Beam Axles - Front, Rear or both.

[Z]

Firstly, thanks to everyone above for giving some thought to these educationally fundamental, but not-directly-FSAE-related, issues. Here is some more general ranting. More specific responses next post...
~~~~~o0o~~~~~

I do not blame Prof. Lewin for any of the teaching errors above. As noted, he does a great job of explaining the subject in an interesting way. The problem is with the modern education system in general, which nowadays seems to be,
"Well, it's all about this humungous jumble of equations, all of which you will have to learn. You have to learn all of them individually, because they are all a bit different. But they are also all kind of the same. Err..., in the same way that these days 'all answers are equally correct', and 'everyone's opinions must be equally respected'. Yep..., that way we can always give all the kiddies a gold-star...".

IMO the best way to teach Mechanics would be more of the Lewin/Mythbusters style of simple, real, and interesting experiments, but with much more honesty, clarity, and rigour in the explanations. This takes no more time than the current method. In fact, probably less, because most of the unnecessary equation-crunching can be dropped. So;

HONESTY - Don't tell lies about what people did or said hundreds of years ago! How is that educational?! An honest historical account is more ethical, and also often more interesting. For instance, in Newton's Definition 1 he defines the "quantity of matter" (= "mass" nowadays) as "... its density and bulk conjointly". Note how we do it the other way around these days (ie. density = mass/volume) .

Also, the notion that "We are cleverer than Newton because we know that General Relativity gives more accurate answers than Newton's ULG..." is nonsense, as noted before. High school teachers might mistakenly suggest this, but University Professors should not teach this sort of slanderous rubbish. Unfortunately, when they all do it, they can all get away with it. And all you students are the losers.
~o0o~

CLARITY - "F = P-dot" is really much easier to understand than "F = mA". I only started to think that way well after I finished my schooling, and I highly recommend it. Lewin often mentions that rotating dynamics are very "non-intuitive". This is, IMO, due to too much "F = mA". And you can forget about ever understanding gyroscopes (the most "non-intuitive" of the lot, according to Lewin) until you move to "F=P-dot". Then it all suddenly falls into place!

BTW, "Angular Momentum" (Lewin calls it L) was in the olden days called the "Moment of Momentum". It is simply the sum of all the "Moments" (= Cross-Products) of the Linear-Momentum-Vectors of the various particles and their Radius-Vectors, taken at a particular point. There is still a bit more explaining required here (maybe with some simple experiments), but seen geometrically it is all quite simple, and it gives "T = L-dot".

In the preface to Bevan's ToM book (ref'd earlier) he says "As so many of the problems which arise may be solved more quickly and easily by graphical methods, particular care has been taken to draw the diagrams correctly...". I note that in Lewin's lectures the "man climbing a ladder" problem is "solved more quickly and easily" in the simple act of drawing the FBD! (Lewin has to work through quite a lot of algebra for the same end result).

Similarly, the "time period of the hula-hoop pendulum" is solved in one, simple, do-it-in-your-head step, based on "equivalent mass systems". (Hint - What length dumb-bell has the same (2-D, planar!) mass-distribution as the hula-hoop?) And the "sliding vs rolling-ball pendulums" (ie. problem asked on other thread) is solved by simply noting the paths of motion, in side-view, of different points on the two bodies. (Hint- Which body has greater changes in its "quantity of motion"?)

Bottom line here, geometrical (or "graphical", as Bevan calls them) methods can give greatly improved insight into problems, and much quicker solutions. Your schools NOT teaching them is your loss.
~o0o~

RIGOUR - It should be constantly restressed that Newton's 3 LoMs are unprovable "Axioms", while most of the other "Laws" are deductions from these. It is a heirarchical system, starting with foundations at the bottom, and then other stuff built on top. The closer to the foundations, then the more widely applicable are the concepts. The further away from the foundations, then, typically, the more simplifying assumptions that have been used, and the LESS USEFUL is that "Law" (see eg.s below).

For a general feeling for how this works, ask the good citizens of Pisa how things go when you get the foundations wrong. Ok, so they do make some tourist-lira out of it now, but that is mainly because people enjoy looking at huge cock-ups. And the good citizens are having to pay quite a lot to prop-up their cock-up, lest it disappear into a pile of its own rubble...

As an example of the heirarchical approach, Kinetic Gas Theory is deduced from Newton's Axioms, typically with a few other assumptions thrown in (eg. the molecules are assumed to bounce off each other like elastic billiard balls). Likewise Bernoulli's Law is deduced from N's Axioms, again with a bunch of simplifying assumptions thrown in. Now, if you happen to forget any of these more superficial Laws, then, with practice, you can always re-deduce them from the very small set you started with (ie. N's I, II, & III). Fortunately, doing this reminds you of ALL those simplifying assumptions. Namely the times when said "Laws" DO NOT APPLY! (<- A hint here to FSAE-aero-guys that Bernoulli does NOT ALWAYS apply!).

An even more superficial example is the "Law of Friction", which barely qualifies for that title. Worth noting that back in the 1960s, when racing tyres started to get ridiculously wide (from 4" to 6"!, then 8"!!, then !!!) there where many experts, those that, ahem, understood the "Laws of Nature", that claimed that "wider tyres won't make any difference!". The "Friction Law" is a reasonably good approximation for hardish and smoothish materials sliding on each other, over a smallish range of pressures. But not much good for soft, sticky stuff sliding on a rough surface. And certainly no good at balancing your car's handling via LLTD and TLS.
~o0o~

Bottom line, it does not take a lot of time to constantly restress this idea that there are different "levels" of Laws (and some SHOUTING might help get the message across in less time ). The fundamentals are by far the most important, and should be understood the best. The more superficial stuff is less important, and if you happen to forget some of it, then no problem, because it is not that accurate anyway...

MOST IMPORTANTLY, never forget that the superficial stuff is usually built on a whole lot of simplifying assumptions, many of which might not apply to your particular problem!

Z

[Z]

I was thinking about this 'everything from 1st principles' point of view and wonder if we as humans skip steps so that we may progress?
...
If everyone had to learn all there is to know from the very basic principles upwards, we'd run out of life before we made any progress!

Jay (and others with similar comments),

I hope I have addressed this sufficiently above. But in case not, just be aware that only a very small part of what you learn in Science/Engineering is solid bedrock. The greater part is [...thinking of metaphor...] like quicksand with a very thin, but hardish looking, crust on it. You can pitch a tent on the latter, but don't go building an office block there (or a Pisa-esque tower ).

And racecar VD is even worse. For example, there is the "Law of Never Letting Your RCs Migrate Sideways". This is pure poppycock that has never been "deduced" from the more fundamental stuff, but has somehow entered the field as an old-wives-tale. It is relatively harmless (it just stops you having "ground level RCs", or horizontal n-lines), but it can waste you a lot of time.

Knowing how to distinguish the important stuff from the trivial nonsense, is, well..., IMPORTANT!
~~~o0o~~~

Originally posted by Ralph:
One last point on all the confusion concerning the terms moment, couple and torque...
Couples in Hartog are designated as C in Meriam as M (same as moment)...
... only one source of clear distinction I could find on Wikipedia under Torque of all places. Did you write that entry?

Ralph,

I don't do any Wikipedia editing. It is too much "design by committee" for me. In fact, I reckon it is accelerating the descent down the S-bend by introducing more and more poorly phrased definitions, and thus legitimising this sort of sloppiness in the eyes of the younger generation. For example (from Wiki- "Torque");
"In US mechanical engineering, the term torque means "the resultant moment of a Couple,"[5] and (unlike in US physics), the terms torque and moment are not interchangeable. Torque is defined mathematically as the rate of change of angular momentum of an object..."
So two different definitions right next to each other!

The second one comes from "T = L-dot", and, strictly speaking, should read as "a Torque CAUSES, and is proportional to, a rate of change of angular momentum". But the double translation, first into algebra, and then back into English, gives the impression that the torque is an end result, or effect, with the L-dot being the cause. Anyway, the whole quote above is very misleading, because it loses the direction of the causality.

Personally, for "a purely rotating, forceful, action" I prefer "Couple". This makes it very clear that for such a rotating action you need at least TWO matched forces (ie. "a couple of..."!). "Torque" would be ok, except that it doesn't stress this "two-ness". "Moment" is far too vague, because it is used in too many different ways (eg. 1st/2nd/3rd - Moment of - Area/Mass/Force/whatever...).

With regard to symbols, I think "T" (often Greek Tau) first started to be used for Couple (which later became Torque) because in Descartes' "Analytic Geometry" (c. ~1600) he used A, B, C for general purpose constants, and X, Y, Z for the unknown variables. This has since become universal, so "C" doesn't really suit a variable vector. Descartes' abstraction into alphabet soup means that even with two whole alphabets (Greek and Roman), and quite a lot of different fonts these days, we still don't have enough symbols to uniquely label all the different concepts (T is also time, L is also length, etc...)

Doing it graphically is much easier because we just draw a different sort of arrow for each concept. So, as in the earlier figures, a ring-like arrow around a normal arrow indicates rotational stuff. Add different sorts of feathers, and you can represent Force, Motion, or whatever you want...

Z

(PS. Don't bother googling images of "Couple Moment". You just get pictures of couples canoodleing...)

[rwstevens59]

Tim.Wright,

I would have to agree with you 100%.

What frustrates me the most is I feel that I should have known better but I took the ride anyway.

Starting to learn VD much later in the game then most students and having a fairly good but ancient (i.e. pretty rusty) understanding of classical mechanics I always had the feeling I came in at the middle of the story while studying the excepted seminal works.

I would be skeptical many times and fall back to drawing very basic FBD's then convince myself that my gut instinct was wrong, because after all the author(s) are the practiced experts, right? I just need to read and study more, I thought.

So, after many fits and starts, a lot of dead end alleys explored I am finally to a point of a somewhat better understanding.

Am l resentful, no. But I am quite disappointed and concerned with many of the sources proclaiming educational content in vehicle dynamics.

[BillCobb]

If you want to be on top of the Vehicle Dynamics game, learn something about nonlinear partial differential equations, the methods to solve them, the ways to characterize their response traits and the means to synthesize a system from known foundation properties that achieves targeted goals.

Otherwise, this subject matter Forum is probably just Vehicle Statics. (Just doesn't sound as cool though, does it ?)

[rwstevens59]

If you want to be on top of the Vehicle Dynamics game, learn something about nonlinear partial differential equations, the methods to solve them, the ways to characterize their response traits and the means to synthesize a system from known foundation properties that achieves targeted goals.

Otherwise, this subject matter Forum is probably just Vehicle Statics. (Just doesn't sound as cool though, does it ?)

BillCobb,

Vehicle Statics it is. Guess I should use V.S. from now on. Being that my mental toolbox is a few wrenches short for an all out assault on better modeling it will be a slow climb up hill. And since my work in this area is strictly for the fun of it, the climb will be even slower. But you are correct of course.

Ralph

[slicktop]

If you want to be on top of the Vehicle Dynamics game, learn something about nonlinear partial differential equations, the methods to solve them, the ways to characterize their response traits and the means to synthesize a system from known foundation properties that achieves targeted goals.

Otherwise, this subject matter Forum is probably just Vehicle Statics. (Just doesn't sound as cool though, does it ?)

I recently finished a 5 dof multibody tire/suspension/chassis model that i used lagrange's equation to solve and simulink to model. Only 2D though... It was a great learning experience. The equations are very tedious to write, easy to make mistakes, and time consuming to track down mistakes. But, in the end, not all that difficult to do. Although, during the process i found myself wondering if it was even worth it - maybe I would be better off spending my time learning Adams instead.

[rwstevens59]

I recently finished a 5 dof multibody tire/suspension/chassis model that i used lagrange's equation to solve and simulink to model. Only 2D though... It was a great learning experience. The equations are very tedious to write, easy to make mistakes, and time consuming to track down mistakes. But, in the end, not all that difficult to do. Although, during the process i found myself wondering if it was even worth it - maybe I would be better off spending my time learning Adams instead.

I guess my only question would be when this model was or will be validated by experimental observation i.e. track testing how much closer to reality was it than the simplified statics type of analysis that has been discussed above? I am not trying to disparage your work in any way nor questioning your approach. I am truly interested in knowing how much smaller your model to observation error was.

Thanks,
Ralph

[slicktop]

No offense taken. I disparage my work all the time. When I get the time, I am planning to post some results in order to get some feedback from the members here. I have not done a comparison of the model to logged data of our car yet or compared it to a statics approach, but it is definitely on the to do list. I have moved on to trying to learn cfd/openfoam so it will probably be a while before I return to the VD model.

The best answer i can give at this time is this: The full vehicle model uses the multibody model to provide the normal loads of the tires, which then uses Pacejka tire model to calculate tire forces, which give the vehicles yaw and sideslip responses in the road plane. Initially though i used a statics approach in place of the multibody model to approximate tire normal loads, and can say that there were differences in the result. Enough to warrant the time spent on developing the multibody model? Can't really say as of yet. I think I might have developed a tool that is too complex to use effectively with my limited manpower. Getting lost in the data can be a problem, i'm quite certain this trap has been discussed here before. I think that may be the lesson here... So I guess I am no help.

[rwstevens59]

I would like to ask the forum members for input and constructive criticism on the attached 2D CAD drawing of the planer view of a twin trailing link torque arm rear suspension linkage layout.

This is a plot of axle movement with respect to body quickly done in response to a question I received regarding the effect of varying effective torsion bar arm length with axle travel. The torsion bar arms are shown as the rectangles. The large circle is the solid live axle tube, the next smaller circle in the triplet is a roller which actuates the torsion arm through line contact with the torsion bar arm and the small circle at the bottom of the triplet is the trailing link radius rod mount to the axle. On the actual car the torsion bar arm roller and rear trailing link heim end are all fixed to the axle via a twin plate bracket.

The question which arises is that this arrangement (twin trailing link, torque arm, panhard bar for lateral location) with the trailing links at static ride height, as shown in black, having an upward angle toward the front should produce roll understeer. It should be mentioned that the torque arm is mounted on a slider and has only one contraint on the axle, that of torque reaction therefore in the sketch its chassis mount point is allowed to travel along the horizontal line shown.

The driveline is considered to be locked and therefore the tire and axle assembly must rotate about the trailing link axle housing mounting points.

The fixed construction points chosen are the trailing arm chassis mount point shown to the right in space and a horizontal line or the torsion arm chassis mount point and the sliders line of action.

So is the roll steer indicated by the movement of the contact patches relative to ground or by the axle housing tube?

MOD RR Suspension.jpg

I would appreciate any input anyone might be willing to give.

I am at a location where I am limited to 2D CAD or a drawing board at the moment and don't have access to my usual array of solid model tools. So a bunch of geometric construction and 2D projection are what I have in the toolbox.

Thanks,

Ralph

[Loz]

So is the roll steer indicated by the movement of the contact patches relative to ground or by the axle housing tube?

That question is a little confusing..

Steering, steered angle, under/oversteer etc. are all relative terms used to describe a change in orientation of the wheel. Through connection to the wheel, the tyre also follows the change in orientation in the general sense. If we consider the wheel and tyre as a rigid assembly, then relative change in orientation of a [u]static[\u] contact patch could be used to assess steered angle, in which case it would be the same as the fore/aft relative movement of each end of axle with respect to some pivot point some where near the middle (dictated by the panhard rod attachments and the ratio of fore/aft movement of the axle on each side due to the trailing arm constraints. Given the tyre and the axles tube are concentric, they should have the same relative change at the tube as the rigid wheel at the ground.

It would be very difficult to estimate the actual change in direction at the contact patch as a result of a steer input without extensive information about the tyre itself, but it would equate to something like the difference between the difference in wheel steered angle and the difference in slip angle (i.e. a difference of 2 differences: e.g. angular change=delta [ delta(SlipAngle1-SlipAngle2) - delta(SteerAngle1-SteerAngle2) ]. It would also be troublesome selecting a definition for the contact patch change that is a true representation of any changes in steered angle (unless of course the tyre is rigid and moves in unison with the wheel in which case we only need be concerned with the change in orientation of each wheel and we are back to using the axle housing).