Suspension Design

The above photo is of RMIT R05 at the Oz 2005 comp, which went on to win FSAE Detroit in 2006. I have posted it as it is a good example of swing axle geometry - without the simplicity.

Reasoning? The short VSA's were an attempt to achieve full camber compensation in roll, noting that our simulations were showing that lateral accelerations were around 8 to 15 times more important than longitudinal accelerations. We were happy to compromise our contact patches in pitch a little to keep the patch flat on the road in cornering.

We had noted that with the track map we had to work with, 10 of the 14 cornering manouevres were entered with no pitch attitude - i.e. no braking. Therefore we wanted camber compensation right from when the car would first start to roll.

The fault? The car would lift the inside rear right from corner entry, and would then transfer all the torque the inside rear when under power - no drive. The team then over a few years progressively dropped roll centres and tightened up the diff (torsen then moving onto clutch packs) to get the power down on exit.

Think of where the c of g of the unsprung mass is - it is at axle height. Now think of where the instantaneous centre is for the VSA - below axle height. Now imagine the unsprung mass inertial force under cornering, and what sort of a moment it will create around the IC of the VSA, and how little moment of inertia the unsprung mass has with such a short VSA...

Instant lifting of the inside rear right from turn in. Terrible when you are trying to get a torsen to work on corner exit. So you can either try to fix the geometry to suit the final drive you have - OR thinking a little laterally, could you find a final drive to suit that kind of geometry?

Hmmm...

p.s. Z asked me to post the above explanation of our geometry (see fantasy car thread) as he has a few of you expressing concern to him that you wont do this sort of geometry because the design judges "hate" short VSAs.

My responses:
- The design judges pointed out to us the design flaws of the short VSAs on our car. If you worried about such things, you might go home and tell your mum that the design judges hated it
- The above car got 3rd in Design at FSAE Cali, and and 5th in Design at Detroit
- If we could have managed to slip through some pinhole in the time/space continuum, it could have been fun to go back in time and redesign our suspension just the way the judges would have "liked". Nice long VSAs. With this newfound knowledge, and a vehicle specifically tailored to thir "liking", I have no doubt we could have achieved 3rd in Design at FSAE Cali, and and 5th in Design at Detroit.

Seriously, don't design for the judges. It is your car, design it for yourself. Trying to second guess what a stranger "likes" will give you a life lesson in futility. And you are being assessed on your knowledge, not how like-able your car is.

Cheers all

Quote:

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Originally posted by Big Bird:
Seriously, don't design for the judges. It is your car, design it for yourself. Trying to second guess what a stranger "likes" will give you a life lesson in futility. And you are being assessed on your knowledge, not how like-able your car is.

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I nominate this as quote of the decade!

Quote:

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Originally posted by murpia:
... a swing axle ... I like the warp-soft / heave-stiff Formula Vee idea quite a lot.

The crunch will be toe & camber compliance, there can be no compromise there...

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Ian,

You got me thinking (always dangerous http://fsae.com/groupee_common/emoticons/icon_smile.gif), and I reckon a Swing-Axle could possibly be the simplest way to do Independent Rear Suspension for FSAE. Here is one possibility.

(Semantic note: I refer to a "Swing-Axle" as a suspension that moves, both structurally and kinematically, about an axis (= the Motion Screw, ISA) that intersects the wheel's actual AXLE. So, typically, the wheel is fixed rigidly to its axle, with this axle swinging about a joint near the car centreline. By contrast, a "Swing-Arm" moves about an ISA that isn't necessarily close to the wheel's axle. Just my usage, though...)

https://lh5.googleusercontent.com/-r...Swing-Axle.jpg

STRUCTURE.
============
1. Only two major components required per wheel, the Swing-Axle and Diagonal-Link.

1a. The Swing-Axle itself is a strong tubular structure that has the wheel fixed rigidly to its outer-end, and has a ball-joint at its inner-end that allows it to "swing" wrt the diff. Also at its inner-end is a "rubber donut" CV that transmits driving and braking torque (more below). The SA thus carries the driving/braking torques, as well as most of the cornering loads.

The sketched SA is a tapered, large diameter, thin-walled tube, since this is the best shape to carry the loads. The large diameter at the outer end minimises camber and toe compliance, negating Ian's (rightful) concerns. The wheel is attached via a splined joint that also locates the outer bearing (use bearing size for scale). I would probably fabricate the axle out of 4130/4140 steel. A constant diameter steel tube, as commonly used on car "prop-shafts", could also be used. A similar sized axle, but with thicker wall in aluminium or CF, is also an option. Or a smaller OD, thicker and tapered wall, one-piece, machined 4140 (or 4340+) hollow bar, with suitable heat-treatment, etc., would also work.

1b. The Diagonal-Link carries the major longitudinal loads from the tyre->wheel->axle->DL->chassis via a 6010 Deep-Groove-Ball-Bearing. (I have done no calcs at all on these sizes, just what feels right. http://fsae.com/groupee_common/emoticons/icon_smile.gif) The DL also carries the vertical loads from the springing (see below). The DGBB is mounted to the DL via a vertical axis "fixed" joint (ie. top and bottom bolts) that allows adjustment of the angle between DL and SA. This is to cater for manufacturing tolerances of the chassis, and adjustments of toe-angle, etc.

I have again sketched the DL as a tapered, sheet steel fabrication, because this is easy to make. It also resembles trees and bones, which know a thing or two about good design. http://fsae.com/groupee_common/emoticons/icon_smile.gif Two tubes in a narrow "V" would also work. Or a CF shell, similar to the sketch.

2. Drive and braking torque must pass from the sprocket/brake-disc, via the "spool" diff, to the SA via some sort of CV joint. I have shown a "rubber donut" because it can smooth a big-single's torque pulses, which may be helpful given that the SA itself will be torsionally very stiff (compared with normal driveshafts). Lateral loads from the wheel are passed to chassis via the SA-inner-Ball-Joint, which is made from a modified OEM steering linkage BJ. The donut+BJ might be replaced with a conventional UJ (= Hookes joint), although this will be torsionally stiffer and doesn't give a "constant" angular velocity. Build-and-test ...?

3. As sketched, the chassis only needs 3 strong-points for the whole rear suspension. The two DLs attach at two forward points near the main-roll-hoop/seat-back/side-impact-structure (perhaps the strongest part of the car). The only other strong-point needed is the differential area, which should already be strong to take the chain loads.

4. All parts are identical on left and right sides, which makes manufacturing and carrying spares easier.
~o0o~

KINEMATICS.
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1. The suspension pivot-axis (= ISA), passing through SA-inner-BJ and DL-front-BJ, should be close to horizontal to minimise bump-steer (given small FSAE suspension travel, this doesn't matter too much). A small slope here can give designed-in roll-steer, but that is polishing.

2. More important is setting static Toe and Camber.
2a. Toe is set by adjusting the rod-ends at the front of the DLs. Shorten for toe-in, lengthen for toe-out.
2b. Camber is set by moving the diff up or down wrt chassis. This could be combined with (ie. added to) the common diff back-and-forth chain adjustment. Note that this sort of chain adjustment requires resetting the Toe.

3. As noted in earlier posts, this suspension has a relatively high "Roll Centre" (= steep lateral n-lines). The longitudinal n-lines are horizontal, giving 0% anti-squat/lift, which is generally a good thing. The implications of these kinematics can all be taken care of by appropriate springing.
~o0o~

SPRINGING.
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1. The main sketch shows a single Anti-Axle-Bounce spring-damper only. This connects to the DLs via a smallish Longitudinal-Link and two pullrods. The pullrods might look to be under high loads, but as noted before the torsional loads through the axles are the really big ones, and I don't see any problems here. Moving the AAB spring, LngLnk, and pullrods, forward into the engine bay would be beneficial, if there is space there.

2. Importantly, the end of the LngLnk is free to move sideways. This arrangement gives zero elastic roll stiffness for the rear suspension. In turn, this implies that all Lateral-Load-Transfer at the rear is "kinematic" (= "geometric" LLT) via the high RC. It also means that the four-wheel suspension is very soft in twist, which is an advantage on undulating and bumpy tracks.

3. If more rear LLT is required, say to unstick the inner tyre and improve performance of the spool-diff in tight corners, then Anti-Axle-Roll springing can be added by constraining sideways movement of the LngLnk (as shown, centre of pic). Many ways to do this, including rubber bungees in tension either side of the LngLnk (just add more loops to increase roll stiffness!). Or overcomplicate to your taste... http://fsae.com/groupee_common/emoticons/icon_smile.gif

4. The advantage of separating the Axle-Bounce and Axle-Roll modes is that the respective spring curves can be tailored to suit your requirements. Here the high RC implies high jacking forces, so the AABounce spring should be droop limited (ie. only extends ~5-10 mm from ride height). This prevents the body jacking up during cornering.

Having short travel of the AAB spring also minimises camber change during acceleration/braking (= pitch couple), and minimises ride height change if you have sprung aero (= heave force). The short travel of the AAB should also be soft for grip over small bumps, with rising rate bump rubbers catering for the big bumps. Meanwhile this suspension can still have very long and very soft travel in Roll, because there is zero camber change in roll. This softness is also good for absorbing big single-wheel bumps.

5. Conventional "independent" springing is also shown at top-left of sketch. If you are in doubt, then you can always revert to this approach. Remember that "any suspension will work, if you don't let it". And this, in fact, is the approach used by many winning FSAE teams!
~~~~~o0o~~~~~

As always, comments and criticisms welcome. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

(PS. [Mini-Rant] The above only possible because I gave up on cable & OS incompatabilities and bought a new scanner! What a farce!!! The ~15 year old scanner+computer worked fine, and had a reasonable editing facility that allowed me to tidy up sketches, compress files, save in multiple formats, etc. The new scanner comes with atrocious software, with one of the very few editing options being "Try Your Luck"!!!!! http://fsae.com/groupee_common/emoticons/icon_eek.gif Idiocrasy, here we come! [Rant Over]

I will try in a few weeks to post a sketch of Semi-Leading/Trailing-Swing-Arms, a very good option for "independent" suspension for current FSAE conditions (off-road is different again).)

Z,

Would you car to comment about combining your longitudinal z bars and the twin beam concepts? I got into a conversation with someone about it and we were trying to figure out if it would be worth doing in two cases, one with a aero package and one without.

Quote:

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Originally posted by Z:
The wheel is attached via a splined joint that also locates the outer bearing (use bearing size for scale).

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Z, you are slipping, shouldn't the wheel be attached by one of those fancy tapered face torque couplings<grin>?

This sort of stuff makes me want to go back to uni.

I was thinking perhaps you could make the longitudinal link have only 1 DOF so you could turn it into an antiroll bar (if deemed necessary) whilst still having it swing up/down for pitch/heave motion. Probably be a compliance hassle though

Z,

Fantastic, thank you for this.

I wish I had the time & skill to put together concept sketches like that. In the absence of both, I'll just let you know where my mind had wandered recently...

Considering a'sidewinder' engine location, I had the idea to use a beam axle with the differential way over towards one wheel. The driveshaft from the engine to the diff could form a longitudinal suspension link. Optionally, the beam axle could have a single joint at the car centerline to instead form two swing arms.

I still worry that the true weight saving over dedicated suspension links and dedicated driveshafts & joints gets lost in the implementation unless the structural engineering is done really well.

Regards, Ian

Rob,

"Would you care to comment about combining your longitudinal z bars and the twin beam concepts?'

I think I covered that in the "Beam Axles" thread. Briefly, IMO, a combination of the "Z-bars" and "Twin Beam" sketches would work very well. A spring between chassis and centre of each beam (acting as lateral Z-bars) would control heave and pitch modes. A longitudinal Z-bar down each side (in any of many practical implementations) would give additional heave and roll control. Twist (= warp) mode thus remains soft.

Importantly, the side-pair Z-bars allow LLTD (actually Elastic Roll Moment Distribution) to be set independently of any heave, pitch, or roll motions of the chassis. And, especially importantly, independently of any twist in the road. A conventional suspension's ERMD, and thus over/understeer behaviour, is greatly affected by the road profile. FSAE has relatively flat tracks, so I showed a soft spring-at-each-corner on the Twin Beam sketch, because no camber change during heave/pitch/roll, and I didn't want to overcomplicate the message.

UWA's 2012 car has very cleverly taken this a step further. Their "W" springs do the job of the centre-of-beam springs controlling heave and pitch. They also kinematically locate the undertray and wheels wrt the chassis, doing the job of my peg-and-slots and BJs. The UWA car then controls roll, entirely independently of the other modes, by a mid-chassis, lateral U-bar connected to the two undertray tunnels, which in turn act as longitudinal "balance-beams".

A very well integrated, minimal parts count design. How they only managed 3 points (out of 200!) in Design is beyond me. Something very wrong there... It is clear to me that the Design score does NOT reflect the car's design, or the student's knowledge... Some more openness and transparency in these decisions would be welcome (might have to rant on the other thread http://fsae.com/groupee_common/emoticons/icon_smile.gif).
~o0o~

"...we were trying to figure out if it would be worth doing in two cases, one with a aero package and one without."

With unsprung (= beam mounted) aero, on FSAE type tracks, I think a simple SOFT spring-at-each-corner would be the best place to start. Next, add the beam centre springs (or just bump rubbers) to tighten up heave and pitch.

With sprung (= body mounted) aero, then short travel beam centre springs, with good bump rubbers, are essential. If excess body-roll is now leading to front-wing or bodywork scraping, or if you are racing on very undulating or bumpy tracks, then short travel, side-pair (longitudinal) Z-bars would be good. You can now remove the corner springs and the car has full control of heave, pitch, and roll, with a fully soft twist mode to cope with the uneven road.

With no aero, but an undulating/bumpy track, then having a soft twist mode is very beneficial. So lateral and longitudinal Z-bars are definitely good. Or just the lateral Z-bars (beam centre springs), together with an anti-roll arrangement like UWA's (which does require some sort of side-pair balance beams).
~~~~~o0o~~~~~

Doug,

"... shouldn't the wheel be attached by one of those fancy tapered face torque couplings<grin>?"

But then some other means would be required to locate the outer ball bearing. http://fsae.com/groupee_common/emoticons/icon_smile.gif (Perhaps a "crush spacer", or second ring-nut...)

FWIW, the axle-to-wheel joint shown is fairly common. Well, the ~1980s 4WD Subarus I having rusting away out back have it on all four corners.

An important trick is the spacer between big-nut-on-end-of-axle and the wheel-mounting-flange (this appears in the sketch as a small triangle). This spacer looks like a fat washer with one conical side, but importantly it has a slit in it so that it is "C" shaped. The nut pushes on the flat face of the spacer, which in turn is pushed into the female cone of the wheel-flange, which in turn reduces the diameter of the spacer, clamping it onto the axle.

Bottom line is that all axial and radial play is eliminated between axle and wheel, so no "fretting" in those directions. Rotational fretting is still possible between inner and outer parallel splines, but this doesn't have the high frequency of wheel load induced fretting. There are ways of positively clamping all degrees of freedom, and still allow the ball bearing to be clamped up during assembly (similar to above, but +++), but that would require a whole lot more words... http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~~~o0o~~~~~

Jay,

"I was thinking perhaps you could make the longitudinal link have only 1 DOF so you could turn it into an antiroll bar (if deemed necessary) whilst still having it swing up/down for pitch/heave motion."

Yes, that would be similar to many current "monoshock" linkages, though upside down. These have a "T-bar" that pivots wrt chassis on a lateral axis. For roll control the leg of the T-bar could flex side-to-side, or the whole T-bar could slide along its pivot axis against springs (as is currently done).

Note that if the AAB spring, as shown in the sketch, has its top mount significantly above axle height, then it exerts a small anti-roll force during body roll (err,... do a FBD http://fsae.com/groupee_common/emoticons/icon_smile.gif). If tension springs are fitted either side of the LngLnk, for roll control, then these will add some rising rate force to the AAB spring, which, in general, is a good thing.
~~~~~o0o~~~~~

Ian,

"... the beam axle could have a single joint at the car centerline to instead form two swing arms."

Ah, yes, this was used very widely by Mercedes around the 1950s. They won everything from Grand Prix's to the East Africa Safari (= today's Dakar) with that sort of suspension. Essentially, take a live axle with diff offset a bit to one side, cut it in half next to the diff, put a single UJ there, and presto!, two Swing-Axles. Their next step was to allow axial plunge of one of the half-shafts (via a spline), which allowed a "low-pivot Swing-Arm" with lesser jacking forces. There must be pics on the web?
~o0o~

"I still worry that the true weight saving over dedicated suspension links and dedicated driveshafts & joints gets lost in the implementation unless the structural engineering is done really well."

Yes. I hope I haven't overcomplicated it by showing the tapered axles. I think using the ~2" diameter 7075(?) aluminium axles used on Rob's previous car, and currently by U of Berkeley(?), together with a lot of the off-the-shelf fittings for these axles, might be a good way to start.

Z

We used a 1.75 OD but they make 2.00 now as well...

http://www.hyperracing.com/pag...tore.aspx?class=1100

Since I am linking a sprint car shop I should take a moment and point out that is was 1994 University of Illinois Urbana #83 car (Finished 7th overall) that was a FSAE legal 600cc spring car that had a sidewinder engine and a 4 link sprint axle that got me thinking that maybe using a solid axle was a competitive direction to go. I wish I had a picture but UIUC took down the pictures of their old cars. This was further reinforced by the 1996 Akron team for showing that a Briggs V Twin with CVT and solid axle could be competitive as well...

http://forums.bajasae.net/foru...f-fury_topic637.html

I was dumbstruck at what Akron pulled off in 1996. There hasn't been anything like it sense unfortunately. Maybe someone will do a Bajamula again one day and use Z's trailing/leading link with interconnection and unsprung aero and show how really good engineers they are. At the very least it would have amazing f*&k you factor since many teams would finish below it. These two cars and their high placement along with my love of F500 cars sealed the deal on my decision to push for the direction we went for the car that eventually ran in 2008 and finished 18th.