How to locate the mass centroid axis ?

[Warpspeed]

The commonly available suspension simulation computer programs require the entry of an effective centre of gravity point at each end of the car located above each axle centerline.

This may be at a different height at each end, depending on how the mass centroid slopes from front to rear. It will obviously pass through the main CG point at the vehicle centre, but how to determine the location of the actual mass centroid, and the respective front/rear heights?

With such a complex distributed structure trying to calculate it theoretically would seem to be an almost impossible task. Is there a practical way to actually accurately measure it?

 

[GregLocock]

There is no such thing.

If you don't believe me check your first year mechanics books.

The programs authors (hacks) may do some hand waving and then claim they are really talking about the principal axis of the moment of inertia, but that is not the same thing.

Yes you can measure the location of the principal axes, using a trifilar suspension, but that's worse than calculating it.

So first of all think about why you need it, then you can figure out a whole vehicle, dynamic, experiment that will tell you where it is.

Alternatively (big hint) just use the cg height of the sprung mass, for typical cars (end of big hint). That's not quite perfect, but it is not bad either.


Cheers

Greg Locock

 

[willeng]

This could be a very interesting thread if we let it roll along a bit, it is a very good question that Warpspeed has asked & many find it a very relevant subject.

A centroid is defined as the geometric centre of a body.
The centre mass is often called the centre of gravity & is defined as the location where all the body's mass or weight can be considered located if it were to be represented as a point mass.
If the the object has (uniform) density & thickness, then the centroid will be coincident with the body's centre of mass.
Conceptually, & in their application to motor vehicles, there is a big difference between a centroid & a centre of mass.

Think about it!!

 

[sreid]

To find the horizontal CG (this is obvious) weigh the car with scales under all four wheels. Then weigh the car again with (say) the rear end jacked up 2-3 feet. A little trig and math will determine the height of the CG.

 

[Warpspeed]

Finding the CG is fairly easy, exactly as you suggest.

The difficult part is finding the axis through which you could rotate the entire sprung mass and have it in complete dynamic balance.

It is like the static balance of a wide wheel rim. Provided the axis of rotation is through the CG it will have perfect STATIC balance. Rotate it at high speed it might show a massive tendency to wobble if major mass is disposed diagonally from inside to outside.

I may be barking up the wrong tree here, but authors of some highly regarded suspension texts suggest the relationship of the mass centroid axis and roll centre heights can be rather important to transient handling.

What they all fail to mention is how to find this centroid axis on a distributed structure as complex as a whole vehicle.

Greg suggests experience shows it to always end up very close to being horizontal, and he is almost certainly correct. But what about unusual or unfamiliar vehicle or drive-train layouts ?

I would like to learn of a practical method of nailing this axis down to some specific dimensions that can then be entered into a suspension computer simulation program.

Just guessing is not really a good way to begin. As the computer geeks so aptly put it "garbage in, garbage out".

 

[sreid]

Warpspeed,

You are completely correct. I am certain that there is no static test that will determine the principle axes and inertia. This may be one of the advantages of complete CAD design.

Years ago I helped in a study to find the CG and moments of inertia of the human body (needed for spacecraft design). We used humans placed in pendulums to find the CG and torsional pendulums to find moment of inertia.

 

[Warpspeed]

I am beginning to think along similar lines, no static measurement can really resolve this problem. Dynamic measurement requires measuring the inertial shift as the mass is rotated or rocked somehow.

Spin balancing of a whole vehicle is a rather scary thought! But a torsional pendulum arrangement operating through a reasonable (but safe) angular displacement may be quite feasible.

As the mass of a vehicle is large, if the measurement was sensitive enough it may not need to move very far or very fast to locate the exact point of dynamic balance at each end.

I am just wondering if anyone else has ever tried this with a whole vehicle, or how it has been done, or if anyone has even thought to try it.

 

[BillyShope]

sreid is correct in saying this is a relatively straightforward problem if everything is in the computer. It's not quite as simple, however, to measure it as he suggests, as the measurement errors can quickly make the results useless.

This has, I believe, come up in another thread, and, at that time, I suggested use of a tabular method to measure the car's CG height. This involves measuring the vertical height to the estimated CG of each component, summing the products of component mass and the measured height, and then dividing by the total mass. The resulting accuracy is, of course, a function of how much time you want to take in these measurements. (This can be done rather quickly on a tube frame race car, but, as you can imagine, not so quickly on a unibody.)

Now, once you have the car's CG, you can calculate the tangent of the "axis" desired. First, sum the products of the component masses and their vertical distance from the car's CG, with that distance being positive upward when the component is in front of the CG and positive downward when the component is behind the CG. Then, divide by the sum of the absolute values of the products of the component masses and their distance...horizontally...from the car's CG. Once you have this tangent, you can add the car's CG height to the product of the tangent and the distance forward from the CG to the front wheels and you have the axis height as it passes through the front wheel plane. Similarly, the situation at the rear can be determined.

If everything's on CAD, I don't see why you couldn't add this as a macro.

Hope this helps.

 

[MoreWing]

Listen to Greg. You're snipe hunting.

The mass centroid axis is a folly that Carroll Smith popularized on racecars, I think in Tune to Win. While I have a huge amount of respect for his work, the old man was just plain wrong on this one. Depending on what you are using it for, a good C.G. measurement and the associated moments of inertia will get you what you want to know.

What software package are you talking about?

 

[BillyShope]

I confess that I don't know the purpose of it all. I'm just saying that the procedure I described will provide what could be called an "axis" of mass distribution for a random array of discrete entities. In other words, I saw it as an interesting puzzle and set out to solve it.

This is what happens when you're retired, start getting all your news off the internet, and no longer have a Sunday crosswords.

 

[Warpspeed]

Well, we are all here to learn, which is why I started the thread. I am not pushing any particular view, just trying to hear a few opinions on this.

So what you guys are saying is that if I slung a massive steel weight very low beneath the front bumper, and another one really high above the rear wing, it would have zero effect on transient handling as long as the centre of gravity remained located in exactly the same place ?

 

[patprimmer]

If that is what they are saying, I would have to disagree as weight at the extremities increases polar moment.

Regards
pat pprimmer@acay.com.au
eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[MoreWing]

a good C.G. measurement and the associated moments of inertia will get you what you want to know

 

[Warpspeed]

Pat, that is the whole point I am trying to clear up in my own mind.

Centre of gravity is a concept that only really works at rest or uniform motion. If you apply tangental accelerations in pitch roll or yaw, the mass distribution also becomes important. Exactly as you say, polar moment is all part of that as well, but only during tangental acceleration.

Suppose you could build a vehicle that had most of its mass concentrated in the front left corner, and the right rear corner. Assume the CG to be located exactly in the middle, the static wheel weights would all be even (assuming sufficient torsional rigidity). I would like to bet the handling characteristics would be rather different between a left handed turn, and a right handed turn. Directional stability during braking might not be too good either. Yet the static wheel weights would suggest perfect vehicle balance.

I am not trying to stir the pot or irritate anyone, just clarify my own thinking a bit.

 

[willeng]

If we look at a cicle track race car with definite weight biasing, isn't this the same thing as moving the mass centroid axis to the left to enhance the handling ability of the car for the given application.

I know they don't turn right or swap directions to good when the weight is biased to the left, so it would seem the mass axis does in fact play a fairly significant role in the overall chassis design!

The (height) of the mass axis at either end of the car would seem to effect things also.

 

[BillyShope]

Would the left/right handling be so very different, warpspeed? I'm not entirely convinced. Reminds me of the common condition on circle track cars, where they use a very high rate spring on the right front. Is this any different than achieving the same roll stiffness with equal rate springs?

 

[BillyShope]

Let me answer my own question (before someone jumps on me). I was thinking, more or less, of skidpad performance. On a circle track car, you can use different rate springs, at the front, to affect performance at the entrance to the turn. By using a higher rate spring at the right front, you tighten the car during braking.

Shouldn't have introduced this in the first place, but this matter of mass distribution just brought it to mind.

 

[Warpspeed]

I can see what you guys are saying. A vehicle is (mostly) a rigid structure, and it has an exact equivalent centre of gravity point located somewhere within. From the physics point of view all the mass can be considered to be located at the CG point. Taking that simple view the actual internal mass distribution is completely irrelevant.

It will also have a polar moment, and an equivalent radius of gyration if you like. This is all true in the majority of situations, but not all.

We all realise that rotating machinery needs to be in dynamic balance as well as static balance to avoid setting up a rocking couple. The concept of a single CG point is just not enough, the mass centroid axis has to be lined up with the axis of rotation to prevent the generation of inertial displacement forces.

Now consider a very softly sprung vehicle with large suspension travel rapidly turned into a corner. The main mass will both roll and yaw on the suspension. This is rotation in two axis, maybe fairly rapid rotation too.

Depending on internal mass distribution, the sudden motion of the vehicle on its soft springs might cause additional displacement forces other than the direct force on the CG.
These might be in different directions at each end of the vehicle, a sort of rocking couple due to mass unbalance if you like.

If the springs are made much stiffer the amplitude will be less, but the rate will increase.

I am not talking about steady state cornering but sudden and very violent maneuvers, and TRANSIENT conditions on a sprung mass.

These extra forces may be so small as to be irrelevant, but I am sure they must exist.

I agree fully that in a gentle steady state cornering situation only the actual CG location is relevant.

 

[GregLocock]

I know of a few practical ways of measuring the orientation of the principle axes. I'll describe two:

1) An extremely accurate modal analysis of the car should be able to identify them. That is, measure the 6 rigid body modes of the car on the tyre stiffness, with a locked suspension.

That has been shown to work for simple systems eg engines on their three engine mounts. I doubt it would give useful results on a car due to experimental errors, and lack of knowledge of the tyre stiffnesses.

2) Again for relatively compact masses you can mount them on a platform in several orientations, and then measure the period of oscillation when suspended by a trifilar suspension. If you accurately measure the setup you should be able to get a good estimate of the principal axes.

This is at least feasible, if rather an enormous undertaking.

There IS a practical method of doing this (I believe it may be on the rig used for measuring roll centre heights/anti dive). I don't know how, perhaps someone could ask Anthony Best Dynamics, who may well sell a rig for this.

But, I come back to: why do you want to know? I think you are mostly interested in weight transfer. So, supposing you set up a pair of hydraulic rams at each end of a car and force it to roll. What 'axis' does it roll around?

Now increase the speed of oscillation of the four rams. Does that axis move? I think it probably will, as the inertia of the sprung mass gets decoupled from the springs and antiroll bars (ie once it is well above resonance). It won't decouple from the suspesnion roll centre linkage of course, which makes it complex.

Here's a better way. If we use two rams, one at each axle. suspend the car from two wires, high up. If we push below the principal axis, at both ends, the top of the car will roll towards the ram as it pushes. If we raise both rams ultimately the top of the car will roll away. If one is too high, and one is too low, then the motion will be complex. Only if both rams are at exactly the right height at each end (and the line joining them, naturally passes through the CG), will the car just move sideways with no other roll or yaw. I think.

Waddayerreckon?


Cheers

Greg Locock

 

[Warpspeed]

Wow ! thanks Greg.

As to why I am curious about all this, it has to do with the rate of buildup of tyre loads during very sudden changes in vehicle direction. I just have this gut feeling that very suddenly applied body roll will not cause a proportional rate of buildup of the lateral weight transfer at each end of the vehicle. It probably will if the lateral acceleration is very slowly applied. If it is rapidly applied, the whole mass may sort of wobble somehow if the axis of roll is far displaced from the axis of mass. The magnitude of this effect may be totally insignificant, or it may not even exist at all. But I am still kind of curious about it.

I like your last idea with the two horizontal rams, it is very ingenious. As you say, the motion will be complex, but it should still be possible by trial and error to get a clean sideways swing when the rams are directly in line with the effective mass heights at either end. Some sensitive accelerometers should be able to detect any tendency to tilt. Some yaw is probably going to be inevitable, but it should not matter.