# Thread: how to design a bell crank for push rod suspension

1. ## CH height : Let's not mix causes.

Z speaks about motion ratio with rising rate and you speak about jacking forces. Not the same thing.

But if you were to consider two cars with different springs but same damping ratio (ie. b1/sqrt(k1*m1) = b2/sqrt(k2*m2), where b is the damping coefficient) won't the car with the stiffer spring come back to it's steady state load distribution quicker than the one with softer springs? Isn't that desirable? How do you come to a reasoning on where you should draw that line [between] better response and road holding ?
I assume you are asking about a quarter-car model driving over a single bump, where the wheel is forced up by the bump, then the suspension-spring pushes the wheel back down, and then after some damped oscillation of the wheel-mass between the suspension-spring above it and the tyre-spring below it, the wheel eventually "comes back to its steady state load distribution". Furthermore, you say that a wheel-oscillation that dies down quickly is better, because "better response" time is "desirable".

Ahh, if only it were so simple!

If it was so simple, then inspection of the relevant (and overly simplistic) equations, such as Oscillation-Frequency = sqrt(K/M), suggests that all you have to do for "optimum suspension" is to keep increasing the spring-rates! Higher K => faster response time => better. Too easy!

But ... you also have to increase damping-rate, in order to keep the same damping-ratio. Err, ... so now the stiffer dampers will increase wheelprint loads on the uphill side of bumps, over and above the increased loads already coming from the stiffer springs. So this doubly increased vertical force, between wheel and car-body, launches the car-body upwards whenever it goes over a bump. And the stiffer dampers also reduce the wheelprint loads on the downhill sides of bumps, which, coupled with the car-body now shooting upwards, can leave the wheelprints hanging in the air. Hmmm, .. so NOT good for tyre-grip. And then there is also the greatly increased drag (= rearward wheelprint-force component) coming from those damper induced wheelprint load changes on the bumps. Aaarrghh, ... not so simple!

Fact is, good suspension on very bumpy roads has long-travel springs with very LOW rate, and VERY LOW values of damping force. Minimum values of wheel-mass also help, but this is limited by stuctural considerations, as well as the fact that larger diameter (= heavier) wheels roll more smoothly over rough roads than smaller diameter (= lighter) wheels. Note also that "wheel-mass" is usually called "UN-SPRUNG" mass, even though it sits between, and oscillates between, the suspension-spring and tyre-spring. It is exceedingly well "sprung" mass!

But, most importantly here, FS/FSAE TRACKS HAVE NO BUMPS!!!

Well, none worth fussing over.
~~~o0o~~~

Claude,

Did you calculate how much the CG would raise with rising rates?
It is a trivially simple calculation.

The more important point is that students say they want rising wheel-rates, usually via rising-MRs, because such rising-rates are supposed to be great at absorbing bumps. The students say this because they see it on motorbikes, and the motorbike PR people are always pushing it. So what the students want is ... to BLINDLY FOLLOW FASHION!

I have yet to hear students ask "What is the best way to get falling-rates? And what shape of a falling-rate curve should we aim for?"

This is despite the fact that a large number of circuit racing cars (perhaps most?) end up with aggressively falling-rates, because these give the fastest lap-times. These falling-rates are arrived at by pure trial and error, and most of the race-teams/engineers who use them do not even realise that their corner-springs have "falling-rates".

Yes, I am talking about "droop limiting" here, which, despite the fancy name, is nothing more than aggressively falling wheel-rate.

Two more points:
1. Some years ago I had quite a few PMs from a student working on rocker geometry with the aim of getting "rising-rates". He eventually managed to get a nice "J"-shaped MR curve, with lowish MR at lower-left of the curve (= full droop), and progressively higher MR towards the top-right (= full bump). But, on closer inspection the curve had its vertical axis (= MR) extending from something like 0.98 to ... 0.99. The MR was all but CONSTANT!

In practical terms, the whole exercise was an utter waste of time. Or "intellectual mastur...", as you might call it . A DASD would give exactly the same performance, but be much quicker to design and build, and have less mass, friction, slop, cost+++.

2. Rocker-geometry is limited in how much "shape" it can put into the MR-curve, and hence also the wheel-rate-curve. Essentially, there are only two sinusoids to work with. At best you get a "U"-ish shaped curve, or part of an "S" on its side. However, a combination of different springs and/or bump rubbers, connected in series and/or parallel, and with optional mechanical-stops to control the ranges of the various elements, allows almost any shape of curve to be produced.

In fact, "droop limiting" is just such a system, in that it uses a "droop stop" (usually the damper-rod) to increase the wheel-rate below static ride-height. This is an exceedingly simple mechanical linkage (so simple that few people recognise it as such) that produces a car performance enhancing wheel-rate curve that cannot be achieved with rocker-geometry alone.

Z

3. ## Ctrl z

Z,

We ran a few simulation in OptimumDynamics, but the differences between the results are very small.

I used linear suspensions with all other parameters (roll center height, camber/toe gain, aerodynamics, etc.) as constants to make sure the differences in the results were only due to the MR variation. I also ran the simulation with a rigid tire stiffness model, to eliminate the effects of tire deflection.

The main conclusion is that you are correct when you say that rising-rate corner-springs pushes the CG upwards. This effect, however, is very small.

You are not correct when you say that, when you have falling-rate corner-springs, the car "jacks down". The car always jacks upwards if you have roll centers above the ground. In a cornering situation, the jacking effect of the tire forces has much higher impact on the attitude of the suspended mass than the rising or falling rates of corner-springs.

I ran lateral acceleration sweeps from zero to 20 m/s^2 at 100 km/h. The baseline setup has a constant MR of 1.0. The setup 1 has an increasing MR that goes varies 0.9 to 1.2 (from full droop to full compressed state). The second setup has a MR that varies from 1.1 to 0.8. These variations were implemented both in the front and rear suspensions.
• Baseline: constant MR=1.0
• Increasing MR: MR from 0.9 to 1.2
• Decreasing MR: MR from 1.1 to 0.8

As expected, the inside spring (left) has a larger deflection for an increasing MR and a smaller deflection for a decreasing MR. On the outside spring (right), the deflection is smaller for an increasing MR and larger for a decreasing MR. See z1

The argument that you wrote in the FSAE Forum is indeed true. The variation of the CG position is larger when you have an increasing MR. However, the difference is very small. See z2.
In this plot, you can see that the CG position is always positive, regardless of the variation of the MR. This is due to the fact that the jacking forces have a higher impact on the variation of the CG position, than the MR.

To illustrate this effect, I removed the jacking forces by placing the roll center of both front and rear suspensions at the ground level: see z3
Now you can see the effect of the variation of the MR. The CG position varies by +0.1 mm for an increasing MR and -0.1 mm for a decreasing MR. This is an exaggerated case, where the MR varies by 0.3. Most suspensions have a smaller variation of MR, so the impact on the CG position will be even smaller.

The reason we removed the tire deflection and the kinematics was to isolate the effect of the varying motion ratios, since it was so small.

When I was running the first few simulations, I was using the full kinematics. The roll center position changed as car rolled, so the jacking forces were also changing. Since the chassis movement in the vertical direction is mainly dictated by the jacking forces, it was very difficult to identify what was the change in cg position caused only due to the variation of motion ratios.

Adding the tire stiffness would only make the effect even smaller, since you would have another spring in series with the suspension.

The change in CG movement with varying MR is so small that it would be "diluted" in the other kinematic effects (migration of roll center).

Claude

4. Claude,

I think it is quite obvious that if you make VERY SMALL changes to the MR-curve, then
... the differences between the results are VERY SMALL.

I am sure that if you modelled a rising-rate MR-curve similar to that used on many motorbikes, namely the type of curve most newbie-students seem to think they need, then the resulting CG-height changes will be much more dramatic.

In fact, that was the point of my Point-1 in previous post, in that spending time tailoring a MR-curve that ends up with only a tiny MR change is ... quite pointless!
~o0o~

The second point of my previous post was to point out that there are simpler ways to get much more dramatic changes to the shape of wheel-rate-curves than using rocker-geometry. Specifically, "droop-limiting" puts a sharp bend in the curve at, or just below, ride height. Very stiff wheel-rate below ride-height, and softer wheel-rate above. It follows that the resulting effects of that sudden change in wheel-rates, such as CG-height, are much bigger.

Coincidently, the resulting body-roll behaviour of droop-limiting is similar, but opposite, to the example that Doug gave in his earlier post. That is, the car-body nominally "rolls" about its inside pair of wheelprints, with no suspension movement of the inside-wheels, and only the outside-wheel springs compressing.

http://www.fsae.com/forums/showthrea...roop-behaviour

If you care to model the CG-height change of a Zero-Droop car, then please give it the same roll-stiffness as the baseline car (and with RCH = 0, no ARBs, etc.). That means the ZD corner-spring-rates have to be HALF that of the baseline car's springs.

(Note the interesting discussion regarding ZD roll-stiffness in the 2005 thread. Nothing changes! Well, maybe I was more polite back then. )
~o0o~

You are not correct when you say that, when you have falling-rate corner-springs, the car "jacks down". The car always jacks upwards if you have roll centers above the ground...
And from the top of your earlier post.
CG height : Let's not mix causes.
Z

(PS. On the 2005 thread linked above I mention the aero advantage of droop-limiting at the bottom of page 2. I think this can be a big factor. Claude gets a mention on page 5 (last page).)