Jacking force

[exFSAE]

Originally posted by Warpspeed:
I really cannot see the value of calculating suspension jacking down to thousandths of an inch, even if that were even possible.

It is probably enough to understand the effect, and have some respect for it.
It only really starts to becomes a significant (and scary) problem with an unusually high roll centre, narrow track, and very low wheel rates.

With a competent purpose built race car with low cg and high roll stiffness, jacking effect is about the very last thing you need worry about.

As with many things in engineering, if you can keep the effect negligible by design, you can probably ignore it, and focus your efforts on much more important aspects.

To me this still comes across as the notion of jacking forces being bad or something to keep to a negligible minimum. Which is just not the case.

[Z]

Originally posted by Moop:
... the correct approach to 3D kinematics isn't taught in engineering curriculum. Where would you suggest we learn it from?

Moop,

That's a hard question. I got lucky being taught by Jack Phillips, whose book "Freedom in Machinery" I have previously mentioned. However, FiM is very long (2 Volumes) and has much more in it than is necessary for a basic understanding of Vehicle Dynamics. Jack worked closely with Ken Hunt (from Monash), who wrote "Kinematic Geometry of Mechanisms". I haven't even browsed that book, but at ~500 pages it might also be more than you need.

Both Jack and Ken were inspired by the work of Irishman Robert Ball who wrote "A Treatise on the Theory of Screws" in the late 1800s. At ~600 pages, and of a general mathematical nature, probably also more than you need. Note though, that while Ball's book was ignored for a long time in the early 1900s, it is now making a comeback in robotics, multi-body dynamics, and so on.

I acquired most of my VD understanding from first principles (Jack considered cars boring). These principles start with Euclid's Elements (especially its well-reasoned approach to thinking about any subject, ie. clearly stated definitions and assumptions -> simple deductions -> more profound stuff...). Next is Newton's Principia, written in the style of the Elements, and explaining the dynamics of point-like masses. Lastly add Euler's Rigid Body Mechanics, and you are pretty much there. This last step can be simplified by replacing each rigid 3-D body by a "dynamically equivalent" system of a few point masses, which gives a fairly easy vector-based understanding of what is happening (mainly in terms of forces and momentums, because F = dP/dt.)

The IMPORTANT POINT is that the 2 x 2-D approach taught in most VD textbooks is a "flat-earth" theory. Good enough for a carpenter laying out the foundations of a house, but not good enough for, say, engineers shooting rocketships into space. Or to put it another way, I happily do calculations with Pi = 3, but I know that it is out by about 1/7, err... or about 0.14159...
~~~o0o~~~

"Our suspension points are laid out in a spreadsheet with 2 x 2D kinematics to pick RCH, FVSAL etc. The points are then brought into ADAMS and the various suspension curves are produced. I've noticed that the swing arm lengths and roll centre heights calculated by ADAMS are always a little bit different than what was calculated in the spreadsheet, but reasonably close. At first I thought it was an issue with ADAMS, but now it's clear that the issue has to do with 2 x 2D vs 3D."

Yes. The 2 x 2-D doesn't account for bump steer, whereas ADAMS probably does. If there is any Offset or Trail (Wheelprint Centre away from Steer-Axis), then different amounts of bump-steer will cause the WC to follow a different path as it moves up-down, hence different n-lines.

Biggish subject, but very briefly (just a taste of the jargon), the Instant Axis and Steer Axis give 2 DoFs between upright and body (ie. up-down and rotate). Thus they are the two zero pitch motion screws (ISAs) that lie on the cylindroid defining this 2 DoF joint. The "spine" of the cylindroid lies on the "common normal" (shortest line) between IA and SA. Position of the steering-tie-rod determines which of the single infinity of ISAs on the cylindroid describes the motion of the upright. So, if no rotation about the SA, then ISA of the upright = the IA. Else ISA is elsewhere on the cylindroid and has some finite pitch. (Much easier with pictures...)
~~~o0o~~~

"Now, if you use the FVSAL and IC heights calculated by ADAMS in your FBDs to calculate the forces transmitted to the sprung mass by the suspension, how is this wrong or any different?"

The difference is that with the 2 x 2-D thinking the "suspension forces transmitted to the sprung mass" are assumed to go through the zero pitch joint of the IA (= a simple hinge, or "revolute"), rather than through a "screw joint". Consider the wheel swinging about a low friction "ball screw", or similar. Any component of force acting on the control-arm (= the "nut"), in the direction of the screw axis, tries to turn the nut. If RH thread, then the nut turns clockwise. If LH thread, then nut turns anti-clockwise. If zero pitch (= the IA revolute), then nut doesn't want to turn at all.
~~~o0o~~~

"Yes, when the unsprung mass is zero, the jacking force ends up being the lateral force multiplied by IC height over FVSAL, which ends up always pointing at the IC, or along the n-line or whatever. With the IC approach, you actually only need the IC inclination angle."

Correct.

"But what happens when the unsprung mass is no longer zero, the unsprung mass has an acceleration greater than zero and you have an overturning moment?(or couple, to make you happy, haha)

The mechanism will still move the tire contact point in the same manner, and so have the same n-lines, but the lateral and vertical forces transmitted to the sprung mass are different. Sticking a vertical force and lateral force at the IC and summing forces and moments allows me to calculate the lateral and vertical forces transferred to the sprung mass. And in this case, I actually do need both the IC height and FVSAL, at least to determine the jacking force caused by Mx and the unsprung mass."

VERY GOOD!

Your consideration of the inertial forces from the unsprung masses (= Wheel Assemblies) makes things much more "interesting", because these forces act along different n-lines to the forces from the wheelprints (very roughly speaking, the inertial forces act along n-lines passing through the WA's CG.)

I have never yet read a VD textbook that comes close to explaining this properly. Or even having a caveat stating that their explanation is a gross simplification. This is also why I said in my first post that understanding jacking forces (ie. those from the wheelprint) is simple, because jacking from inertial WA forces is several levels higher...

Again very briefly, and simplifying it to 2-D front-view, with ground level ICs (horizontal n-lines), and a given lateral G. Inertial WA forces acting through inboard ICs with very short FVSALs (less than half track) counteract the body roll of the sprung mass alone (ie. less roll angle). ICs on the car centreline makes no difference to body roll. Infinite FVSALs give roll as if the WA masses are part of the body (ie. more roll than body alone, because body now heavier but has same spring stiffness). Short FVSALs and outboard ICs significantly increase body roll.

Note that these WA forces that cause different amounts of body roll act internally to the car. The overall Lateral Load Transfer stays the same.
~~~o0o~~~

"I was only talking about front view above, but the exact same thing applies in side view."

Not really. A complete consideration in 3-D is much more interesting.

For example, a wheel that rotates as it rolls along the ground, and also rotates in yaw as it goes around a corner, requires a gyroscopic couple to act on it to keep it upright. This couple comes from the car body and the reaction increases both LLT, and the body's roll angle. Same effect with an engine with East-West crankshaft which rotates in the same direction as the wheels. So when going around the same radius corner, at the same speed, this engine causes more outward LLT and body roll when in low gear (high revs) than when in high gear (low revs)!

An E-W engine with "reversed" rotation (ie. backwards to wheels) reduces LLT and body roll. But by how much? Is it possible to lift the OUTSIDE wheels when cornering, say with a fast reving, reverse rotation, heavy flywheel?

Quite an easy calculation, but it definitely requires 3-D thinking!
~~~o0o~~~

I need a drink....

Z

[STRETCH]

Originally posted by Z:

Can you explain why you think that "all the tyre forces feed into the chassis at the IC for that wheel"?

Is this the only point they can act?

Z

Z,
I never said this is the only point. If you actually read my post, rather than jumping to condescending comments, I was simply suggesting this point for taking moments around the sprung mass, to help explain the jacking force concept to the OP. Obviously its the line of action that is important, but given they were asking about changing net tyre loads, I thought it was an appropriate simplification - the same reason I didn't even mention the effect of unsprung inertial forces... Nevertheless, for this 2D approach, why not use the IC? Their coordinates are generally readily available in the suspension data one passes between suspension programs, and you can quickly plot them in front or side view to visualize your 'n-lines'.

[Z]

Originally posted by STRETCH:
I never said this is the only point. If you actually read my post, rather than jumping to condescending comments...

Lee,

Thanks for the reply. I did read your post, several times. From that reading I reckon a newbie would most likely conclude that the IC is the only point where "all the tyre forces feed into the chassis". (Ooops.... Hope that didn't sound too condescending... )

Anyway, you say "... why not use the IC? Their coordinates are generally available in the suspension data..."

Most off-road racers with wishbone suspension have them equal length and parallel. Even wishbones that are unequal length and non-parallel can have them go parallel somewhere in their travel. In both these cases, and many others, the ICs are at "infinity".

Where would you feed the forces into the chassis in this case? (<- spoken in least condescending voice possible... )

What do you think of Danny's preferred FAPs? (ditto)

Or what about using the "Roll Centre"? (-"-)

Can you see why new students get confused?
~~~o0o~~~

Danny,

What is special about your FAPs?
~~~o0o~~~

Can anyone think of another, perhaps easier, point to use?

Z

[STRETCH]

An infinite swing arm length gives zero vertical component, and zero x infinity is zero.

Maybe you can answer a question about your n-lines... How do you account for the fact that the slope of this line changes as a function of tyre squash (something not captured by a kinematics package)?

[Z]

Originally posted by STRETCH:
An infinite swing arm length gives zero vertical component, and zero x infinity is zero.

Lee,

Noooo!!! There are countless examples in Mechanics where "zero x infinity" = finite result. A relevant one here is a finite couple, which can be thought of as an infinitesimally small (=zero) force acting at the end of an infinitely long lever arm.

Parallel, but not horizontal, wishbones have an "IC" that is at infinite lateral distance (left or right), but also infinite altitude (up or down). Taking the horizontal tyre force (Fy) and applying it at the infinite altitude (or let's just say "very high") IC gives a very large moment about the CG in one direction. Taking the vertical tyre jacking force and applying at the "very large" lateral IC position gives a very large moment about the CG in the other direction. Adding the two moments gives a quite reasonable (= small) moment of the n-line force acting about the CG.
~~~o0o~~~

"Maybe you can answer a question about your n-lines... How do you account for the fact that the slope of this line changes as a function of tyre squash (something not captured by a kinematics package)?"

Well, different tyre squash at left and right might tilt the whole car, but this does NOT change the n-line slopes wrt body. Compliance in chassis, wishbones, upright, BJs, etc. might change the whole geometry a bit, but this is a separate (and important) structural problem (ie. not kinematics).

"N-lines" are simply the directions in which a particular linkage (in this case the suspension control arms) can carry forces without the linkage moving. IMPORTANTLY, any forces that do not lie along n-lines must be carried by some other structure, which in the case of suspension is the spring-dampers, ARBs, etc.

The above is as per your original post, where you correctly stressed that this whole "jacking" business is about the distribution of forces internal to the car (ie. between control-arms and spring-dampers). I'm mainly ranting about your choice of the IC for the calculation (there is an easier point ).

(BTW, the concept of n-lines (= "normal-lines", aka "right-lines", because at right-angles to direction of motion) was developed in the 1800s. The lines drawn through the "pin-ended-links" in the 2-D sketch used to find the IC are n-lines (because "no" motion possible along them). A "contact normal" between a cam and follower, or between two gear teeth, etc., is also an n-line. They are everywhere, and are very useful simplifying tools.)

Z

[STRETCH]

Originally posted by Z:
Well, different tyre squash at left and right might tilt the whole car, but this does NOT change the n-line slopes wrt body. Compliance in chassis, wishbones, upright, BJs, etc. might change the whole geometry a bit, but this is a separate (and important) structural problem (ie. not kinematics).

Z

I disagree. Take a front view, and say both front tyres are squashed the same amount, but due to kinematics the IC (which is above ground) height does not change, the n-line ("all the straight lines that pass through the wheelprint and are perpendicular to its path-of-motion") will now have a shallower slope...

[Z]

Originally posted by STRETCH:
I disagree. Take a front view, and say both front tyres are squashed the same amount, but due to kinematics the IC (which is above ground) height does not change, the n-line ("all the straight lines that pass through the wheelprint and are perpendicular to its path-of-motion") will now have a shallower slope...

Lee,

Oops..., sorry, yes, I agree.... sort of... (I must have been thinking of mainly parallel n-lines (IC a long way away) when I made that quote. Also see point 2 below.)

Considering just 2-D front-view, the three lines drawn in the find-the-IC sketch (upper and lower link and tyreprint-to-IC) are all n-lines. So also are all other lines that pass through the IC (because these are all "normal" to the motion of points moving around the IC). So if the tyreprint gets squashed upwards, with upright, body, and IC all fixed in space, then yes, the n-line through the tyreprint will have a shallower slope.

But now both the IC and CG heights, relative to the new ground level (which is at tyreprint height) are less than they were before. So calculations of moments of tyreprint forces about the CG also change.

A similar issue occurs during hard cornering, when the Fy ground-to-tyre forces cause the tyreprint "centre" to move significantly sideways.

There are two approaches to dealing with the above.
1. Keep track of the moving tyreprint centre under different load conditions, and then adjust IC height, CG height, n-line slope, etc., to suit.
2. Consider an idealised "wheelprint centre" that stays in its proper fixed position wrt the rest of the kinematics, so that n-line slopes or IC positions stay the same. Then add tyre "moments" (mainly Mx in this 2-D front-view) to account for the different load conditions that move the tyreprint about. Standard "tyre data" seems to follow this second approach.

Z

(BTW, in 3-D space there are "three infinities" of n-lines associated with the motion of any one body wrt another. This is a lot of lines, but also a lot less than the total of "four infinities" of all straight lines in 3-D space. "Four infinities" means that four separate numbers, each of infinite range, are required for the specification. So only "three infinities" of points in 3-D space (because only x, y, z needed...).)

[ChassisSim]

Hey Guys,

Sorry for the hold up in getting back to this. I've had my hands full on some other matters.

Z In response to your questions and I think some other questions that are out there I think it might be time to clarify a few things.

First things first, Force Application Points (FAP) are a direct corollary of doing Free body diagrams of suspension geometry linkages. This is covered in year 1 of any mechanical/aerospace engineering degree worth its salt and is the back bone of why Mechanical/Aerospace engineers can design structures that don't fall apart. That is a fact of life and if you don't like it I suggest you take it up with a higher power.

Bill Mitchell did an excellent analysis of the whys and ramifications of FAP. Here is the link for the article,

http://www.neohio-scca.org/com...e%20Dynamics2007.pdf

The proof is in black and white and Bill and I came up with the same answers totally independently.

Also as I discussed in the video and my book, The Dynamics of the Race Car these Force application points apply laterally and horizontally. They are also the true drivers of what is happening with so called Jacking forces. If you don't believe me work through the analysis (hint - undergrads reading this - that means you)

However the real proof of the pudding is in the eating. Bill Mitchell is incredibly well respected in formula as diverse as NASCAR and IndyCar and WinGeo is one of the industry defaults for suspension geometry software. FAPs are also the back bone of suspension geometry calculations and roll and pitch moment calculations in ChassisSim. We have customers in fields as diverse as F3, GP2, Sportscars, FIA GT and V8 Supercars and if they have measured up their geometries correctly their suspension correlation is outstanding.

On this one the facts speak for themselves.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

[STRETCH]

Originally posted by Z:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by STRETCH:
I disagree. Take a front view, and say both front tyres are squashed the same amount, but due to kinematics the IC (which is above ground) height does not change, the n-line ("all the straight lines that pass through the wheelprint and are perpendicular to its path-of-motion") will now have a shallower slope...

There are two approaches to dealing with the above.
1. Keep track of the moving tyreprint centre under different load conditions, and then adjust IC height, CG height, n-line slope, etc., to suit.
2. Consider an idealised "wheelprint centre" that stays in its proper fixed position wrt the rest of the kinematics, so that n-line slopes or IC positions stay the same. Then add tyre "moments" (mainly Mx in this 2-D front-view) to account for the different load conditions that move the tyreprint about. Standard "tyre data" seems to follow this second approach.

Z

(BTW, in 3-D space there are "three infinities" of n-lines associated with the motion of any one body wrt another. This is a lot of lines, but also a lot less than the total of "four infinities" of all straight lines in 3-D space. "Four infinities" means that four separate numbers, each of infinite range, are required for the specification. So only "three infinities" of points in 3-D space (because only x, y, z needed...).) </div></BLOCKQUOTE>

And you still think this is easier than just applying forces at the IC? The only point that is ALWAYS on the force line, from ACTUAL tyre contact patch (which moves as you say with load/pressure/camber), and also through the FAPs described above, is wait for it... the IC.

I rest my case