What the 'Fric' is it?

[DaveW]

A nice background to the Williams active suspension:

More formally recorded in US patent 4861066, August 29 1989, I believe. Probably similar to the system used by Williams F1 in 1987. It would appear to require a supply of hydraulic fluid, using a pump labelled 32 in the patent.

[mep]

So far I was under the impression that the system connects the heave elements in order to supress pitch. Now, I have realised that it might be possible that the cars are actually less pitch sensitive as expected. The exhaust blowing can make the aero very tolerant to varying rear ride height, which basically cures the original problem rather than working around it. It might also be easier to control pitch, with nonlinear springs and bump stops. However, the cars can be sensitive to roll especially on the rear axle due to the proximity of the rear wheels to the floor. Then it makes sense to interconnect left and ride side. In the simplest form are only the rear sides connected to each other. In a roll case causes a compression of the outside cylinder a compression of the cylinder connected to the inside tire. This would transfer spring load but it should not change tire load. However, I have to think a bit more about that and other causes. In general I would say that it is not beneficial for mechanical grip and the tires can suffer under that. The increased downforce in corners outweighs this at least for a single lap (qualifying). The systems of other teams might look more like my initial though, where the front and rear heave elements are linked. This might cause less problems with the rear wheels.

An evolution of the simple left to ride link stated above could be to connect the rear wheels to the front wheels. Mercedes is apparently linking the anti-roll bars. Level of complication rises easily with this.

[DaveW]

... However, the cars can be sensitive to roll especially on the rear axle due to the proximity of the rear wheels to the floor. Then it makes sense to interconnect left and ride side ...

But don't forget other solutions, for example roll centre heights. Normally suspended race cars frequently have a higher rear roll centre heights specifically to control roll angle in turns, I think.

[techF1LES]

[ringo]

This is quite good. Something new, something with substance.
It chops down all that jibber jabber on imaginary nonesense in the media.

I'm just rambling, here but reading the article;

Overall we have sprung and un sprung mass equations, and moment of inertia about the pitch axis?

Ok a few questions, for equation 1, which denotes downward movement, why use the front damper rate at the rear force part of the equation?
Are you assuming they have the same damping rate?


When you put fric into the equation, to get eq 5, it seems that you are combining the displacements of front and rear correct?
And this is acting on 2 additional springs. How do you suggest these springs are physically located in the car, and having that combined displacement acting on both?

Correct me if i'm wrong, but equations 5 seem to be the same as equation 7.
You made mention of substituting the Fric displacements back into 5, but why do this if it's already done? or was is just so readers can follow?

Any how it's a very good piece. Fric is basically a longitudinal sway bar as suggested. I feel ride height gimmick can be implemented, but that doesn't relate to the vibration theory you have in your article.

[DaveW]

All that is happening in the FRIC system is that we are adding an extra spring by combining front & rear damper movements.

I think that Danny's equations are a "parameter based" linearised solution. Nothing wrong with that, except that it is not necessarily helpful when trying to design and assess a "real" system.

[mep]

Maybe it is time to discuss a bit how to model such a system.
Dave, could you go a bit more into detail what you mean with: “parameter based linearised solution”?
What other ways of modelling exist? Or how did you model it?

I start of by showing the model I created for it. Hopefully a schematic is enough to understand because I don’t really want to write down all the equations behind that. As I see it, the difference to Danny’s model is that I have an additional mass splitting up the interlinked spring stiffness. From Danny’s picture it is not quite clear how he connects front and rear. In my case, a compression of the front heave cylinder does cause a movement of the oil (m4) to the rear resulting in a compression of the rear cylinder (see the small arrows). Therefore front and rear axle move up and down together (in phase). The picture below illustrates this by showing how the car would response to a suddenly applied down - force to the front axle. Once the system has settled down, the pitch angle change is reduced because the front axle compresses less as it has transferred some of the load to the rear. That is what you desire.

The problem is the transition time, where the interlinked suspension has significant oscillations. Interesting to note is that front and rear axle oscillate 180° out of phase. It is basically doing the same as a Newtons cradle, the front and rear axle bounce off the stiff connection. This is where I see the biggest drawback of the system. On the other side it is the beauty of science that noting comes for free.


[youtube]http://www.youtube.com/watch?v=0LnbyjOyEQ8[/youtube]
It looks a bit suspicious that Danny got such a clear advantage on every braking event without mentioning any drawbacks. If things are that easy as he tries to make them look like all teams would have been using it long time ago.

[ringo]

Where are the equations by the way? I can't really take your assumption as gospel, without the reasoning behind the assumption; the phase angles and lag and stuff.
It would be easier to make sense of your diagram as well.

Why is your interlinked mass linked to the ground?
Also why have damping on the FRIC springs?

[mep]

Ringo, I already mentioned that it is a lot of work to write down the complete equations for this. But if you really can’t live without them I might do it later.
Btw. I think I noticed a couple of wrong indices at Danny’s equations. Basically front and rear mixed up a couple times.

Why is your interlinked mass linked to the ground?

That is just a different way of damping it. Actually it would be connected to the sprung body mass but in a way that it does not cause any pitch or heave movements therefore in the model it is referred to be connected to the ground.
The idea was to dampen the oil movement between the axles as a flow control valve would do. To increase the control over the pitch velocity but in the end I did not use it very much and had the value put to zero so you can ignore it. I might spend some time playing with that later.

Also why have damping on the FRIC springs?

For the same reasons there are dampers on the springs?!
Dampers just help you to gain control over systems which suffer under oscillations.

[ringo]

You may not need to dampen them since it's linked to the main suspension. The main dampers will dampen their oscillation.
The same goes for the mass.
Your equations should be in matrices form as well, as your system will have multiple degrees of freedom with that mass in the middle and with those additional springs.

[DaveW]

Dave, could you go a bit more into detail what you mean with: “parameter based linearised solution”?
What other ways of modelling exist? Or how did you model it?

I prefer your model. I especially like the additional freedom in your model (X4), which allows some account to be taken of fluid flow restrictions.

Danny allocated Kric_f & Kfric_r to front & rear stiffness, without acknowledging that, in a fluid coupling with no gain or loss in fluid, there must be a relationship between the two. I concluded, that whilst is possible to approximate the equations in the way he did, I requires some work to achieve sensible results (i.e. it should work if the parameters are estimated correctly). For example, he did say in his example,

I should also add that I biased the FRIC effects totally at the front.

which implies that he assumed Kfric_r was zero, I think, which would not be reasonable.

[mep]

You may not need to dampen them since it's linked to the main suspension. The main dampers will dampen their oscillation.
The same goes for the mass.

Yes true.
Increasing the damping coefficient of the conventional dampers would achieve the same. Apart from the connection of the mass to the ground (or sprung body), which in my opinion is a quite smart option.
When this model was generated the initial idea was that the heave dampers are replaced with hydraulic cylinders. The suspension would keep its side dampers for roll and single wheel bump. It is then not desired to increase their damping rate as this would affect those modes. F1 teams have the possibilities to custom design the required parts. Ideally they would then have a combination of a heave damper, with heave spring plus a hydraulic cylinder and on top of that an inerter. Then you don't need damping in the connection anymore. Especially the inerter might be helpful to react against the oscillations. It is another thing I should try.
Note that so far this is one of the most simple forms of FRIC.

[DaveW]

What other ways of modelling exist? Or how did you model it?

Using mep's excellent diagram, but assuming Khyd is infinite, M4 & Cground are both zero, and a reservoir of volume StVol is inserted in the hydraulic line close to M4.

Quasi-statically, the hydraulic pressure (charged to nominal value of Po) will be the same everywhere in the link, and the force (+ve compression) acting in parallel with the normal suspension will be proportional to +Po*Af at the front axle and -Po*Ar at the rear axle, where Af & Ar are the link front and rear actuator cross-sectional areas.

Movement in the suspension (Zf & Zr) will change the volume of the reservoir, from StVol to a dynamic_volume = (StVol - Zf*Af + Zr*Ar), which will, in turn, change the internal pressure. If it is assumed that Boyle's Law applies, then (still quasi-statically) the pressure will change to a dynamic_pressure = Po*StVol/(dynamic_volume).

Two (at least) more assumptions are required.

I assumed that Khyd was infinite. This is not quite the case, although a "de-gassed" fluid is close. Gas dissolved in typical installations reduces the bulk modulus significantly. It can be assumed, perhaps, that the effect of the gas can be included in the reservoir, reducing its volume (and perhaps removing the reservoir altogether), whilst keeping the assumption of an incompressible fluid.

The other assumption was "quasi-static", implying that the internal pressure was the same everywhere. This is not a bad assumption at very low frequencies and where no fluid passes between the actuators. Otherwise, it is required to model the pressure drop required the move fluid between the actuators. Suspension velocities (DZf & DZr respectively) are available in my model, and I modeled the "Flow_Pressure" as Cs*(DZf*Af + DZr*Ar), See, for example, here (Equation 2.9). This is the bit I was most unhappy with - I like mep's inclusion of a damped mass (M4), but that would have increased the model "freedoms", which I was a major change for me.

There you have it, I think. The contributions are

Front_Load = (Dynamic_Pressure + Flow_Pressure)*Af
Rear_Load = -(Dynamic_Pressure - Flow_Pressure)*Ar.

The parameters to play with are a daunting Po, StVol, Af, Ar, Cs as well as other changes that might be made to existing suspension parameters (especially spring rates &/or pre-loads).

It should be advised, perhaps, that in a front/rear installation the nett pressure in the actuators should be constrained, to recognize that cavitation can occur.

You may note that the equations cannot directly be written in the form used by Danny Nowlan (Dynamic_Pressure is inversely proportional to actuator displacements), but deriving an equivalent "linear approximation" should be fairly simple.

Edit: Made a sign change in the dynamic_volume equation - courtesy of mep.

[DaveW]

Interestingly, perhaps, this reference gives an estimate of "Cs" equal (in my case) to:

• 64*mu*Pipe_Length/[pi*(Pipe_Dia)^4]

in equation 2.9 (mu being dynamic viscosity).

This suggests that the system "time constant" would increase by a factor of 16 if the connecting pipe diameter was halved (something that F1 engineers are prone to do as a matter of course "Why does need to be any bigger than a brake pipe?") ....

[ringo]

MEP, It's quite possible the mass of oil can be ignored. The order of forces far surpass any effects the oil mass may have.
This is why the equations would have been good to have. An example would have show why maybe the oil mass can be ignored.

Why would you say the front and rear oscillate 180 degrees out of phase? Just curious.