is quite hard and is an ongoing process throughout designing and testing the car.

Ideally you'd want a different spring/damper setup for each driving situation, which can be obtained with active damping. But I wonder what the performance gain of it exactly is and furthermore, I wonder if the effort put into it is worth it. You'd need a very sophisticated laptime simulator to even get a remotely good idea what the performance gain is. But maybe a team that has tried active damping can shed some more light into it.

[Claude Rouelle]

mmalinoski

"Remember that the steady state response of a sinusoidally excited 2-nd order system will also be sinusoidal with a phase angle “lag” between the input and output (suspend a water bottle on a rubber band and move your hand up and down in a sinusoidal fashion and observe the vertical displacement of the bottle. If you have never done this before, I highly recommend it! Observe the point at which your hand moves up, while the inertia of the bottle pulls it down.)"

Fill the bottle with water or oil only 1/2 of the capacity and also observe the water level change..

[Goost]

I realized yet again that the code (alone) is probably not very easy to follow. Attached some notes on how to add the relaxation to the quarter car.


By the way, I enjoy linear systems because they're easy to manipulate and visualize. I actually design this stuff with a nonlinear full-car model + kinematics + nonlinear dampers + yada yada . I don't mind sharing more if people have specific questions but for now this discussion is probably more relevant and enlightening for all.


~~~

Responding in order:

~

MCoach,
The MATLAB codes I posted include relaxation length in the 1/4 car model, may help to see what it does there where the model is already familiar? Softer definitely helps with ride I think you've got it, and 'pretty soft' is 'pretty good' for grip too. Maybe the problem only starts when you see that you can get the tire on the ground faster, the trouble is that the extra oscillation it takes to do that may lead to loss of grip since the tire 'can't keep up' with the suspension. Also, in general lateral relaxation is significant compared to longitudinal if that helps. Excited to see your stuff when you get a chance!

~

mmalinowski,

Thanks for the sim. I summarized what I think the key contribution of that to the discussion is: namely the fact that at 'speeds' higher than the corner frequency (yea it's 4th order but you know what I mean) lower damping decreases excitation, and at lower speeds more damping decreases excitation. I know you know this stuff, but man did it take me a while to see that concept is the first hint at why bilinear dampers may be a good idea. The trick is turning 'frequency' into 'speed'...

So if the damping force direction is opposite to the velocity direction, it is still dissipating energy. Do I misunderstand? I think this is why we plot F/v curves and not DampingRate/v curves.

That paper is a good one! Georg Rill has written some stuff on dynamic tires that is not particularly rigorous, but definitely helps explain. Also Pacejka in his book and ~3 papers and his student's theses. Of course all these are strictly tire<->ground interactions and don't at all speak of the damping affecting it. All that to say, the things you are saying definitely follow from that paper, but I think it's easier to think of it like:

Fy_magic_formula = Fy_actual + tau*dFy_actual

tau = sigma/V - the relaxation time constant
sigma - the relaxation length
V - vehicle forward velocity

Not sure about the lateral deflection methods, but I think you are assuming too much to say Mx is only a function of Fy and Fz since the sidewalls can twist/compress. Like if you add camber there is probably a moment just because of the geometry of tires.

As far as dampers tuning the tire temperatures - You're spot that it will change the temperatures: but do you get more grip because the tires are hotter, or do they get hotter because you have more grip??? haha

Sorry so many words, no need to respond to all.

~

Dmuusers

Good point about the spring rates. You are free to critique for sure, obviously simplified a lot to get a quarter of a race car suspension and especially a tire into ~ 30 lines of actual model code.

~

Claude and Dmuusers

I am always curious when people say 'to do this properly you must consider XYZ Q and P and etc...' whether they want to discuss it more or toss it as unattainable. I think you are both on the 'discuss it more' side of this, but unfortunately these threads often die with posts like that. Let's let this thread develop into all the things you mention!

~

Claude,
Thats a great example and a great way to teach a very complex concept in Dynamics. Different frequencies of bouncing and you get different amplitudes and a phase shift. Usually do it with keys and a rubber band - I'll try it with a half-full (not half-empty! haha) bottle when I get home tonight.

[Goost]

mmalinowski,

sorry but one more thing:
on your frequency response plots, I assumed that the input is a force (Y=force at contact patch) since you called it transmissibility. If not, is it constant amplitude position/velocity/acceleration with frequency?

Realistically a road profile can't have high amplitudes at high frequencies since there isn't that much energy there. Some lit. suggests that constant velocity is close enough approximation (if you can access SAE tech papers, see Kowalczyk 2002-01-0804 if you're interested).

[BillCobb]

A couple of things gentlemen:

Tire force generation (relaxation) is NOT 1st order, its 4th order at best just from the mechanics of the parts involved. Don't ignore MZ (is that Misses Z?). It should be obvious that the Pneumatic Trail theory is out and about WRONG in this regard. Mz really isn't driven by Fy, it' the Fx distortion that produces it. Get out your toy car tires and play with them on your desks.

Tire are not really round. They are lumpy. and also have radial run-out. Thus the self excitation potential. (Hands off of that one).

Above all, keep in mind that tires are distance traveled devices. That's why we call it 'roll-out' when looking for truth.

Relax.
You'll need some information first.
Just the basic facts.
Can you show me where it hurts?

(guess that dates me, eh ?)

[MCoach]

Bill, were you listening to the same radio station I was yesterday? (Oh dear, the music I've grown up with...)

On the peumatic trail, Pacejka actually changes his calculations between his original model and his newer iterations on the "magic formula" models. His original calcs use the deformation of Fx, but the new ones refer to the lateral force for these things. I didn't dig too much into why, but I thought I remember a note somewhere of better compatibility with the rest of the model and poorer overall correlation with Mz.

So, back with some numbers from our car. With an unsprung frequency of about 40Hz, including what was estimated to be the tire vertical stiffness of 500lb/in (making a very active effort to not bring the TTC data into this conversation) our damping rates put our front damping rates at .70 for the sprung mass and .35 - .45 (depending on degradation on tire mass) for the unsprung mass, with a vehicle weight of 520lbs with driver.

I played around with high speed damper settings for a while and the lower damping ratio I targeted, the more my calcs started to charge shape from bi-linear. Eventually my eyes almost popped out of my head when I accidentally hit a high speed damping ratio target of .01 and the target profile turned into a pretty comparable output from the Penske regressive curves. As I moved back towards a range of .05 - .25 the digressive rates began to show themselves. I find that pretty interesting and am very curious to test this out with regards to tire grip and driver feel. I'm curious if there are any adverse effects from such things.

[DougMilliken]

... our damping rates put our front damping rates at .70 for the sprung mass and .35 - .45 (depending on degradation on tire mass) for the unsprung mass, with a vehicle weight of 520lbs with driver.
As you play with the damping of unsprung and sprung, it might be instructive to spot in points on Olley's plot of damping and mass ratios? See Fig 6.25, page 353 in "Chassis Design", SAE R-206. While he used a linear damper, maybe there is a clever way to add in velocity (and/or frequency) dependence?

[BillCobb]

You need to monitor the wheel travels. As they found out in the early F-Car program, dents in the hood are customer dis-satisfaction points.

There are some very real durability issues to damper parts if you don't have blow-off capability. Deflected disc valving could not take the pounding.

Boyz In Da hood, not Dents...

[ChassisSim]

MCoach,

This is a really thoughtful thread that you have started up and it raises some really good points that everyone can benefit from.

Firstly let's talk about employing damping ratios to spec your dampers. This is the procedure I adopt,

1) Start by calculating damping ratios based around the 1/4 car model and using the main springs.
2) If your crazy enough or want to take it to a higher level use state space analysis.
3) Refine using a transient simulation like ChassisSim or Simulink. If you using ChassisSim pay attention to your damper histograms.
4) Always validate on track.

The reason I say to start with the quarter car model is it's a simple tool. This allows you to get your head around what all this means so you don't make any silly mistakes. Also the reason I say start with the main spring as opposed to the roll spring is that typically the roll rates are higher than the ride rates so the roll modes die of faster. As you get better you can incorporate that in but this is a good start point.

As for digressive damping I wrote an article about this in Racecar Engineering and I'll dig this up shortly. They key thing to tuning those dampers is taking a close look at the damping velocities and then dialing what you want with damping rates.

This whole discussion on damping rates really rams home why I went down the transient route with ChassisSim. In my experience dialing in the dampers has always been a critical tool for tuning race car performance.

BTW - I just posted this on the ChassisSim blog and my Vehicle Dynamics Corner thread.

http://www.chassissim.com/blog/chassissim-news/using-damping-ratios-and-eigenvalues-to-specify-racecar-damping

I've pitched it a high level but I hope you get something out of it.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

[Claude Rouelle]

High speed input and the nature of damping rate…..

Here are 2 simple, practical, outside the box additional perspectives

1. What do you call low speed and what do you call high speed? Some people define an arbitrary “border” damper speed of 1”/sec (or 25 mm/sec) under which the damper is considered at low speed and over which the damper is considered at high speed. Some others will look at their damper Force Vs, Speed graph and will call the low-high speed transition the speed at which the slope of the Force Vs Speed changes (basically that is the speed at which the shims around the piston get enough force to be bended and leave and easier flow, less restriction to the damper fluid to get from one side of the piston to the other).
Whatever the definition of low and high speed is you may want to look at real data of your damper in the form of a damper speed histogram. You will see that you ALWAYS spend a majority of your time at low speed, even more on a FSAE / FS track which is most often smooth (OK you will tell me everything is relative so I will simply say that a FSAE / FS track much smoother than let’s say…. Sebring) and also FSAE/ FS track does not have curbs (except one in track; Brazil where the cones in one corner have been put in a manner that the driver has to ride the karting race track curb otherwise he will hit a dozen of cones.) So I do not say that high speed damper tuning is not important but if your damper spends 90 % of its time at low speed and 10 % and high speed, you suddenly realize that high speed tuning is not that important

2. The second thing to look at is WHERE on the race track your damper is at high speed. My experience is that damper high speed is often reached on bumps which are on circuits straights (unless, again, you have high curbs at corner apex or exit). Damper tuning have a considerable effect on tire temperature and tire wear; I have seen teams destroying their tires because they had a lot of high speed damping control that was essentially use in the circuits straights … where grip count less.

[MCoach]

Danny, thanks for that, I think I've listened to every video you've posted through Chassis Sim, I just let them run in the background while I'm at work.

Claude, you always have interesting input and keep us thinking.

Doug, I've look at the Olley information the past few days and think I have an idea of what I'm looking at now.

I have a Matlab model that I made a while ago that applies a constant damping coefficient to a perturbation into a tire-spring-mass, sprung-mass-damper chassis model. I'll go back to this and change it to a few different input styles to see what I get. Doug brought up the point of linear damping from Olley compared to bi-linear or otherwise so I want to see the effect of tire acceleration compared to damper response equations. Frequency related? Digressive FvsV look up table? I'll get back to this as time allows.

The thought process for looking at acceleration is to then look at jerk, with Force being on the tire relative to the masses * accelerations (getting all complicated in here) and the thought of 'slowing down load transfer' that is typically talked about for sprung mass in roll, pitch, etc through springs are dampers being applied to the tire itself. If load variation is degrading to grip, then looking for minimizing that variation would seem like a goal. How true to life this? I don't know. I'm going to explore it and see what happens. I'll share results if they look pretty.

Erik, I've been contact with Dave Williams on this subject and he corroborates that minimal energy absorption seems to be best but not "NO DAMPING". The idea being that the suspension is nothing more than an RLC circuit and the goal is the use as little energy as possible to filter the input is an idea I read about but appears to be incorrect. Dave directed me to read some Malcolm Smith articles to set me straight...

I'm not sure if I feel like I am going in the right direction, but it's exciting (kinda like rallying through the forest with an amateur co-driver who can't keep up)

[Jay Lawrence]

MCoach,

Apologies if this was already obvious to you, but you might want to have a look at inerters (or J-dampers. Essentially dampers based on acceleration rather than velocity). These were used in F1 for a while, specifically to minimise load variation due to frequencies at the tyre excitation level. So (I think) the application is very true to life.

[MCoach]

Jay, inerters are an odd, rarely covered source. I find them very interesting because the concept isn't new but the understanding of how to create one and use it is. I might have had a slight obsession with finding out as much as I could about a year ago... I designed a theoretical fluid inerter based on a quarter midget damper but haven't had the chance to actually put it together or try it out yet. From afar in CAD it just looks like a normal spring and damper assembly. ;)

[mech5496]

MCoach, let's say that I might had the same interest a while back! :P The RLC cirquit analogy is really nice for a car damper/spring IMO. BTW "J-dampers" are sometimes used in tall buildings to balance them dynamically during earthquakes and that was what got my mind working on them. Any plans to put one of your quarter midget based dampers together really quick n' dirty just to prove the concept?

[MCoach]

I only have enough functioning dampers around to keep our cars running, but if someone were to offer me a damper to modify and play with for a while, I might be interested in developing a few things for here and there and send it back. :)

I'm aware of the tuned-mass dampers and other sorts of inertance damping in buildings and that's actually where I went to dig up documentation on them. I think it was like an old 1960s (not sure it was really that old...) document that walked through the design of a tuned mass damper for a tall building that I finally understood how they play a part. Unfortunately I used poor documentation techniques and don't remember where it was. It was some document that was scanned and uploaded to the internet.

Speaking of F1, I took a page out of their book for my current rear suspension concept, just trying to package the damp :P thing is becoming a little difficult with the rest of our modifications.

On the related subject of damping, I had our guys outfit our car with solid rods for dampers yesterday for some heat + tire pressure testing, which unfortunately ended after only about an hour and two collapsed bell cranks. It was enlightening to see the difference in handling and especially transient situations when everything happens relatively instantaneous and without the chassis damping effect. It was true that our tires were almost as hot as the prvious day when we went testing with dampers but from much shorter run times.

With the dampers I noted that a pressure change over the range of 10 psi yielded the same lap times within a range of .3 seconds (neither faster just within the range of fastest laps for each setting), but the feedback from the drivers was very curious. Whenever the pressure was increased, the car was said to snap and respond quickly (expected, higher cornering stiffness) but lap times felt slow (unexpected). The lower the pressure that was run, the more each driver said that they felt more in control (expected) and felt lap times decreased dramatically even though there would be a small difference, if any, negative or positive (slower times still felt faster to driver). The FTD of the day was run by one of our newer drivers on high tire pressure even though he thought the car "felt slow and had no grip"...struck me interesting. When tire pressures were at the lowest points of the range the vehicle would exhibit a characteristic that I can only describe in this way, and maybe someone can help me describe what's happening:

stand on one leg, now lean over such that your CG is at the outside of your foot, so you're starting to balance by partially lifting the inside of your foot. Now,with one foot still in the air, try to lean back towards center and take a small jump to the side of which you have your foot raised. It takes an extremely long time to accomplish compared to standing with your CG still within the bounds of center to foot and jumping.

The car seems to exhibit something similiar to this at low pressures when transitioning a slalom and seems to increase in probability of occuring the higher the speed attempted. The car may take the first slalom just fine, but then fails to respond to any sort of input during that second or third slalom input. I've felt it myself and seen it from other drivers where they will turn in and the car seems unaffected, continuing along it's original path. I wish I could describe it in detail further, but usually at this point the driver usually panics that they've DNF'd by plowing or missing the slalom cone. The car will not snap back like a whip, nor spin, nor slide out indefinitely, just after a certain time lag or speed decrease, returns to life as normal. It puzzles me to no end.