Posted by: drracing | July 14, 2013

Audi R18 Modeling – part 3

Finally back on the modeling process of Audi R18 in rF, it is now time to deal with (probably) the last topic: suspensions.

Although they are, in general, a less easy to evaluate parameter to overall performance, they are still a key element in a race car and, as a consequence, also in a race car virtual model. Actually, most of the times they are, anyway, one of the strongest influencers in how the driver “feels” the car and can actually use it to his best, being the suspensions one of the main tuning parameters in a competition vehicle.

As probably most of you will well know, suspensions have several tasks to fulfill in a racecar: they are responsible to keep, in the best possible way, the wheels in contact with the road, still transmitting loads to the body and from the body; this implies that they also define the position of the body with respect to the ground (together with tires, that also acts as springs) thus also influencing aerodynamics forces, because of ground effects.
The way a suspension moves with respect to the car body also has a huge influence on forces exchanged by tires with ground, because it defines the angle at which the tires will be in contact with the road in different (perhaps critical) situations (braking, steering, rolling, accelerating, etc): to say this in two words, suspension kinematics. In a wider picture, we can also include the steering system in the list of suspensions components, since its position and the way it influences wheel angles are strictly related to what also suspension arms do in this respect.

In a road car, suspensions also defines how big are the loads and accelerations experienced by the human bodies sitting in the vehicle (comfort), but normally this is not a sensible problem in a race car.
On the other hand, some of the implications connected to body movement (and speed and accelerations) control have also an influence on the way the loads changes at the tire contact patch and so on how effectively tires are used to produce “grip” from a pure mechanical perspective: if loads at wheels interface with ground varies much and quickly, normally “mechanical grip” (so the grip coming purely from the interaction of tire with ground) reduces (and this phenomenon is more evident in tracks where road surface is bumpy). And here we already have the need for a compromise: to have less load variation at contact patch (and thus more mechanical grip), you would probably want to have a soft suspension (lower stiffness) and not too much damping (up to a certain point); on the other hand, if your aero loads are (highly) sensitive to ride height (distance of the body from the ground) or you anyway want to be close to the ground with your underbody (to lower the CG, for example), than you probably would be happier to have, overall, a very stiff suspension, so that ride heights don’t change too much with increasing downforce, or because of bumps, or during brakings (when load transfer will increase the magnitude of the vertical force acting on the front axle reducing at the same time the magnitude of the one acting on the rear), etc. Moreover, with stiff suspension setting normally a race car is quicker to react, but can become unpredictable and more difficult to “understand” at the limit. This is a very first and quick overview of the eternal debate soft vs stiff. Although, to say soft or stiff doesn’t mean much in itself…

Last, but absolutely not least, suspension design and tuning have a central influence on how and how much weight is transferred side-to-side (on a certain axle) in cornering situations and front-to-rear in acceleration or braking situations.
This is why suspension stiffness (in heave and roll modes) and damping are some of the most important parameters that are changed by Race Engineers to tune a race car.
Changing spring and antiroll bars stiffness, damping coefficients and, more in general Total Load Transfer Distribution, you can heavily influence the understeering-oversteering tendency of the car, together with its way of reacting in transients situations, like corner entry. Once again, sometimes you have several problems at the same time and to change a parameter could be good to solve one of them but not the other.

Who wins?  Better to help tires or to help aerodynamics? Better to solve a problem in corner entry, middle or exit? Or maybe is there a way to solve them all, at least partially or at least in certain situations? And which is the solution that could potentially give you more advantage in term of lap times?

These are some of the (difficult) questions that designer and race engineers try to answer (every race weekend or in design phase) when they lose their hairs trying to help their drivers to gain the last tenths that, in certain races, could make the difference (and here we are still completely ignoring reliability and strength issues). The bad thing is that it is not only difficult to find the right answers to these questions, but it is also very difficult to verify if, at the end of the day, your answer (setup choice, design, etc) was really correct or not, since very often there are so many things working together at the same time and influencing the final result, that it becomes very hard to isolate which one has produced what (just to mention one of them, track conditions are never exactly the same in two different sessions; the same can be said for two different set of tires or for their behavior when worn; luckily enough, at least in simulations these variables can be isolated!); although it is of primary importance to always understand what is causing what. As a very good engineer (Claude Rouelle) once said in one of his seminars, you need to know why you are fast, not only why you are slow, otherwise you will not be able to be fast again tomorrow. And in this regard, to have a good and sensible drivers is crucial. But this is another story.

Let’s now focus on the modeling of Audi R18 suspensions into rFactor.

In general, when modeling a suspension you normally want to identify to main groups of parameters: dynamic parameters (stiffness, damping, masses, inertias, etc) and kinematics parameters (so, actually, how the suspension is allowed to move based on the constraints we put in place and, more specifically, how the wheel will move with respect to the ground or to the body).

Let’s start with suspension geometry, so actually where attachment points between each suspension component and the adjacent ones or between control arms and chassis are located. Suspension geometry directly defines how the suspension will move with respect to the body, so, namely, kynematics.
Audi R18, as the greatest part of purpose built race cars, uses a double wishbone scheme, with push rod at the front and push rod at the rear in 2011, then changed to a pull rod from 2012 on. An interesting point about nearly all modern top level race cars, is that they normally use a 3 springs-dampers layout, both at the front and at the rear and Audi LMP1 contender makes no difference in this respect. It’s difficult to know wether Audi guys use a real third spring, just a bump stop or a spring that starts to act only after a certain wheel travel has been achieved. One of the pictures you can find in my flickr page seems to suggest that, at least in Spa, they were using the first solution at the front. But the third spring look very small, leaving me with some doubts.
What is anyway pretty clear about this devices is that they help a lot to disconnect the corners stiffness to the axle stiffness and to decouple roll stiffness from heave stiffness, making also easier to better control ride heights without hurting too much mechanical grip in low speed corners.
This will be the object of further studies i want to do with this model, also connected to the damping ratios in heave and roll.

Let’s see how suspensions can be modeled in rFactor. I am aware of at least three kind of suspensions that can be simulated with this software: double wishbone, solid axle and McPherson strut.

In road cars, very often the connection between each component and another or between suspension components and chassis are done by rubber elements, called bushing, which are sometimes designed on purpose not to be (so) stiff in certain direction (mainly for comfort reasons, but also for vehicle dynamics connected purpose, like toe correction).
In race cars, compliant connections are the last thing you could want, mainly because it would be something very difficult to predict, both from an engineering and from a driving perspective. Normally, the connections are done through very stiff joints, like ball joints for example, where friction, as well as hysteresis, are tried to be kept as low as possible.
I have honestly never tested myself how stiff a race car ball joint is, but I think it can be simulated as a “no compliance” connection also under very high loads, at least if the ball joint itself was properly chosen/designed by the designer. I have always modeled them this way and normally had good correlation with real data. There are actually other components in a suspension that are not as stiff as one could expect and that are normally not simulated as compliant (not only in rFactor but in also in a lot of high level and very expensive simulation tools). See for example my post about rims, a couple of years ago.

Back on topic, rFactor simulates the suspension as a series of rigid bodies (with own mass and inertia) connected together by joints that can be chosen from a rose that includes ball joints (they take out 3DOF, leaving only rotational movements free), hinges (- 2DOF) and a joint+hinge (-5DOF).
Actually, control arms are simulated through another constraint called “BAR” which force to bodies (or two points belonging to two different bodies) to maintain always the same reciprocal distance in a certain direction in space (BAR axle) thus taking out 1DOF: so a wishbone, for example, is made of two bars, each one representing a beam of the arm. This means that in rF control arms have no mass and no inertia and that all the unsprung mass and inertia must be concentrated in wheels and spindle (including also arms, brakes, tires, rims, upright and bearings mass). This is a simplified way to represent things compared to, say, a proper multibody software like ADAMS, where also arms (can) have their own inertial properties; but since control arms mass (control arms are the only bodies in a suspension that have a CG which is not really close neither to the chassis or to the wheel) are pretty small compared to the overall unsprung mass, this doesn’t have such a big negative impact on the results. Except from this approximation, rFactor way to simulate suspensions behavior is very similar to a “proper” multibody package.

Now that we know how suspensions can be defined into rFactor, we can potentially model our one. Bur first, we need to know hardpoints locations and we have to estimate how big the unsprung mass is at each front or rear corner.

Tackling the second point first, I had some good indications from some engineers working with similar cars about how big the unsprung mass should be for an LMP1-like vehicle. I think a reasonable value should be around 45-50 kg per wheel (here we talk about the current very big LMP1 tires). This is a lot if you compare, for example, with an F3 car. But these cars have nearly double of an F3 weight and much much more downforce.

Regarding hardpoints locations, instead, the first thing I did (as for the other topics) was to gather as much information (in this case, mainly pictures) as possible to start immediately with a feeling of how front and rear suspensions look like. Actually, this has led to the first issue: as I said, Audi suspension layout has changed between 2011 and 2012 (with a major change at the rear, where Audi has switched from a pushrod solution built up on a gearbox only partially made out of carbon fiber to a pull rod design on a full carbon fiber gearbox) and it was not easy to find good pictures about the first year.
My procedure has been to try to measure from the best pictures I found the main dimensions needed to draw suspension geometry, using some other (more or less) known dimensions as a reference (to identify “the scale” of the picture). The idea is very similar to what is shown in Mulsannerscorner, when Mike found main cars dimensions using a basic 2D CAD tool, thus identifying, for example, car wheelbase and overhangs.
On this regard, this task has been a bit easier for the suspension attachment points placed on the chassis and on the gearbox, but I found nearly no pictures (at least not close ones) of the wheel side (here suspension hardpoints are nearly completely hidden by brake covers), thus requiring a bit more intuition and common sense on this side; it was anyway still possible to identify the main tendencies/choices and to the draw something that at least should resemble to the real counterpart.

Once this work has been done and I finally had an idea about the approximate locations of the main hardpoints, I input all the data into an suspension kinematics software to check if the suspension behaved “correctly”. In this phase, I checked, for example, that bump steer was as close to zero as possible and that other indexes (like roll steer, scrub, roll centers position and migration, etc) was in a range that, basing on my own experience (and looking to the suspension from pictures) could make sense. Of course, this has required some points to be slighlty moved and so, finally, the suspension has been modeled more through the work I have done with this software than using pictures (and that has been true above all for the wheel side harpoints locations, as I already said, I had very few picture showing accurately enough where they are). But still, the boxes defined through pictures study have been respected quite closely (I just moved the hardpoints slightly) and the general look I got at the end of the process was very similar to the one you could see in Audi´s photos (I tried to move the hardpoints the minimum amount possible). Much more interesting, the work I have done with this software has confirmed some of the features I would have expected (not only looking to the pictures but also from my experience), like roll centers position and camber gain.

In this sense, my work has focused mainly on the pure kinematics, so on how the wheel moves with respect to the body. I have not investigated at all, for example, rocker designs, which play a huge role in defining, for example, wheel rates and wheel damping coefficients (through motion ratios, so namely how much the wheel move vertically compared to the spring). I have ignored them mainly for three reasons:

  • it was nearly impossible to get useful pictures showing their shape or dimensions, above all at the front
  • rocker cannot be modeled in rF, at least not as bodies or as bars, like control arms. To design constant or progressive/digressive motion ratios in rF other means have to be used
  • wheel rates and damping rates are anyway some of the most tuned parameter in a race car: it is pretty common to change spring/Antiroll bars stiffness in order to change car behavior or to change damping to tune car way of performing in bumps or in transients situations. So, although without knowing the motion ratio, i will probably never get to the exact wheel (or damping) rate that Audi engineers use on the R18, I could still allow some freedom in spring stiffness and damping coefficients choice so to cover as more as possible the range I think they are playing in.
    In all the race cars I have worked on, I normally changed my spring stiffness in 100 lb/in steps, rarely I did 50 lb/in steps changes (although this was valid for cars using normal coil springs, not torsion bars as Audi does; I honestly have not experience with cars equipped with this kind of springs). Moreover, sometimes motion ratios were very close to 1, thus leading to a nearly perfect equivalency between spring rate and wheel rate.
    So I set a step dimension in this order of magnitude and then I chose, as base setting, a stiffness value that was giving me a reasonable unsprung mass natural frequency (normally very stiff aero cars are in the range of 5-6 Hz for sprung mass vertical stiffness).

To do so, I modeled the suspension in a way to have a motion ratio as close to 1 as possible and as constant as possible, “tricking” somehow the software for the absence of a rocker. On this side, a very important help came from Niels Heusinkveld (probably the most informed man about physics modding for rFactor), who kindly and patiently explained to me rFactor “language” for suspension hardpoints coordinates definition. As you may imagine, infact, rFactor works completely another way compared to a proper Kinematics software or to a multibody one, with respect to reference system definition, as well as with how the hardpoints are then moved in game. It is easy very easy to take a wrong way, if you don´t know this “language”.
Basing on Niels advice and example, i created my own tool to input the right numbers into rF, starting from the input i got from my suspension kynematics software (which, on its side, received the input from my previous pictures study or, for other models, from an hardpoint list). Basically, i built up an excel sheet to have immediately harpdoints coordinates in “rF language”.

As for the other phases of the modeling process, this one has been again also a chance to look to Audi choices and to try to understand why they have designed their components in a certain way. Looking for example to R18 front suspension you can see, first of all, that control arms are pretty short (Audi´s chassis is not that narrow at the front), with the lower ones being slightly longer than the upper ones, because they are attached to the chassis below car front nose supporting structure (picture 1, 2 and 3).
Short control arms normally lead to some kinematics compromises (scrub could be an issue, for example: in general, short arms make harder to control how angles changes with wheel travel), but, in my experience, when dealing with limited wheel travels and when control arms attachments are located with a grain of salt, this issue could be overcome. This is what i have found playing around a bit with my model’s front suspension hardpoints, although of course i cannot know if Audi Engineers came to the same conclusions/locations. Let’s say, if my intial assumptions were right, we should be at least close. Anyway, I don’t expect wheel travels of such a race car to be very big, above all at the front (maybe some 20 mm? that’s at least what I see in my simulations logged data).
Another thing which is pretty evident is that top and lower control arms are more or less parallel. This normally leads to a very small camber gain (which means that camber doesn´t change much in heave, so when wheels move up vertically with respect to the body). This is a philosophy I understand and, honestly, agree with (at least for front suspension), since such a design normally gives a better control of tires contact patch in braking situations (since your camber gain is small, you can expect camber not to change so much in brakings, thus leaving tire contact patch to have more or less the same dimension as in static conditions) but still you can use other means (see Caster, for example) to influence camber angle in cornering, so when you actually need camber effect on cornering force. Caster is normally an important player with such a geometry: it also moves the inner wheel down with respect to the body when steering, thus increasing the load pushing on it in corners and counteracting load transfer effect in a stronger way as soon as more steering angle is used (this typically happens in small radii corners, where you normally tend to have more understeer).

The only undesired effect I see with an aggressive caster angle at the front is the need for bigger forces to rotate the steering wheel, but normally cars like LMP prototypes use some kind of power steering to help the drivers.
And actually, looking to the pictures I have found, it seems that Audi use quite a significant amount of caster at the front. This was something already visible in Audi R15 (see this and please note how far back is top wishbone attachement point to upright compare to lower one: Audi R15 front suspension): probably, R18 uses less caster (at least, I think this would be reasonable since they now have such big tires at the front), but still it is pretty clear that they have some. How much exactly? Difficult to say from the very few pictures showing the wheel side I have found or i could do when i was in Spa (the best picture i found showing a bit how big is longitudinal span between upper and lower wishbones upright attachments is this one).
I know for sure that some other (more customer oriented) manufacturers used something in the region of 7° to 10°, but of course I have no direct info about Audi. I would anyway expect Audi not to be below 10°.
I also suspect that, on wheel side, the pushrod is attached to the upright, instead of being connected to the lower arm. This leaves room to also create an effect similar to the one from caster (that pushes the inner wheel down when steering), if the pushrod attachment has a longitudinal offset compared to the steering axle.
Unfortunately, this later feature cannot be implemented in rF, as far as I know. If anybody knows a different story, please let me know!
Another thing you could notice looking to Audi R18 front suspension attachments is that upper arm rear connection point to the body seats sensibly lower than the front one. This is a tendency you can see also in Formula 1 car where, anyway, one could think it could also be done to help aerodynamics (see picture 4, 5). The effect of this solution should be is to produce a pretty big anti dive effect, with the top upright hardpoint moving backward when the wheel moves up with respect to the body. An interesting side effect of this solution is that as more the wheel travel increases, the more also caster goes up, because of the rearward movement of top wishbone attachment point to the upright. I don’t if this is something Audi Engineers have even considered or if their reasons to design the suspension this way was different.
What i can tell for sure is that, according to my calculation, this effect is pretty strong and can be seen very well when analysing sessions data because the front springs don’t displace much although longitudinal acceleration and weight transfer being pretty big.

What about the rear?

Rear suspension shows the typical compromises connected to need to leave room for the diffuser and to attach the arms to the gearbox case.
What can be immediately seen is that both top and lower wishbones are attached to the upright pretty much forward, very close to the rim edge. Looking from top, you could also see that the rear beams of both upper and lower wishbones are attached to the gearbox forward of the halfshaft exit and, as a consequence, slightly forward of the wheel center as well. Still looking from top, it is also clear how the Tie Rod is the only suspension link to seats rearward of the wheel center.
As I said, I can see the reasons of such a design both from a structural and an aerodynamics perspective. The wishbones are located in a way they can leave room for the diffuser (above all the lower one; the upper one could maybe be less compromised, but i guess they put it where it is also for packaging reasons), still managing to face loads in an efficient way in acceleration (where you would probably expect them to the hardest work). The Tie Rod, on the other hand, being attached to the upright far away from the “steering axis”, can help to increase toe stiffness.
Looking from the rear, it is pretty easy to see how the wishbones are not parallel, thus leading probably to some camber change in heave. This is something I have seen very often in single seater cars as well and, again, it makes sense to me. Since rear wheels don´t (or shouldn’t, at least) steer and you cannot benefit of caster effects, the only mean you have to compensate for negative camber loss in roll is to add some camber gain in your kinematics.
Also, in rear view Tie Rod is located more or less between upper and lower wishbone. In open wheels race car, this is normally related to aerodynamics optimization (it is in the diffuser exit area), don´t know exactly if in a sport car this choice can play a similar role.
Finally, if we look to the suspension from side view, you can see that, as we could expect, the rear suspension feature some antisquat (you could see that the front attachment to gearbox of lower wishbone seats higher than the rear one, while top wishbones has its attachment points at a more even height). That is a normal solution, above all with ride height aero sensitive cars like these.

A final note about front and rear roll centers height. Although roll centers are a controversial concept that not everybody accepts (or at least not everybody look to it the same way), Audi seems to have a very conventional solution, with the front RC seating clearly lower than the rear one. This is, in my experience, a very common choice, not only for race cars.

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