Tire Torment

[Gareth]

Hello All,

I'm going to give this a shot - a decent thread about tires, dampers and all in all fun vehicle dynamics stuff...that I hope will stay civil.

Here are a few things I've been thinking about and was wondering if anyone else has any experience with them:

1) For those who have the TTC data, have you watched the fun videos of the tire on the belt? I was there last summer when they were testing some of the 10" wheels and I couldn't get over how much vertical deflection occured during the slip angle sweeps. This is one of the reasons for the oscillation in the raw data - the machine's controller was having difficulty keeping up with our unusually low spring rate tires. If you plot the raw data you'll see that there's a significant change in the effective spring rate of the tire at higher loads and higher slip angles. I suppose the actual spring rate may not change significantly, but the vertical deflection is substantial. Also, I'm not sure how representitive the TTC data is of this effect at higher slip angles as the sandpaper belt seems to generate a great deal more grip than we commonly see, thus pulling more of the rubber out from under the wheel and perhaps not affecting the spring rate quite so much.

Now, I haven't really begun to think about how this might affect things in the frequency domain, but it does make me realize that there are some serious flaws in how we consider our lateral load distribution. Simply, if we use the method shown in RCVD then the tire is lumped with in with the ride rate which is in parallel with the anti-roll. In fact, the wheel rate and anti-roll are in parallel and the tires are in series with them. If you had a rigid suspension (go-kart) with no kinematic roll, then you still have body roll on the tires and potentially diagonal load transfer. The reason why this concerns me is if you're looking at linear pot data to get an idea of what your LLTD might be, then you must also take into account your tire. On top of that, if you tire's spring rate is changing with slip angle, which is exactly when you'd be rolling, your actual LLTD is difficult to obtain. Has anyone else looked at this effect?

2) Have any teams been looking at how to deal with grip disturbance/tire load variation at ride frequencies (> 5Hz)? I suppose I should break this down into two parts:
a) Does anyone have any experience with how it changes the shape of the SA vs Fy plots? My thinking is that the linear region should stay pretty much the same as it's mostly driven by elastic deflections of the tire. I would also have to think that the main consequence is that the 'roll off' would happen sooner as sliding may be induced sooner (ie: in the grip/slip model suggested by Hallum, the rubber 'snaps back' at lower deflections). We've done some simple calc's based on the Pacjeka fits using the steady state grip values at various loads to estimate how the grip may change, but I'm curious about the dynamic effects.

b) What means have teams tried to reduce load variation? I realize this is mostly done in spring and damper tuning, but what methods have been used to quantify change seen at the contact patch (other that lap times)? I resolved that springs are generally chosen based on response. We've been running very soft to make up for a bumpy Silverdome parking lot, but more recently we've been liking a stiffer setup and that's for response reasons and as far as I can tell, nothing to do with load variation.

There are some interesting SAE papers on 4/7-post testing where a rig is used to excite the car through the tires (not rolling) and the response is measured using load cells under the wheels and accelerometers on the pans, hubs and chassis. The method I was trying to develop used a setup like this. The 4-post would do a frequency sweep to excite the car within typical ride frequencies. The sweep maintained a constant peak velocity, so it started out low freq, high amplitude and ended with high freq, low amplitude. One of the papers suggests this is a good way to get roughly the right energy input at all frequencies. Yes, it's not as good as a 'shaped' white noise input as is also suggested, but it's a lot faster. The max velocity is varied until the linear pots show roughly the same velocity histograms as are seen on the track, thus approximating the energy input typically seen on a particular surface. Next, the accelerometer data is used to calibrate a math model of the car. I was using a 7 DOF simulink model (pitch, roll, heave, +4 tires) and the parameter estimation toolbox. Unfortunately I couldn't get my model to correlate with the data, mostly due to time constraints. With more time (and some money...who wants to hire me to do this stuff???) I would have found my model constants and then performed a DOE to 'optimize' my output (contact patch load variation) by varying damping rates. Essentially this would have given me a new setup to try next (ie: revalve the dampers and shake the car again). This method is iterative, but should reduce the number of 'guesses' to find a good solution. I know I have been ignoring pitch and heave sensitivity in all this, but seeing as we don't have wings on our car, I was thinking it wasn't such an issue. Depending on how it went, I was considering adding a 'cost function' to the optimization routine to help bias between 'perfect' load variation and pitch sensitivity. The model is linear, thus it cannot handle digressive dampers, though that could be built in if I made the simulink model more complex at the expense of run time. I would think you would still want to look at low speed damping using linear pot data and/or something like the methods on the OptimumG website.

Has anyone been doing anything else interesting in this respect?

3) Lastly, have teams been writing their own lap time simulations? I would like a tool that I can use quickly to help understand track data. What I mean is that sure, we could spend lots of time to setup a full ADAMS model and send it around the track all day, but it takes a long time to run and typically doesn't deal with things like tire temperatures and load variation. Has anyone written a tool that can be 'calibrated' using track data that can help us understand the attitude of the car around the track and some estimates of the tire forces involved? I know it's kind of a holy grail, but wouldn't it be nice to have something like that you could run a fast DOE on to help suggest setup changes? Or what about macros to search for interesting events in the data? I know some of this is being done at a professional level, but I'm curious if there's FSAE teams out there taking a crack at it. I've been considering writing a quasi-steady state lapsim just to get a better understanding of the vehicle dynamics involved. That model could then be modified to take into account a local load variation coefficient, a tire temperature model, or maybe a non-linear tire spring rate as per the above discussion.

Okay, that's it for now. I figure this should kick-off some interesting discussion so I'd love to hear some feedback on it. I really don't want anyone telling me that I should build a car and stop worrying about this kind of stuff because I've built 5 of them and I've earned the right to some mental masturbation.

G

[GSpeedR]

Originally posted by Gareth:
Hello All,

I'm going to give this a shot - a decent thread about tires, dampers and all in all fun vehicle dynamics stuff...that I hope will stay civil.

Here are a few things I've been thinking about and was wondering if anyone else has any experience with them:

1) For those who have the TTC data, have you watched the fun videos of the tire on the belt? I was there last summer when they were testing some of the 10" wheels and I couldn't get over how much vertical deflection occured during the slip angle sweeps. This is one of the reasons for the oscillation in the raw data - the machine's controller was having difficulty keeping up with our unusually low spring rate tires. If you plot the raw data you'll see that there's a significant change in the effective spring rate of the tire at higher loads and higher slip angles. I suppose the actual spring rate may not change significantly, but the vertical deflection is substantial. Also, I'm not sure how representitive the TTC data is of this effect at higher slip angles as the sandpaper belt seems to generate a great deal more grip than we commonly see, thus pulling more of the rubber out from under the wheel and perhaps not affecting the spring rate quite so much.

[quote]Now, I haven't really begun to think about how this might affect things in the frequency domain, but it does make me realize that there are some serious flaws in how we consider our lateral load distribution. Simply, if we use the method shown in RCVD then the tire is lumped with in with the ride rate which is in parallel with the anti-roll. In fact, the wheel rate and anti-roll are in parallel and the tires are in series with them. If you had a rigid suspension (go-kart) with no kinematic roll, then you still have body roll on the tires and potentially diagonal load transfer. The reason why this concerns me is if you're looking at linear pot data to get an idea of what your LLTD might be, then you must also take into account your tire. On top of that, if you tire's spring rate is changing with slip angle, which is exactly when you'd be rolling, your actual LLTD is difficult to obtain. Has anyone else looked at this effect?

Yeah, I don't think anyone will argue that using your linear pots to determine load transfer is ignoring a fair amount of the whole picture. You are really only given a measure of the elastic weight transfer occuring through the springs and dampers (strain gauges on the P-rods is a better way but few teams do this). The geometric weight transfer occuring through the wishbones/links is not being measured.


2) Have any teams been looking at how to deal with grip disturbance/tire load variation at ride frequencies (> 5Hz)? I suppose I should break this down into two parts:
a) Does anyone have any experience with how it changes the shape of the SA vs Fy plots? My thinking is that the linear region should stay pretty much the same as it's mostly driven by elastic deflections of the tire. I would also have to think that the main consequence is that the 'roll off' would happen sooner as sliding may be induced sooner (ie: in the grip/slip model suggested by Hallum, the rubber 'snaps back' at lower deflections). We've done some simple calc's based on the Pacjeka fits using the steady state grip values at various loads to estimate how the grip may change, but I'm curious about the dynamic effects.

The effect of tire load variation is heavily dependent upon the vehicle speed or, more correctly, wheel angular velocity. Tires must build lateral and longitudinal force when they are given a set of inputs (slip angle, slip ratio, normal load, etc.). A tire in general takes around 1/2 to 2/3 of a revolution before the tread surface has reached its "Steady-state" deflection. If you are rapidly changing the normal load of a slowly moving tire then it will produce substantially lower grip forces as force never gets the time to build up. So you can't really analyse the problem using static tire equations where grip is produced instantaneously...before discussing this with one of my professors I was assuming that you could use the regular Pacjeka equations but with an "effective" RMS normal load, but this does not account for the tire angular velocity. Your best bet is to model the tire's response (estimate it) and incorporate it into your Simulink model.


b) What means have teams tried to reduce load variation? I realize this is mostly done in spring and damper tuning, but what methods have been used to quantify change seen at the contact patch (other that lap times)? I resolved that springs are generally chosen based on response. We've been running very soft to make up for a bumpy Silverdome parking lot, but more recently we've been liking a stiffer setup and that's for response reasons and as far as I can tell, nothing to do with load variation.

Drive on smoother tracks. http://fsae.com/groupee_common/emoticons/icon_smile.gif You said you have a 7 DOF Simulink model going (with 4 1/4 car models), model it. You can perform a parameter sweep of spring rate and (linear) damper constant through a randomized bump input. One of your variables will be wheel center height minus the input height. This is your tire deflection. Now you sweep damper and spring settings and look at the resulting changes in tire spring, there should be a point where RMS tire deflection is minimized. A non-linear damper model will give you much better insight as what the hell to do with your high speed damping.


There are some interesting SAE papers on 4/7-post testing where a rig is used to excite the car through the tires (not rolling) and the response is measured using load cells under the wheels and accelerometers on the pans, hubs and chassis. The method I was trying to develop used a setup like this. The 4-post would do a frequency sweep to excite the car within typical ride frequencies. The sweep maintained a constant peak velocity, so it started out low freq, high amplitude and ended with high freq, low amplitude. One of the papers suggests this is a good way to get roughly the right energy input at all frequencies. Yes, it's not as good as a 'shaped' white noise input as is also suggested, but it's a lot faster. The max velocity is varied until the linear pots show roughly the same velocity histograms as are seen on the track, thus approximating the energy input typically seen on a particular surface. Next, the accelerometer data is used to calibrate a math model of the car. I was using a 7 DOF simulink model (pitch, roll, heave, +4 tires) and the parameter estimation toolbox. Unfortunately I couldn't get my model to correlate with the data, mostly due to time constraints. With more time (and some money...who wants to hire me to do this stuff???) I would have found my model constants and then performed a DOE to 'optimize' my output (contact patch load variation) by varying damping rates. Essentially this would have given me a new setup to try next (ie: revalve the dampers and shake the car again). This method is iterative, but should reduce the number of 'guesses' to find a good solution. I know I have been ignoring pitch and heave sensitivity in all this, but seeing as we don't have wings on our car, I was thinking it wasn't such an issue. Depending on how it went, I was considering adding a 'cost function' to the optimization routine to help bias between 'perfect' load variation and pitch sensitivity. The model is linear, thus it cannot handle digressive dampers, though that could be built in if I made the simulink model more complex at the expense of run time. I would think you would still want to look at low speed damping using linear pot data and/or something like the methods on the OptimumG website.

Has anyone been doing anything else interesting in this respect?

Myself and another guy on our team made a similar model using a State-Space handling model (also linear) which had roll, yaw, and side slip (lateral velocity). The State-space model is pretty easy to make but is linear, so we pulled the dampers and tires out as subsystems and entered them into the model as inputs. We input steering data from track testing and outputted handling responses as we changed the dampers, springs, and chassis around. We used it to validate builds on the dampers we designed. If we were better at Matlab then we could have a 10-11 DOF handling model combining your stuff and our stuff. I spoke with the damper guy at ETS who did this exact thing and I may try to waste my time doing it too...as soon as I get some.


3) Lastly, have teams been writing their own lap time simulations? I would like a tool that I can use quickly to help understand track data. What I mean is that sure, we could spend lots of time to setup a full ADAMS model and send it around the track all day, but it takes a long time to run and typically doesn't deal with things like tire temperatures and load variation. Has anyone written a tool that can be 'calibrated' using track data that can help us understand the attitude of the car around the track and some estimates of the tire forces involved? I know it's kind of a holy grail, but wouldn't it be nice to have something like that you could run a fast DOE on to help suggest setup changes? Or what about macros to search for interesting events in the data? I know some of this is being done at a professional level, but I'm curious if there's FSAE teams out there taking a crack at it. I've been considering writing a quasi-steady state lapsim just to get a better understanding of the vehicle dynamics involved. That model could then be modified to take into account a local load variation coefficient, a tire temperature model, or maybe a non-linear tire spring rate as per the above discussion.


I would love to use that but I wouldn't want to make the model.

[GSpeedR]

Shit I just made a post on topic...there went my streak.

[Kerry]

For a short time I was considering building a simple shaker rig that would maybe shake one wheel or a set of wheels to measure the individual load variation on each wheel. I would still like to take a stab at it but I don't think the time invested vs. lap time reduction would justify the project. It'll have to be something to do after competition/graduation.

I am currently working on developing a 14-DOF car model that could potentially be used as the "meat and potatos" of a lap time simulator. The major road block I am hitting is a method for finding the locations of each of the suspension points as the car moves. I thought I had a viable solution, but recently I discovered that it only works MOST of the time. Does anyone have any ideas? What method do programs like Mitchell or ADAMS use?

[Kevin Hayward]

Gareth,

First up, great post ... tough questions. I think everything you raised deals with very real issues in these cars, issues that have all been discussed at length back at our Uni. In the end a lot of our solutions were the type to go around the problem rather than solving them.

1) Treating the anti-roll bar and the tires as you have mentioned will give an incorrect result. The equations can easily be changed to correct this. Not a big issue with UWA, where we never ran rollbars of any significant contribution to roll-stiffness. In fact I'm not sure we ran any comps with rollbars attached. Doherty brings up a good point of using strain gauges on the push/pull rod. Only issues with them would be accuracy vs. cost vs. time. We have attached our own previously and calibration, with temperature correction is not an insignificant problem. Recently in a test with a professional team, we encountered a similar problem with the sensors drifting even though they had been installed by a very reputable company. (Unfortunately cannot mention names of the team or company here).

Also had the opportunity to work with data from cars with rideheight sensors in addition to strain guages, slip angle sensors, and linear pots. The tire stiffness is a function of a whole lot of things. To make things worse to get the stiffness a lot of sensor channels have to be included, this induces a fair amount of accumulated error. In the end it appears that approximating a linear stiffness, while not being super accurate is a pretty good compromise.

Getting around this you can have a reasonable idea of which direction you want the LLTD to go at any given point around the track. You know the things you can change and roughly how much they will change the distribution. While you may not know the exact "real" number you have a lot of tools to do relative changes. This only really becomes an issue when changing tires, at which point there will likely be a lot of testing anyway, during which you can asses the relative change from one set of tires to the other.

I don't want to be dismissive of the issue, but this is one I don't lose sleep over.

2) No experience with a). To reduce load variation and increase response we put our effort into developing a kinetics system for the UWA cars ... It works very well.

While developing the first kinetics system we had a student working on a 7DOF shaker simulation. As in your situation callibration was an issue due to time. That was my last year with the team, so I'm not sure if they continued the work, or if they have found it particularly useful. Another student had modelled the dampers quite well and had good correlation between our damper dyno tests and his models. He is currently doing a PhD and is looking further into the kinetics system. I would not be surprised at all if he has some sort of advancement of the 7DOF model using an interconnected damper simulation.

Unfortunately due to student turnover and the learning rate of people I have serious concerns that this may be reaching the limits of what a FSAE team may be able to implement with vehicle dynamics. For a fair amount of time put into this work (the 7DOF sim) we saw very little applicable results to making our car better. There are other areas I would concentrate on in the shorter term. Actually it would be more along the lines of what you suggest in 3)

3) I have written a quasi-steady state lap time simulation, and am very certain that we are not the only team to have created one. Depending on the complexity employed they are not that difficult to start, and provide immediate interesting results. A lot of what I did was done personally and for a PhD I have not yet completed. Very little of what was learnt has been applied to the racecar, apart from helping to validate quite a few assumptions. I was linking my sims to a heuristic solver to help suggest changes and some interesting things come out ... which I wont mention here http://fsae.com/groupee_common/emoticons/icon_smile.gif The model I used did not take in tyre temps, but could be modified with a lot of the data we obtained. I do not see this as being overly difficult.

After I left one of the students took on the task of creating an open loop transient vehicle simulation and has had some very interesting and immediately useful results.

I would be putting most of my mental masturbation time into furthering the development of these sorts of simulations. They provide information that is useful to the whole team, a very real way of understanding where the design time should be spent on the vehicles, as well as being able to be developed piecemeal while providing useful information at each step.

in this I think we are much better off than most professional raceteams. For a professional raceteam your performance is almost certainly in tuning. Hence models need to be super accurate and painstakingly calibrated. For FSAE the design is so important that relative effects can often be more useful. This reduces the need for precise accuracy quite a lot. In perspective:

Pro Team : Buys car -> Test -> Calibrate -> Sim

FSAE Team : Sim -> Design -> Test -> Calibrate

Basically each year our sims get more accurate, but they are almost immediately useful. For pro teams a lot has to be in-place before simulation becomes useful, a heck of a lot if you want to trust the sim to make quite small trackside changes.

Anyway, hope that gives a little insight into how we did vehicle dynamic things while I was at UWA.

Cheers,

Kev

[kwancho]

I've got the beginnings of a state-space simulation from my vehicle dynamics class, and my question is how to apply that simulation to making design decisions. Do you use it to select the ideal spring rate or damping? Or to decide whether a light, single cylinder car is faster around a track than a heavier four cylinder?
Perhaps my tire model is too simplistic. Right now it works off cornering stiffness, with a drop off at increased loads. I'd like to plug in some of the TTC data to get a better representation of the tires, but I'd like to know that somewhere in the end is a benefit to our car.

[GSpeedR]

Alex, for the tire model you can use a look-up-table and just enter your TTC data right in there. Input slip angle and vertical load and output the lateral force.

Kevin, you mentioned one of your team members made a damper model. Is this a lumped parameter hydraulic type model (MSC Easy5 or an equivalent program) or a CFD/FEA model? I attempted to make a combined CFD/FEA model to subsequently model fluid flow with shim deflection but gave up when Fluent told me it was impossible with their code. I am seriously impressed if you guys managed to do that.

[Kevin Hayward]

No CFD by the time I left. Pretty sure it was lumped paramter, would have to check with Nando (maybe he will post if he sees this).

The validation was quite impressive though, and when speaking to the guys at Kinetics I was left with the impression that the CFD really only becomes useful when there is high levels of turbulence. One of the guys knew of some CFD work on dampers going on in Europe. Me ... well I'm just ignorant on the topic.

Kev

[Jersey Tom]

You guys are way too knowledgable for me.

Damn do I wish we had ANY vehicle dynamics classes here.

[mtg]

Originally posted by Kevin Hayward:
Pro Team : Buys car -> Test -> Calibrate -> Sim

FSAE Team : Sim -> Design -> Test -> Calibrate

Kev

You pretty much nailed it there. This is why I think FSAE is the best racecar series to be involved with as an engineer.

It will interested to see what comes out of this discussion (which is WAY beyond the scope of most "pro" race teams).

[Gareth]

Okay, not enough time right now for a full response, but so far this thread is going great!

What about using the pull/pushrod forces for evaluating contact patch load variation? I know this is used at some levels of racing, but the problem is that it ignores the tire between the upright and the ground. It occurs to me that the stiffer your tire is, the better this measurement gets. Ie: With a rigid tire you don't have a second spring interacting. On aero cars with stiff tires and wheel rates I would think that measurement gets worse, but I'm not sure. I should do some quick and dirty studies to find out how well and when it correlates. We strain gauged our pullrods on our 05 car, but never had the amplifiers working properly. Had we that data then I would have used it during the 4-post work to calibrate the max velocity as well as the shock speed histograms.

I agree pushrod forces seem to be the best way to look at LLTD...something I'd like to believe I would have thought of had we gotten them working. I suppose I should harp on the new team to get them going.

Doherty - You say the affect of load variation is wheel speed dependent and I see what you're saying about the transient response of the tire to the varying loads. Do you have some feel for how that would change the shape of a SA vs Fy plot? I don't have time to properly think this through right now so more to come...

What degrees of freedom were included in these various lap sims? Was a friction circle assumed and used to generate load transfer, or was a tire model used. I've heard that it's common to use bicycle models for this type of sim to reduce compute time...though this may be for aero cars that roll very little. Or what about using a bicycle model to generate accelerations at each point on the track and then using that data in a more complex model that could be used for looking at pitch/roll etc. How appropriate is it to use the TTC Pacejka fits in a sim like this? There is no combined braking/cornering data so that model is not particularly useful in that regard. I've heard of doing simulations with a fixed laptime (time and distance based acceleration inputs obtained from track data) and then doing parameter sweeps to minimize the slip angle each tire is working at while maintaining yaw rates. Anybody doing anything like that?

Okay gotta run. I'm happy this thread is thus far filled with reasonably intelligent discussion. ;-)

[Kevin Hayward]

A couple of comments on the lap sim I made:

- Definitely not a bicycle model. A bicycle model may be adequate to look at aero and longitudinal CoG position I think it falls far short of being able to look at important things for FSAE, like ackermann and camber change. It does become a little more difficult when all 4 tires have different slip angles, different cambers and different loads, but I believe for modelling FSAE cars this is essential.

- The tyre model I used was a curve-fitting one like the Pacejka model. It was a function I made myself in order to increase speed. It follows the shape of a Pacejka model very well until well after the peak. This didn't seem to be a huge problem to me as a quasi-steady state lapsim generally assumes a perfect driver, and the tires will end up operating close or below the peak values for grip. Unlike myself the simulation does not like entering corners sideways. Because my lap sim was designed to use an optimisation algorithm I needed really good speed, and for me the numerical solving solutions for Pacejka were not fast enough. I have used a Pacejka model in it earlier, and it could easily be substituted back in, just at the cost of a little speed. To combine cornering and braking I used an eliptical fit on the lateral and longitudinal with a shape factor (that allows to define how the "corners" of the elipse look. Not the best tire model, but your sort of pretty limited of what you can use for these sorts of sims.

- The tyre model is the weak link in the whole thing, which is to be expected. One of the other advantages of the Pacejka model replacement I created is it enable easy creation of "fantasy" tires. This basically allows the user to put in penalties for a given tire based on tuning experience etc.

The example I give here will be the Goodyear R065 tire. From our experience we found the Goodyear tyre to be incredibly senstive to wear due to camber. The sidewalls were considerably stiffer than the Hoosiers and the edge of the tire less rounded. As such we could have a fast setup that had increased negative camber, but would chew the tires out very quickly. This sort of thing does not show up very well on the TTC results. The tyre model I created has two variables to determine the effect due to camber. First there is a camber thrust parameter, and then a camber degredation parameter. By increasing the camber degredation value the lap simulation would end up penalizing a car with tires with too much camber.

The danger of this approach is that you could apply false knowledge or assumptions. Generally I prefer to make my model fit the data as best I can with no penalty factors.

...

As for optimizations I think that parameter sweeps are useful but limited. Obviously there are quite a few parameters and they are most definitely not all independent variables. Doing something like a DOE helps to find out the variables that will have the most immediate effect. However following a DOE approach will lead to what could be a local rather than global minimum.

The whole purpose of my Lap-sim (for my thesis) was to apply algorithms that pretty much put all the variables into a big pot and let the computer sort it out. The end result is that you avoid a lot of local mins as well as having a good idea of how important certain parameters are.

Kev

[Schumi_Jr]

I've got a couple thoughts on this.

1) Everyone else pretty much hit this one on the head. It is worth noting that the Pacejka model doesn't account for the change in rolling radius or vertical rate of the tire with slip angle.

2) a. This is obviously a very important effect. This is why a FSAE tire with 50lb of load doesn't have a COF of 3. As Doherty already said because of tire relaxation (slip angle hysteresis) the cornering stiffness and limit grip are affected. Since most FSAE corners are at similar speeds I think it is safe to neglect speed effects. With out an understanding of this concept then it will be difficult to make any gains from the methods you describe in 2 b). I got hammered in design judging because we focussed so much on reducing load variation without quantifying its effect (just because you read something is important in a textbook doesn't make it important!) There is a compromise between maintaining tire attitude, aero attitude and reducing load variation - if you don't first understand the relative weighting of each parameter it is difficult to solve this problem. I think that a good solution can be found with a strong understanding of theory and the courage to run some "un-conventional" set-ups that in theory reduce mechanical grip.

3) With the benifit of hindsight I think that making your own simulation is probably the best approach. You will learn way more than if you just use a canned software program and will probably land a job with a race team. I would caution against doing any DOE optimizations since your model lacks the fidelity to find an optimum solution. Think about how complicated a car is to model. Your tires (and aero) are hugely simplified and your optimization can blindly lead you in the wrong direction. Look at where your tires are operating, then use your common sense and whatever tools you have to bring them where they produce the most grip. If you are doing more than that you are probably over-engineering the problem.

[Charlie]

I've always thought, as Kevin said, that a team with a basic lapsim can really knock out a fantastic car in a hurry. The small amounts of sim work I did really saw good results and were satisfying. Unfortunately I was so involved with other stuff on the car, (like cost and presentation http://fsae.com/groupee_common/emoticons/icon_redface.gif ) never got a chance to go further.

It doesn't have to be too complicated, the tire data is the key. You don't even really need shocks in the model in my opinion. Just a real simple thing would tell you so much about track widths, wheel bases, ackerman, power curve, etc. It'd be an awesome thing to have.

[murpia]

Originally posted by Alex Kwan:
I've got the beginnings of a state-space simulation from my vehicle dynamics class, and my question is how to apply that simulation to making design decisions. Do you use it to select the ideal spring rate or damping? Or to decide whether a light, single cylinder car is faster around a track than a heavier four cylinder?
Perhaps my tire model is too simplistic. Right now it works off cornering stiffness, with a drop off at increased loads. I'd like to plug in some of the TTC data to get a better representation of the tires, but I'd like to know that somewhere in the end is a benefit to our car.

Alex,
Your sim, even with the simple tyre model, sounds perfect for analysing the big design decisions, which is exactly what I would use a sim for. As Charlie posts above, you can decide the mass, track, wheelbase and CoG height trade-offs for different vehicle concepts, such as lightweight single and heavier 4 cylinder etc. Run the concepts through some 'virtual events' and look at the best overall combined score.

An important thing to consider is the 'robustness' of your results. Are they highly sensitive to small changes in any input parameters? Or does a smooth range of inputs produce a smooth range of results. At this level of abstraction from reality you are looking for confidence-inspiring trends not absolutes.

Considering that the major input that drives results will be your tyre model then you should analyse a range of potential tyre characteristics either side of the data you have. Look out for sudden steps or discontinuities, at this level of sim you want to avoid them. This applies equally to a 'simplified' model or measured data.

At the vehicle concept level you can certainly neglect complications like dampers and even (and this will be contentious) detailed suspension and steering geometry. You are looking for the big trends here. Once you have a 'winning' concept then you can refine it more, but I suggest that simulation be used to set the adjustment range limits of parameters such as spring rates, Ackermann, etc. rather than absolutes - do the rest at the test track. You can also simulate to decide if everything need be adjustable. If you can get back to e.g. the same US gradient and laptime by adjusting both camber gain and roll couple distribution together, consider if one can be fixed...

Note that many of the most useful results won't necessarily be vehicle dynamics related either. Consider the percentage full-throttle time per lap (fuel consumption and cooling system), time on the brakes (brake system energy dissipation requirements), average speeds (cooling system and aerodynamics), etc. Involve the powertrain guys and define your torque curve(s) and gear ratio options.

This will involve a number of iterations of course. You need to prepare design concepts for a number of potential candidate vehicles to a level where you can be confident the input data is good. (A possible shortcut would be to take published data from other teams). Then once you have analysed each one you will have a lot of data ready to improve that concept and be more confident of the next iteration's results. Brakes is a good example, initially just assume the same brake system for all concepts, then once you can simulate the difference between the heavy and the light concepts, the brakes can be adjusted to suit (the light car gets even lighter...).

Sorry to slightly hijack the original thread on tyres, but I feel strongly that this form of simulation usage is one of the most valuable learning possibilities for FSAE competitors.

Regards, Ian

[Nick McNaughton]

murpia, a lot of what you're describing doesn't require simulation, it can be calculated straight from data acquisition. If you're keen, a lot can be done with a simple quasi-steady state longitudinal model and some track data. That's probably the best bang-for-buck stuff out there.

Charlie, you're spot on when you say the tyre model is key to even the simplest of simulations. Validation of the basic stuff is the second most important aspect. There's a decent paper by Siegler and Crolla that goes through most of the stuff thats important, SAE number 2002-01-0567.

Marc, I've had some luck with calibrating the contact patch 'lag' experimentally, but it's an iterative process looking at a few different cases before you get something that works for all of them. Even then it's not perfect, but it's a lot better than assuming things happen instantaneously. Without modelling a bumpy track it's going to be difficult to get around the 'chatter' that happens when you get near the peak force.

Also, not all tyre models are made equal. While there's a lot of talk about the load variations in the tyre data, that's far from the biggest issue. http://fsae.com/groupee_common/emoticons/icon_smile.gif

So far, I'm yet to believe any model's predictions of tyre drag caused by cornering.. if they'd measured the driving torque when doing the tyre testing we might be able to figure it out, but without it we're just guessing.

I can't help but think that with student resources, the best thing a model can do is point you in the right directions, and show you the most worthwhile things to go and test. It'd take a team of people a whole lot of time to come up with genuinely accurate results for all aspects of a few different vehicle's performance characteristics. Bang for buck gets worse the more detail you include, but there's definitely merit in building proper models bit by bit each year, if only for team continuity of vehicle dynamics knowledge.

[kwancho]

Ian -
Makes sense. I think what I have to do is get the TTC data working with the model, and then make up a representative autox and enduro track.
Oh, also, how do you guys model your driver? I tried a couple different methods (heading error, which worked too slowly I think, and slip ratio, kind of a traction control, which I think is more accurate). My prof suggested aligning torque, but that's hard because max force is beyond the peak of max aligning torque, and that all changes with normal load.

[Nick McNaughton]

Alex, I haven't tried it, but there's a few methods covered in freely available papers if you google 'vehicle simulation driver model'.

It seems as if a reasonable estimate of the velocity profile of the path you want the model to follow is a good start. If I were to have a crack at it I'd probably use a yaw rate error approach with a speed dependant look-ahead function to figure out what's about to happen. Some sort of detection of tyre force saturation for each end of the car is probably a good idea too... and being able to step back to a previous state to have another crack at it if the model messes it up might help.

It sounds like it would be a slow and painful process..

[Kerry]

You can probably make a lot of design decisions without a "human" driver model so long as you consider the assumptions you are making by doing this (avoid creating a steering system that requires more force to turn than the driver can produce). The plan for my model is to start by using telemetry (TPS, brake line pressure and steer angle) as inputs. Design changes and probably (hopefully?) even setup changes would cause the car to take a different path rather than completing the same path in a different amount of time.

The next step would be adding a "perfect" driver model that would follow some line around a course. This would allow lap time comparisons to evaluate design changes, but the lap times would have little hope of matching actual lap times. The final step would be a calibrated "human" model to predict actual lap times, but as far as I can imagine, predicting actual lap times is the only situation that would require a human model.

[kwancho]

Originally posted by Nick McNaughton:
Alex, I haven't tried it, but there's a few methods covered in freely available papers if you google 'vehicle simulation driver model'.

It seems as if a reasonable estimate of the velocity profile of the path you want the model to follow is a good start. If I were to have a crack at it I'd probably use a yaw rate error approach with a speed dependant look-ahead function to figure out what's about to happen. Some sort of detection of tyre force saturation for each end of the car is probably a good idea too... and being able to step back to a previous state to have another crack at it if the model messes it up might help.

It sounds like it would be a slow and painful process..

Yeah, some type of look ahead would be nice. Sheesh. My driver kept driving straight off the skidpad.

[murpia]

Originally posted by Kerry:
You can probably make a lot of design decisions without a "human" driver model...
...but as far as I can imagine, predicting actual lap times is the only situation that would require a human model.
Many (most?) 'professional' simulations don't use a 'human' driver model. Generally, a trajectory is generated (either from logged data or a survey) which is known to be smooth in curvature. The simulation solver will calculate accelerations (both lateral and longitudinal) at the limit of tyre grip, engine torque and brake torque, to minimise the time spent following that trajectory. Often the solver will look for the tightest part of a corner as a reference point and assume minimum speed and maximum lateral acceleration at that point. It will then apply engine torque acceleration forwards from that point and braking torque deceleration backwards. At some point the forwards acceleration from one corner will 'meet' the backwards braking from the next and you have 'joined up' your lap.

Of course there are many possible sophistications on this theme depending on how complicated you want to construct your solver, but the basic concept is that the simulation can never choose alternative 'lines' around a corner, like a human could. For many applications of simulation work this can be entirely adequate.

Regards, Ian

[VinceL]

Sorry for changing the subject, but I figured this would be the perfect thread to ask this question. Can anyone recomend a good book on vehicle dynamics simulation.

[Nick McNaughton]

murpia, the quasi-steady state simulation method that you're describing ignores the influence of the driver and transient vehicle behaviour by its very definition. FSAE driving has far more transients than most forms of racing, and there's a wide variation in driver skill. As a result, it's important to apply a hefty pinch of salt to whatever a QSS sim tells you about highly transient driving, or try to come up with fancy ways of adapting the technique to better suit the problem.

Having said that, it's a great way to get started and very powerful if you keep its limitations in mind.

[murpia]

Agreed, but the points I wanted to make are:
1) a simulation, even a basic one, is a very valuable tool to use when deciding how to proceed with a car design.
2) teams shouldn't be put off developing a simulation just because the task of developing a driver model is difficult, not to mention adding a whole extra layer of uncertainty into the results requiring additional validation.
Regards, Ian

[ben]

It's worth pointing out that unless you validate (i.e. measure) all the things like slip angles and compliances they're going to be of limited use.

Unless you measure them how do you know the model was any good?

Simpler models that generate easily measurable parameters like steer angle Ax, Ay, speed will probably give more meaningful correlations because you can accurately measure these things on the finished car.

The more I work with tyres, the more concerned I am by some of the tyre models used in VDS. My suspicion is that things like effects of Ackerman would get swamped if you just used Pacejka.

"All models are wrong. Some models are useful."
George Box, industrial statistician

Are we sure the usefulness goes up just because the complexity of the model has?

Ben

[murpia]

This makes for an interesting read:
http://www.bosch-motorsport.de/content/language2/downlo...al_LapSim_V.2006.pdf (http://www.bosch-motorsport.de/content/language2/downloads/Manual_LapSim_V.2006.pdf)
with the free download here:
http://www.bosch-motorsport.de/content/language2/html/3050.htm
Regards, Ian