anti dive setup

[Moop]

While the n-line/instant centre approach is a better approach(imo) to understand steady-state/transient geometric load transfer and how the geometric suspension forces result in changes in body attitude, I don't think that it tells the entire story.

I can't make a picture right now, but consider the classic 4 bar linkage representation of a vehicle suspension in front view. You have the chassis as one link and two swing arms + hubs as the other two links. The swing arms are pin jointed to the chassis and at the ground. We know that the instant centre of the chassis wrt the ground is at the intersection of these links, or the geometric roll centre.

Because the instant centre of the chassis is below the chassis link's centre of gravity, we know that when the chassis link rolls for whatever reason, it also must translate in Y for its motion to be consistent with its kinematic constraints. Basically, because of the kinematic constraints, the chassis cannot roll without also having some lateral motion. This effectively increases the inertia of the chassis to this combined rolling and translating motion and is exactly what the parallel axis theorem tells us.

Neglecting this lateral motion and just considering the forces transferred makes no difference in steady-state, but it will make a difference in transients/dynamics.

This is similar to the case of a simple pendulum, where you can either analyze its motion with 2 equations of motion and 1 kinematic constraint, or one equation of motion in the generalized coordinate. The only difference here is now the pendulum has a rotational degree of freedom and rotational inertia.

In terms of controlling the roll motion have a read of this SAE paper and consider this:

• When the outside damper is hard on the bumpstop. The outside wheel vertical movement becomes zero while the inside still moves. Your roll centre (as in the roll motion axis) is now the contact patch of the outside wheel.
• Now consider the point just as the bumpstop starts to engage. The outside wheel rate is increasing and its movement is diminishing. The inside wheel continues to move into rebound unrestricted. The motion roll axes is then somewhere in betrween the CL and the outside wheel is it not?
• Now forget the bumpstops and realise the a simple rising rate suspension is going to have this same effect.

Then ask how is it in any way valid to transfer your body roll inertia to the geometric roll centre with the parallel axis theorem???

What happens here is the exact same thing that happens in side view that Z has talked about in the past/complained about how people don't understand it.

Consider a 2D chassis mass in front view(no wheels) with heave and roll degrees of freedom and no kinematic constraints from the suspension, and also suppose the chassis only has corner springs. In the case where the tracks are symmetric and the spring stiffnesses are equal, if you write out the equations of motion for free vibration, the mass matrix will have a diagonal of zeros and the modes of the system will be uncoupled, ie. pure heave and pure roll.

If you instead make one of the springs stiffer than the other or one of the half tracks larger, the mass matrix will be full and the modes of the system will be coupled. The modes will be a roll mode with a bit of heave and a heave mode with a bit of roll. This is the same idea that you're talking about in your first and second bullet points.

I'm not entirely sure how this all comes together when you put the kinematic constraints and asymmetric springing together though, but it would make sense if they continued to have the same effect they have when analyzed by themselves, plus some additional effects potentially due to their interaction.

The annoying part though is that, at least in the general case, to analyze it you have to solve the equations of motion and equations of constraint at the same time, which is into the realm of DAEs and multi-body dynamics.

[Z]

Posts are coming thick and fast now...

First (the last bit of) the disappointing stuff. Namely, just how hard it is to communicate these essentially spatial ideas here. In the ancient Greek forums they would all stand around a sandbox, and with long sticks they would draw lines, and curves, and point to various intersection points, and ask "Do you mean this 'centre' here?" So much easier, IMO...

Anyway, I'll do a sketch tonight, and then the scanner (ughhh, much profanity...), and the Picassa upload (groaan...)...
~~~o0o~~~

Thank you to Ben and Tim (and others) for supporting the idea that it is easier to look first to the wheelprint n-lines for this sort of analysis, rather than RCs and PCs. Here I should note two things.

1. To find a R/PC you must first locate the relevant wheelprints, and then from a kinematic study of the two independent suspensions you must locate the two wheelprints' n-lines. The last step of locating the intersection point of the two n-lines, which gives the R/PC, is largely redundant (not needed for calculations), except perhaps for use in loose conversation such as "It has a high Roll Centre" (vs "It has steep n-lines, err, lateral, that slope up-to-centre...")

2. Both Mark Ortiz and Bill Mitchell have been promoting the idea of thinking in terms of the "force-line slopes", rather than R/PCs, for at least ten years (possibly more than twenty...). This for reasons similar to mine above (and more below). "Control-arm-force-line slopes" might be an even more accurate term, maybe with "passing through the wheelprint" thrown in there as well. "N-lines" (aka "normal-" or "right-lines", because at right angles to path of motion) is the general term used throughout the wider field of Kinematics for the last ~200 years (eg. it is commonly used in robotics nowadays). So "n-lines" is a short phrase with very wide application.

(BTW, congratulations Ben on the new job...)
~~~o0o~~~

Some general comments.

The word "transient" can mean "whenever the "quantity of motion" of a body changes because of the forces impressed on it". (Nerd Note: Newton's definition of "quantity of motion" = our "momentum".) As such, a car at constant speed and radius on a Skid Pad is, in a very real sense, in a "transient" state of motion (its momentum vector keeps changing direction).

As is done on the Jacking Force thread this sort of "transient analysis" is easily done in a standard "Statics FBD", by using d'Alembert's Principle and having an appropriate "inertial reaction force" added to the other "real" forces to bring them to equilibrium. In the Jacking Force diagram the inertial reaction force is Fi (which implies "transient"), and it is in equilibrium with the two wheelprint forces and the gravitational force Fg.

The more common understanding of a "transient" in VD is when the body is wobbling about (in R/P), so that the spring-dampers are expanding/contracting. Such rotational "transients" are also easily analyzed using d'Alembert, and simply require the inclusion of some "inertial couples" (say, "Ti.roll") in an otherwise bog-standard, Static FBD.

I stress this here so that you students DO NOT THINK THAT YOU MUST HAVE a big, complicated system of 2nd order ODEs, plus Matlab+++..., to be able to understand these things.

The key point is that a force vector F, acting on a particle of mass m, for a period of time dt, will cause the particle's current momentum vector P, to change in length and direction in proportion to F. Essentially, you just add dP, which has same direction as F, and length proportional to F.dt, to the end of old P, to get your new momentum vector P+dP, at the end of that particular timestep dt (ie. NII is F = dP/dt, NOT F = mA!).

For extended bodies (ie. not point-like particles) you change their angular momentum vector L each time step in a similar way to above, but by using the couple T acting on the 2nd MoIs of the body. This is very easy in 2-D, but requires knowledge of the body's "inertia tensor" in 3-D, and is perhaps best done using Euler's Rigid Body Equations (still quite easy).

All this is very graphical and much easier to explain on a blackboard (or a stick in the sand...).
~~~o0o~~~

HenningO,

I see the biggest problem, by far, in talking about Roll or Pitch Centres, is that there is a very strong implication that these are "the centres of the motion". Almost everybody seem to fall for this, including Claude a lot of the time... I will post a sketch showing how wrong this is soon...

Both these "centres", when taken as "points where forces can be added together", could equally be called the "Heave Centre". This is because with non-horizontal n-lines, and unequal n-line forces, there is a vertical control-arm-force-component passing through this point that acts to lift the car. Of course, if you start thinking in these "Heave" terms, then you must not forget to also include the horizontal CA-force-component acting through this point as well!

The SAE/ISO definitions of the RC are especially disappointing because they only define it in terms of its height, so not really a "centre" at all. By omitting the horizontal location of the RC these definitions do not account for the vertical ("jacking") force's affect on body roll, and so, indirectly, have resulted in much heated debate on these pages! (Aaaarghh, ... how many words!!!???) Also, depending on L/R split of the wheelprint Fy forces, the same suspension can cause the body to Heave EITHER up OR down. This seems to be totally ignored... I have another sketch (in another box) that explains this, that I will try and post soon.

"But when you want to look at the non-suspended weight transfer, the height of the IC with respect to the non-suspended CG location becomes highly relevant. Additionally, when we start to look at Mx from the tire, then the ICy with respect to the contact patch location becomes highly relevant. All of these three effects will change the weight transfer and/or suspension deflection."

Agreed, and these effects were covered to some extent on the Jacking Force thread. The Wheel-Assembly ("non-suspended") mass effects can also (IMO quite easily) be analysed by considering the suspension's n-lines passing through the WA's CG. Gyroscopic effects (also on the JF thread) can also be understood using n-lines, but require a few more of them. As noted earlier, n-lines are an old and reliable concept used throughout Mechanics.
~~~o0o~~~

Lao Tzu (old Chinese philosopher writing in "Tao Te Ching") "There are so many names, is it not time to stop?"

I'll try and post some pics soon...

Z

[DougMilliken]

On the question of terminology, MRA vehicle dynamics simulations can be traced back to work done in the 1960's and early 1970's at CAL and GM (see history chapter of RCVD). The vehicle input deck (originally on punch cards!) calls for the side view kinematics as "longitudinal force anti" (different directions are anti-squat, anti-lift, etc). It also carries that naming scheme to the front/rear view case with "lateral force anti" for independent suspensions. I guess this is now sometimes called "force based roll (or instant) center", but we never used that terminology.

The underlying analysis (several large, detailed reports) is designed to work with K&C output. GM developed piece-wise K&C capability in the 1950's and 60's and then designed/built a comprehensive rig called the Vehicle Handling Facility (VHF) in the early 1970's--located at the Chevy Engineering Lab in Warren MI. Tom Bundorf has put together a slide show with pictures of many of the special test rigs--we host it at:
http://www.millikenresearch.com/Vehi...yRTBundorf.pdf (bottom of the Olley book page).

Back to "longitudinal & lateral force-anti" -- one of the standard K&C tests that was developed was to clamp the chassis to ground, apply longitudinal or lateral forces (or combined) to the tire footprints and measure the change in load. For drive wheels (ie, anti-squat on rear wheel drive), the longitudinal test is run with the driveline locked. With the brakes locked the longitudinal test results were reduced using the F/R brake bias. Tests could be repeated at different ride heights if desired. The change in vertical load (delta), resulting from the horizontal force was curve fit (linear and nonlinear options), and that became part of the vehicle description for the computer simulation.

[jpusb]

This thread went crazy.
May I contribute with a question, or should I say, an additional point of view. A lot of talk in this thread has been going on about (and maybe it didn't touch this enough) if going far in the car model, and what it accounts for, is worth the time in FSAE (and this is not yet clear to me). Going back and remembering this is FSAE, I will add my question which adds the driver variable to the pot. What are your thoughts on RC (or n-line slopes, IC, anyone you like fits the question) values and value fluctuations with lateral accel. and their importance or relevance when you put an amateur driver on the car?. What do you think the average amateur driver works best around?

If I may, I can rephrase that question to a more practical one (and this includes not just the end-view case but also lateral or longitudinal case). Claude gave an example in which two different designs can give the same Steady State (SS) results (roll angle, weight transfers, etc) but behave very different in transients. To that, I think we can all agree (I hope so), but, where (in this thread, and in the design process) do you think we should input the driver? Of course testing is where the driver has more input and where you get to know what he likes or works best for him, but a good design should have input the driver in the design process (and many people don't). A particular setup may be faster (clock time around a lap, sector, whatever) in SS and simplified TS analyses but the whole real package includes a driver that can read/feel these things and a vehicle that is rarely in SS (FSAE again) so, thoughts?. Will an amateur driver get an advantage from an anti-whatever setup? Do you think it is better if everything goes through the shocks? Of course in this topic, previous experience is precious, but initial thoughts and reasons may lead to a good initial setup.

JP

[Z]

ROLL CENTRE vs INSTANTANEOUS MOTION CENTRE.
============================================

Earlier I said that a car's "Kinematic Roll Centre" (same as its "Force-Based Roll Centre", namely the intersection point of the car's lateral n-lines), is in no way related to the car-body's "Instantaneous Motion Centre". Why so? And how do you find the IMC?

Firstly, it is important to note that when doing calculations of FORCES acting on the car-body, such as the FBDs shown on the Jacking Force thread, you only have to consider the ONE SINGLE BODY. That is, you only need one reference frame, with, say, only one origin, and only one X, Y, (and Z) axis.

BUT!!!, when studying MOTIONS you MUST consider at least TWO DIFFERENT BODIES (or, equally, two different reference frames). It is completely pointless to try to describe the motion of a single body with respect to ... itself (?), or with respect to ... nothing much at all (???). A motion is always that of BODY-A, WITH RESPECT TO, BODY-B (or referance-frame/cartesian-axes-A, wrt, frame/axes-B, etc.). Maybe this is why some people find Kinematics harder than Statics.

Here we consider the motion of the "car-body" with respect to "the-ground" (= the road, the Earth, Terra Firma...).

Secondly, as noted ad nauseam elsewhere, the 3-D motion of car-body wrt ground is best described via the concept of the "Motion Screw" (aka ISA). That is, at any instant the car-body translates parallel to, and rotates around, an Instantaneous Screw Axis that resembles a momentary "screw joint" between body and ground. (Important note: this "screw joint" serves only to describe the relative MOTION. It is incapable of transmitting FORCES.)

However, this 3-D stuff is a bit difficult to explain clearly with just text and simple sketches, so here I dumb it down to 2-D. Because of this dumbing-down you should ignore all motion in-and-out of the plane of the sketches, and any rotations other than those entirely in the plane (ie. around an axis perpendicular to the plane).
~~~o0o~~~

So, at the top-left of the sketch (below) is an end-view of a car, notionally cornering to the right (ignore the fact that this "cornering" cannot happen in this 2-D picture...). As a result of the leftwards centrifugal force acting on the body, the body has rolled a little bit to the left, and ALSO the whole car has slid some distance to the left (remember, all this is WRT the ground).

From a simple analysis of two points (A and B) on the car-body, at two successive moments in time (0 and 1), we find the 2-D Instantaneous Motion Centre of body wrt ground (well, it is only really "instantaneous" when dt -> 0). In this case the "IMC" is a long way under the car. If the car's Roll-stiffness was greater (ie. less roll-angle), or the road was slipperier (ie. more sliding), then the IMC would be even further underground.

(In case you are wondering why the car has moved left, even though it is "cornering" to the right, this is due to the dumbing-down process of moving from 3-D to 2-D. It might be better to think of a strong wind blowing from the right, which pushes the car to the left. This wind represents the centrifugal force and acts along a Line-of-Action that happens to pass through the car's CG. Or perhaps think in terms of the SAE RC-height test where a lateral (leftward) force is applied to the car body...)



At the right of the sketch is a car similarly cornering to the right (or being blown leftward). But this time its outer (left) wheel has hit a curb that has briefly given the tyre very high lateral stiffness. With stiff Roll-mode springs, softish Heave-mode springs, and an above-ground KRC/FBRC (ie. n-lines sloping up-to-centre), the car body has only rolled leftward a small amount, but it has "jacked-up", or "heaved", quite a lot. The end result is that the IMC is now a long way to the left of the car. Less body-rolling, and/or more body-heaving, puts the IMC even further to the left.
~~~o0o~~~

So is there any time when the IMC can be coincident with the KRC/FBRC? Certainly, yes, and this is the case that many (most?) people consider to be the norm. But this only happens IF BOTH WHEELPRINTS ARE EFFECTIVELY PIN-JOINTED TO THE GROUND!!! Buckley's chance of that ever happening!

Putting this into 3-D terms, each wheel would have to be rolling along some sort of track, such that each "wheelprint" could not move laterally or vertically wrt the track. (Check the fairground rides for hints on how to do this - ie. extra "guide" rollers). Anyway, what we are talking about here are tyres of infinite lateral (ie. cornering) stiffness, which is unrealistic.

Unfortunately, in static tests, such as the SAE RC-height test, the tyres ARE approximately "pin-jointed-to-ground" because of static friction (as long as you neglect sidewall lateral deflection). I reckon this is one of the main reasons that Heave motions are so often neglected in VD analysis (ie. the "RC" should be called the "Heave/Roll Centre"). As seen at the right of above sketch, Heave motions typically require the track dimension to change, so can NOT happen when the tyres are pin-jointed-to-ground.

Note that a real car with normal tyres, an above-ground RC, and TOED-IN wheels, will heave upwards even when travelling in a straight line. You can try this by strapping on some ice or roller-skates, get some speed up, spread your legs like the n-lines, then toe-your-feet-in. Or try toeing-out ..., ouch!
~~~o0o~~~

So now we can reconsider Moop's post above (and many of Claude's on other threads), where it is suggested that in this end-view the car-body can oscillate in a roll-motion with the centre of this motion being the KRC/FBRC. The implication is that, if this is so, then the "parallel-axis-theorem" has to be used to increase the effective MoI of the system, above the "normal" MoI of the body about its CG.

My view is that the above is only possible if the wheelprints are (unrealistically) "pin-jointed" to the ground. More likely is that a roll oscillation will take place about a Motion Centre that is very slightly below the body's CG. As the top of the body rolls leftward, the KRC (which is significantly below the MC) moves rightward and pushes/pulls the wheelprints rightward. Body rolls rightward, KRC pushes/pulls the wheelprints leftward. The wheelprints follow an "S-shaped" path along the road.

Furthermore, as the tyres follow this S-shaped path, their Fy forces, which are always opposed to the direction of side-slip, act to damp the roll oscillations (dampers always exert a force opposing their motion). Thus, if you are calculating the amount of roll damping needed to suppress roll oscillations, then not only is the roll-mass-MoI number smaller than in the parallel-axes/roll-about-RC case above, but there is also extra damping from the tyres thrown in for free.

Note that this is a very different situation to a car SUDDENLY entering a corner, with the tyres suddenly pushing the car-body's KRC towards the inside of the corner, and thus causing sudden, and significant, body-roll. This is a very different problem to "roll-oscillations", and requires a different amount of damping to completely absorb the energy (ie. to stop the body-roll at its steady-state angle).

Bottom line, there is a big difference between a "centre" which describes a point at which forces can be added together, and a "centre" which is used purely to describe relative motions (with NO FORCES acting there). Sometimes these two different types of "centre" might share the same spot (eg. pin-joints in 2-D linkages...). Often they do not (eg. RC and MC above).

Enough for now...

Z

(PS. Why did my scanner give the black-and-white sketch a blue background? Did I ask for that? (NO!!!) Why is the file ~200 kb when it should only be about 50 kb?? Why is the grumpy old-fart starting to foam at the mouth??? )

[Z]

Jpusb,

Brief response to your questions.

1. Effectively "suspensionless" cars have won FSAE (ie. very stiff springs). So "optimising" the kinematics (RC height/migration/etc.) vs spring-stiffnesses, etc., is NOT of the utmost importance (in FSAE!).

2. The best thing for your drivers is lots of seat time. When they become reasonably good they will drive around any smallish faults in the car setup.

3. So bottom line is to get something built quickly so the drivers get a lot of practice. Roughly modifying an old car so that it has highly adjustable suspension (ie. lots of cutting-and-butting of frame++) at the beginning of the year is a good way to give your drivers seat time in "different" types of car. I would bet that a good driver in a non-optimal car will easily beat a novice in the "most optimal" car.

That said, IMO horizontal n-lines (end-view and side-view) cause the least problems.

Z

[ben]

Great info as ever from Z.

To answer the anti-dive question from Jpusb in my own way; in my experience anything above 25% anti-dive tends to be perceived negatively by the driver. This is another version of Z's comments about relatively horizontal n-lines being least problematic.

Unfortunately "Ben said" or "Z said" are not acceptable design tent answers (rightly so...). In this situation testing with a real driver is infinitely preferable to trying to infer what the effect of the anti-geometry will be from a simulation with a poor (or no) driver controller and a non-existent transient tyre model ;-)

Ben

[murpia]

...

1. Effectively "suspensionless" cars have won FSAE (ie. very stiff springs). So "optimising" the kinematics (RC height/migration/etc.) vs spring-stiffnesses, etc., is NOT of the utmost importance (in FSAE!).

...
Z

Nor in many other formulae. One thing that does need reinforcing though is the ability of the suspension to distribute forces accurately. Non-engineers (or poor ones) will equate lack of suspension _movement_ with lack of suspension (period). Hence I mildly object, Z, to your phrase 'suspensionless'... Lack of suspension movement does indeed diminish the role of kinematics and easily understood 'static' parameters start to dominate: 'static' camber, 'static' toe, etc. By 'static' I refer to what you would measure on a 'flat patch'.

Lack of suspension movement does not however mean loss of control over suspension forces. Controlled & tunable roll stiffness distribution front to rear is still present in a car with 'stiff' suspension while obviously absent in a car with 'no' suspension. Even if to the naked eye on the track the motion of the chassis relative to the wheels will appear similar. F1 cars appear to have 'no' suspension save the tyres, but in fact have exquisitely tuned, ultra-low friction, low-compliance suspension designs specifically to control the roll stiffness distribution as well as possible.

If you decide to adopt stiff suspension to diminish the importance of the kinematics, you need to place additional effort in characterising the effect of the other compliances in the system on roll stiffness distribution. Chassis torsional stiffness get the most attention but there are lots of others. There is a handy shortcut though, if you can fit pushrod loadcells like any serious formula car would have. They neatly eliminate all the compliance effects (including the tyre vertical stiffness) and report the truth. If your suspension design model, or (Claude's 'magic number' spreadsheet) is telling you your car has 55% front roll stiffness but the pushrods are telling you 51.5%, believe the pushrods...

Regards, Ian

[Claude Rouelle]

The difference between the basic Excel 1st magic number (the one of the ratio of the front / total "elastic" weight transfer) spreadsheet and the "reality" (that is as much as you trust your load cells and pushrod strain gauge) is effectively due to
- tire stiffness being one of them (change only the front or only the rear tire pressure and you won't have the same ratio)
- the chassis torsion stiffness
- the chassi torsion stiffness distribution (for the same total Nm/deg you can have the front stiff and the rear soft ... or vice versa... think about how Go-Karts are tuned)
- the chassis torsion damping
- all other suspension, rim etc...compliances
- possible asymmetrical aero effect (in the car setup, and/or side wind, and/or aero yaw angle)
- of course the damper and inertias.

In any case whatever the car, the tires, the driver, there are too many parameters to be spot on in your calculations; you work in delta, in quantified effect of the variation of one of the parameters (spring, ARB, weight distribution etc...) on this "magic number"

I have been using this spreadsheet AND the pushrod strain gauges on several race cars. Every time we changed one of the car setup parameters we saw pretty much the same VARIATION (not the same absolute number) on the both the excel spreadsheet and the strain gauge data. It makes you both more self confident (after a while you know which direction a given setup change will influence the car behavior why and by how much) but also humble because you know there is a difference between real number and reality, mainly from compliances and damper.

[Z]

To anyone reading this thread and wanting more information, here is a link to a post on Migrating Roll Centres that I just put on the Jacking Force thread (ie. similar to above discussion, but perhaps more appropriate on the JF thread).

Z