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MKII Suspension Analysis: Front Suspension

41K views 97 replies 24 participants last post by  timmyc 
#1 · (Edited)
Finally got arround to modeling up the front suspension on the MKII in optimum K. The analysis and discussion for the rear suspension can be found in this thread

As before, it is based on my own measurements of my car with Tien S-tech springs, which lower 1.5" according to Tien. Stock is based on raising the car 1.5" from what I measured. Green = stock, red = lowered 1.5", and Blue = Lowered 1". As before, body roll is to the right, aka car is in a left hand turn, so the right is the outside wheel, should be the dashed line in the graphs. As with the rear analysis the choppy parts of the graphs are due to the program not knowing how to handle excessive roll center migration.

First, the graphs.

Roll vs camber:


Roll vs Toe:


Roll vs Roll center migration:


Roll vs Spring Displacement:


The first thing I noticed with the front is that lowering it actually REDUCES roll center movement compared to stock. This I found to be very strange, but as far as I can tell my model is fairly accurate. I'm really not sure what is so different about the front geometry that this occures. One thing not shown on any of the graphs is the actual location of the roll center. Stock it is about 1" above ground level and when lowered 1.5" it is about 3" below ground level, so you can see how it drops siginificantly more than the CG when you lower.

Another interesting thing about the roll center. Stock, it moves toware the inside of the turn. When lowered it doesnt move as far, but it now moves toward the outside of the turn.

The other strange thing is that it APPEARS from these graphs that if your going to lower the front you are better off lowering it more rather than less. Dropping it 1.5" seems to have a better effect on roll stiffness and roll center movement than does lowering only 1".

The front seems to experiences a reduction in roll stiffness when lowered, just like the rear. However, it doesnt appear to be quite as severe, and in fact the spring displacement vs roll becomes very linear when you drop the front 1.5", compared to the rear where it was linear stock.

As with the rear, lowering has a slight negative impact on the camber curves.

The front appears to toe in the direction of the turn, and lowering only increases this tendency. Not a big deal either way in my opinion.

******************************************************

Now a bit of analysis of the front and rear at the same time, Roll center migration:


This is where things get a bit crazy. As you can see, at stock height the front roll (Solid Line) center moves quite a lot, the rear (Dashed Line) hardly moves at all, and both move toward the inside of the turn.

Lower it 1" and now the rear moves a lot and the front moves a little. The rear is still moving into the turn, but the front is now moving OUT of the turn.

Lower it even more and now they are atleast moving in the same direction, rear still moving a lot, front moving not quite so much.

Now, if this is right this will cause the roll axis to swing out in the rear and stay centered in the front when lowered. This should tend to cause the rear to lift (due to roll) when lowered, increasing oversteer. Stock the front swings out and the rear stays centered, which should lift the front, reducing oversteer. Sound right?
 
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#53 ·
In autox, narrower is better, much better. Making the car 4-6" wider is very bad.

Otherwise, what you are saying is mostly correct, though if you lengthen the LCA you may also need to add more caster to compensate for the same increase of SAI that I experienced.
 
#55 ·
You can't build the bumpsteer spacer into the LCA, as that won't move the ball joint. You have to space the ball joint down relative to the hub.
 
#56 ·
rnoll98 said:
In autox, narrower is better, much better. Making the car 4-6" wider is very bad.
We were all surprised how much we gained by taking an inch out of each track of our '08 SAE car. The new car was about 10% down on power and was running a full second quicker than the old car on a sub-30-second course, both with the same competition driver. It's like getting free lateral acceleration.
 
#57 ·
bentheswift said:
We were all surprised how much we gained by taking an inch out of each track of our '08 SAE car. The new car was about 10% down on power and was running a full second quicker than the old car on a sub-30-second course, both with the same competition driver. It's like getting free lateral acceleration.
Another way to imagine this. If your car is 6" wider, it's like offsetting the cones in a slalom that far the 'hard' way. Road racers don't have this issue because they have so much more space between turns.
 
#59 ·
When we were trying to decide on track width for our new FSAE car, I did some quick & dirty calcs in Matlab for a steady state corner with varied track widths, basically just seeing whether the benefits of the reduced weight transfer from a wide track outweight the benefits of making corners effectively a larger radius by having a narrower car. In a steady state corner it showed that wider was better, but I haven't yet been able to work out a good way to model the effects on something like a slalom. Regardless, I went with my gut and decided to reduce the tracks by a reasonably significant amount, so it's good to hear some anecdotal support for this :)
 
#61 ·
Driftin_AW said:
When we were trying to decide on track width for our new FSAE car, I did some quick & dirty calcs in Matlab for a steady state corner with varied track widths, basically just seeing whether the benefits of the reduced weight transfer from a wide track outweight the benefits of making corners effectively a larger radius by having a narrower car. In a steady state corner it showed that wider was better, but I haven't yet been able to work out a good way to model the effects on something like a slalom. Regardless, I went with my gut and decided to reduce the tracks by a reasonably significant amount, so it's good to hear some anecdotal support for this :)
For a slalom just assume the wider the car the longer the distance it has to travel and, as a result (assuming grip was constant), the slower the speed through the slalom because of the increased amount of steering input (more turning) needed.
 
#62 ·
I certainly have no qualms with the fact that a narrower car will tend to be faster through a slalom, but what I'd really like to do is to numerically model a basic car going through a slalom so that I can get a feel for the significance of the effect of changing track width, so that I could compare this to the loss of speed in a large corner and work out roughly what track width would make a good compromise, based on a certain ratio of importance of steady state cornering ability versus transients/slaloms.
 
#63 ·
Driftin_AW said:
I certainly have no qualms with the fact that a narrower car will tend to be faster through a slalom, but what I'd really like to do is to numerically model a basic car going through a slalom so that I can get a feel for the significance of the effect of changing track width, so that I could compare this to the loss of speed in a large corner and work out roughly what track width would make a good compromise, based on a certain ratio of importance of steady state cornering ability versus transients/slaloms.
My gut tells me until you get to the extremes, what you make up in a slalom will always be more than what you lose steady state, assuming track width is the only variable.

Also, be careful what you call steady state. Most autox courses are a series of offsets (even if not true slaloms). On a given course you probably have 10% of your inputs doing steady state cornering--defined as having enough room to setup wide and finish wide without having to compromise to get the car setup for the next turn. The rest of the time you're focusing, to varying degrees, on getting the width of the car over far enough to get a good line through the next corner.
 
#64 ·
Yeah I appreciate what you're getting at with respect to what is and isn't steady state/how little true steady state you'll see in an autocross course - ultimately though speed, even in a slalom, will be limited by the ultimate/steady state lateral acceleration ability of the car.
 
#65 ·
Driftin_AW said:
Yeah I appreciate what you're getting at with respect to what is and isn't steady state/how little true steady state you'll see in an autocross course - ultimately though speed, even in a slalom, will be limited by the ultimate/steady state lateral acceleration ability of the car.

As an instructor, and driver, my fastest slalom times have been ones where my hands never stopped the wheel. I think this would apply to FSAE cars as well. Assuming little/no wasted motion, if your hands are constantly moving that means the wheel is moving as slow as it possibly can (simple velocity/distance over time), and the tires are happiest because the loads on them are being changed very smoothly. If your hands are always moving, the suspension is always moving, and you aren't in steady state.

I see your point. Bottom line is if the car grips better it'll go through a slalom faster. No argument there. But you could have great steady state on smooth asphalt and crappy dampers and suck in a slalom. The difference between what we're saying is probably just semantics, but the "steady state" people talk about in road racing rarely if ever happens in autox.
 
#66 · (Edited)
Ok, I went back and did some more analysis on the RCA question, and now I definetly think that its a good idea to add these to the front only.

The graph below shows the lateral movement of our front roll center over 1 degree of body roll. The red line shows what the roll center does on a car lowered 1". The blue lines show the movement of the front (solid) and rear (dashed) with the addition of a RCA. Not only does it move a whole lot less, it also moves in the same direction as the rear, instead of in the opposite direction.


All of the above I already knew. However, looking at vertical movement: After 1" of lowering the front roll center is just below ground level, the rear about 1" above. Adding the front RCA brings the static height of the front to about 2" (this I already knew). However, I hadn't noticed before the vertical movement that you get on a lowered car. The front roll center may start out below the rear, but as the car rolls it quickly climbs (and the rear drops a little). Adding the RCA raises the front roll center above the rear (this is rare in my research), but atleast they now move in a nearly parallel manner. Before I was concerned about the idea of having the front roll center higher than the rear, mainly because it seems so rare. But after seeing how quickly the front moves above the rear, I don't think it can possibly be a bad thing to go from the large movements to almost no movement, even if the static condition is a little higher in the front. It only takes a half degree of body roll on a lowered car to put it there anyway. I think its better to start there, and then move in a more predictible manner. This can be tuned arround. Whereas it would difficult to tune arround the massive movements seen in the uncorrected case. As before, the red curve is the front roll center movement, the blue curves are the front and rear with the addition of the front RCA.


Thoughts?

One other thing. I discovered that if I tell optimum K to calculate based on a fixed roll axis the previously seen errors and annomolies (as points go to infinity) go away, and you get nice data out of it. The data doesn't appear to be changed, it just is now consistant. Since I have read a lot of things lately that say that the car doesn't REALLY roll about the roll center I don't think its too big of a deal to do calculations about a fixed axis, rather than one thats way outside the wheel base and is producing errors.

Thoughts on that?
 
#67 ·
On the subject of lateral roll center movement and whether the car really rolls about that point -

I started reading this thread recently as I consider some suspension mods on my AW11, and all the plots of lateral roll center had me bothered, especially when I started thinking about how I should calculate roll stiffness if the roll center had moved way off to one side. Logic suggested that if the car is rolling about the roll axis, then roll stiffness should be calculated as the sum of torques of the spring forces about that axis. But my conclusion was, if the car really pivoted around an axis not under the center of the car, then the spring farther from the roll center would compress more than the extension of the spring closer to the roll center (if the roll center was between the wheels), and the total spring force would be greater than the weight those springs are holding up. If the roll center was outside the wheels, both springs would compress! That would make the car rise until the spring force equaled the weight, i.e. the inside wheel's spring extension would equal the outside wheel's spring compression assuming linear springs. In steady state cornering (no braking or linear acceleration) this would be true for each end of the car separately. Equal and opposite spring deflection seems to imply a "pivot axis" midway between the wheels, so that makes it seem that the car always rolls about a point midway between the wheels (assuming the suspension is mirror symmetric), regardless of the lateral position of the roll center.

So then, what does the lateral position of the roll center really tell us? I haven't got that one figured out yet.
 
#68 ·
That is assuming that your spring deflections ARE equal ;). There are what are called "jacking forces" at work in suspension that WILL actually cause the suspension to compress or extend further than would be implied by simply assuming the weight of the car being reacted through both springs.

Now, I'm not saying that the car ACTUALLY rolls about the roll center, especially when that point is hundreds of inches outside the wheel base. A lot of the reading I have done indicates that the kinematic roll center (the one I am calculating here) is of limited importance in suspension design.

However, I still believe that it can be a useful theoretical tool. While the car may not actually roll about the roll center, I can say that a well designed suspension WON'T see the roll centers moving hundreds of inches, and also shouldn't see the front and rear moving drastically in opposite directions.

To be honest I don't myself have a super firm grasp on what the lateral position really "means" (the vertical position should be a component of roll stiffness, and it effects camber gain). I tend to look at the lateral movement more as a check. If the roll centers don't go shooting off into the sunset, then I can move forward and work on other aspects of the geometry. If they are moving drastically, then that is something to be fixed first. It is POSSIBLE that lateral movement doesn't really effect anything, but my feeling on it is that the lateral movement should be kept within the wheel base, at the very least.

Hopefully I didn't just contradict myself a whole bunch, and hopefully I didn't forget anything. Hopefully that was helpful too :)
 
#69 ·
You're right, I did ignore the jacking forces, which blows my whole argument that the sum of the spring forces has to hold up the car. I could argue that since the roll centers are close to the ground that I intentionally chose to ignore the jacking force, but that would be somewhat overstating the completeness of my thought process. :)

I did find this helpful writeup, the analysis seems sound and is clearly presented. it looks like its from a real SAE engineer, not just a hack on the internet like me.
William Mitchell roll center article

(back up to the main page www.neohio-scca.org to find the link to the rest of their "competition clinic" material)

I do think that at the very least, large lateral movements of the roll center must be an indication that one of the instant centers is zooming off toward infinity, meaning that at least one of the wheels is running out of camber gain. That alone seems like a valid reason to try to keep the roll center lateral movement reasonably contained.
 
#70 ·
mhleary said:
I do think that at the very least, large lateral movements of the roll center must be an indication that one of the instant centers is zooming off toward infinity, meaning that at least one of the wheels is running out of camber gain. That alone seems like a valid reason to try to keep the roll center lateral movement reasonably contained.
Absolutly, that is is definetly something I have seen in my analysis (one of those things I had forgotten). The roll center is really just an "average" of the two instant centers (as its location is defined by the relationship between the contact patches and the instant centers), so movement of the roll center implies movement of the instant center. I have chosen to post mostly roll center data here since I think it illustrates my point, while simplifying it to the point that hopefully more people may be able to get something useful out of it.
 
#71 ·
Great article! Note the the RC for the heavily loaded outside tire (uh, make that the Force Application Point) is lower than for the lightly loaded inside tire. My read is that means more body roll in real life and less weight jacking than you expect from looking at the kinematic RC.
 
#72 ·
I finally got arround to reading that article (very good by the way, I have spent a lot of time looking for similar information and but somehow didn't find that one).

Anyway, I urge everyone to read it, but I wanted to point out this:

Stability results when the FAP(Force Application Point)-CG moment arm remains constant as the vehicle rolls. The chassis ?takes a set? rather than constantly seeking a new equilibrium. This can be expressed by minimizing the lateral movement of the KRC (Kinematic Roll Center) as the vehicle rolls. But this is an artifact: there are more direct ways to calculate this; namely with the change in FAP height resulting from ride. It should be one-to-one. (An easier way to visualize this is from the viewpoint of the chassis rather than the world. The FAP point should be constant as the wheels and tires move up and down.)
So THATS what lateral roll center movement does for (or against) us!
 
#75 ·
Interesting thread, i've just read through it again (First read it ~2008).

I'm approaching things from a slightly more practical angle, and after seeing the Phoenix Power rack ends I'm currently designing my own outer steering rack ends with built in adjustable spacing. Once i've built a prototype and some front RCAs to space down the BJ i will let you know how it feels.

I was planning on setting the amount of downward spacing of the rack ends the same as the RCA thickness at probably about 15mm- Alex i believe you used equivilant spacing in your model? I chose 15mm as it seems to be about the amount of spacing on the PP rack ends.
 
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