Steering Geometry Question

[Ran]

Hello all,
My name is Ran and I've never actually posted although I’ve been following closely for the last 4 years or so
My question is this: In a lot of high caster applications like karts or cross karts I’ve noticed a phenomenon of self aligning steering, but only to a certain steering angle. I mean that if you turn the steering it would have a tendency to return but only up to a certain angle (I don’t mean the hysteresis effect of the tire). This can also be felt while the vehicle is stationary. For instance, turn a kart steering wheel 15 degrees and you feel a torque resisting, but turn it all the way and the aforementioned torque changes direction. I.e the torque from the steering wheel now wants to keep the wheels turned. I’ve noticed this in a few road cars as well and have been trying to find the reason for it. As it seems the tire aligning moment isn’t changing direction yet as I’m talking about a situation where you’re far from the limits of adhesion. So if I understand correctly maybe this is caused due to the car’s CG going down with the high steering angle, caused by the fact the car changes height because of the steering axis inclination WR to the YZ plane? Has the car has now found a lower equilibrium WR to the ground (hope this is understood correctly)?

Thanks guys.

[Jersey Tom]

The stationary case should be pretty simple, no? There will be some compliance in the whole steering system, and some torque spring effect in the tire itself - for small angles it will spring right back. As you put more steer into it you're just dragging and scrubbing the rubber against the ground - it will resist this but then will stay where you put it.

Dynamic / high speed rolling is quite a bit different, but one thing at a time.

Also not sure what you mean by "the hysteresis effect of the tire."

[Ran]

Thanks for the reply.
What you said is what I meant by "hysteresis effect". That being the scrubbed tire not returning to the straight ahead position.
I'm talking about a different phenomena, the steering not returning but "wanting" to turn more. If you turn a kart wheel a certain (large) angle not only will the steering not return a small angle, it will actually turn more.
Hope this is clearer.

[Tommy Cookers]

..... So if I understand correctly maybe this is caused due to the car’s CG going down with the high steering angle, caused by the fact the car changes height because of the steering axis inclination WR to the YZ plane? Has the car has now found a lower equilibrium WR to the ground (hope this is understood correctly)?.

the manufacturers want it a cartain way (natural stability not increasing with steering angle ie at lower speeds/greater angles)
this is achieved by a steering geometry where the steering axis is chosen to intersect the wheel rolling radius above its mid point
this geometry is anyway convenient in other ways (offsets etc)

(CG height change relative to the steering axis is the key ? with other steering geometries this relative CG ht can even increase)

though the effect discussed is desirable, with small wheel diameters it cannot be sustained over the full range of steering angles
as I think you are finding
such geometry works better with relatively large wheels ie in motorcycles
(small or large wheel diameters meaning small or large relative to the necessary, rather fixed, mechanical trail)

[Ran]

By that do you mean the tire's Fz has now moved enough (because of caster effects moving the contact patch center of pressure) enough to create a torque arm in the opposite direction compared to small steering angles?
Does that produce a situation which wishes to turn the wheels into the corner?

[Tim.Wright]

I think that is most likely. Bear in mind that the steering geometry is largely designed to have the tyre lateral force and aligning moment giving you the steering torque. Without them, it could be reasonable that at higher angles some of he gravitational component of the steering torques reduces. I'd be a bit surprised if it really goes negative though.

[garygph]

IIRC on a kart you must take care to not ignore the toe change. There is a point where if you turn a little more the toe dramatically changes to more toe out and the inside tyre feels like its being dragged along. Maybe you have witnessed that happening and thought it had something to do with the caster not noticing the toe change?

[Jersey Tom]

There are definitely ways of getting the tires to a condition where the natural "self aligning torque" is reversed (and wants to pull in the direction of the force rather than oppose it). Magnitude can be pretty big.

No magic to it either. Though I'd be very surprised to be seeing that in road cars other than certain times driving over uneven roads, the steering wanting to follow some of the irregularities. What I'm thinking of is more pure flat road stuff.

[Ran]

This is not a kart-only condition. I've seen this in many regular cars (Pug 106 for instance) and it happens even while stationary so toe has a negligible effect as the tire is not rolling and has no real slip angle.

[Ran]

There are definitely ways of getting the tires to a condition where the natural "self aligning torque" is reversed (and wants to pull in the direction of the force rather than oppose it). Magnitude can be pretty big.

No magic to it either. Though I'd be very surprised to be seeing that in road cars other than certain times driving over uneven roads, the steering wanting to follow some of the irregularities. What I'm thinking of is more pure flat road stuff.

I am familiar with this condition in high load situations close to the tire's peak Fy. Are you referring to this or to a geometric thing as Tim said?

[Greg Locock]

It certainly does occur on road cars, including BMWs.

The static case is the easiest to think about, it has a lot to do with front view geometry, and side view geometry. The simple cure is to increase mechanical trail. Effectively the wheel flops over to full lock. These days you are less likely to see it because with EPAS we can always motor the wheel;s back to straight ahead if there is no driver input.


Dynamically it is very easy to get torque out of phase with yaw velocity at non zero frequencies. An interesting test is to drive at a moderate latacc and then wiggle the wheel, then plot SWT vs yaw velocity. We'd like them to be in phase, roughly, and certainly not in antiphase.

[Jersey Tom]

Are you referring to this or to a geometric thing as Tim said?

Neither

Dynamically it is very easy to get torque out of phase with yaw velocity at non zero frequencies. An interesting test is to drive at a moderate latacc and then wiggle the wheel, then plot SWT vs yaw velocity. We'd like them to be in phase, roughly, and certainly not in antiphase.

Not difficult to reverse at zero frequency either...

[Ran]

It certainly does occur on road cars, including BMWs.

The static case is the easiest to think about, it has a lot to do with front view geometry, and side view geometry. The simple cure is to increase mechanical trail. Effectively the wheel flops over to full lock. These days you are less likely to see it because with EPAS we can always motor the wheel;s back to straight ahead if there is no driver input.


Dynamically it is very easy to get torque out of phase with yaw velocity at non zero frequencies. An interesting test is to drive at a moderate latacc and then wiggle the wheel, then plot SWT vs yaw velocity. We'd like them to be in phase, roughly, and certainly not in antiphase.

Could you explain the mechanics behind these two cases?
What causes the wheel to flop over? Is it the Fz line of action moving around due to steering axis inclination and location as said before?

In the dynamic case, what would affect the tires' phase? Is this primarily caused by tire construction and design?

[Tim.Wright]

In a dynamic case, the steering torque is not just a function of the tyre force and aligning moment but also the kingpin geometry. BMW have (I believe its still currently the case) a virtual lower arm made up of 2 links instead a single A-arm. As a result their caster trail and scrub radius change a lot with steering angle.

I don't know for sure, but I suspect that this is partly responsible for the "particular" feeling of the BMW steering.

[Greg Locock]

We first noticed both these effects on a dual ball joint arm suspension based on a BMW, which as it turned out had the same problems but worse.

Yes, with dual ball joints the motion of the virtual steering axis relative to the contact patch is crucial for low speed returnability. Jacking can be used to help as well, ie castor. We changed MT to amplify the castor jacking effect.

The high frequency dynamic effect is not easy to explain, we just tried a few different things that were under our control until it went away.

I'm not convinced the two are necessarily directly connected, the SWA used in the dynamic test wasn't enough to really move the steering axis.