CFD - General

I'll write this up while I wait for the drier to finish.

I'm sure as soon as I get into the meat of any CFD or FEA I'll get comments of criticism. Some out of genuine concern and interest (cool), others just so they sound like experts while really just being a dick (not cool).

The accuracy of such analysis always comes into question, and rightfully so. In my limited experience doing designer-level structural FEA in college, and just from watching some stuff at work, good results inevitably come down to the following:

1. Assumptions made. Could be assuming your upright material is isotropic and homogenous (more or less true on billet, not at all on a weldment!) or that flow around an airfoil is incompressible.
2. Boundary conditions / loads / constraints. Maybe it was just CU, but FSAE students seemed notoriously off in this regard, just from inexperience.
3. Refinement of mesh. Pretty self explanitory. Capturing fine details (be it a Gurney flap or a non-radiused corner for a stress riser) requires localized mesh refinement.
4. What you expect to get out of it.
   

As an example of 2 & 3, on one of our FSAE cars we had a highly-loaded structural part (wheel hub). Billet aluminum, with material properties well-defined. Design criteria was based on von Mises stress, with FOS=2. The part had a thin tube section of about 0.06" wall thickness. I believe the mesh used globally in the model was 0.10 - 0.12". Additionally when I looked at it years after, the constraints were off. As a result, the first time driving the car this part sheared as soon as the driver got on the brakes. FOS=2, not so much.

On the other hand, we designed the same part years later with a different method. Billet steel. I think it actually wound up being lighter than the aluminum one (steel rocks). Design criteria again based on von Mises stress, with FOS=1.2. May sound low, but 20% is a lot of overshoot! Very carefully looked at the constraints and conditions with a highly refined mesh. Part never failed.

Good examples of how changing a few small things has a big impact on results. For this 2-d CFD work I'm not looking for absolute numbers. I'm interested in directionality in how to increase negative lift, reduce drag, look at effects of Gurney's, etc. Hopefully I won't get in too much trouble.

Unsteady 2-d flow simulation

A preview of things to come in the blog?



Very possible.

Darren Engwirda put together Matlab code for a 2-d mesh generator, and 2-d Navier-Stokes solver. Pretty slick and easy to use. We shall see how well it works.

Static cross-weight

While I'm at it I might as well get into cross-weight. You might be thinking...

Well who cares on a road racer? Besides I can just corner weight the cross load out.

Just you hold on a minute. Two things to think about...

First, what is it and what does it do? Percentage of load taken up on a diagonal. I do it as the percentage of load taken up by the RF and LR, but either works. On an oval setup it's a good trick to get power down better out of a corner. With a cross-weight > 50%, you are "preloading" load transfer to the outside on the front axle, and the trade is you can "preload" load transfer to the inside on the rear axle. Having extra load on the LR tire in that case will let you get on the throttle earlier and more confidence. Obviously the trade off is the car will understeer more since you're overloading the RF more.


On a road course car, cross-weight > 50% will give you asymmetric balance, particularly on-center. Car will understeer left and oversteer right. Not what you want when trying to tune the car. Having looked at some of the telemetry from my guys' FSAE car last year they had that issue, and I'm kinda curious now if they had a cross-weight problem.

When doing corner weights, you can get rid of static cross-load by lengthening or shortening pushrods and such. Now that I think about it though, I suspect you could be fooling yourself by doing this, particularly if you have asymmetric wheel rates. Asymmetric wheel rates are surprisingly easy to get if your manufacturing isn't perfect or if your spring rates aren't all the same. Having measured springs on the FSAE car, there's a damn lot of variation. Four springs all stamped "300 lb/in" could easily range from 290 to 340.

An interesting way to check would be to take corner weights with and without the driver.

The above example are some representative FSAE numbers. It shouldn't be too hard to position the seat on centerline. While I'd expect the F/R load split to change a bit when the driver gets in, the cross sure shouldn't! Cross changing with vertical load, or acceleration, could lead to some weird stuff... if you put a different driver in, as fuel burns off, or even if you just get onto a section of track with some banking.

In the above example, if everything had been manufactured perfectly and air pressures were set, I'd suspect maybe the RF and LR springrates are a bit higher than the LF and RR. A swap of the LR and LF springs might fix it.

Food for thought.

Hopefully I'll get back to more design-related stuff soon. Been busy with other crap, and gotta drive up to Buffalo at 430am tomorrow morning...

Preload and bump stops

It appeared there was some speculation or confusion elsewhere as to the impact of spring preload on handling. Bump-stops are related. Both are important parameters. Unfortunately I don't think we really appreciated what they all did when I was on FSAE.

Balance is essential to good race handling. Balance inevitably comes down to managing dynamic tire conditions. Load is one aspect.

I think most people get the basics. More front bar (or spring, or damper [momentarily]) = more lateral load transfer relative to the rear = more understeer. The opposite is true for adding rear stiffness.

If you were to put your race car on an SPMM, you could generate a plot similar to what's below... looking at lateral load transfer as a function of chassis roll angle. Rough indicator of cornering balance. Ideally you'd want load transfer as a function of lateral acceleration (Ay)... the two plots are related but not the same.


Anyway. This might be a typical baseline setup with no preload, not hitting bump stops, and linear installation ratios. The slopes, and difference in magnitude between front and rear load transfer are what's important. In this example it's pretty straight-forward. The front has a higher roll stiffness, takes a higher percentage of the load transfer, and all other things being equal (50/50 corner weights, same tires all around) the car would probably understeer slightly. The feel should be very progressive and predictable.

If you were to add a hell of a lot of front preload, it may look something more like this.


If your tires and suspension were infinitely rigid, that initial slope would likewise be almost vertical. The front suspension is locked. Since the tires have a spring rate and inevitably there's compliance in your suspension, the rate is just very high.

There was an article in Racecar Engineering that (I believe) claimed lots of front preload would help a car "cut in" on entry from extra heat into the outside front tire. I find that hard to believe. It's no different than having a stiff anti-roll bar that "switches off" after a given amount of displacement. There are other reasons I won't get into, and I can also vouch for SPMM plots.

Until I see instrumented track data that proves otherwise, to me, I'd think front preload will "numb" the handling on-center.

Bump stops I am damn sure of, and the way they behave backs up my thought on pre-load.


If you roll onto a bump stop in the rear, your rear roll rate is going to increase substantially, very quickly, and rapidly shift the balance to oversteer.

The point of all this being, unless you manage it all carefully, going overboard with preload and bump stops and what have you can make for really non-linear or bizzarre handling. If you don't need it, or can't justify the reasoning for it... why bother?

Further clarification on Mz and Mx

Thought about this some more, given that a few people asked about it. Best way I can think of each of them is a dynamic measure of where the force center of the footprint is.

When making a simple vehicle model you might assume tire lateral force acts right under the centerline of the spindle. This isn't the case. Due to the black magic of tires, the lateral force trails the centerline, which is what gives rise to pneumatic trail and aligning torque. Mz is really a measure of how the pneumatic trail is changing, and where that "Fy action point" is moving around. Since yaw moment is dependent on Fy cross-multiplied by the distance from the "action point" to the CG, the fore-aft movement measured by Mz does affect your vehicle balance.

Likewise with Mx, in a simple model you might assume your track width to be constant or just a function of how much lateral scrub your suspension generates. In reality as the tire deflects under lateral load, the center of pressure ("Fz action point") deflects as well and your track width changes length or shifts over (deflects toward inside of turn). That in turn will definitely modify your lateral load transfer!

Bottom line, they're both important and non-trivial.

If I were running a MechEng department... [Some of this stuff is really practical!]

...I'd want a class for "Practical Application of Engineering Tools." 3000 or 4000 level, based heavily in Matlab. Probably 4000 level, since MCEN3030 - Computational Methods, is a junior class and pretty much murders you. Back then I eventually got decent at Matlab from having it thrown at me mercilessly, but when I got to work I couldn't do anything PRACTICAL with it. Like.. how to load a damn Excel file. Matlab has so much built in stuff it's unbelievable and I didn't know about any of it.

On the other hand, a bunch of crap that was just theory without application, as far as I was concerned, is really practical! Bode plots for example, who knew!! I sure didn't. I think I either skipped that lecture to work on the racecar, or it was when I had sliced my finger open on a lathe. (Freak accident, but don't EVER think you're the master of the machine. It can, and will get you).

Anyway. Don't let anyone try to fool you into thinking ride quality isn't important on a racecar. It's critical. There's a reason why professional race teams put a lot of time in 7-post ("shaker") testing.

What is a 7-post test? You put your vehicle on a special contraption, and shake the hell out of it. More precisely you recreate the disturbances and undulations the car is going to experience on a racetrack.


Why? We know that tire load variation is bad for grip. If you didn't know that, it's easy to conceptualize. If your suspension is stiff as a brick, if you had rigid links instead of springs, the car would chatter, skip and bounce over the race track. The whole reason for having a suspension is so it can be compliant and ride easily over bumps without upsetting the tires and chassis. The ratio of input from the ground, to force passed up into the vehicle, is transmissibility.

Where do Bode plots come in? It's a way of plotting signal amplification (transmissibility) and phase lag versus input frequency.


Changing masses, spring rates, and damping rates will change the shape of your curves. If I know what the major frequency content is of my suspension in a critical part of the track (big braking zone, corner exit, whatever) I can adjust my suspension rates to deaden that vibration out and increase my mechanical grip.

Wheel rate, tire rate, and damper rate are easy enough to get, as are the sprung and unsprung mass at a corner. If you knew the tire damping rate (hint hint) you could in theory fire up Matlab, play with some of your rates, and do a form of virtual 7-post testing. The Bode plot is a good way of seeing at a glance if your suspension is doing what you want or if you're moving in the right direction. Up until now I just thought it was some silly thing without a practical use.

As an aside, since at each corner of the car you have a sprung and unsprung mass, you'd think one would be acting as a mass damper relative to the other. For a long time there's been the phrase that you want to "always reduce unsprung mass." Generally I think this is true. There may be the case though that you could tune your unsprung mass to go along with everything else and really zero in on the frequency response you want.

Aw snap.

Ohhh... yea...

I gotta give it up to the folks at the F1-Info site, wow. Some amazing photos and drawings.

This... is a beast. 1972 flavor of the 312B-2. I do kinda like that extra fairing that blends the roll hoop into the rear wing, and the NACA ducts which feed the oil coolers.

Also the '70-'71 312B-1...


And the '69-'70 312B