Force Based Roll Centers

[Erich Ohlde]

How are force based roll centers different from kinematic roll centers?

[Erich Ohlde]

How are force based roll centers different from kinematic roll centers?

[F1engineer]

If you calculate them correctly they are identical.

Most of the standard text books show a method of calculating the roll centre which is based on the intersections of lines in the planes of the wishbones (eg Milliken, Bastow). Several commercial suspension analysis programs use this method also. A roll centre calculated with this method is usually refered to a the "kinematic roll centre". Implicit in this method are various assumptions which may or may not be valid for a particular suspension. Unfortuanately the text books seldom explain what the assumptions are, so a mythology has grown up that the calculation is correct in all cases, and that there are two roll centres kinematic and force.

If you have a kinematic package you can calcuate the intantaneous centre directly, from the vertical and lateral velocities of the contact point, the angular velocity of the wheel about the longitudinal axis and the vertical and lateral position of the contact point. By comparing this with the standard text book calculations you will be able to see what the assumptions of that method are. You can validate by calculating the roll centre with a force based and comparing.

I suggest you look at the following aspects for an SLA suspension:

i) The pin joint which attaches the upright to wheel.
ii} The influence of the trackrod particuarly when it is not in the plane of a wishbone and is of a different length to the wishbones.
iii) The effect of wishbone inboard hinge lines which are not parallel to the car centre line in plan view.
iv) The effects of wishbone inboard hinge lines which are not horizontal in side view. (anti squat and anti dive)
v) The effects of castor, KPI, trail and offset when combined with the above.

If you analyse a SLA with the inboard wishbone hinge lines parallel to the car centre line. Zero Camber, KPA, Castor, Offset and Trail and the trackrod exactly in line, in front view, with the wishbone points, the calculations will all give the same result.

You can calculate the force based roll centre by building a fea model in strut and beam elements. When you have the calcs correct you will get the same results.

When calculate the IC from the contact point velocities, you will note that the calculation is not dependent of what sort of linkage you have. ie the calc is the same for SLA, Mac strut, 5 link, beam axle, mumford link or anything else you care to invent.

[ben]

The velocity of the contact patch gives the instantaneous centre of rotation of the wheel, and obviously that would be the approach to take rather than assuming lines drawn through 2D intersections.

The problem you then have is how this relates to the motion of the sprung mass and the load transfer when cornering. If a wheel has an instantaneous centre of rotation that isn't in plane with the track surface then there will be some lateral/vertical force coupling - i.e. a lateral force at the contact patch will create a vertical reaction force. The magnitude of these forces depends on the lateral force, which in turn determines the vertical forces.

The kinematic roll centre model doesn't model this coupling and that is probably it's main fault.

Ben

[F1engineer]

No, the roll centre defines the coupling. That is what it is! There is only one roll centre. You can calculate it by a force method or a kinematic method and if you do the calcs right you get the same answer.

For a linkage with one degree of freedom the resultant force at a point must be perpendicular to the velocity vector of that point or as the linkage moves there will be work done. Work = Force * Displacement in the direction of the force. If work is done it is not a degree of freedom.

When you do the calcs by the fea method above you will see that applying a lateral to the contact point gives an resulting vertical reaction and the force vector at the contact point is normal to the velocity vector of the contact point calculated by the kinematics.

[Brian Evans]

Bill Mitchell has updated his software to calculate force based roll centers. That strongly implies that kinematic isn't the same thing.

http://www.mitchellsoftware.com/ForceBasedRC_1.htm

Brian

[D J Yates]

My explanation of the force based roll centre:

A free body diagram will show that forces applied through the suspension will cause angular and linear acceleration of the sprung mass. The roll axis is simply the instanious axis about which the sprung mass is oscilatting (euler's theorum). To find this would require all the suspension forces, the roll angle and roll rate at any given time. As i'm only interested in the car's yaw rate, lateral acceleration and attitude at any given time - why would i want to know where the roll axis is if i already knew the roll angle!? I honestly can't see the point.

In short, calculation of the force roll centre requires more information than you are likely to have at the design stage and provides little/no useful information. The kinematic roll centre, although not entirely accurate, is a useful design tool.

[Marc Jaxa-Rozen]

SAE paper #983033 has a good example of an "integrated" approach to this, and it's pretty easy to implement. When you throw in the non-linearities and geometric characteristics, there's definitely a difference between the force-based approach and the textbook method with a typical FSAE geometry, but honestly, manufacturing tolerances, stiction, compliance, etc. probably have a much bigger impact...I wouldn't lose sleep over it.

[Frank]

"but honestly, manufacturing tolerances, stiction, compliance, etc. probably have a much bigger impact...I wouldn't lose sleep over it."


SO TRUE

[ben]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by F1engineer:
No, the roll centre defines the coupling. That is what it is! There is only one roll centre. You can calculate it by a force method or a kinematic method and if you do the calcs right you get the same answer.

For a linkage with one degree of freedom the resultant force at a point must be perpendicular to the velocity vector of that point or as the linkage moves there will be work done. Work = Force * Displacement in the direction of the force. If work is done it is not a degree of freedom.

When you do the calcs by the fea method above you will see that applying a lateral to the contact point gives an resulting vertical reaction and the force vector at the contact point is normal to the velocity vector of the contact point calculated by the kinematics. </div></BLOCKQUOTE>

The instant centre defines the coupling of each wheel, but the roll centre is determined by both, this means you need to know what the lateral force distribution is.

If 100% of the Fy comes from the outside tyre the thing is rotating about that CP. The centre of rotation will be different if 50% of the force comes from each tyre.

You need the lateral force distribution to determine the roll centre, but you need the roll centre to determine the lateral forces, it's not a closed-form solution, hence why the kinematic roll centre is still used.

Ben

[F1engineer]

Yes, you need to know the distribution of lateral loads. That why it makes no sense to talk about lateral migration of the roll centre.

However there is a far more significant effect on the front axle. When cornering you invariably have steering lock applied and that means that the front tyre lateral forces are no longer in a transverse plane.

[CMURacing - Prometheus]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Frank:
"but honestly, manufacturing tolerances, stiction, compliance, etc. probably have a much bigger impact...I wouldn't lose sleep over it."


SO TRUE </div></BLOCKQUOTE>

my apologies for diverging a bit, but...

does anyone take this into account when designing the suspension? for example, when i used Mitchell for our front suspension last semester, I knew the inboard (chassis) mounting points were difficult to get correct, so I tried to keep them as easy fractions to calculate. Then, since we tend to use CNC machnining for the uprights, I let them run off into the thousandths of an inch to get the characteristics I wanted.

thoughts?

[ben]

Thoughts?

If I could be bothered I'd do a tolerance analysis and look at how sensitive key parameters were to +- 1-5mm in any of the pickups. I believe the Lotus kinematics package has this functionality as standard.

F1engineer - Excellent point about the direction of the forces. Most force based models in the literature (The Clemson Nascar one being a good one) tend to calculate lateral/vertical and longitudinal/vertical force coupling separately using front and sideview instant centres.

I assume you would advocate a single coupling equation with the resultant in-plane force and the instant axis? Or just using ADAMS...

Ben

[Kevin Hayward]

Mike,

While at UWA I definitely took the sensitivity of manufacturing into consideration. However not in any formal manner. Rather you found the paramters that changed the result the most and either:

A) changed them to a region that was less sensitive. For example having longer rocker arms and allowing the slight increase in mass.

or

B) Have extra care with the manufacturing of the components involved. For example the UWA cars of the last 3 years have a relatively small steering arm at the upright. It is incredibly important that tolerances in the steering hardware is very tight to reduce the effects of this. (More so than other areas of the car).

This sort of process allowed us to prioritise the effort in manufacturing. Who cares if you chassis is a little twisted if the suspension points are in the right place.

We were working towards more formalised methods such as robust design methodologies but as with everything time to implement these properly was always short.

Kev

[Sisyphus]

I'm curious about how the geometry packages you guys use to compute the roll center and camber change treat tire sidewall stiffness.

I'd guess the stiffness of even the current low profile tires is low enough that the lateral load transfer across the chassis is enough to change the height of the hub carriers above the ground and therefore affect the camber. I think the tire stiffness was one of the measurements made in last years tire characterization project so you know what it is.

Has anyone studied this affect of tire deflection on camber?