Beam Axles - Front, Rear or both.

[Will M]

Originally posted by Z:
A few weeks ago on the "suspension for spool" thread I said I would post a sketch of a Twin Beam-Wing concept. I think this is a more suitable thread, so here it is (warts and all ).



(Edit: Made image bigger.)

Main features:

* This is an "aero above all" car. Everything else is there just to support the aero. I figure "drive on the ceiling" at less than maximum FSAE speeds (ie. DF=W at <100kph, (maybe <70kph?)). And more is possible!

* Aero is direct acting on the wheels, and easily adjustable for F/R balance via the flaps. Since wings are close to ground, and with wheels as skirts/end-plates, drag is low (no induced drag). The streamlined fuselage and wheel pods also lower drag for good economy.

* The aero centres of pressure are unlikely to be exactly above wheel axle lines, so some force acts on chassis through BJs causing some pitch/heave. This can be fixed by either; a) not worrying about it, b) reshaping the wings, or c) interconnecting the wings with two torsionally flexible spars running alongside the chassis and attached flexibly to the beams on their axle lines. Extending this last solution sideways gives a full width "live" undertray.


* Finally, a first year or "limited resource" team can do this car without the aero. Use a RE, B&S, or similar engine and you have a simple lightweight car that is quicker to build than the usual wishbones-and-pull/pushrods&rockers-everywhere cars. And, all other things equal, it will have high grip and benign handling because of soft springs with no camber change (not possible with normal independent suspensions).

Comments and criticisms welcome!

Z

Z,

With the softer springs you should see more travel and I estimate from your drawing that a 2cm travel will cause about 2.5 degrees for caster change in the wheels and angle of attack for the aero (assuming the front and rear aren't linked). You might only see that much travel under heavy braking or hitting a bump and it might not make a big difference but it is another design consideration I wanted to point out.

[mech5496]

How the hell did you figure that "2.5 degrees of caster change"?

[Will M]

mech5496,

Unless I am completely not understanding the idea (I am not a suspension guy really) this should be right. Also I got the 45cm from Z's drawing.

William

[Z]

Originally posted by Will M:
I got the 45cm from Z's drawing.

William,

Actually, it is 50cm (lower right of picture).

Aerofoil AoA will only change about half your figure under extreme braking (even with +/-2cm F&R), but regardless of AoA the downforce can be kept fairly constant with the right profiles (ie. maintain a constant gap to ground). If the two main BJs are closer to centre of wheelbase (in side-view), then less AoA and castor change during pitch. Also there is quite a lot of anti-dive/lift in the kinematics, which lessens pitch under braking.

But the main point here is that you do NOT want to do a lot of braking or accelerating. Fast cornering, and a "constant speed car", is best!

Also, the wings as shown are mainly for ease of construction. Just a "plywood" add-on to a simple beam-axle suspension suitable for a first year team. More advanced and powerful aero is hinted at in my quoted text in your first post.

Lastly, lots of castor change (+/-10+deg!) over bumps is NOT a problem. And FSAE tracks don't have bumps!

Z

[mech5496]

Actually you could have NO (or very limited) pitch under braking by designing a certain amount of anti-dive and using a dedicated pitch/heave "spring" and "damper" (a polymer puck could replace both), directly on the sliding mechanism, so it does not affect roll at all. What's more, what is so bad about a degree of caster change?!

[Will M]

I am actually a big fan of this car architecture, I'm just trying it for possible weak areas. The main problem I see with dynamic caster change is if it went from positive to negative or the other way around that could be disconcerting for the driver. Caster change is not bad, like bump-steer it is a knob you can turn but you do have to think about it.


Z,

Also. If you were building one of these how much adjust-ability would you add? If the geometry was locked in the beam could be very stiff and light... Maybe two sets one adjustable and then a second fixed one...

William

[Z]

William,

"How much adjustability?

Good question. I didn't want to put too much detail into the earlier posts, but I'll briefly cover this important issue now. What follows applies to teams that are fairly new to racing, which is pretty much all FSAE teams, and certainly any that might try beam-axles (because very few examples to "learn from" (ie. copy )).

The following also applies to any suspension type on smooth track circuit racing. So this is mainly about going fast around tarmac corners. Top of the list is most important, and less important further down.

Important Suspension Adjustments for Fast Cornering.
==============================================

1. Tyres - Type (carcass/compound), Size, Pressure, Rim Width.

2. Static Toe - to +/- one tenth degree.

3. Static Camber - to +/- one degree.

4. Front/Rear Roll Rates - ie. LLTD or ERMD (same things). Note Pitch/Heave rates are important for sprung-aero cars, but not considered in detail here.

5. Dampers - just enough to suppress resonant bouncing on above springs, or on the tyres.

6. Kinematics - RC heights, anti-pitch, camber recovery, etc.
~~~o0o~~~

Note that things like Ackermann and compliance are also very important in FSAE (in fact, close to top of list, depending on details), but will leave that for another time. Also a spectacular cock-up on something like Kinematics (say, severe rear bump toe-out) will push it to the top of list. And also not considering Z-bars (can be added later).

So from the above, and IMHO, the biggest gains come from lots of testing of different tyres, their hot pressures (anything from 0.5 bar (7psi) to 2+bar (30+psi) can be "optimal", depending on...), and also rim widths, which can make a big difference.

On the other hand, any kinematic issues can be covered by other adjustments (again, unless you truly stuff it up). A brief example is Formula Vee, which mandates Beetle suspension with ground level front RC and ~axle height rear RC, but corners as fast as any other similar single seater on same tyres (hint: high rear RC compensated by zero rear roll rate springing).
~~~o0o~~~

So for a beam-axle FSAE car I suggest the kinematics be non-adjustable, as in the sketch. That is, roll and pitch axes (strictly speaking, the beam's "cylindroid") as low as practical, which is just above floor level (to allow room for the brackets, bolts, etc.). (See note re: De-dion below.)

The spring-dampers can be direct acting as in sketch. LLTD adjusted by changing springs or, for fine adjustments, small changes to the angle or axle mounting points of the S-Ds might be used. Preferably do NOT use any ARBs, but if you must, then use only one (say, a stiff one at rear to compensate for a "spool" differential). Do not overcomplicate this! There are much bigger gains elsewhere.

That leaves the two big ones on the suspension front, namely static Toe and Camber angles.
~~~o0o~~~

FRONT AXLE - Static Toe is easily adjusted via the steering tie rods. I suggest building one structurally efficient beam, then adjusting Camber and Castor (less important) at the king-pin. This is an opportunity for some good detail design, but even a crude overweight design won't cause too much harm here (as long as it doesn't break!).

REAR AXLE - More options here.

Live Spool, as one tube wheel-to-wheel. Here Toe and Camber are fixed at zero, but it is important to make everything stiff enough.

Live Spool, as two half axles with spline/CV at centre. This is the reason for the four bearings (eg. "pillow blocks"?) in the sketch. Toe and Camber now easily adjusted by moving relative position of inner and outer bearings for each half-axle.

Live Differential. This is as above, but with any sort of beam mounted differential (eg. open/LSD). Again, Toe and Camber easily adjusted.

De-Dion, with chassis mounted differential of any type (open/LSD/spool). This option may make the final drive easier, since the diff location is fixed wrt engine. This requires CV'd half-shafts and stub axles at the beam ends of similar type to independent suspensions. I suggest the stub axle housings have some means of adjustment for Toe and Camber, if only to correct for manufacturing tolerances of the beam. These can then also be used for "tuning". Again, a good opportunity for quality detail design!

Important De-Dion note. The side-view kinematics, or anti-pitch, changes when the diff is chassis mounted. A layout as in the sketch, but with De-Dion, will have lots of pro-squat under power. This can be ignored with a low power engine, or a beam-centre bump rubber (aka "third-spring", or "lateral Z-bar", as mentioned by Harry above) can be used to limit squat (axle bounce) but allow roll. Alternatively, a different kinematic location can give anti-squat (higher pitch axis) while maintaining a low roll axis. This is a quite simple structural change, but will require a sketch to explain it properly...
~~~o0o~~~

I also discussed suspension adjustments on this old thread.

Z

[Charles Kaneb]

Z,

A couple things I've run into while trying to convince my team of the merits of a car with suspension other than A-arms all round:

1. With the required cockpit volume, side impact intrusion prevention, front and rear roll hoops, and supports for said roll hoops, you end up with a very torsionally stiff center section of the car. I'll mail a dollar to anyone with results showing a currently legal car with end-to-end torsional stiffness of less than 800 lbs*ft/degree. Any significant torsional deflection would have to be concentrated in a very small area near the back of the car. At this point, you'd have committed to weld in a nonadjustable twistable element with unknown damping properties that, if karting experience shows anything, will gradually change over a couple dozen hours of racing. Even if you figure out how to get good properties from this, there's nothing that says a tech inspector won't require you to weld in some supporting bars at competition.

2. I haven't had the time to draw up and do the stress analysis for a preliminary design of a beam axle rear end. I do not know whether it will save weight, or how much. The heaviest components in an FSAE suspension right now are the axle cups, the axle bearings, and the spring-damper units. If a beam axle rear end is not set up to be extremely stiff in roll, your sprocket will tip about the X-axis, and motorcycle chains or synchronous belts do not tolerate this well at all. A De Dion rear end is at least as complex as any double wishbone setup.

3. Vehicles which are soft around the Y-axis (twist mode) are used in many applications. Outside of racing and certain military off-road vehicles, there are very few vehicles where the main differences between success and failure are peak tire grip and controllability near peak tire grip.

My main experience with operation of a vehicle with a soft twist mode near its dynamic limits was on a driver-training day for garbage-truck drivers. The garbage truck consisted of a torsionally flexible twin-rail chassis with a rigidly attached cab, above which was "floated" a garbage compactor/storage box on flexible mounts. The truck entered a fairly tight, constant radius 180 degree turn, at a speed such that the tires squealed slightly. The chassis deflected about the Y-axis, storing up strain energy and keeping the inside rear tires on the ground. So far so good. Then the corner ended. The driver straightened the wheel. The chassis released its stored energy. The compactor box was tossed several inches in the air and landed in a slightly skewed orientation on the chassis. Meanwhile the rest of the truck wobbled back and forth...

4. Almost every chassis rules change since the start of FSAE has been anti-kart; in addition, up to 1/5 of the team score is in a design event with judges who are unlikely to have experience with design and optimization of karts. Just to get this out of the way, a kart with a 450cc motocross engine and a working vacuum traction system would absolutely wipe the floor with every FSAE car ever made. First, we're required to have some form of "working" suspension. Second, we're required to have a reasonably torsionally-stiff chassis. Third, we are required to have wheels that are at least 8" diameter (and no remotely competitive tire smaller than 10" exists); the resulting 18"+ tire diameter means that the suspension system must handle a large Y-bending moment during cornering and a large X-bending moment under braking. It will be lighter and cheaper to handle these moments with a small amount of material far away from the centerline of the axle than wih a large amount of material near it. Finally, the aerodynamic downforce generating components we're allowed to have are not terribly sensitive to roll or twist - more to pitch and heave.



The advantages of a fewer-moving-parts suspension have been heavily cut back by practical and rules constraints, while the risks of moving to one include possible disqualification, rules changes which would ban the car for next year and make what we learned about how to make one of these cars handle irrelevant, and a very real possibilty of a design-event score that's so bad it would wipe out any dynamic event gains this thing could make. When we build a car with four-wheel independent suspension by A-arms, with constant-rate passive springs and passive dampers, we are not simply polishing a turd - we are selecting a design that has proven to be at least OK at its job and will not be banned or drop-kicked in design.

[Z]

Charles,

Thanks for comments. Here are some brief responses.
~~~o0o~~~

1. The mandatory chassis safety parts (roll-hoops, side impact,...) form most of the chassis for the Twin-Beam concept. No more torsional stiffness is needed, because beams allow soft springs. I would not suggest adding any extra torsional "softness" to the chassis, again, because the soft corner springs already give enough softness. The advantages of longitudinal Z-bars is that they can give a completely soft twist-mode, even with a stiff chassis and stiff roll-mode, this latter being necessary with wishbones with small camber gain (long FVSA). Also the Z-bars make handling adjustments (ERMD) very easy.
~~~

2. I think the possibility for weight reduction by using beams over wishbones comes mainly from the much simpler chassis with its smaller number of hard points.

You say "A De Dion rear end is at least as complex as any double wishbone setup."

I have to disagree. I reckon a detailed study of a De Dion would have it roughly half as "complex" (time to make, etc.) as double wishbones. Likewise, there are many other simple suspensions that are almost never considered. The "proof" of this is that almost all FSAE teams use the completely unnecessary push/pullrods-&-rockers, so they are clearly not concerned by useless complexity, and make no attempt at "simplicity". Well, other than talking about "KISS".
~~~

3. "Outside of racing and certain military off-road vehicles, there are very few vehicles where the main differences between success and failure are peak tire grip and controllability near peak tire grip."

Well, how about every farm tractor ever built.... and all the earthmoving machines....? All of these rely on massive grip, so almost always have a completely soft twist mode. (BTW, to be successful in motorsport you just have to keep your sponsors happy, and back of the grid is no disadvantage.)

"The garbage truck consisted of a torsionally flexible twin-rail chassis ... The chassis released its stored energy ... the rest of the truck wobbled back and forth..."

And therein lies the problem with providing a soft twist mode with a spring capable of storing a lot of energy. Better is completely soft, like tractors, forklifts, ride-on lawnmowers, etc., etc..
~~~

4. "...while the risks of moving to [a fewer-moving parts suspension] include possible disqualification, rules changes which would ban the car..."

Any comments from someone on the Rules committee???

"When we build [the standard suspension] we are not simply polishing a turd - we are selecting a design that has proven to be at least OK at its job and will not be banned or drop-kicked in design."

The sad part is that a "NO suspension" car would also be "OK at its job" in FSAE, but a lot easier and cheaper to build, and probably faster because lighter, more testing time, etc.

The really sad part is that you really are all "Polishing A Turd". And in building the "PAT" car very few students learn how real suspensions work, because real suspensions have to cope with real roads which have real bumps on them, whereas FSAE tracks are unrealistically smooth.

Z

[Will M]

The debate that a go-kart is better fitted for an FSAE track than an FSAE car is has been going on at least since 5 years ago when I started reading this forum and probably stated 15 years ago. So there have been about 50 to 200 competitions since the debate started. We are not politicians doomed to argue about which century old econ book is best, we can objectively prove this one way or the other. Surely at least one FSAE official owns a decent shifter car. The test is simple, before each dynamic event they take their kart out and put down a time. This would give an objective comparison and would be a good way of checking track conditions. Getting decent historical data for FSAE is a real pain (the event book has car data but no results, and the online results have no car data). This would give at least one bench mark, and could be used to compare events in different years and locations to each other.

William