Regarding the front and the rear ride frequency

[Edward M. Kasprzak]

But thanks to progress over the last ninety odd years this rather simple 2-D problem has been dumbed-down to 2 x 1-D problems (ie. two totally independent, and unrealistic, 1 DoF spring-mass systems).

I think it's worth noting that a scenario exists where it becomes mathematically correct to treat the front and rear as oscillating independently. It depends on the value of the pitch inertia relative to vehicle mass and CG location.

[ben]

Originally posted by Tim.Wright:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">So, the $64,000 question: Will the front of the car now oscillate at some fixed frequency?

It doesnt matter one iota. Nobody cares.

We use the ride frequency to get a baseline value for the spring rate and then we move on. The final spring value is then refined after looking at load tranfser calcs, full vehicle simulations and test data. </div></BLOCKQUOTE>

You're right Tim. However, if I was going to be charitable towards Z I would say that the idea of using a simple calculation to get in the ballpark then testing and refining (i.e. development engineering) to get a final answer is an insight that is missed by a lot of students in the competition.

It's the "how do I calculate the right answer" syndrome. If more people were honest about what a given model can and more importantly can't do we'd avoid a lot of these debates.

Ben

[Will M]

"All models are wrong, but some are useful" - George E. P. Box

-William

[Moop]

While I don't agree with what Z says about automotive engineers or his tone, I do agree that it seems a bit silly to speak exclusively in terms of front/rear ride frequencies, given how simple the analysis is.

For a block with a heave(x) and pitch(y) degree of freedom(about its centre of gravity) and springs at the front and rear(no dampers), the spring compressions at the front and rear are -x + a*y at the front and -x -b*y at the rear. If heave is positive up and pitch is positive forwards, then your equations of motion are simply
m * x double dot = Kf*(-x+a*y) + Kr*(-x-y*b)
I * y double dot = b*Kr*(-x-y*b) - a*Kf*(-x+a*y)

with some rearrangement, you can write the matrix equation
[ x double dot] = [ -(Kf+Kr)/m________(a*Kf-b*Kr)/m ] [ x]
[ y double dot] [ (a*Kf-b*Kr)/I_____-(a^2*Kf + b^2*Kr)/I ] [ y]

The brackets are supposed to look like matrices/vectors. I had spaces but had to replace them with underscores because the forum wouldn't display the spaces. This forum could use something funky for writing equations!. I checked it and it looks right, but I'm tired so I might have messed something up.

This is obviously the equation of a simple harmonic oscillator. The positive square roots of the negative of the eigenvalues of this matrix will give you the two natural frequencies of the system and the two eigenvectors will give you the two natural modes. There's no reason why the eigenvectors have to yield pure front spring displacement with no rear displacement, so the eigenvectors will be some combination of the two degrees of freedom. I think this is the bouncy pitch and pitchy bounce modes mentioned in the damper chapter of RCVD. With these eigenvectors you could calculate the instant centres of these two motions.

I started trying to find an expression for the eigenvalues but algebra became a PITA - maybe I'll finish it later and see if I can find the fantabulous expression Ed is referring to. I haven't done so yet, but it's pretty easy to plug this into an Excel spreadsheet to calculate the eigenvalues/vectors numerically.

Of course, this was without any damping. I'd imagine the modes would change with damping maybe? I'm not 100% on that - my ODEs prof mostly skipped over matrix ODEs.

But I guess it really depends on what you're concerned with. If you're more concerned with talking about roll stiffness distribution, then this doesn't matter at all and you can speak in terms of ride frequencies. If you're more concerned with flat ride for a production car or perhaps the way your chassis movement affects your undertray, then it would be more important to look at it with this approach.

I also think that the suspension kinematics would have an impact on this. The way I see it, the sprung mass doesn't have a pure pitch degree of freedom like our block does, since it unfortunately has suspension arms/sliding pillars/trailing arms. Instead, it has a pitching while moving forward a bit and possibly up a bit degree of freedom.

[GSpeedR]

Moop, Ed is referring to the case where (a*Kf-b*Kr) = 0, which means that the K matrix have is diagonal and thus the 2 equations decouple. In this case, the two modes will be independent: a pure pitch input will result in no bounce response and vice versa.

Edit: to complete the picture that Moop started...

If we change our coordinates from bounce/pitch to zf/zr [zf=bounce-a*pitch; zr=bounce+b*pitch] then we have another special case:

m*a*b - I = 0

where the front and rear suspensions are fully decoupled (assuming we have still met our a*Kf=b*Kr case above) and an input at the front suspension has no effect at the rear and vice versa. Give it a try. Note that the above 2 clauses are pretty difficult to obtain in practice, plus you might find working with body modes to be much easier.

[Z]

js10coastr,

"Following that logic, "stress" is fiction too since we can't measure it... we measure strain and then calculate stress."

I would measure force and a cross sectional area to calculate stress. I might measure strain if I wanted to estimate modulus of the material. Frequencies are easy to measure. Just count the number of peaks, troughs, whatever, of some cyclic phenomena that repeats itself over a given time period.

But the important point is that the word "frequency" suggests the frequent (= "numerous") reoccurrence of the same single event, or cycle. To suggest that a car has a single "front ride frequency" is like saying that Beethoven's Fifth consists entirely of the single note "middle-C".
~~~~~o0o~~~~~

Tim,

"They are typical examples of terminology and methods used by people who actually build cars for a living mate...
It doesnt matter one iota. Nobody cares."

I take this as confirmation (possibly from someone in the auto industry?) that modern car designers are a bunch of gibbering idiots that use whatever buzz-phrases they think will make them sound clever, but as for actually building better cars, well "Nobody cares"!!!

"We use the ride frequency to get a baseline value for the spring rate and then we move on..."

So, for example, you choose a "ride frequency" from the range in the Optimum G Tech Tip;
1. Passenger cars (soft springs) = 0.5 - 1.5 Hz,
2. Sedan racecars (medium) = 1.5 - 2.0 Hz,
3. High DF racecars (rock hard) = 3.0 - 5.0+ Hz,
With Frequency = (1/2.Pi).Sqrt(K/M).

And what brilliant insight does that give you, other than that you can have soft, medium, or hard springs?

Why don't you use the simpler "static deflection" to get your baseline value? Eg. (using the same numbers as above, rounded);
1. Passenger cars = 100 - 11 cm,
2. Sedan racecars = 11 - 6 cm,
3. High DF racecars = 3 - 1(or less) cm
With Deflection = W/K.
(W=weight)

Oh, yes, it's not nearly as clever sounding, so it won't impress your bosses, will it? But you don't care anyway, which I am sure is very cool...
~~~~~o0o~~~~~

Edward,

"I think it's worth noting that a scenario exists where it becomes mathematically correct to treat the front and rear as oscillating independently. It depends on the value of the pitch inertia relative to vehicle mass and CG location."

Agreed! I note that there are an infinite number of possibilities of this happening, but these are only one infinitieth of all possibilities. Less cryptically, for each of the infinite possible CG positions (longitudinally in 2-D side-view) there is an infinite range of possible pitch inertias, but only one of these pitch MoIs (per CG position) will give independent F&R oscillation.

I find it disappointing that no one else has yet shown any interest in this real (ie. observable, measurable...) side-view behaviour of cars (Edit: See PS below). FWIW (to the students), and very briefly, there are two fundamental harmonics (because 2 DoF system). One has its oscillation centre outside the wheelbase, and the other inside the wheelbase. These are respectively, and loosely, called the "bounce" and "pitch" modes. When excited by any input at either axle both fundamentals combine to form a "beat", within which is a varying amplitude and wavelength. In the special circumstances of above paragraph, the oscillation centres coincide with the axle lines and constant frequencies can be observed.

All this very easy to understand with simple geometrical calculations. Students might try "Chassis Design... Olley" book by Millikens and Edward for one approach (I think the explanation can be simpler and more insightful).
~~~~~o0o~~~~~

Ben,
"If more people were honest about what a given model can and more importantly can't do we'd avoid a lot of these debates."

and William,
"All models are wrong, but some are useful"

My main concern here is that by using a model of separate "front and rear ride frequencies" the suspension engineers are giving themselves a metaphorical lobotomy. The car is cut into two halves in the very first design meeting, and henceforth there is never any communication between respective F&R design teams.

"What the... You want to CONNECT the front and rear springs!!!
But what sort of F&RRFs will that give???
Aaaaaaargh!!!... Go away, you're hurting my brain!!!"

Yep, "Idiocracy" here we come!

Z

PS. Moop, you posted just as I was writing this. I haven't checked your equations, but I reckon you've got it. The geometrical analysis is very simple, just a couple of lines and circles. The gist of it is that you replace the real car with a "dynamically equivalent" (*) system of two springs under two masses (* ie. first 3 MoIs, for springs and mass, are equal to that of the car). These represent the fundamental harmonics, and their locations are the oscillation centres.

PPS. GSpeedR, as above... Good to see that some of you are interested in what actually happens.

[Tim.Wright]

It was exactly my point, that the ride frequency is only used to tell you if your springs are soft medium or hard, nothing more.

Let me ask you some questions.
What extra insight do you reach by using a rigid body with pitch inertia in your calculations??
Why do you (incorrectly) assume the body is rigid?
Why arent you speaking of hysteretic friction in the suspension and tyres?
Why don't you account for the installation stiffness of the suspension?

To me the answer to these questions is exaclty the same as the answer to why we calculate the front and rear frequencies seperately.

The $64k questions is, how would YOU arrive at a set of spring rates for a car?

My main concern here is that by using a model of separate "front and rear ride frequencies" the suspension engineers are giving themselves a metaphorical lobotomy. The car is cut into two halves in the very first design meeting, and henceforth there is never any communication between respective F&R teams

The is complete BS. The car isnt developed seperately front and rear, I dont know where you got that idea from.

[GSpeedR]

Tim, maybe you understand the assumptions made when making (hopefully very quick) calculations using separated ride frequencies, versus using rigid body coordinates, versus adding extra DOFs and nonlinear elements, etc. However, I don't think everybody on this forum fully understand what these assumptions entail.

"Good enough and move on" is a good way to create bad engineers.

[Tim.Wright]

While I do agree that these simplifications are generally taught without the disclaimer that they are gross simplifications (and I think this is the only point where we are actually all in agreeance), I still don't see any reason to over complicate a problem which in the grand scheme of things is quite a small part of the overall picture.

I also disagree that "good enough and then move on" is such a terrible way to work. If you reach a solution that is "good enough", any extra time spent dicking about with it is a complete waste. The springs are a perfect example. What exactly do you gain by calculating the pitch and bounch frequencies using the pitch MOI (which nobody know accurately anyway, not even OEMs!!!) as opposed to a simple frequency calculation which requires only the sprung mass and its longitudinal distribution??

Then consider the fact that the spring value will change during the design phase as you trial different geometries for anti-dive, roll centres, roll gradients etc. Then once the car is built the springs will again change from track to track and from driver to driver. You will quicky see that all this masturbation over how you arrived at your initial spring values was a complete waste of time.

[GSpeedR]

Here's the issue: At some point, somebody is going to have to analyze and characterize this racecar, whether it is done at the early stages of development, or at some intermediate level, or 1 week before competition. It sounds like you jump directly from looking up ride freqs from OptimumG's website straight to looking at results from your 35 DOF ADAMS model after you've finished the vehicle(?).

How long does this analysis really take (how much time are you wasting)? If you are completely developing a vehicle on your lunch break, then OK there may not be enough time. Yes, various factors will change the parameters involved so you may have to do it again...write a program in Matlab. There is a significant amount of effort that goes into simplifying the results of hugely complex systems so that humans can understand it and make decisions with it.