Suspension Design

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@ Warpspeed: How would steering the rear wheels change the rear slip angles on a skidpad?

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Now that is a really interesting question.

Individual wheel steer angles should probably not be thought of as being just relative to the chassis, but referenced to the steer angles of all the other wheels on the car....

Seat of the pants experience suggests that any sudden changes to steer angles at the back, even significant lateral compliance at the back, can produce some very unstable dynamic handling. Even though steady state skid pad testing may seem fine.

Having the rear wheels always pointing rigidly dead ahead seems to be a fundamental requirement for fast stable transient response to steering input, as well as straight line stability.

Once you have that, a bit of tweaking of the roll axis inclination can put the icing on the cake.

Every time I have had rear wheels flapping about, there have been huge wide eyed pants wetting problems for the driver that don't go away.

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Originally posted by Owen Thomas:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"> I am still trying to get my head around the concept of how steering the rear wheels will get you around a skid pad any faster.

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Not sure if rhetorical question. Regardless, steering the rear wheels in the opposite direction of the fronts generates an opposite slip angle, which generates (outwards) lateral force. Inward lateral force at front + outward lateral force at rear = larger yaw couple (than without 4WS). Larger yaw couple = larger yaw rate = faster turning. Faster turning means you can have a larger tangential velocity (aka speed) to get around the same radius corner.
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A correction here: larger yaw couple = larger yaw acceleration (alpha) = faster turn in. There is a discussion on how greater yaw acceleration can reduce lap times in this thread:
http://fsae.com/eve/forums/a/t...7348/m/824105905/p/9

I can think of three ways that 4 wheel steer may improve skid-pad times:

1. The skid pad is taken below the tangent speed (correct me if I’m wrong), so the car will take the corner with the front axle further from the inside of the corner than the rear axle. In other words the car will corner with a nose out attitude below the tangent speed, and a tail out attitude above it. This means the centre of mass must travel on a larger radius to avoid clipping cones with the inside rear wheel than it would need to if it could travel at the tangent speed.

Steering the rear wheels in the opposite direction to the fronts can reduce or eliminate the nose out attitude of the car, allowing the centre of mass take a tighter radius without clipping cones. For the same lateral acceleration a smaller radius will give a higher yaw rate (omega) than a larger one, meaning the car will complete a lap of the skid pad quicker (skid pad lap is 360 degrees).

2. Skid pad should be close to pure steady-state cornering because the first lap in each direction (where the yaw rate will be established) is not timed. This means the car is undergoing lateral acceleration only; and as such requires the resultant force acting at the centre of mass to point towards the centre of the turn, with no resultant yaw couple.

When the front wheels are steered a component of the force from the front tyres now acts longitudinally, and does not contribute to the lateral acceleration.
By steering the rear wheels in the opposite direction to the fronts; the required steer angle on the fronts will be reduced. The component of the force at each tyre that acts laterally is related to the cosine of the steered angle; which means that the amount of lateral force lost by steering the rear wheels is less than the amount gained by reduced steering angle of the fronts. The result is the car will be able to achieve higher steady-state lateral acceleration with four wheel steering than without.

3. Lastly steering the rear wheels allows for dynamic toe adjustment (aka Ackerman) to be applied to the rear wheels as well as the fronts. This may enable a closer to ideal slip angle to be achieved on the inside rear tyre.

This is mainly me thinking out loud, so corrections/criticism is welcome.

Excellent reply nowhere fast. If we agree that skidpad is close to being a steady-state event then, to summarize what you said, the primary effect of rear steer is to adjust the vehicle sideslip angle. You have mentioned several follow-on effects.

Warpspeed, this is a good observation and the reason design judges frown upon (uncontrolled) rear toe compliance:

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Seat of the pants experience suggests that any sudden changes to steer angles at the back, even significant lateral compliance at the back, can produce some very unstable dynamic handling. Even though steady state skid pad testing may seem fine.

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Once we're talking about transients the use of rear steer becomes very "interesting". "Good" or "bad" would depend on how it is implemented.

Owen Thomas: One way to think about the interaction between tires making lateral force and tires making yaw moment is to study the Milliken Moment Method diagrams in Chapter 8 of RCVD. Keep in mind that at steady-state the yaw moment on the vehicle must be zero. Thus, the relative amount of lateral force each end of the vehicle must contribute is dominated by the yaw moment requirement. Of course there are other contributors to yaw moment besides lateral force, but the relationship between the lateral forces, the fore/aft CG location and the yaw moment is a great starting point.

Axel,

"Take this for example: The Ford twin I-beam.
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What you have here is a swing arm with a rather wide [front-view] instant center. If you were to design double wishbone to hit these same instant centers on the same chassis, your arms, while there would be 2x the number, would be about .25 the length. I would say that the size and packaging would be a tip towards the wishbone... "

It is indeed the "packaging" advantage that makes the double-wishbone so common on production cars. They were first developed so that the mid-front engine could be pushed further forwards between the two front wheels, thus making the whole car more space efficient (bigger passenger space in smaller envelope).

BTW, the Ford twin I-beam is what I call a Semi-Leading Swing-Arm. Its pivot axis is about 30 degrees off lateral, passing through the ends of the I-beam and torque-reaction-arm. I will try to cover these this week (but silly season now in full swing!).
~o0o~

"Now, one thing that I'm going to throw out there for consideration ... is the "Jacob's Ladder""

The Jacob's Ladder, Watt's Linkage, and even the SLA Linkage (in front-view), are all variations of similar "planar 4-bar" linkages. That is, they all have a "frame" (link 0) connected to two straight links (links 1 and 3), which in turn are connected to the centre link (link 2). These linkages are useful because they can all give approximately straight line motion at a certain point on their centre link.

Move to 3-D linkages and it is possible to get exact straight line motion in a given plane. An example is the "scissor" linkage that controls the steering of the sliding-pillar suspension on aeroplane nose wheels. This "scissor" linkage is a good option for controlling lateral motion of beam-axles.
~~~~~~~~~~o0o~~~~~~~~~~

Tony,

"With many (most?) other front suspension designs, the bump steer problem may be far from simple to solve satisfactorily."

IMO, bump-steer, front or rear, is an easily solved problem with most supension types (in FSAE). Assuming you are using a normal toe-link (rather than something more exotic), the simple solution is to start with a long toe-link (preferably starting near car centreline, so ~60 cm long), then attach to a long steer-arm (ie. distance on upright from steer-axis to toe-link BJ at least ~10 cm long). If the ends of the toe-link are at the right heights (which should be adjustable), then the bump-steer for the +/- 2.5 cm suspension travel should be small enough to be unnoticeable.

BTW, the above Ford twin I-beams have criminally negligent amounts of bump-steer, all through attrociously bad design that could have been easily fixed! Many rollovers!!! http://fsae.com/groupee_common/emoti...n_rolleyes.gif
~o0o~

"I am still trying to get my head around the concept of how steering the rear wheels will get you around a skid pad any faster."

This already covered by Ed and Nathan. I will add to Nathan's list that rear counter-steer will give larger body side-slip angle, which could give a significant aero sideforce, especially if huge wing endplates are used.

To restress the main point of rear counter-steer, it is to increase YAW ACCELERATION. With normal front-only steer it is only the front wheels that exert a force that yaws the car. Counter-steering the rear wheels allows them to exert a similar yawing force, doubling the potential yaw acceleration. The tricky part is to control that yaw acceleration so it doesn't run away on you. Below is how I described it on the 4 Wheel Steer thread.

"If you watch nature documentaries you see the big cats using "active rear steer" when they chase their dinner. The rear briefly steers out [counter-steers] on corner entry (all in one big step), then immediately steers (or pushes) inward [= same steer]. (The tail also swings around for "active yaw and roll control".) Downhill ski racers also "hop" the rear of the skis outward on corner entry. But both of these have extremely capable active control systems!"

That is, a very brief period of rear counter-steer to get the right yaw velocity, then immediately switch to rear-straight-ahead (or even same-steer) so the rear exerts the necessary centripetal cornering force.

Z

Z, I disagree with bump steer being a simple problem.

With crossed I beams, both tie rods would need to be made the same lengths as the I beams, and these long tie rods would also need to cross over.
Not impossible, but not exactly a neat solution.

While I agree, longer steering arms would tend to make the steering less sensitive to any bump steer errors arising from the front view SLA motions.
it also magnifies the bump steer errors created by caster change introduced by any anti dive.

As the front upright tilts with changing caster, the steering arm and relative outer steering ball joint height changes, and it does not then follow the simple arc the tie rod end is constrained to follow.

Many very simple suspensions look good, until you start seriously thinking about bump steer.
In many cases that simple suspension may need a much more complex steering linkage which kind of defeats the initial purpose.

The best practical steering solution for a beam front axle is probably to bolt the steering rack direct onto the beam. That has a lot going for it for both simplicity and pretty good geometry, and should not be underestimated.

If I had do design and build a very simple car ultra quickly, with extremely limited resources, that is how I would very likely go about it.

By the time you add up all the unsprung weight that MUST be there, the added extra weight of a light weight steering rack would be negligible.

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Originally posted by Warpspeed:
I disagree with bump steer being a simple problem.

With crossed I beams, both tie rods would need to be made the same lengths as the I beams, and these long tie rods would also need to cross over..

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Tony,

No, no, no...

In plan-view each I-beam has a longitudinal "torque-arm" going backward from just inboard of the wheel to the chassis rail (ie. to about 0.6 m behind axle line). The screw-axis for the wheel passes through the I-beam and torque-arm chassis attachment bushes, so about 30 degrees back from lateral. Being a "Swing-Arm", the I-beam's screw pitch is zero (ie. it is a revolute joint = simple hinge).

For zero bump steer the steering tie-rod's inner BJ can lie anywhere on the screw-axis. A convenient place is close to the intersection point of the two front wheel's screw-axes, namely close to the centreline of the vehicle and about 0.3 m behind axle line. A steering linkage similar to most latter 1900 US double-wishbone cars would be suitable (ie. no more complicated than any other suspension type).

BTW, Ford used a slightly simpler steering linkage that steered both wheels towards the driver's side whenever one wheel moved up and the other down. Lots of rollovers of short wheelbase F100's on righthand corners here in Oz. Mine had a long wheelbase, but even so it managed to fall over one night (though it was "tired and emotional"...).

In FSAE, I reckon a team has to make a spectacular design cock-up to get their bump-steer wrong. However, I accept that this does happen. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

(PS. R&P-on-the-beam gives a small amount of roll understeer. For the minimal roll angles in FSAE this is not a problem.)

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Originally posted by nowhere fast:

2. Skid pad should be close to pure steady-state cornering because the first lap in each direction (where the yaw rate will be established) is not timed. This means the car is undergoing lateral acceleration only; and as such requires the resultant force acting at the centre of mass to point towards the centre of the turn, with no resultant yaw couple.

When the front wheels are steered a component of the force from the front tyres now acts longitudinally, and does not contribute to the lateral acceleration.
By steering the rear wheels in the opposite direction to the fronts; the required steer angle on the fronts will be reduced. The component of the force at each tyre that acts laterally is related to the cosine of the steered angle; which means that the amount of lateral force lost by steering the rear wheels is less than the amount gained by reduced steering angle of the fronts. The result is the car will be able to achieve higher steady-state lateral acceleration with four wheel steering than without.

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This makes sense regarding tire force vectors relative to the chassis-fixed coordinate system. However, once we have added (opposite) rear steer and the vehicle again reaches a steady-state condition, it will have a larger magnitude of body yaw relative to the CG heading. Have the tire force vectors changed relative to the turn center (or, equally, relative to the vehicle CG heading) compared to the front-steer less-yawed vehicle?

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Originally posted by Z:In plan-view each I-beam has a longitudinal "torque-arm" going backward from just inboard of the wheel to the chassis rail (ie. to about 0.6 m behind axle line). The screw-axis for the wheel passes through the I-beam and torque-arm chassis attachment bushes, so about 30 degrees back from lateral. Being a "Swing-Arm", the I-beam's screw pitch is zero (ie. it is a revolute joint = simple hinge).

For zero bump steer the steering tie-rod's inner BJ can lie anywhere on the screw-axis. A convenient place is close to the intersection point of the two front wheel's screw-axes, namely close to the centreline of the vehicle and about 0.3 m behind axle line. A steering linkage similar to most latter 1900 US double-wishbone cars would be suitable (ie. no more complicated than any other suspension type).

BTW, Ford used a slightly simpler steering linkage that steered both wheels towards the driver's side whenever one wheel moved up and the other down. Lots of rollovers of short wheelbase F100's on righthand corners here in Oz. Mine had a long wheelbase, but even so it managed to fall over one night (though it was "tired and emotional"...).

In FSAE, I reckon a team has to make a spectacular design cock-up to get their bump-steer wrong. However, I accept that this does happen. http://fsae.com/groupee_common/emoticons/icon_smile.gif

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To have a substantial amount of bump steer in an FSAE car's amount of wheel travel, you're right there. Getting it as low as possible however is a fun thing to keep the suspension designers busy and out of the manufacturing guys hair...

As for the twin I-beam, as my avatar shows, I have the earliest iteration of said suspension (1966 F100) and I never honestly noticed the bump steer until I got to college (never really thought a whole lot about suspensions until then) and then I only ever notice it when I first jump back into it for the summer. However, you're correct, and not just on bump steer. The camber change of these is also criminal (same qualm with swing arms, but that discussion is upcoming still...)


For something that was made for 30+ years with no design changes to really speak of, there aren't many good pictures out there of this setup (as of 84, still no swaybar. As of mid 90's, still criminal bump steer induced roll over). Here's a shot for those unfamiliar:

http://1.bp.blogspot.com/_UeLVY2Znz-...0/IMG_3190.JPG

Now, lets add in the screw axes:

http://img.gawkerassets.com/img/187x...g/original.jpg

Here, you can see the point that Z is referring to (If I'm understanding correctly) and you can see where the bump steer comes from. However, this is pretty significantly behind the centerline of the axle, and it is in the center of the chassis. Not sure how exactly you'd package your steering box in the center of the chassis, especially with an engine there.

That is exactly what I was referring to AR.

For it to work properly, a central steering box would have to be located about in the middle of the sump where your two red lines cross.

To move the inner ends of the steering tie rods forward to a much more practical location, the tie rods must be both much longer and cross over.

Just for clarification, rear wheel steer (and 4 wheel steer has NO effect on max lateral capability. It (obviously) thus has NO effect on the vehicle's understeer gradient. Simply stated: Only effects directly or indirectly related to cornering force dependency affect understeer, hence no effect on lateral capability. Knowledgeable readers should recall that you remove the Ackerman gradient from the net lateral acceleration gain to calculate understeer. If you have rear steer (only) or in addition too, its effect must be factored into this calculation. Since its driver activated (an input) and not a response (output) it's not a playa by definition.