Quantifying the effects of tire load variation

[JT A.]

Ok, so if two tires are put in 2 different situations:

1) A tire held at constant 10 degree slip angle and constant 250lb Fz for some amount of time.

2) A tire held at the same slip angle, but Fz is a sin function that averages 250lb, varying above and below it with some amplitude and frequency.

In theory tire 1 will produce a higher average Fy than tire 2. As amplitude and frequency of the Fz variation increases, the average Fy for tire 2 decreases. This is one of the most important considerations in deciding ride frequencies and damping characteristics (ride comfort is low priority in race cars, and wing height/orientation is only important if you have wings, which most of us don't).

So I've been trying to figure out 2 things:

Question 1: Physically, what causes TLV to reduce lateral/longitudinal grip?

I haven't found an explanation in my books, and my only theory so far has to do with hysteresis of the rubber. While a tire is being loaded, it takes more force to compress the tire than when it is being unloaded. With steady loads, u is always going to decrease with higher load, but the deflection of the rubber increases contact patch area and "mechanical interlocking" of the rubber with the road, which slightly offsets the decrease of u. But in a transient case with load being increased rapidly, u is decreasing due to load sensitivity, and the rubber is not deforming as much as it would in steady state due to hysteresis, so there isn't as much gain in contact patch area & mechanical interlocking to offset the loss in u.

I may be completely off-base here, so if there is anybody that actually knows could you set me straight please?

Question 2: How can I quantify it? I want to quantify the amount of mechanical grip vs spring rate, the tradeoff between a car with high ride height, soft springs, vs low ride height, stiff springs, etc. All I have is TTC data, which is tested at mostly steady Fz's. I also have a quarter car model where I can define a road profile and accelerations of the sprung mass, and it will output a log of Fz throughout the simulation. Of course it can not correlate Fz's to Fy's, because the tire model I have made from the TTC data is only valid in steady state. Has anybody else tried to look into this analytically? If so, what approach would you recommend?

[BillCobb]

Useful procedures for getting answers to your questions and some understanding as well, can be found in two of the sections in the TTC Forum in "Tire Models/Tire modeling Technology". The threads on 'TIRF Data Hysteresis Removal' and 'Simulink Evaluation of Tire Surfaces' should lead you to a Simulink processing experiment to incorporate the hysteresis lag distance you compute into a frequency sensitive element. All you can get is a first order approximation (its really not but 1st is pretty close), but the phenomenon is reproduced pretty well. Sorry, but the Mz transient response can't be determined in a similar manner because it's 3rd order with dominant high order terms.

When you run your frequency sweep of the tire response model in Simulink with the transient approximation added, you will see a frequency dependency. You can then do your 4 or 7 post simulation of the car and get some direction for your 2nd question.

These are relatively small tires with short relaxation parameters, but don't be fooled by expecting relaxation lag to correlate well with cornering stiffness or peak Fy, etc. And, its load dependent. Tthis ought to factor into your tire, pressure and rim width selection process, too. Your driver will appreciate your extra effort, so to speak...

[JT A.]

Thanks, your powerpoint slide raises a lot more questions, but at least I have a direction now.


Let me make sure my understanding is correct so far...

So you start with a surface fit of the raw data and a matlab function to that outputs Fy=f(Fz,SA,IA). Then you make a simulink diagram that simulates sweeps on a tire test rig. You add the relaxation function with a time constant. Here's where it gets fuzzy for me:

It says the time constant is arbitrarily set at 0.1s. Is that just an initial guess? Or is there some way to obtain a correct value to start with?

Anyways, after that, simulink outputs a Fy-SA curve with simulated hysteresis. The next slide shows a curve of shift index vs correlation coefficient. I have no idea what either of those are. I assume correlation coefficient is the correlation between the simulated sweep and the raw data. Is "shift index" somehow related to the time constant used in the relaxation function? Meaning you just vary the time constant until the correlation coefficient is maximized, and that is the relaxation time? Once you have a relaxation time, you multiply that by the belt speed to get a relaxation distance, correct? Finally, I assume you would do this at several loads and come up with a function of relaxation distance vs load. For a first-order approximation, is relaxation distance only dependent on load or is it also dependent on rate of slip angle change?

That process (assuming I am anywhere close to correct in my understanding of your method), would give me the "slip angle lag". What I want to model is the "load variation lag" (at least right now, I will definitely do something with slip angle lag in the future). Are they the same? Or can I find it using the same method, by holding SA and IA constant in the simulink diagram while varying Fz? I don't believe the TTC raw data comes with a sweep of constant slip angle and varying load, so I'm not sure what I would correlate the simulated sweep with in order to find the correct time constant.

[exFSAE]

I could tell you, but then I'd have to kill you.

Seriously though... this is a topic you probably won't find much public domain information on.

Consider though - how much ride content do you really expect to have? Low speeds, fairly flat surface (at MIS anyway). Is spending the time going down this route going to get you more speed, or is it more or less a dead switch?

If you want to start to quantify it - test it! Theory is nice, but results are what ultimate matter. Come up with two packages with equivalent mechanical balance (FLLTD for example) - one with high spring and/or damping rate, one with low. Go run some laps on your favorite track. Transient handling aside (which we know will feel differently) - how much does this change your mid-corner peak lateral G's? Should be able to get a read very quickly on whether or not its critical.

It's fun to try to figure these things out, but ultimately there's a long list of development items which will all contribute to your lap time. Critical engineering skill is being able to sort those into the ones which are most impactful and master those first, before diving into minutiae.

[Z]

JT A.,

Regarding Q1, I suggest the following two ways of looking at it;
~~~o0o~~~

1. As a first step consider normal frictional behaviour. We have a block of some substance sitting on a smooth horizontal surface. A vertical force Fz pushes the block down, and a horizontal force Fy tries to move it sideways. Given a friction coefficient Cf, we know the block will NOT move if Fy < Cf.Fz.

We now add a varying component to the vertical load Fz. When Fz increases, nothing changes - the block remains stationary. But, when Fz decreases, and if it decreases far enough that Cf.Fz < Fy, then suddenly the block slides - a completely different behaviour. It is important to see that this behaviour is NOT symmetric, and is in fact very NON-LINEAR. The pluses do NOT cancel out the minuses.

This is the mechanism via which vibration loosens bolts, etc. It is not an accurate answer to your question (because wheels also roll), but it is a start.
~~~o0o~~~

2. With tyres I think it is important to have a good physical understanding of the mechanism at work during axial (Fy) loading (these are not clearly explained in any book I have read). At the core of this understanding is "tyre relaxation length" (itself a rather odd term).

Just briefly (and simplified), I see this mechanism as having the "tyre tread-hoop" and "wheel" as two separate bodies that are connected by a spring and a CV joint that allows some relative axial and yaw motions. So the tread-hoop can take a different steer angle to the wheel, and also move axially (left-right) relative to it. Simplistically, the tread-hoop likes to roll in the direction of travel, but the wheel can have a "slip-angle".

Anyway, consider the wheel and tread-hoop rolling straight ahead. Suddenly the wheel is steered N degrees, but its axle/upright/etc. is constrained to keep moving straight ahead. It takes some rolling distance (and hence also time) for the tread-hoop to acquire its yaw angle and axial displacement wrt the wheel (this can be seen on slo-mo video). Importantly, while this is happening the axial (Fy) forces are relatively low, gradually building from zero to the full Fy value for that Fz and slip-angle. This "full Fy value" is achieved only when the "spring" coupling the tread-hoop and wheel (ie. the sidewalls + air pressure, etc.) reaches its full distortion.

With regard to your question, if the Fz force varies significantly, for example to the stage where it is close to zero for part of the cycle, then at these times the tread-hoop realigns itself to the wheel, and thus only delivers a low Fy. It is only after the Fz increases, and the tread-hoop has time to move relative to the wheel, that the system as a whole can carry any Fy force.

So, a stiff suspension on a bumpy road might have the wheel Fzs cycling between zero and 2x static-Fz. The tyre tread-hoop/spring never gets a chance to reach its full distortion (always being brought back to zero at low Fz), so the Fy cornering force remains very low. The pluses during high Fz do not have time to compensate for the minuses during low Fz.

So, ON BUMPY ROADS, SOFT SUSPENSION = HIGH GRIP! http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~o0o~~~

To quantify this (Q2), you could try some kind of mathematical/computer model of the above mechanism. Then compare with real test results.

Z

[exFSAE]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">To quantify this (Q2), you could try some kind of mathematical/computer model of the above mechanism. Then compare with real test results. </div></BLOCKQUOTE>

Or, the other way around.

[Buckingham]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Question 2: How can I quantify it? I want to quantify the amount of mechanical grip vs spring rate, the tradeoff between a car with high ride height, soft springs, vs low ride height, stiff springs, etc. All I have is TTC data, which is tested at mostly steady Fz's. I also have a quarter car model where I can define a road profile and accelerations of the sprung mass, and it will output a log of Fz throughout the simulation. Of course it can not correlate Fz's to Fy's, because the tire model I have made from the TTC data is only valid in steady state. Has anybody else tried to look into this analytically? If so, what approach would you recommend? </div></BLOCKQUOTE>

One of the biggest obstacles you face in performing a ride model analysis is that you do not have consistent input (like in F1 or NASCAR where the track is permanent and the racing line can be reasonably consistent).

Your 2nd biggest obstacle is that your damper is in reality much more complex than a simple Force-velocity curve. There is plenty of hysteresis here.

Thirdly, a 1/4 car model sounds neat on paper, but an anti-roll bar system and chassis stiffnesses will have a measurable impact on how the model responds. (rear damping can affect front tire load variation).

That being said.... can you use your 1/4 car model as a guide to help you come up with a few different packages to test? probably.

Try performing a sine sweep to characterize your system over the broad range of frequencies that you think you will see.

Since we know the 1/4 car model is really nothing more than a rough approximation, look for large scale trends and then test those trends on the track.

[Z]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by exFSAE:
Or, the other way around. </div></BLOCKQUOTE>
exFSAE,

The trouble with doing real tests first, and only doing the computer simulation after, is that it is too easy to get the right answer.

"...and now we'll just tweak this little parameter here, aaaand ..... perfect match! Aren't we soooo clever..."

Colourful Flow Diagrams are a good example of this in modern engineering. They are great "predictors" when the real answer is already available. Not so good otherwise.

My point is that a "model" (math/computer/whatever) is only worthwile if the model can give you the answer, without you first having to give the answer to the model!

Z

[exFSAE]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">exFSAE,

The trouble with doing real tests first, and only doing the computer simulation after, is that it is too easy to get the right answer.

"...and now we'll just tweak this little parameter here, aaaand ..... perfect match! Aren't we soooo clever..."

Colourful Flow Diagrams are a good example of this in modern engineering. They are great "predictors" when the real answer is already available. Not so good otherwise.

My point is that a "model" (math/computer/whatever) is only worthwile if the model can give you the answer, without you first having to give the answer to the model!

Z </div></BLOCKQUOTE>

I don't quite agree with that assessment.

Math models can be great tools, or a gun with which to shoot yourself in the foot, depending on your confidence level in the fidelity of the thing. Could very well invest a lot of time and effort in development only to have it lead you to the wrong answer or down a dead end.

Model validation always comes first before using it as a predictive tool. This has been the case with all professional work I've done, most certainly including simulation development at the pro motorsport level. That DOES mean having a few real test cases AND establishing what "correction" factors (if any) are necessary to improve the fit to real world responses.

Knowing that you have to do some tests to validate a model, you might as well get those out of the way first to see if this whole process is even worth doing.

It's entirely possible that TLV amounts to fuck all on a FSAE car, or at least absolutely pales in comparison to the impact it has at a typical Cup, Indy, or F1 car event.

I could easily see it taking at least a week if not substantially more to do all the development of the math model and package it in a useful tool. That's a lot of time. More logical alternative IMO is to do a quick track test and back-to-back two extremes of the spectrum for ride quality (or better yet, an A/B/A). If you DO see an appreciable difference in your saturation G's, OK... pursue it further. If it doesn't do shit, then scrap the whole idea and move onto more relevant things.

Just my 2 cents.

[Z]

exFSAE,

Firstly, I am a great believer in building it asap, and then getting it out there and doing real world tests. Then modify and retest, etc. In many cases this is the quickest, cheapest, best way to a good result.

But this doesn't work for really big projects, like huge bridges, or rocketships to the moon. All the trial and error can get costly. So here you need a good "predictive" model. This is somewhat like the difference between "interpolation" (quite easy), and "extrapolation" (often a lot harder).

You say, "Model validation always comes first ... establishing what "correction" factors (if any) are necessary to improve the fit to real world responses."

My problem with this is that I have seen too many times the simulation gurus take the "real world responses", load them into what could be an empty box, tweak a few "correction factors", and then pull out the correct result, and demand a wheelbarrow of cash for their efforts! (More specifically, the racecar simulation has the car going fast on the straights, slower on the corners, and then guru gets a +/- 0.001s match to the real laptime by slightly tweaking the "global grip factor"!).

My problem with these overly-simplistic-models-plus-tweaks is that they only give limited understanding of what is really happening, so the chance of improved design is likewise limited. There are countless details I could go into here, but for now "caveat emptor". http://fsae.com/groupee_common/emoticons/icon_smile.gif (Edit: (Couldn't help myself.) One example might be an FSAE LapSim that does NOT consider the car's Yaw MoI, but nevertheless gives results accurate to 0.001s. So the students think "Yaw MoI isn't important. We've done the Sim, it's spot on...")

A good predictive model gives reasonably accurate results every time, without any "tweaking". For example, Newton's "F = P-dot" (ie. F=dP/dt, NOT F=mA) has never required any tweaking to give results as accurate as any instrument can measure. Thus Newton II gives deep understanding, which is useful when designing things that move.
~~~o0o~~~


You say, "It's entirely possible that TLV amounts to [not much] on a FSAE car..."

We might be talking about slightly different things here, but drive any ground supported vehicle over a bumpy enough road and it behaves like a hovercraft, ie. NO GRIP!

A stiff suspension on corrugations is worst, and you can forget about any cornering grip. The size of the corrugations is a big factor (they only have to be small if the frequency, or speed/wavelength, is high), but in general;
SOFT SUSPENSION = BETTER.

Z

[exFSAE]

You do indeed need good predictive tools for building bridges, aircraft, spacecraft. These CAE tools are all extensively validated before they are ever used "for reals." Even if I'm using something like ADAMS, which has had people banging on the solver for years and have high confidence in it in general - I'm still going to do some verification that I've set up my models or templates correctly. Maybe a quick comparison against K&C data.

For other commercially available software that hasn't been as extensively "beat on" by professionals, I'll do a bit more thorough verification. For something done in house, I want even more extensive checks before I use it to make critical path engineering decisions. Doing this sort of combined in & out of (x-y) plane dynamics work there are potential pitfalls all over the place.

Now you do make the good point that using one data set or data point for model validation is a joke. Very easy to set model parameters to match one data point exactly - though when you use those parameters on another case your quality of correlation may be worse. Definitely requires several examples to identify model parameters which best fit over a range of conditions.

Still, I come back to the point of wanting to prove level of significance. If we drive a FSAE car around in a rock quarry - sure - your "grip" (itself a nebulous term) is probably going to suck. But for a typical FSAE event, or the one any team is looking to travel to - what's the level of significance?

I think back to running at the Ford Michigan Proving Grounds. Ride effects there are probably insignificant to handling in comparison to say compliance rates or tire setup. Could spend a day screwing with high speed dampening and ride rates and such and probably get nothing appreciable out of it - or that time would have been better spent elsewhere.

So. For any given event you're planning to hit, I think it's good to do a quick litmus test to see if it's worth investing the time in pursuing further. Effective use of time is key in this series IMO.

[BillCobb]

Consider this:

Here is a decent question from the Steering Systems Group on LinkedIN:

http://www.linkedin.com/groups...oback=%2Egmp_1873982 (http://www.linkedin.com/groups/I-want-know-root-causes-1873982.S.62079267?qid=2c22c136-e1af-4c6f-8b1a-f04b9063666e&trk=group_most_popular-0-b-ttl&goback=%2Egmp_1873982)

Pretty straight forward question, but look at the 'answers'. These are the kinds of answers usually given by engineers who 'test' by changing parts and go out on the track to evaluate their progress. This is what I call 'Old School' engineering. You work like a mechanic, you talk like an optometrist ("Is this better or worse?") and the hesitation in you answer(s) hint at a lot of doubt in your ability. Plus, you hardly ever know the 'why' of a part change result. Your cars tend to have a lot of adjustment holes and weldment in them. And you get skewered in a presentation to management.

In this case, if you had a decent simulation (and I don't mean an Erector Set program [multibody dynamics]), you would know the cause of this phenomenon and how to eliminate it once and for all.

Industry mechanics only make 1/3 to 1/2 of New School engineers. We call them technicians.

Now can any of you tell us the analogy to a power transister in a hydraulic assisted steering system and what it takes to make it not shedder'? This makes a terrific Simulink model. Use a simple parabola for the control valve profile.

Or just order a truckload of different valves and t-bars and tierods and steering damper parts and a couple of barrels of hydraulic fluid. Then get down and dirty.

[exFSAE]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by BillCobb:
Pretty straight forward question, but look at the 'answers'. These are the kinds of answers usually given by engineers who 'test' by changing parts and go out on the track to evaluate their progress. This is what I call 'Old School' engineering. You work like a mechanic, you talk like an optometrist ("Is this better or worse?") and the hesitation in you answer(s) hint at a lot of doubt in your ability. Plus, you hardly ever know the 'why' of a part change result. Your cars tend to have a lot of adjustment holes and weldment in them. And you get skewered in a presentation to management.

In this case, if you had a decent simulation... </div></BLOCKQUOTE>

'Decent' is the key word. Just because someone makes a simulation or math model does not mean it is an accurate predictor. You don't know the confidence level in the predictions until you validate it - after which point you can comfortably use it to make engineering decisions.

That's the point here. Already in this example there's a fundamental assumption being made in how one would go about this math modeling that from previous work on this very topic - I don't agree with.

Leaning too heavily on the side of "old school" engineering, or tinkering as the case may be, is indeed something that can get you left in the dust by competitors who are taking an approach based more on total system understanding.

On the other hand, I think it's MUCH more dangerous to be too heavily on the side of "new school" engineering when you have blind faith in a predictive tool and then you make a very wrong decision based upon the results. That's where you'll be skewered in a presentation to management, or your team principal, or the man whose name is on the side of the race shop. It can be a common pitfall of newly graduated FSAE alumni going into industry, and one of many poor engineering practices which are soaked in when we're in college.

Consider this: When you're brand new to a team or organization and trying to justify your pay by appearing competent... you don't want to be THAT guy who points the way to a poor solution because you were overconfident in your tools.

When it comes to developing new simulation tools... there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – there are things we do not know we don't know.

It's that last one that will get ya.

[Moop]

Regarding tire load variation - is it typically calculated as a function of frequency in a frequency sweep? I mostly see it referred to as an RMS value and that's what it's referred to as in RCVD. But an RMS is just one value of a given time history, which is where I'm getting confused. I thought I could maybe make some time slices around each frequency and calculate the RMS tire load change in that slice, but I feel like I'm missing something obvious because this seems pretty hack.

The reason why I ask is in my current 4 post model, I'm looking at the transfer function of tire deflection*tire stiffness over road input as a measure of tire load variation. It lets me see relatively the impact of various parameters on the tire load variation, but it doesn't let me get back to say a sinusoidal load fluctuation(of the given RMS value) at each frequency that I could use to see how the actual cornering force is affected by the road undulations.

I suppose I could feed the tire load history through the relaxation function to get a rough idea, but I'm more interested in using this in a lapsim to degrade the grip based on the road input, and possibly try to include the effects of heave variation's contribution to tire load fluctuation via changing CG height(which the 4 post model doesn't capture unfortunately...). Including the effect of pitch variation would be cool too, but we're not an aero car yet and even if we were, I'm not sure how I'd capture the effect of varying downforce/aero distribution in a steady-state simulation.

Essentially, I'm interested in determining a performance index for 4 post testing that's more than a guesstimated weighted average of transfer functions that's worked well in the past(or never been used in past if you're me, haha).

Of course, this is all theory in my head right now. We have adjustable dampers this year so I'll do a skidpad test to see if the tire load fluctuation is worth pursuing or not.