Skewing roll axis and its effects on handling

[GSpeedR]

During a discussion on a separate website, we were discussing load transfers during lateral cornering, ie. no longitudinal acceleration. The general opinion was that if there is only lateral acceleration, then there will only be lateral load transfer; you would understand that after reading the Carroll Smith books. However, if you've taken an intermediate dynamics course (Euler and Lagrange based rigid body dynamics), then you'll have experience with motion transformations, which can be applied here. If you have a skewed roll axis, which is now angled sideways, then I believe the car will transfer load longitudinally under "pure roll"�. The lateral inertial force, oriented at the CG, will cause the vehicle to rotate about its roll axis (even though the roll axis is no longer parallel with the longitudinal axis of the vehicle). This is because of the rigid constraints that the suspension places on the vehicle: the roll axis is defined by the suspension and determines the motion path the sprung mass will follow. The motion of the vehicle (which is about this skewed roll axis) must be resolved about the body-fixed axes of the vehicle, which we chose to be the inertial axes if we are smart. Now we have a rotational acceleration about an axis with components in both the roll and pitch plane, and this rotational acceleration causes a transfer of load in both the lateral and longitudinal directions (and also a roll and pitch angle). This makes sense to me, but please correct me where I have made a mistake. The above is consideration of the sprung mass only (as a rigid body), so if we want to include the unsprung mass, we have a multi-body problem which probably has to be numerically solved.

I believe that the above is not only true, but provides a great way to tune handling. A skewed roll axis is present when the RC on one end laterally migrates a lot more than the other. I know that the geometric roll center typically moves to the inside of the turn as the vehicle continues to roll, I believe the "force-base"� roll center will do the same, but I'm not completely finished with my ADAMS yet. Anyway, say you limit the lateral migration of the front, while allowing the rear to migrate significantly during cornering; as lateral acceleration builds, the component of longitudinal weight transfer builds as well. You dump a lot of weight on the fronts during braking, but then you transfer more and more back to the rear, so you have more weight on the rears when you nail the accelerator after the apex. Possible problems would be under steer as rear grip increases under lateral forces, and difficulty in roll axis control: you need a damn good model or you may be taking weight off the rears instead.

A vertically inclined roll axis is similar but turned 90 degrees. Now we have roll-yaw coupling, where a lateral force causes a roll moment and a yaw moment. Most FSAE cars I know have a downward inclined roll axis (rises as you go back), which would cause a yawing moment which yaws the vehicle out of a turn. Maurice Olley described this as a sort of "roll damping"�, because the tire forces will provide a lateral force that tries to unroll the vehicle, all of which is proportional to the vehicle speed. If you angled it the opposite way, then you would have fast turn-in response and a vehicle that tried to rotate itself into a turn as it rolled...good or bad depending on how good your driver is. =) This is a much easier situation, because we aren't relying on dynamic movement of the roll/force centers, and we could keep the axis locked in place through all phases of cornering.

Maybe this is common knowledge for many here, but I've never seen a thread discussing this. Has anyone given this thought before (or after reading)? Anyone have any experience and results they'd like to share?

Sorry for the long post.

Chris

[Badi]

Doherty,

I believe your logic is correct if you make the assumption that the vehicle rolls about the roll axis. So the question is....does a vehicle actually roll about its roll axis. The answer to this question is no. The terms roll center and roll axis are unfortunate misnomers that have led to this widespread belief by even experienced people in the vehicle dynamics field. There are several good SAE papers that go into great detail to dispell this myth('Asymmetric Roll Centers' by Bill Mitchell is the first to come to mind). The 'official' SAE definition of the roll center is the HEIGHT where tire lateral force acts on the sprung mass , there is no mention of a geometric roll center or its lateral position(RC lateral migration is another myth). Ask yourself this question: If a car has assymetric spring stiffness(for a fixed overall roll stiffness) left to right would that effect its roll behavior relative to symmetric springs. If a vehicle actually rolls about it geometric roll axis then the answer would be no. Some simple calculations prove the correct anser to be yes. Others on this board have caught on to this point...feel free to chime in.

[GSpeedR]

Badi,

That is a valid point. My argument would be that the vehicle rolls about some axis at an instance of time as it is a rigid body. I did speak of geometric RCs, but I don't feel my theory neccessitates them at all. The sprung mass will have a roll axis whether you believe in RCs or not: The motion of a rigid body (the sprung mass) in an instance of time can be defined about a set of axes, which, in this case, are created by the constraints of the suspension...roll, yaw, and pitch. Euler's Equations still apply here. My question was for a car experiencing "pure roll" due to a lateral inertial force, which is a simplification since motion about a single axis is rare, but still as valid IMO.

The lateral migration was assumed from an ADAMS "force-based" RC analysis, which we get it moving inside laterally. The sprung mass does have a roll axis and a pitch and a yaw axis, and where this roll axis crosses the suspension planes I call the "roll center". I definitely agree that this RC probably can't be found by drawing control arm lines.

I see no reason why the roll axis can't be skewed (you state that there is no lateral migration). The sprung mass is like any other rigid body, with rigid contraints that determine its DOFs.

I don't know, maybe others agree with you.

[Frank]

i was kinda thinking a "skewing" roll axis meant your roll resistance distribution changed with the G's encountered

i was also wondering if a "calibrated" driver can feel the "skewing"
ie can a good driver detect the actual movment of the mechinism?

besides.. its a piece of cake to stop it skewing...

the ratio of (outboard) distance of upper and lower pickups is the key

[Storbeck]

You can't have longitudinal weight transfer without longitudinal acceleration. The front of the car weighs so much and the rear of the car weighs so much and no matter how that weight is distributed between the two front and two rear wheels it has to be the same.

This stuff is difficult to explain with a blackboard and ten pounds of chalk let alone with pure text, so I might not understand what you're saying correctly. But if I do, I think the flaw in your theory is that you are picturing the car rotating about a fixed, though imaginary axis. The axis doesn't necesarily have any relationship with the classic projected line roll axis, but it is rotating about some imaginary fixed axis. The problem is that the axis that the car rotates about is free to constantly move.

If you have a rigid body and put a force on it to rotate it about some fixed axis that is not perpendicular to the force, the rigid body may have an acceleration that is not in the same direction as the force. If this happens there has to be a reaction force in some direction different from the above mentioned force. The car has no reaction force in any other direction than lateral if you're talking about lateral acceleration.

It is quite possible under pure lateral acceloration, for one end of the car to come up or go down due to the geometry of the suspension, which would sort of imply a roll axis that is not parralell to the ground,(or the car, however you want to think about it), but this has no effect on weight transfer during steady state lateral acceleration.

I suppose we're talking about dynamics so I have to say something about free body diagrams. So draw a free body diagrams

My $.02

[Z]

An interesting subject, and as Storbeck says difficult to explain in "pure text". Here are some random thoughts.

Regarding 3-D motion: Everyone keeps talking about rotation about an axis - there is a bit more to 3-D kinematics than just rotation... I harped on about this in the "Vehicle Dynamics" thread (starting page 2). But actually it doesn't make much difference here...

One thing that does make a difference is if you are talking about "steady state" cornering, where the car's body has stopped "rolling/pitching/yawing/etc." (ie. dampers not moving), or if you are talking about the transient phase where the body is moving from upright to leaning outwards.

In the steady state condition there is mainly load transfer radially outwards from the centre of the curve (as Storbeck says). If the car has large oversteer (tail out) this includes car coordinate lateral (outwards) and longitudinal (rearwards) components of load transfer. Depending on the car mass distribution there might also be a small component of lateral/longitudinal load transfer similar to that in the next paragraph.

In transient conditions there can be load transfers in pretty much any direction because the body is generally NOT rotating about one of its principal axes (so like any spinning "dynamically unbalanced" object it will try to "wobble"). Because of the low angular velocities I think any load transfers here would be small. Whether or not they are negligible could be found through Euler's equations.

Chris (Doherty) says "The sprung mass is like any other rigid body, with rigid constraints that determine its DOFs". Not really. There might be reasonably rigid constraints between the wheels and the body, but the wheels themselves are sliding all over the place on the road (ie. they are not rigidly constrained to the road or inertial space, and thus cannot constrain the body).

I think it is better to think of the 4 wheels applying 4 forces (and 4 small couples) to the body, and the body then being a "free body" that will accelerate accordingly. Perhaps think of it as a rocket ship with a rocket-thruster at each corner (and then call yourself a "rocket scientist" http://fsae.com/groupee_common/emoticons/icon_smile.gif). As the body moves (accelerates) a small increment in a particular direction, the forces change (the springs get more or less compressed, etc.), the acceleration changes, another small increment of movement, etc., etc...

Z

[ben]

I like Z's idea of thinking about 4 forces and moments being applied rather than implicitely thinking about a physical constraint.

This is how models in ADAMS work. The tyre is actually a six-component force at the wheel centre.

Claude Rouelle mentions inclined roll axis' and talks about a combined roll/yaw motion. As Z has pointed out though the actual load transfers caused by this may be small because the angular rate is relatively low.

With regard to the original post, An inclined roll axis (in traditional terms) is the result of more anti-roll percentage at one end. The biggest effect of running different anti-roll percentages is the frequency of load transfer.

Ben

[Z]

Originally posted by ben:
With regard to the original post, An inclined roll axis (in traditional terms) is the result of more anti-roll percentage at one end. The biggest effect of running different anti-roll percentages is the frequency of load transfer.
Agreed. A "roll axis" that slopes down at the front (normal for many production cars) has a lot of "kinematic" anti-roll (ie. high "RC") at the rear. This causes "kinematic lateral load transfer" at the rear wheels as soon at lateral forces develop at those wheels. The "elastic" load transfer is only felt at the wheels (all of them) as the body develops a roll angle and springs compress/extend, which takes some time.

Above I said that load transfers due to "dynamic imbalance" of the rotating body would be small. I have just done some rough calcs and they are not always so small.

So, consider a car during steady state cornering about a small radius corner, with relatively high speed and hence high angular yaw velocity. Note that there is no roll or pitch motion, just the car rotating about the centre of the corner (as if it is sitting on the edge of a merry-go-round). If the car's body has its longitudinal principal axis sloping steeply down at the front, then as well as the normal lateral load transfer, there is also a longitudinal load transfer towards the rear. Imagine the car as a dumb-bell sloping down at the front, calculate the centrifugal forces (acting radially out from the vertical axis at the centre of the corner) on each half-mass, and resolve these centrifugal forces into car coordinate lateral and longitudinal components. Since the longitudinal components are at different heights front and rear they give a pitching moment.

Note that this "steady state" longitudinal load transfer is only significant for cars with steeply sloping principal axes that are cornering at high yaw rates (small radius corners), or more likely spinning after an accident. It has nothing to do with "front and rear CG's", although it might be interpreted as such.

Z

[clausen]

God that dumbell thing is going my head in. I'm going to have to come back to it http://fsae.com/groupee_common/emoticons/icon_smile.gif

[GSpeedR]

I will respond to everyone as best as I can.

One note is that I purposefully avoided using the term "steady-state" (at least I should have). Steady-state cornering isn't really valid when you have rolling/pitching/yawing acceleration. Let's keep it at: Only an inertial lateral force at the CG...no longitudinal inertial forces.

Frank - not sure what you mean by outboard pickups...do you mean A-arm attachment points?

Storbeck - Weight transfer is not a result of translational acceleration, it is a result of rotational acceleration (think of the CG on the floor...you can have plenty of lateral accel but no lateral weight transfer). If there is a rotational acceleration in the pitch plane, then this moment would be reacted by vertical forces at the front or rear tires aka longitudinal weight transfer. There is still no longitudinal acceleration at the CG. In your example about a car pitching under only lateral acceleration, something has to cause this increase in pitch angle.

Z - I completely agree that the motion of the vehicle is not about a single axis, but about three all of which can change in time. The same equations could be used for the more general case, but would be more difficult to explain and harder to calculate. Actually, what you described about 4 forces applied to a sprung mass was how I was thinking...so I guess "rigid contraints" is a bad way to describe it. In my simplified scenario (roll axis angled sideways), the tires were locked in place, which apparently you shouldn't assume.

The inclined principle axis makes perfect sense, and I would guess that a typically FSAE car definitely would have an inclined longitudinal principle axis...ILPA for short =)

Ben - So (according to traditional terms) are you saying that a vertically inclined roll axis would be a result of additional roll stiffness at one end, or the other way around?

I guess that the tracking of a moving roll axis is more of an academic exploration than a practical tuning tool. I still would draw a line between the RCs given to me by ADAMS and call that the "roll axis" (though I am worried about oversimplifying the coupling between the front and rear suspensions) . You could perform multiple iterations and visualize how this axis moves due to suspension changes, keeping in mind that larger relative RC movements would lead to increased longitudinal load transfer components...Or, you could just run the whole ADAMS model and not even bother with intermediate steps like the above. Let the computer do the work for you, and you don't have to worry about overly specific situations ie pure roll. hmmmm...

Chris

[Storbeck]

Z-I am having trouble picturing what you are saying about the dumbell. Is this a dumbell angled so one end is higher than the other, then we are putting a force on the ground beneath the centroid of the dumbell perpendicular to it's axis, and it is accelerating in only that direction? If we are talking about pure lateral acceleration changing , then we have to be talking about a change in the radius of the curve, which would also cause a change in angular velocity. Is this the situation that everybody is talking about?

Are we talking about weight transfer, that can be caused by accelerating the car either laterally or longitudinally, a situation that can be maintained for a relatively long length of time(indefinitely for lateral) or are we talking about lifting and lowering the car or one end of it which would cause a change in normal load for only a very short amount of time, and can only be caused by a change lateral or longitudinal acceleration?

I thought we were talking about steady state lateral acceleration. If your lateral acceleration is changing you can have changes in ride height at one or both ends of the car, which would cause a change in normal loads for the end of the car that is lifting or lowering. Not really weight transfer though because it is possible to have the normal loads get higher at both ends of the car at the same time. If you have a level roll axis that is very high, both ends of your car will rise with increased lateral acceleration, and while they are begining to rise (accelerating upward) they will both have slightly higher normal forces. Unfortuneatly when are begining to stop rising (the upward velocity gets smaller, so accelerating downward) they will both have slightly lower normal loads, till they settle at steady state. This is jacking, it seems like something to be avoided to me. I don't want a sudden increase then decrease in normal load when I have a change in lateral acceleration.

If you did it more at one end of the car than at the rear, you would have normal load distribution that changes with changes in lateral acceleration, I sure don't see how this could ever be a good thing though.

I also don't see how it could be significant unless you have the roll axis really high or really low, (which basically means really high or really low roll centers) I think if you step back and look at what is being discussed here, it's just another way of looking at jacking caused by a very high roll center in the rear and a very low roll center in the front, which would give you a steeply sloped roll axis. I am of coures refering to imaginary roll axis or roll centers, not the projected line deals we normally talk about.

Another $.02
Andy

[Z]

Originally posted by Storbeck:
Z-I am having trouble picturing what you are saying about the dumbell.

Andy,

Firstly, I agree with what you say about the momentary jacking forces. These cause (momentary) heaving or pitching of the body whenever the lateral forces at the tyres change, and these motions are the direct result of changes to tyreprint normal (vertical) loads. But these are only momentary effects, which also reverse themselves between beginning/end of the movement, as you have said.

What I was getting at with the "dumb-bell" is an effect that is constant during steady state cornering. I will try to explain.

Picture the car in "steady state" on the skid-pad. Or think of the car sitting on the outer edge of a merry-go-round, like some of the children's rides at the fairground. The car is fixed to the merry-go-round - no heaving/pitching/rolling/yawing... As the merry-go-round spins (or the car corners), what are the forces acting on the car? Well, a vertical gravitational force, and equal and opposite upward road-to-tyre forces, but we will ignore those for now (and aero drag, etc.). Also a horizontal "centrifugal" force at the car's CG that is directed radially outward from the central vertical axis of rotation, and an equal and opposite centripetal force at ground level. This is what gives the lateral load transfer. Any other forces? Yes, but not obvious! (Because so far we are only considering the "CG", but whenever a solid body rotates we must also consider its "mass distribution".)

Now imagine that the car's "mass distribution" is not horizontal, but it slopes down at the front. Ie picture the car with its nose on the ground and its rear high up in the air, so that its longitudinal principal axis is sloping down at front. Or picture the car's mass distribution as being simplified to just two half-masses, with the front half-mass low down, and the rear half-mass somewhat higher. This is the "dumb-bell" I was talking about. Note that the car is still in steady rotation about the vertical central axis (ie. it is still "fixed" to the edge of the merry-go-round). Also the car's longitudinal axis is tangent to the edge of the merry-go-round, so the central rotation axis is on a line that is perpendicular to the car's longitudinal X-axis at its CG. (Ooohhh, for a simple sketching facility!!!)

Now look in plan view at the centrifugal forces acting on each half-mass of the "dumb-bell". The force on the front half-mass is directed outwards and forwards relative to the car's axes. The force on the rear half-mass is directed outwards and rearwards. Ie the forces are not purely lateral, but are radial (ie. diverging) from the central axis of rotation!!!

So, because of the forwards component of centrifugal force low down on the front of the car, and the rearwards component of centrifugal force high up on the rear of the car, there is thus a nose-up/tail-down "inertial" pitching moment (couple) acting on the car! This inertial couple is resisted by changes to the front(-) and rear(+) vertical tyre loads.

(Catch my breath...) You can also work this out using Euler's equations and rough estimates of principal moments of inertia, etc. (This is quite simple - I was going to include it, but this post is already tooooo long! http://fsae.com/groupee_common/emoticons/icon_frown.gif)

Anyway, most "Mechanics" books have an example of aeroplane propellor blades, where they show that the "twisted" blade tries to untwist itself because of the centrifugal forces acting on its leading and trailing edges. Basically the same thing as above. You can also think about the car, tilted 45 degrees down at the front, spinning about a vertical axis passing through its CG.

If the "X" principal axis is close to horizontal, and the angular yaw velocity is small (larger radius corner), then the longitudinal load transfer is also very small (probably less than that due to aero drag, or a slight tail-out attitude). A car spinning after being hit in an accident will have a bigger "dynamic imbalance" of this type.

Hope this helps. http://fsae.com/groupee_common/emoticons/icon_smile.gif


Chris,

Denny posted his car's principal axes directions in the "Value of inertia of student car..." thread, in Dynamic Events section. His longitudinal X-axis only slopes 5mm/m from horizontal. He also has a sideways skew to this axis, so that might also cause some funny load transfers. Again, Euler's equations on "the back of an envelope" should tell if these are significant effects...

Z

(Edit: Added some more comments... Going away for a week, so hope the above is clear http://fsae.com/groupee_common/emoticons/icon_confused.gif)

[BFCoordinates]

DohertyWins!

I hope you realize what you're going to be doing ...

The tires generate forces on and moments about the vehicle, and you will have to resolve these forces/moments along the Body Fixed Coordinate system.

Now you could resolve them along the Inertial reference frame, but then your mass properties will vary with time. Now if you are Mr. Hamilton out in california, with your expensive computer numerical simulation, you may not mind your intertias dependance on time, but for me, I like them to be constant.

Quote DohertyWins!

"The above is consideration of the sprung mass only (as a rigid body)"

bpbpbp real bad assumption!

[GSpeedR]

Hahaha

I just got a call on my cellular telephone from Mr. Newton. He says that he and Mr. Euler won't help me solve these equations, he only sets them up. I also got a call from a friendly gentleman working at Maplesoft who claims he will be happy to provide me with a solution, but he refuses to help me set them up.

BFCoordinates: please chaneg your username to GackAttack immediately.

Everyone else: Sorry. We're losers. http://fsae.com/groupee_common/emoticons/icon_cool.gif