Suspension Design

[Z]

Way back in December 2012 (page 9) I wrote a rather long post describing the various types of Swing-Arm suspensions. There I said that Semi-Leading&Trailing Swing-Arms are my second favourite type of suspension for FSAE. They don't have quite as good overall properties as Beam-Axles, but they are perhaps the structurally simplest solution, so in that way are well suited to FSAE.

So here is a sketch of how I would do Semi-Leading&Trailing Swing-Arms.



Some comments (much of this also covered in the above link).
~~~~~o0o~~~~~

1. KINEMATICS - These Swing-Arms have a short "Front-View-Swing-Arm" that gives "100% Camber Compensation". This means there is no wheel camber change during cornering, regardless of any amount of body roll. The penalty of short FVSAs (not seen on Beam-Axles! ) is that the wheels will have camber change when the body pitches due to accelerating or braking forces, or heaves due to vertical forces from sprung aero or big bumps. FSAE is mostly about lateral cornering forces, with lesser amounts of longitudinal or vertical forces, so this type of front-view kinematics (for independent suspensions) is preferable (ie. better than very long FVSAs). See also Geoff's and other posts on previous pages.

The side-view kinematics have the front wheels' longitudinal n-lines rising slightly up-to-rear, so giving a small amount of anti-dive. At the rear the longitudinal n-lines are such that there is some anti-lift under braking for outboard brakes, but with inboard brakes there is a little pro-lift, and with inboard drive there is a little pro-squat. (Hint: Draw side-view n-lines in the plane of the wheel, and see that they intersect a little above ground near the front wheel. Note that the n-lines for a Swing-Arm are ALL the straight lines in 3-D space that intersect the SA's pivot-axis (= its ISA).)

This side-view behaviour is generally OK for FSAE type racing. The pro-squat is not suited to drag-racing (where large anti-squat is better for good launch), but in FSAE such issues are adequately fixed with Anti-Axle-Bounce springs (see below).

At the front wheels bump-steer is mainly determined by steering tie-rod position (its centreline should pass through, or close to, the SA pivot-axis). Note that a little bump-steer at the front is not too bad, because the driver can correct for it. At the rear the Swing-Arm pivot-axes (ie. their ISAs) should be close to horizontal to minimise bump-steer.

Sloping the rear pivot-axes up-to-front gives bump-toe-out, and so roll-oversteer. This is generally bad for passenger cars (car spins out of corner), but may be good for an FSAE car that understeers through slaloms and hairpins. Sloping the pivot-axes down-to-front gives bump-toe-in and roll-understeer. I suggest it best to keep the pivot-axes horizontal, and then fine tune with static-toe adjustments (see below).
~~~~~o0o~~~~~

2. STRUCTURE - The chassis structure required for these S-L/T Swing-Arms is about as simple as possible. I see this as their biggest advantage. All the SA-to-chassis attachments (BJs or bushes) are at the perimeter of the floor. These attachments are at the centreline of the front bulkhead (where strong structure is required for the pedals and IA), at either side of the front and main roll hoops (which are required by the Rules), and under the drivetrain/diff (which must also be strong, least the engine fall out).

A flat floor can join all these points, and this is well suited to carrying the mainly horizontal loads from the SAs. Having all these attachments in the flat floor plane also simplifies jigging and manufacture of the chassis. All this major structure is at the lowest possible part of the chassis, so giving a lowest possible CG. The vertical loads from the wheelprints, which are carried mainly by the spring/dampers, can be fed from the Swing-Arms to the chassis by any convenient path (more below).

In the sketch the structure of the Swing-Arms themselves is a hollow sheet-steel fabrication. IMO this is easy technology to learn, can be done with simple tools, and gives the best strength and stiffness-to-mass properties. Thicker aluminium sheet could also be used, or carbonfibre if you really like the smell, sticky fingers, and extra time and cost.

Importantly, ALL FOUR SWING-ARMS ARE IDENTICAL. This means only one jig is required and fewer spares needed (eg. only have one spare, and it can replace any corner). There are important "Production" advantages here. Namely, once you figure out how to make one good one (ie. which welds to do first, where to rest your elbow while welding, etc.), you can then produce high quality items at high speed.

The two rear "uprights" are also identical, as are the front "upright/king-pins", and all axles and bearings are very similar (for lower spares count), but some parts of the front steering are different (too many funny angles! ).
~~~~~o0o~~~~~

3. SPRINGING - Given that suspension is NOT a very important performance factor in FSAE (rigidly sprung cars have won), a very simple spring-at-each-corner is shown, because it will do. So a conventional spring-damper is drawn at each corner, which feeds its loads into any convenient point on the chassis. These dampers have a Motion Ratio of about 0.6+ (damper/wheelprint movement). This is more than enough for lightweight FSAE cars, and the supposedly magical MR=1 is NOT necessary. In fact, I have shown the spring-dampers neatly tucked away because there is more to be gained from good aero flows than silly MRs!

As noted above, the main disadvantage of these types of Swing-Arms is excessive wheel camber change during heave or pitch motions of the car. The easiest solution is to fit Anti-Axle-Bounce springs (these covered extensively in other posts). These "lateral Z-bars" are essentially the same as the "third-springs" used on many modern aero racecars.

I would possibly implement AAB springs as lateral centre-pivot-leaf-springs (see "Z-Bar" sketch somewhere), mainly for neat packaging and low CG. Perhaps go to an Archery store for inspiration (ie. a lightweight and stiff centre section with the pivot, and lightweight flexible fibreglass leafs at the ends). Zero-droop+rising-rate-in-bounce is also good, and easily done with this type of spring. Other options also possible...

If you use AAB springs as above, then these should carry most of the weight of the car (ie. they control pitch and heave). This way the corner springs really only have to carry the roll forces, and since body roll doesn't affect wheel camber angle, the corner springs can be quite soft. This, in turn, means that the chassis is subject to only low torsional loads, and thus high torsional stiffness is less important. Furthermore, the soft corner springs give the whole car a softish Twist-mode, which is a good thing if the track has any undulations.

Of course, longitudinal Z-bars can also be fitted, giving a completely soft Twist-mode, and thus very predictable and easily adjusted handling balance. (Might have to do another sketch of these one day to show various practical implementations...)
~~~~~o0o~~~~~

4. REAR CAMBER & TOE ADJUSTMENT - This is shown at bottom-left of the sketch. A one-piece Swing-Arm-From-Chassis-Out-To-Hub-Bearings would be simpler, stiffer, lighter, etc., but then camber and toe might be harder to adjust, and different SAs would be required for each corner.

The joint shown is essentially a three bolt flange, but with capability to vary the spacing between the three corners of the equilateral triangular flanges. The two forward bolts use shims (eg. washers) to vary the top and bottom spacing and thus adjust camber-angles. The rearmost bolt uses a threaded adjuster in the SA to give finer adjustment for toe-angles.

The "upright" has spherical surfaces machined into it, and these are clamped by the bolts and cup-like washers. This is necessary to accomodate the misalignment when making adjustments. Note that the three bolts are always parallel and with constant alignment to the SA, but the upright moves "out of square" wrt the bolts.

The bolt sizes, etc., shown in the sketched joint would have similar strength and stiffness to a one-piece SA+Hub, although it is slightly heavier. However, this joint should be considerably stronger and stiffer than many FSAE wishbone+uprights because the load paths are more direct, and the "balls" are clamped tight and thus don't have any of the usual freeplay.

For the record, the sketched joint only positively constrains 5 DoFs between SA and upright. The sixth DoF, a rotation about the rearmost bolt, is only constrained by friction. It is quite easy to positively constrain all 6 DoFs (yes, this has been covered before ) but that is harder to sketch, would require a bit more machining, and is most likely not necessary. Other variations are possible, but the above joint should do...
~~~~~o0o~~~~~

5. CENTRE-PLANE STEER-AXIS - The "upright" at the front wheels might seem rather novel (err, unless you play around with tractors ). It uses a three-bolt joint as described above to attatch the Swing-Arm to the king-pin. Camber adjustment is done through this joint, with toe being done through the steering linkage. Castor adjustments would require the piece between SA and king-pin, which is different L and R, to be a "change part" (you should NOT need to change castor in mid-comp).

The main differences in the sketch to normal FSAE cars is the use of Tapered-Roller-Bearings for both king-pin and axle, and the very compact overall packaging. These bearings (30ID x 55OD) are more than adequate for the loads, and IMO much better than the 68xx Deep-Groove-Ball-Bearings commonly used for FSAE axles. FWIW, for a given mass TRBs carry much greater loads than DGBBs, and can have better installation stiffness. The main disadvantages of TRBs is slightly higher friction (Mu=0.002 vs Mu=0.001 for BBs), and consequently lower MaxRPM.

One of the main advantages of this design is the low steering friction under very high loads. Here I am thinking of serious aero downforce and the resulting 3+G cornering loads ... minimum! As such, the "upright" (ie. the "king-pin" shaft + outer-housing of the axle bearings) should be made of reasonably good quality steel. A 3" square bar of 4140 would do for a start, hollowed out with "speed holes" as far as you dare.

A similar but different design for the front king-pin/steer-axis can be found on the Citroen 2CV, and is a good alternative.

Close to centre-plane Steer-Axes are quite common in FSAE these days, which is good because they work better than the massive Offset + SAI (= KPI) that used to be common. However, if tyre distortion due to low pressures or excessive negative camber start to give funny steering feel during mid-corner braking, then adding a small amount of Offset (= scrub radius) can help. This is most easily done with wheel spacers (between wheel and hub), or using a wheel with different "offset".

The sketch was done primarily to show that centre-plane steering is feasible in a 6" wide, 10" diameter wheel, with the brake-disc outboard of the Steer-Axis, and relatively large steer-angles are possible (30 degree outer, 45 degree inner).
~~~~~o0o~~~~~

As always, comments and criticism welcome.

Z

[Jay Lawrence]

I may be missing something, but I would imagine that the rear camber/toe adjust system would be quite difficult to operate in practice. I would also think that the tolerancing and matching of the bolted components (I'm assuming those washers around the 'upright' are domed to accomodate the misalignment) would be very critical and possibly prone to becoming misaligned if the bolts aren't torqued perfectly.

[murpia]

Hi Z,

Nice concept and fantastic drawings as usual.

My concern with this is the weight of the swing arms compared to a 5-link version with very similar geometry. I agree with the geometry justification & the sensible load paths into the chassis. The swing arms as drawn need to resist bending forces from the springs, dampers & lateral Z-bars.

The 5-link version would use simple tubes with rod-ends at each end, creating triangulated structures. Co-locating the inboard pickups reduces the chassis compexity compared to double-wishbone.

So at the rear we have 2 roughly longitudinal links from a common chassis pickup out to the top & bottom of the upright. Then 2 roughly lateral links from a common chassis pickup out to the top & bottom of the upright. Plus a toe control link and a push or pullrod. Camber & toe are adjusted with LH & RH rod end threads slightly altering the link lengths.

Without a detailed design & stress analysis I can't answer the question which is lighter for equal camber & toe stiffness. I do know I'd rather fabricate the simple tube suspension links than the swing arms.

The front is more complex depending on steering requirements. An Audi A4 style virtual steering axis could be used, or a separate steering upright and suspension upright (think Ford RevoKnuckle, GM HiPer Strut or see RC cars). Again, a detailed design & stress analysis would be required to determine the solution with the best stiffness vs. weight.

My preference is for push or pullrods & rockers rather than direct acting suspension. In fact I think the lateral Z-bars would be easier with rockers (more a gut feeling than a rigorous analysis...) Or, to implement axle heave springs gaining much of the benefit of the lateral Z-bars with less packaging concerns.

Regards, Ian

[Warpspeed]

On anything I have ever built, the wheels, tires, hubs, discs, calipers, driveshafts, and uprights all end up weighing vastly more than the unsprung portion of the actual suspension linkages.

Unsprung weight may appear to be a disadvantage of some suspension configurations, but in practice the actual real final numbers may not differ by as much as might be imagined.

[Z]

Jay,

The rear camber & toe adjustment joint works with "agricultural" tolerances. I have made similar joints (different application) using an ancient Chinese lathe, V-belt driven from a washing machine motor, and with only manual feed of cross-slide and saddle. Most really old machinery that was hand made (eg. from castings or blacksmith's hammer followed by hand filing) required similar consideration of DoFs, loose tolerances, etc. Studying such old machinery is very educational. Anyway, as long as the clearances are right it will work.

Note that all three bolts have to be loosened before making any adjustment.
~~~~~o0o~~~~~

Ian,

I agree that most students would be more comfortable making the arms from 5 tubes. Conventional rod-ends could be used for camber & toe adjustment at the upright, but I would prefer something similar to the sketch. I say this because normal rod-ends invariably have more flex (more complex load paths), and can develop free-play, which all adds up to more camber and toe compliance. The "home-made rod-ends" in the sketch have a more direct load path (no shear strain of the bolt-through-ball), and the clamping always eliminates free-play.

Nevertheless, the LL style 5-tubes+rod-ends-at-upright at least eliminates 2 rod-ends at the chassis, so is a good start...
~o0o~

With regard to weight, I think of it this way:

1. Five tubes of (say) 1.6 cm diameter, by 0.16 cm wall thickness, by 50 cm long, weigh,
5 x Pi x 1.6 x 0.16 x 50 x 7.85 = ~1600 gm = 1.6 kg

2. One big (!) tube of 8 cm diameter, same wall thickness, same length, weighs,
1 x Pi x 8 x ....... = 1.6 kg = exactly the same (because 5 x 1.6 = 8) !

3. Two tapered tubes of 8 cm diameter at one end, zero at other, same thickness and length, weigh,
1.6 kg = exactly the same!

All the above examples use exactly the same amount of sheet metal, just wrapped up in different ways.

Anyway, as sketched the Swing-Arms would be slighly more than 2 kg each (assuming 1.6 mm sheet, = 1/16", or 16 gauge), because they don't taper to zero as per the third example above.

More importantly, reducing the 5-tubes to 1 mm wall thickness reduces their weight to ~1 kg, and my SAs would be about 1.3 kg. BUT! 1 mm thick tubes of 16 mm diameter are easily buckled when hit by the rubber cones, or even by rough handling (eg. picking car up to put in trailer). I reckon the sketched SAs, in 1 mm thick 4130, would survive super-student jumping on them with his work boots!

Furthermore, the Y-shape of the front SA, which gives it the large possible steer-angles, would be a bit more complicated as a tubular spaceframe (ie. would require two extra, shorter tubes). And as Tony pointed out most of the mass at the corners is in the tyres, wheels, hubs, etc. Typical FSAE "unsprung" corner weight is about 15 kg, with 10 kg being very lightweight. The 0.3 kg extra above, for much stonger suspension, is worth it, IMO.

Bottom line is that I discovered a long time ago, through trail-and-error and a bit of laziness, that folded sheet-steel structures work very well indeed. It is a worthwhile technology to learn, and very easy.

Or put another way, triangulated spaceframe structures are good for students who are still learning (don't let the triangles get too narrow!). But Nature seems to prefer doing everything in bending, and in single-shear, and with all those other FSAE taboos. I'll stick with Nature.

Z

[Chevalier]

Hi all,

The other night I was thinking about my time leading an FS team and found a thread (linked on page 9 of this thread) discussing Lancaster Links. Lo and behold there was a picture of "my" car.

The guys that commented on that thread gave it a bit of a panning. Some of which I don't think was entirely justified (obviously! everyone will defend their car!).

I am interested in what is being discussed here as I have always (perhaps stupidly?!?) thought that the LL system was a great, simple solution to FS suspension that was only really let down by our lack of resources and thus ability to execute it properly. Anyway, I posted the below on the other thread and will repeat here for peoples information/discussion.

Note: That pic of our car doing the rounds doesn't really do things favours. I don't know when it was taken but the ride height looks sky high so the geometry of the suspension and driveshafts and all that just looks a bit rubbish to begin with. That said we did have to run it quite high for none suspension reasons I don't really have time to go into right at this moment!

--------------------------

Long story short, I was the team leader of the 2009 Lancaster team and whilst this evening thinking back to my uni days I found this thread and was surprised to see a picture of "my" car. I know the original post was three years ago and the original posters are probably long gone but I felt compelled to respond and defending things. I would be interested in discussing things further if people are interested too.

Firstly that year we had a team of just five masters students (two of which were useless and just made more work for the other three!) a bit of help from some 3rd years, and a budget of about £10k for EVERYTHING including events costs etc. We also did a lot of the fabrication ourselves. I cut/welded most the chassis and did a lot of machining of components myself. It was a car the team built, not a car a sub-contractor or technician built. So with such finite resources a lot of things just got built after five minutes of back of fag packet design.

Anyway to answer a few questions/comments:

- There are no rod ends in bending. Also the LL system reduces the number of rod ends required as the inner pivots only require bushes rather than rod ends.

- The LL system has the advantage that it has excellent camber control in roll but sacrifices camber control in bump. This I think is obvious to all.

- For FS at Silverstone the track is flat so bump isn't really a problem and Braking/accelerating is controlled with a good dollop of anti-squat/anti-dive.

- In its "pure" form the links would join at the middle. By moving them slightly apart you encourage a small amount of camber gain in roll to compensate for compliance/tyre deflection that pushes the wheel into positive camber.

- The car can be set up with very small static cambers to improve traction.

- In ordinary double wishbone set ups the top and bottom bones are in tension/compression respectively. By joining them up at a single node these forces into the chassis are "cancelled out" to some extent.

- Yeah ok the rockers and push rods don't look great (in fact the car looks rather un-set-up in that pic). The judges panned us for the angles of these. But they were just put there cos we needed somewhere to put them (built not designed!). Another possible disadvantage, you must use push rods.

- The hyperbole of "best suspension in 40 years" or whatever I think is just the journalism. They have to make a magazine interesting to read. It's not a technical paper after all!

- Driveshaft plunge was a bit of an issue, in fact it caused an unforseen problem on the test pan at the event so we missed the early dynamic events whilst this was repaired.

- Brake lines at the back is criticism for the sake of criticism. Utter rubbish! When has any FS car suffered a rear end shunt?! A shunt from what? In the very very chance event that it did happen the fronts would still do plenty enough braking to pull you up safe anyway.

Anyway, it finished the endurance event. Better than many other could achieve (including, I remember the Red Bull team (Graz?!)). And survived a spin and backwards trip into the gravel! Zero driver training and not having time to sort the traction control plus a damp track meant we were slow and sideways; but the concept worked!

If the LL system was developed to a level that double arms are by every team every year I can't see why they wouldn't work. Maybe I am just blinkered in defending my car!

Interesting to enter into discussion on this if people want.

---------------------

Cheers all,
Malcolm

[Z]

Malcolm,

Thanks for sharing your experiences with the LLs.

Over the last half year or so (since page 9) I have had a few students PM'ing me and intending to go with LLs next year (for all the good reasons previously mentioned). Unfortunately, so far it seems they have all been outvoted by other team members who insist the car be built with "a real racing suspension". This coming from team members who know nothing about suspensions! And, worst of all, these are teams who have failed in previous years to build a running car! Ah well, young people and peer group pressure ...

Anyway, some questions:

Q1. Is there a CV joint at the outer end of the driveshaft, or is it just a splined coupling?

Q2. Given your experience with the LLs so far, what would you do differently next time???

Z

[Chevalier]

Hey Z,

To answer your questions, plus a few extra thoughts. I will try to be brief but it doesn't always work out as I like to be sure I am understood!

Q1. There are tripod style cv joints at both ends of the drive shaft to (obviously) transmit drive and accommodate the "extreme" drive shaft plunge. The CV at outer end was moved out as far as possible and became housed in the upright. This was to make the shafts as long as possible in order to reduce drive shaft angles.

Q2. That is tricky one... The car that was pictured on page 9 was the car the team and I built for FS 2009. That was four years ago and my final year at uni. Since then whilst occasionally thinking about such things I have never really sat down to seriously give it thought. Real life and other such things tend to get in the way! But a few thoughts I have had...

1. I have pondered the idea of how to mount the spring/damper units low down, preferably on the floor. But the obvious problem being that the pivot is effectively at floor level and that leads you to using an upwardly angled push rod.

The key benefit to this in my eyes (other than the obvious CoG etc.) would be that you could really easily build what would basically be a ladder frame chassis that all the suspension would work off. This would be easy to make with excellent precision and you would have a rolling chassis in no time. The rest of the structure could then be made as light and as minimal as possible just to comply to the regs.

2. Mono-shocks and air springs. Kind of conflicting again. I have long pondered air springs as a cheaper and lighter option. Also, we used cane creek shocks/springs and there was basically too much adjustment. Most teams I think struggle for testing so a more basic shock system set up well I think would be better than a fancy system set up badly.

A mono-shock system would also reduce cost. As you are basically de-coupling roll/bump with the LL I think a mono-shock system would work well, although I admit I haven't actually given this more than 2 minutes thought at the moment. If you ran a mono though I doubt an air shock would be beefy enough to cope with the weight of two axles.

3. The whole thing just needs building with a bit more finesse and precision than we managed! But we did the best with the limited time/resources we had.

4. More recent Lancaster teams split the top and bottom wishbones. They still pivot along the same axis but they are separate arms. Our systems the top and bottom arms were welded together at the pivot point. I guess this just makes fabrication easier for them but I'm not sure.

Cheers,
Malcolm

[Z]

INTERCONNECTED SPRINGING - TWO WHEELS AT A TIME.
=================================================
The subject of interconnected springing is currently being discussed on this "Roll Rates in RCVD" thread. I am adding these notes here, mainly to keep as much of my "Suspension Design" ramblings on the one thread.

The simplest way to "spring" a car is to put one spring in control of each wheel, namely a "spring-at-each-corner" suspension. At the other extreme a single spring can be connected to, and be in control of, ALL the wheels via some sort of linkage. Search with keywords "Balanced Suspension", "Kinetic suspension" +++.

For now, let's consider the simplest types of interconnection, where a single spring interconnects the chassis and TWO wheels only. The only clear explanation of this particular subject that I have ever seen was an article by Mark Ortiz in RaceCar Engineering magazine in the late 1990s (maybe '97?). There may be other sources for this information, but it is definitely NOT mainstream VD.

If you students apply enough pressure now, then maybe one day Claude will start teaching it. Claude???
~~~~~o0o~~~~~

DEFINITIONS - These covered in more depth elsewhere, but a brief recap here:

* U-BARS and Z-BARS - These are descriptive names given to torsion-bar versions of interconnecting springs. The names refer to their appearance when seen in plan-view and fitted to a car in the "usual" manner. The difference between these two types of spring is that the lever-arms on U-bars both point in the same direction, while the lever-arms on Z-bars point in opposite directions.

The functional behaviour of these springs can be implemented in many different ways (eg. with leaf, coil, or other spring types, and via mechanical, hydraulic, or other linkages...). The important functional differences are;

* U-BARS - RESIST DIFFERENT movements of their ends/wheels (ie. when one wheel moves up and the other wheel down, or vice versa), but ALLOW SAME movements of their controlled wheels (ie. both wheels move up, or both down) with no resistance, other than maybe some friction.

* Z-BARS - RESIST SAME movements (= both up, or both down), but ALLOW DIFFERENT movements (= one up and the other down).

So functionally U and Z-bars are complementary to each other.
~~~o0o~~~

* ALL-WHEEL-MODES (of a four-wheeled, rectangular pattern, vehicle) - These are different ways of describing the motion of all the wheels as they move wrt the car-body. There are many different ways to define these (in fact, four infinities!), so the following is only a taste.

HEAVE-MODE (aka Bounce-mode) - All four wheels move in same direction (either up, or down) by the same amount. So +1 cm of Heave-mode might have all wheels moving up, wrt car-body, by 1 cm.

PITCH-MODE - Both front wheels move up by the same amount, and both rear wheels move down by the same amount. A different, and equally valid, definition for a car with 40F:60R weight split might have "+1 cm Pitch" as front wheels up by 1.5 cm, and rears down by 1 cm. This corresponds to the car pitching about its CG.

ROLL-MODE - Both right-side wheels move up, and both left-side wheels move down, by the same amount.

TWIST-MODE (aka Warp-mode) - One diagonal-pair of wheels move up, and the other diagonal-pair move down, by the same amount. Again, a different definition might have the front wheels moving 50% more than the rears, to better describe a Twist motion about a 40F:60R car's CG.

Note that early work on these concepts (1930s to "active suspension" era in F1) usually had the definitions rather rigidly defined to be "all equal" movements of the wheels, up or down. This can then introduce calculational difficulties when the CG is not at 50% wheelbase (ie. the researchers talk of "mode-coupling", and insist that the Warp-mode must exert a force to help balance the handling).

IMO these difficulties are most easily overcome by REDEFINING the modes so that they better suit your particular problem (and you are free to define anything in any way you want!). This allows the Warp/Twist mode stiffness to always be zero.
~~~~~o0o~~~~~

So far, so simple.

Now what happens when we start fitting U and Z-bars to cars with four wheels? Here is a summary of all the possible interconnections when using either two U-bars, or two Z-bars, between the various possible pairs of wheels. We are looking for the effect these springs have on the various All-Wheel-Modes described above.

U-BARS.
=======
1. Between End-Pairs (ie. one U-bar connects the front-pair of wheels, another U-bar connects the rear-pair).
Stiffens Roll and Twist (Heave and Pitch free).

2. Between Side-Pairs.
Stiffens Pitch and Twist (Heave and Roll free).

3. Between Diagonal-Pairs.
Stiffens Pitch and Roll (Heave and Twist free).

Z-BARS.
=======
1. Between End-Pairs.
Stiffens Heave and Pitch (Roll and Twist free).

2. Between Side-Pairs.
Stiffens Heave and Roll (Pitch and Twist free).

3. Between Diagonal-Pairs.
Stiffens Heave and Twist (Pitch and Roll free).

Again, quite simple. These symmetrical two-wheel interconnections always stiffen up two of the all-wheel-modes, and leave the other two free. But what does all this mean in terms of overall car behaviour?
~~~~~o0o~~~~~

CONCLUSIONS (briefly).
====================
* Importantly, the above description is only for "linear" behaviour. That is, when the lengths of the lever-arms at the end of a given (U or Z) torsion-bar always stay in the SAME RATIO throughout the range of wheel travel. Typically (by design, or by accident) the effective lever-arm lengths will change by different amounts, so giving a rising-rate, or falling-rate, behaviour at each end, and a different force ratio between the ends. This non-linear behaviour can then "add stiffness" to the above "free" modes. This can make a real mess of your best laid plans, or it can be used to considerable advantage (see below).

* In general, anything that stiffens the Twist-mode is, at best, unnecessary, and at worst, VERY BAD (I will explain why in a later post). There are exceptions, but if your suspension layout starts with a zero-rate Twist-mode, then it is usually VERY EASY TO ADD more Twist stiffness. But if your suspension starts with a lot of stiffness in its Twist-mode, then it is all but IMPOSSIBLE TO SUBTRACT that stiffness (ie. it requires a total redesign).

* So of the U-bars, we can cross out the end-pair (#1) and side-pair (#2), because they add Twist stiffness. Note that end-pair U-bars are the all too common ARBs (which are considered mandatory in FSAE, by some Design Judges!). Likewise, we can cross out the diagonal-pair Z-bars (#3).

* Diagonal-pair U-bars (#3) are potentially useful, but have disadvantages. The diagonal interconnection can be difficult to package with a mechanical linkage. Also this arrangement does not control Heave, so some other springing must be used to hold the car up (quite important!). Perhaps worst, the Pitch and Roll stiffening are inextricably linked. So, if you want a stiff Roll-mode, say for flat cornering, then you MUST also have a stiff Pitch-mode. This might be acceptable for a racecar, but a soft(ish) Pitch-mode contributes greatly to ride comfort of passenger cars. The Spanish "Crueat" (spelling?, and maybe Portugese?) hydraulically interconnected suspension uses a variation of this type.

* This leaves end-pair and side-pair Z-bars. Both these control Heave, which is very useful as it is the mode that you MUST have (lest the car drag its belly along the ground).

* End-pair (or lateral) Z-bars are common these days in motorsport, and are usually called "third-springs" (more accurate would be "seventh and eighth-springs", given that they came after the 4 x corner-springs + 2 x ARBs). IMO these have evolved almost entirely by random trail-and-error selection, with next to no deep theoretical understanding. Nevertheless, they work well for big-aero cars because they can greatly (and non-linearly) stiffen Heave and Pitch, and thus provide a stable aero platform while leaving Roll and Twist UNAFFECTED. UWA 2013 car's "W-springs" are end-pair Z-bars.

* Finally, side-pair Z-bars are perhaps the best of all the above options (though the rarest!). Heave and Roll generally have to be the stiffest of the four modes (passenger or racecar), and they carry the largest, and similar, loads (ie. statically each bar carries half the car's H weight, and at high-G cornering the oustide bar carries close to the total car weight = H/2+RollLLT). Also, for given Gs, Pitch-longitudinal-load-transfer during acceleration or braking is less than Roll-lateral-load-transfer during cornering by the ratio of Track/Wheelbase.

Bottom line, side-pair-(longitudinal)-Z-bars have a lot going for them, and are very easy to implement (see next post). And by arranging the linkages to be rising-rate at each end of the bar, they can also control Pitch. (I call this "pendulum springing" and it comes almost for free, which may be why BL-Austin-Morris used it in the 1960s+). However, this rising-rate method has limitations, and smaller, lighter, dedicated end-pair Z-bars (one or two) can be used for more precise control of Pitch, with no stiffening of the Twist mode.

More coming...

Z

[Z]

"THE NEW PACKARD TORSION LEVEL SUSPENSION".
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(by F. R. McFarland, presented June 15 1955, and in SAE Transactions Vol 64, p284 1956, 560026.)

I made some comments about this paper on the "Roll rates..." thread (linked on previous post, page 25). Below is Figure 1 from the paper, and my interpretation of the system.

In the image the "Main Load Torsion Bars" are longitudinal-(side-pair)-Z-bars. The "Z" shape is quite apparent. IMO, all things considered, this particular layout is possibly the best way to do longitudinal-Z-bar suspension, both on production cars and many types of racecars. So also quite suitable for FSAE.

The entire torsion-bar+lever-arms lies in a horizontal plane at the bottom of the car, so is easy to package and gives a low CG (ie. all the "spring mass" is at the lowest possible position, and big springs, ie. for off-road or luxury cars, can be quite heavy). The front lever-arm cranks outward, allowing easy connection to the wheel, while giving room for the front-wheel to steer. This lever-arm can be in unit with the lower wishbone, or else it can be connected to the suspension by a flexible link (Packard tried both).

The rear lever-arm must now crank inward (to form the "Z"!). So the main body of the torsion-bar angles out towards the rear of the car. This allows the rear lever-arm to connect to any convenient point on the rear suspension. In this case the connection is by a short "pullrod" to the live-axle control-arm (= "Rear Axle Torque Arm"). Similar pullrod-like connection could be used on any independent suspension.



Other comments:
* The "Compensator Bars" at the rear act as simple corner springs (ie. no interconnections), but both can be simultaneously adjusted to reset rear-ride-height (hence "Levelizers"). This is important for a very softly-sprung luxury car, and is described as "an answer to the stylist's prayer"! IMO an adjustable lateral-Z-bar would be much better here.

* The "Rear Stabilizer Link" is a Watts-linkage for lateral control of the live-axle. This was deliberately made quite soft laterally to reduce "harshness". IMO this is poor design for too many reasons to cover here. Well, just one being rear-axle-(over)steer during cornering! Many ways to fix this, but they didn't...

* A "Front Stabilizer" (ie. lateral-U-bar) is also fitted. This, and the "Rear Axle Torque Arms", both act as ARBs, thus stiffening both the Roll AND Twist modes. IMO this shows a lack of deep understanding of the whole system...

* IMO the Packard engineers didn't seem to grasp this whole concept nearly as well as the French, who were doing this sort of thing twenty years earlier. The whole paper seems to be focussed on the side-view, 2-D behaviour of the car in "bounce and pitch". Admittedly, they had better understanding of these motions than is currently the case with the modern concepts of "front and rear ride frequencies" (see extensive ranting elsewhere! ). But nowhere in the paper is any Twist or Warp-mode behaviour mentioned. Well, except, and only (!), the last Summary point "8. Reduced torsional stresses in frame.").

* Note that to understand Twist-mode motions, you have to think in 3-D, with the four wheelprints starting in a horizontal plane, and their vertical motions taking them out of this plane. By comparison, the "bounce and pitch" motions discussed in the paper are contained entirely in a 2-D, side-view plane. This limited 2-D thinking seems to have prevented the Packard engineers from fully appreciating the advantages of a soft Twist-mode.

* Finally, the paper starts by noting that "automobile developments seem to appear in cycles", such as manual to automatic gearboxes, straight-8 to V-8 engines, and so on. It ends with "The time is ripe for a cycle of development in automotive suspensions ... it would seem that within the next 2 to 5 years, we should see some radical changes in suspension design.". (My emphasis.)

Well, that didn't happen! And a good indicator of why not is in the subsequent discussion to the paper. The other manufacturer's engineers quite clearly did NOT understand the Packard system (not even its dumbed-down, 2-D, side-view version), as they gave some completely false criticisms of it. Having led with this bulldust, they then launched into a marketing spiel about how great their suspensions were!

Ahh, nothing changes...

More in a few days...

Z