Suspension Design

[mech5496]

What Pete said! It is a common thing here, especially between new team members, as they cannot get their heads around "how it is possible to lose camber WRT road when the kinematics program says I have 0.5deg/deg camber gain?".

[stever95]

Pete and mech,

Thanks for you responses. I'm still caught up on defining body roll though. I often try to relate vehicle parameter changes to two different vehicles, to see the effect on weight transfer. Let me explain.

Assume the 4 wheels of the vehicle are fixed to walls of your shop so that there is no change in inclination angle with lateral force on the CG, and deflections in sus components are negligible.

Case 1: With an inelastically sprung vehicle (go kart or similar), imposing some lateral force on the CG of the vehicle will cause weight transfer, since the CG is above the ground. No roll, simple weight transfer calcs. No camber gained because no suspension travel.

Case 2: With a sprung vehicle, a lateral force at the CG will cause the suspended mass to roll (about its roll center?), compressing the outboard springs and expanding the inboard springs. Roll is proportional F.lateral and roll stiffness (another question for another time). But as you know, weight transfer is NOT a function of roll stiffness, which means this spring compression does not, in a steady state, change the Fz on each tire. Still not 100% confident in how that works, but I bet a good FBD will clear things up.

I suspect, then, that the only reasons to reduce body roll are to decrease turn in response (time it takes for car to "take a set"), decrease ground clearance variations (highly aero dependent undertrays, high downforce aero, etc), OR if body roll is so excessive that you run out of shock travel and lift up the inboard wheel(s). Obviously the last one would require you to not fix the wheels.... but you get what I'm saying.

What really mucks up this analysis is if you allow an inclination angle, but I am not convinced that if you unbolted your wheels from the walls, you would end up with anything different! Why would the wheel have a tendency to change its orientation to the flat road (read: pick up the inboard wheels if it must use up all available shock travel before doing so?? If inclination angle is truly how you have described it, and you must depend on camber gain to counteract it, how does a go-kart's wheels seem to remain at 0 degrees inclination?

Sorry for long post... just trying to get my whole thought process out there!

[mech5496]

... But as you know, weight transfer is NOT a function of roll stiffness, which means this spring compression does not, in a steady state, change the Fz on each tire...

TOTAL weight transfer is not...but think what will happen if you have an infinitely stiff spring on the rear and a super-soft spring on the front. How much of that weight transfer will be taken by the front and how much by the rear (i.e. what your LLTD is going to be?) Tip: LLTD is one of the main tools to tune US/OS in a car...

Reasons to limit roll, besides the ones you mentioned, include camber LOSS by suspension geometry. As Pete mentioned if your camber gain is below 1, your wheels lose camber WRT road (kinematically that is, as you also lose camber due to compliances). Karts do not roll (other than tire squash), so their kinematic camber is constant WRT road, compliances removed. Same holds true with a beam axle...

[SomeOldGuy]

Not a suspension guy, but I believe you are not considering the other 4 springs in the system...

The tires will also provide some roll to the overall system and that is why the angle of the wheel plane will change, even when you do not have camber change due to kingpin and castor.

[stever95]

Mech,

Thanks again for chasing this issue with me... I understand what you say about LLTD, it has come up several times in several books. Herb makes it abundantly clear with a couple of examples around page 15, from memory. But the big picture that I still don't understand from a physics standpoint is why a sprung vehicle has a tendency to tip over (unfavorably change inclination angle) in cornering. You sound very sure of this - if there's a reference you know of somewhere explaining it I'd be deeply appreciative.

Not a suspension guy, but I believe you are not considering the other 4 springs in the system...

The tires will also provide some roll to the overall system and that is why the angle of the wheel plane will change, even when you do not have camber change due to kingpin and castor.

Are you referring to sidewall deflection, or the wheel rate being affected by tire spring stiffness? I guess the former would sort of cause a change in inclination angle, but I don't understand how its spring stiffness would come into play. Can you elaborate?

[BillCobb]

During lateral forced maneuvering, tire tread migration (or more correctly wheel migration away from the tread) due to sidewall deflections induces moments about the spindle that are reacted by the suspension. These moments can be quite large. There is an induced body roll reaction to these
'overturning' moments that can be quite substantial and amplified/attenuated via the 'roll by camber' SDFs of the axle. It goes without saying that spindle and wheel bending is also in play and taking you further away from the performance characteristics of suspension members made of unobtanium. The range of roll camber SDFs in typical vehicles is surprisingly large and has both signs. This affects the TLLTD and thus the vehicle's understeer and roll gradients (deg/g). A weak total roll stiffness and strong roll camber coefficients can induce a disturbing amount of roll velocity and its corresponding treachery. Because of the way tires behave, (as weakening force components, just the right recipe of tires, SDFs and dampers can cause a vehicle rollover at low speed no matter what its cg height, in the hands of a skilled driver and now even more fun with sophisticated driver robots which sense peak roll velocity. Tire relaxation (response time) is an interesting player here, too. Camera views of tire carcass torture during heavy steady state and transient cornering maneuvers are fascinating. I posted a video some time ago on YouTube of Calspan tests of a tire receiving a reverse steer type MX test. It ain't pretty. People are surprised that the tire doesn't air-out, but when it does, the MX change followed by the metal rim digging into the pavement can produce a decent 360 and some high "Dancing with the Stars" scores. This was the Explorer problem. Lowered tire pressures from a ride improvement process coupled with the normal air permeability (leakage with time) rate even got the attention of the US Congress. But, I diverge...

Unanticipated overturning moment loads usually result in suspension component fatigue and stress fractures that can be embarrassing for all involved, too. "I hate it when it does that" has a familiar ring...

[stever95]

Bill,

Thanks for your reply. I have to say, I'm pretty perplexed by a lot of what's in your comment. I still have a fundamental mis-understanding of "body roll," but certainly you aren't saying that it is completely due to tire tread migration. So the answer is still out there..

Nevertheless!

When you say that sidewall deflection induces moments about the steering, are you referring to lateral Fz migration relative to the upright?

What is the 'roll by camber' SDF you speak of? Why would this play with TLLTD? Roll velocity? I am behind on the SDF acronym

[Z]

Stever95,

I have been away for a while, so missed much of this. You ask,

Body roll definition ... have I been wrong all along?
=======================================
...
In "Chassis Engineering," Captain Herb makes a couple of statements that have really thrown me off...
...
... camber gain ...
...
I haven't read anything that clears this up in RCVD, Valkenburgh's Racecar Engineering and Mechanics, or Carroll Smith's stuff. And I've drawn more FBD's than I care to admit...
...
[then in later post]
... Assume the 4 wheels of the vehicle are fixed to walls of your shop so that there is no change in inclination angle with lateral force on the CG...
...
What really mucks up this analysis is if you allow an inclination angle, but I am not convinced that if you unbolted your wheels from the walls, you would end up with anything different!...

Firstly, I think this could all be explained very quickly if we had a simple sketching facility here on this Forum. But none, so I'll try with words.

A crucial point is that this whole issue of "Camber-Gain" (aka "Camber-Compensation", "Camber-Recovery", and many other terms) is really very simple.

1. This is purely a matter of the Suspension Kinematics. So,
NO FORCES (ie. no "Statics" FBDs),
NO DYNAMICS (ie. no F = P-dot),
NO COMPLIANCES (ie. no structural flexing of anything),
NO TYRE MODELS (ie. no rubbery stuff, just wheels that are dumbed-down to rigid discs),
and NO OTHER CONFUSING REAL-WORLD COMPLICATIONS.

2. Furthermore, this is purely a 2-D KINEMATICS issue, as seen in end-view of the car (ie. either front or rear-view).
~o0o~

So, sketch an end-view of a simplified Car-Body. Add simplified 2-D Suspension attached to Car-Body at its inboard side, and attached to simplified Tall-and-Narrow-Wheels with rounded tops and bottoms at its outboard side. Add a simplified flat Ground for all this to sit on.

Define "Wheel-Camber-Angle" as the relative angle between Wheel-reference-frame-vertical and Car-Body-reference-frame-vertical. Quite easy to measure, because all in 2-D. For example, if both "verticals" are parallel, then WCA = 0 degrees. Worry about directions for +/- later. (Usually Wheel-top leaning away from Car-Body means WCA = positive.)

Define "Body-Roll-Angle" as the relative angle between Car-Body-vertical and Ground-vertical. Worry about directions for +/- if you have to write a VD-sim-program...

Define "Wheel-Inclination-Angle" as the relative angle between Wheel-vertical and Ground-vertical. Again, worry about +/- when you have to get real numbers.

Next, and IMPORTANTLY, assume the Wheelprints (ie. the bottom surfaces of the Wheels) are always in contact with the Ground. In fact, you might define "Ground-vertical" as being perpendicular to the line through the two Wheelprints. Also, DO NOT ASSUME that the Wheels are "fixed to walls of your shop". And ignore any Heaving motion of the Car-Body, so assume that its CG is always at the same height above Ground.

Finally, come up with some sort of rigorous definition of "Camber-Gain" such that whenever there is finite Body-Roll-Angle but the Wheel-Inclination-Angle remains unchanged from when the car's BRA = 0, then "Camber-Gain = 100%"...
~o0o~

On the other hand, if you want to make a career of this, perhaps by writing books or giving seminars, then standard practice is NOT to give any definitions at all. Instead, introduce as many different buzz-words and phrases as you can dream up, never do any sketches, spend as much time as possible talking about "tyre-curves", and "magic numbers", and miscellaneous "centres", and try to make everything appear as complicated as possible. Much, much easier for you...

If the above still doesn't make any sense, then please post some sketches explaining your thinking, and where you are having difficulty.

Z

[stever95]

Thanks for laying things out, Z. I was looking forward to your response. I'll get to work on some more sketches. Or a cardboard model, or something.

[ChristianChalliner]

Stever95,

Cardboard models are great for everything, likewise lego, it makes understanding movements much simpler and is good for testing various ideas quickly before you run with them. For example, yesterday myself and our chassis guy had a three hour long conversation with a faculty advisor about how both front and rear suspension systems worked, trying to explain with words and drawings was difficult but once a model was made from some lego he immediately understood. By a similar notion it is very good for force visualisation as thin pieces will deform giving you instant results, much faster than building an ANSYS sim, more fun and more reliable too!

Which reminds me, i intend to update my build thread over the next few days, you might be interested

Thanks,

Christian