Front and rear roll angles

[Komodo86]

I have done a fair bit of mathematical and 3D modelling of independent automotive suspension systems, and have come to the conclusion that the in pure steady state cornering no matter what the combination of springs, ARB/sway bars, motion ratios or linkage geometry, the roll angle (ignoring the tyre flex component) is always determined by the deflection of the spring and that the load they see on each axle will directly correspond to the rate of the spring, meaning that they will deflect such that the wheel movement and thus roll angle, is the same at each end of the vehicle.

It has been suggested by an experienced engineer, that this is not the case and that the front and rear axles DO roll different amounts, however the mechanics of this were not explained. Surely if such a case was true, this means the chassis must be twisting to accommodate the difference in roll angle? In a typical modern chassis with say 15,000Nm/° torsional rigidity, surely the amount of differential roll, if any, must be negligible to the point of not being worth considering?

 

[GregLocock]

He may be thinking about the tire deflection contribution. He may be thinking about the torsional stiffness. He may be thinking about something subtle. Or he may be wrong.

However 'the load they see on each axle will directly correspond to the rate of the spring' is a bit worrying as it ignores the effect of RCH, at first glance.





Cheers

Greg Locock


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[Komodo86]

By that I mean the roll angle is dependent on the spring deflection, which is dependent on the spring load, which is dependant on the spring rate AND the other contributory factors, RCH included. Assuming all else held equal, then the load is proportional to the spring rate.

 

[BrianPetersen]

For modern unibodies, the amount of torsion in the unibody is not very much. Body-on-frame trucks might have a bit more twist. Older models with less frame rigidity, might have a lot more.

If you neglect the torsion in the unibody and you are on flat ground, then there is no choice but for the roll angle to be the same front and rear (neglecting tire compliance). The geometry dictates it ... up to the point where you lift a wheel off the ground in hard cornering. There are some front-drive vehicles notorious for lifting up the inside rear, and some rear-drive vehicles will lift up the inside front.

 

[Komodo86]

I guess my next question is, should we, or can we neglect it?

At what torsional stiffness does it become enough of an issue to warrant attention? The car in question is relatively weak, only 5000Nm/degree.

 

[BrianPetersen]

What's the total roll moment at, say, 1 g of lateral acceleration?

If the vehicle weighs (say) 1500 kg and the center of gravity is (say) 0.667 m above ground then the total roll moment is 1500 kg x 9.807 m/s2 x 0.667 m = 9807 N.m. Call it 10,000 N.m.

So if the total roll moment is applied to the chassis - implying that all the weight of the car is at one end with no roll stiffness on that end, and none of the weight of the car is on the other end which is somehow being constrained to have no roll - it'll twist by two degrees.

Back that assumption off to something realistic, and the chassis twist is probably not going to be very much compared to the suspension deflections, but just enough to drive owners crazy with squeaks and rattles - or make it so that the doors won't open if someone uses a scissor jack under one corner.

 

[GregLocock]

while 5000 isn't great, it doesn't have to be a basket case.

Cheers

Greg Locock


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[Komodo86]

I see. So lets assume a 1000kg car, 1G acceleration, 55% front weight distribution and CGh of .5m

The total roll moment is 9810N x .5m = 4905Nm.

The front roll moment is then 4905Nm x .55 = 2698Nm

The rear roll moment is then 4605Nm x .45 = 2207Nm

The difference is 490Nm, which at 5000Nm/degree is .098° or 0°5'53"

Correct thinking on that one? I would consider that level of twist fairly irrelevant if it correct.

 

[Komodo86]

Should the roll stiffness distribution not be counted in that calculation somewhere also?

 

[NormPeterson]

Yes, because the chassis torsion distributes in accordance with it as well as in accordance with the longitudinal CG position.

I'm still not sure what your basic question is.

Are you perhaps referring to Bob Bolles?


Norm

 

[Komodo86]

"I'm still not sure what your basic question is."

Don't worry, neither am I. I guess I am just trying to expand my understanding of vehicle dynamics, it would be nice to have some way of checking the amount of twist imparted on a chassis for a given set of parameters, even if it is only a rough estimate.

I have no idea who Bob Bolles is.

 

[NormPeterson]

You could do "springs in series" calculations combining the chassis torsional stiffness forward of the CG with the front suspension roll stiffness (you'd scale that 5000 overall torsional stiffness upward), doing a similar calc for the rear, and dividing the total roll moment accordingly. It may be better to determine the roll moment based on the CG longitudinal position and height and a line drawn between the front and rear geometric roll centers if there either roll center height is at a significant height (as it tends to be with stick axles). Picky and probably unwarranted for this purpose would be to use the sprung mass and its CG rather than the overall numbers.

Bob is a US circle track chassis guy (author, magazine editor, consultant) who frequently writes in terms of what the front and rear of a car "want to do" in terms of roll.


Norm

 

[Komodo86]

I guess what I am not understanding first and foremost, is that my calculations for roll angle on each axle will give me exactly the same amount of wheel displacement each end, no matter what the combination of springs, bars, track width, weight dsitribution, motion ratio or roll centers. Now this to me just makes sense, but then if it is true, it does seem to suggest that in pure roll, the chassis is not twisting?

Obviously, add in braking or acceleration and it all goes a lot more complicated...

 

[BrianPetersen]

The only way the chassis is not twisting (at all) are if the torsional stiffness is infinite, or if the distribution of roll stiffness taking into account the geometric roll centers and springs and antiroll bars at each end is exactly the same as the weight distribution.

Calculate the amount of total body roll based on total roll stiffness front and rear of the complete vehicle, then knowing that number, calculate how much resisting moment there is from the front end and from the rear end. I betcha they won't match the weight distribution. They shouldn't except for a minor miracle, or unless the suspension was specifically designed for them to match (which is not a good way of doing it).

 

[Komodo86]

The cars in question are around 62% front weight, but have around 65% of the roll resistance taken by the rear axle.

If the load transfer calcs tell me I get wheel displacements of .63" front and rear, then chassis has one roll angle of 1.3° over a 58" track width. I am having difficulty seeing how this then relates back to the chassis.

Are you suggesting that the numbers I should see for front and rear wheel displacements should be different? That would obviously cause twist.

 

[NormPeterson]

Crudely, you can think in terms of the rear axle dragging something like 27% of the roll moment away from the front axle (where it would go if the chassis was infinitely rigid torsionally and the front and rear suspension roll resistances were equal). That 27% of roll moment being dragged off to where it wouldn't go otherwise will certainly cause chassis torsional deflection once you let the chassis become realistically flexible.

If a glorified order-of-magnitude guess helps you any, a single mass model I put together some time ago for a car of similar torsional stiffness with 54% front weight and roll resistance taken 59% up front resulted in a little under a quarter degree of chassis twist at 1g lateral acceleration. I wouldn't attempt to extrapolate from that if I were you.


Norm

 

[TC3000]

If it makes it easier to visualize/understand, you can try an calculate it for two "half" cars.
Imagine the car is split at the CG, and that the front part and the rear part would need to resist roll independently.
If there is a different roll angle for the front half and the rear half of the car, then you "twist" your chassis/structure,
which can be seen as a torsional spring. If the chassis would be perfectly rigid, the difference in roll angle will be taken
up by the tyre as deflection. Ignoring chassis twist and other structural deflections for a moment, the tyre deflection is
inverse proportional to the axle deflection (if we assume same vertical stiffnesses of the tyres).
Add the tyres as additional springs in series to the suspension springs into your model, and then you can see, that while
roll angle in relation the ground plane is the equal front and rear for a rigid body, the displacement can be split between the
two springs.
I think (but could be wrong) that this is what your mate referred too, as this is quite commonly done in the racing fraternity.
They will measure the suspension deflection and then calculate a "roll angle" for the front and rear, which most of the time is
not equal. The difference is taken up by chassis deflection (which for a half decent modern race car, shouldn't be much), and the
tyre deflection, thereby this gives and indication of what the tyre loadings are at the different axles.
If the chassis structure is sufficient stiff (> 10x tyre stiffness), the difference in suspension roll angle gives and indication
about Lateral Roll Moment Distribution or Lateral Load Transfer, which can be used as a handling tuning parameter.
If the structure which connects front and rear is not stiff enough, you twist a additional spring, which is also largely undamped.
If this is the case, the amount of LRMD you can achieve is limited, you can stiffen one end, but all it does is twist the chassis more.
If you have a stiffness issue (maybe with some historic race cars)you are better off, trying to aim for close to equal roll suspension
roll angles front to rear, to minimize the load put into the chassis (torsional spring).

Total Roll Angle (Body to ground) = suspension roll angle + tyre roll angle
I think your mate referred to suspension roll angle not total roll angle, and the suspension roll angle can be different front to rear
and most often is.

 

[Komodo86]

My model is done as you say, as two different, separate axles each with their own roll stiffness.

When calculating each axle, the total elastic load transfer/total wheel roll rate will always end up equal.

Equal roll rates in the suspension would mean no chassis twist.

Here's some of my workings.

Vehicle mass = 2575lbs.
Track front = 58"
Track Rear = 58"
Front weight distribution 62%
CGh = 22"
RChF = 2"
RChR = 5"
Axle height = 11.75" (F+R)

Spring rate
Front - 250lbs/in
Rear - 250lbs/in
Motion Ratio
Front - .7
Rear -.7

Gives a wheel rate of 123.5lbs/in front and rear.

Unsprung mass
Front - 66lbs
Rear - 62lbs

ARB (simple model)
Front
Diameter - 26mm
Length - 32"
Arm - 12"
Motion ratio - .55

Gives a wheel rate of 161lbs/in

Rear
Diameter - 22mm
Length - 32"
Arm - 6"
Motion ratio - .59

Gives a wheel rate of 379lbs/in

In total, we have a front wheel roll rate of 161+123.5 = 284.5lbs/in and a rear wheel roll rate of 379+123.5 = 503.5lbs/in.

Now, based on those parameters, at 0.8g lateral acceleration I get

Total load transfer - 744lbs
Front LT - 280lbs
Rear - 464lbs

Front unsprung LT - 22.17lbs
Front geometric LT - 40.40lbs
Front elastic LT = 290lbs - 22.17lbs - 40.40lbs = 218.7lbs.

Rear unsprung LT - 19.76lbs
Rear geometric LT - 58.99lbs
Rear elastic LT = 464lbs - 19.76lbs - 58.99lbs = 385.39lbs.

218.7lbs into 284.5lbs/in = .77" wheel deflection at the front.

385.4lbs into 503.5lbs/in = .77" wheel deflection at the rear.

 

[TC3000]

I think your "problem" is that you assume infinite stiff tyres in your model.
Calculate what the force are the contact point would be, for your 0.77" wheel deflection or better any given roll angle, in your model
You can assume tyre vertical stiffness with ~300-330 N/mm --> 1700-1900# for a common touring car racing slick or whatever values you may have from your tyres.
If we assume a flat road and equal tyres front and rear, the tyres will deflect differently, if I assume 300N/mm stiffness I get a difference of ~ 0.288° for your values. With total values of ~1.65° and ~1.36° roll rear and front, with the suspension providing ~1.05° roll and the difference comes from the tyre deflection.

 

[NormPeterson]

More basic than that.

In order calculate chassis twist, the model must assume that the chassis might actually twist, and where the necessary torsional input is located. "Springs in series" should have been a big enough hint.


Norm