Beam Axles - Front, Rear or both.

[Z]

FRONT BEAM-AXLE, Suitable For Car With Front-Overhang.
==============================================
Here is another sketch of a Beam-Axle, this time suitable for the front of an FSAE car that necessarily has some front-overhang. This might be because an off-the-shelf engine prevents the driver sitting further back, so their feet end up forward of the front-axle.

(As stated many times before, I believe a driver-entirely-within-the-wheelbase design is best VD-wise, although I accept that this is not always possible when working under some Team constraints. In fact, this sketch was prompted by Christian's similar design on his thread. Because this sketch is in part a derivation of Christian's work, it is not necessarily what I would do if starting entirely from scratch...)

Also squeezed into the sketch are some ideas that might be useful for very different cars. For example, the "Side-Mounted-...-Brake-M/Cs", that allow the Front-Bulkhead to be positioned immediately in front of the pedals. More below...
~o0o~

OVERALL CONCEPT - This is a "Model-T-Ford" style, low-mounted (ie. underfloor) front-beam. The major dimensions can be found, roughly, from the small three-view detail at the bottom-left of the sketch. The wheels and tyres are nominally 10" x ~6+" wide. The Steer-Axis geometry is "centreplane" and should package with the maximum steering-locks shown.

The beam feeds the major road-to-tyreprint loads to its main "Apex-BJ" that connects to chassis at floor level and close to the middle of the car. Thus any heavy chassis structure needed to carry these major loads is low and centrally positioned, thus giving overall low-CG and low-Yaw-Inertia. The beam has only four connections to chassis in total (not including steering). The two main Kinematic constraints are low down and on the car centreline, so allow easy chassis jigging and fabrication.

Spring-Dampers are Direct-Acting, and feed their loads in a close-to-straight path from the wheelprint to a mandated strong part of the frame in the FRH to upper-SIS node. Note that different lengths of DASDs can be accomodated by having the upper-SD-BJ connect to a "frame-bracket" that looks like a frame-tube cantilevered down-and-out from the FRH-SIS node. As long as this tube is aligned with the SD-axis it will be strong and stiff enough, even if it is quite long, say ~15 cm. At most, some small "gusseting" of this tube to the FRH or other frame tubes might be required. Create this bracket with Craftsmanship, then check with Engineering-Analysis, or better yet, do a real Load-Deflection test.

Lateral control of the beam is via a "wishbone" and "Ball-In-Tube" joint, detailed at top-right of sketch. Note that the similar front-beam on the first of my sketches back on page 2 could also have used a similar, but longitudinally much shorter, form of lateral constraint. The Peg-&-Slot used in the page 2 sketch is perhaps simpler in that case, because its Front-Bulkhead is just BEHIND the beam.

Here the B-I-T joint is simply a conventional "spherical joint", with its "ball" bolted firmly to the front of the wishbone, but with its "outer-race" allowed to slide longitudinally in the cylindric housing attached to the chassis (ie. attached to the mandated very strong FB here). The cylindric housing might have an internal bronze sleeve for a "proper job", but not really necessary in FS/FSAE. In fact, the "ball" just has to be reasonably stiffly constrained laterally, but allowed to move a small amount longitudinally. A rubber bush inside the cylindric housing would do the job.

The combination of the B-I-T joint at front, and the Apex-BJ at rear, gives the beam as a whole an 0.8 metre wide "base", along the centreline of the car, to resist any "yaw" (ie. "steer") motions of the beam. This gives very stiff directional control of the beam.
~o0o~



BEAM STRUCTURE - The entire beam is fabricated from folded sheet steel, typically 1 - 3 mm thick. With the dimensions sketched I would suggest mostly 1.6 mm thick (= 1/16" or 16 gauge). This is thin enough to easily fold, and thick enough to easily weld. Some details of the fabrication techniques are shown at the bottom-right of the sketch.

Most of the tubes are folded into octagonal cross-sections, about 60 mm across flats for the main tubes. In fact, the main-beam would be marked out with folding lines ~30 mm apart for the horizontal/vertical faces, and ~20 mm apart for the "bevelled corners". These octagonal cross-sections mean more corners to fold than square or rectangular sections, but the folds are only 45 degrees rather than 90 degrees, and more folds better stiffen the flat faces against buckling.

Also shown are two "reverse folds" at the edges of the sheet where the tube's "seam" is later welded together. This requires extra folding work (I would clamp the sheet so it overlaps the edge of heavy steel table, and use hammer to make these small, sharp-edged folds), but it makes TIG welding of thin sheet, say <1 mm, EFFORTLESS! NO filler rod used, just melt the two lips into each other. A conventional butt-weld can also be done, perhaps with an aluminium backing-bar to prevent burn-through of thin sheet.

The two tapered torque-arms are made with the folding lines converging at the narrow end to ~half the distance given above. So near the Apex-BJ these torque-arms are ~30 mm across flats. A nice gusset can be welded into this Apex-"V" to stiffen everything up. Use a BIG BJ here, perhaps 10 mm ball-bore. Smaller will save negligible mass, and will soon wear-out and start rattling.

The most highly stressed parts of this beam are the "elbows" where the SD-lower-BJs attach to main-beam-to-torque-arm nodes. Here the torque-arms are merged with the main-beam so they meet the outboard part of the beam, which rises up at ~45 degrees, at a mitre-joint cross-section of about 100 mm wide, x ~80 mm high. The rising part of the beam then tapers to meet the next outboard horizontal section, which is ~60 mm octagonal inboard, morphing to 60 mm SQUARE outboard. Folded sheet structures allow lots of fancy stuff like this!

IMPORTANTLY, all the mitre-joints (aka "lobster-backs") MUST have internal webs! Well, you can try without, but the structure is greatly weakened. These webs prevent the corners from crushing under bending loads. (Do some force diagrams of the skin-stresses!) The webs can be the same thickness sheet as the outer skins, or can be twice as thick with a lightening hole in the middle. The thicker webs can make the welding procedure easier, or not, depending on details...

The amount of gusseting required at the various joints is best determined as follows. Make rough trial-run beams, then LOAD TEST TO DESTRUCTION! Note where the skins first start to buckle, or buckle the most. Gusset said weak points. RETEST TO DESTRUCTION ... until whole structure is giving up UNIFORMLY. So, NO WEAK POINTS.

BTW, I made a half-scale, half-beam (ie. only one side of centreline) out of about half a cereal-cardboard-box + sticky-tape, in about one hour while watching telly. Hot-melt-glue-gun does a better job of "welding", but is messy, and, err..., kids have "hidden" it! This sort of Cardboard-Aided-Design makes it very easy to decide where "faces and edges" should go, and gives a quick and accurate indication of how the structure will fail, so where more section-size/webs/gussets are needed.
~o0o~

STEER-AXES - My preference is the Inverted-Tractor-KPs as detailed on this SLT-Swing-Arms post. Compact, strong, stiff, low-friction...

Alternately, a more conventional upright can be used, as shown at top-left of sketch. This has Camber-Adjustment by shims between the beam and a small "Top-BJ-Carrier". This gives Camber-Change = Steer-Axis-Inclination-Change, which is OK. Castor-Adjustment is made via swapping different Top-BJ-Carriers, which move the Top-BJ fore-aft. Castor should only need to be adjusted occasionally in early testing, so "change-part" restrictions in the Rules are NOT a problem.

A big-ish question here is do you carry the vertical Fz loads of this conventional upright via the lower-BJ, or the upper-BJ, or both? I know what I would do... but I prefer the Tractor-style...
~o0o~

Last bit next (10k char limit!!!)

Z

[Z]

(Last bit from above...)

SIDE-MOUNTED BRAKE-M/Cs - These are carried on an "L"-shaped pedal-tray bracket, which can slide fore-aft and is fixed in position by a single spring-loaded pin at the base of the left-side FRH. The front of this bracket also carries the throttle-pedal (not shown) and is located sideways and up-down by some simple "slide-rails".

The foot loads on the brake-pedal are transferred rearwards by two pullrods connected to the side of the pedal. Note that this puts the pedal structure under considerable torsional loads, so it should be fabricated as a hollow sheet steel structure (as above!), NOT as a pretty, but flimsy and expensive, billet-machined 7xxx part. The pullrods actuate two "pull-type" M/Cs, which in turn connect to a vertically oriented balance-bar, just in front of the FRH.

The advantages of this system over the more conventional "M/Cs in front of pedals" are:
1. Significantly shorter chassis for less overall mass, and MUCH less Yaw-Inertia because the heavy Front-Bulkhead is as far rearwards as possible.
2. The M/Cs and balance-bar are moved rearward for lower Yaw-Inertia again.
3. The brake-pedal, M/Cs, and balance-bar are all a planar mechanism so can use low-friction revolute joints (eg. needle rollers) everywhere, rather than higher friction sphericals, thus giving more accurate brake-balance.
4. Adjustment of brake-balance is within easy reach of the driver (ie. under his left knee), without the need for the usual messy cables, etc. (BTW, the detailed balance-bar design has been thought through (it is simple and easy to make), but no room to sketch it...)
5. The large brake-pedal loads (ie. ~2 kN) are fed back to a central and strong part of the car, namely the base of the left-side FRH.
~o0o~

Enough for now...

Z

[CWA]

Z, it's slightly off topic and I'll admit I haven't read all of the text in your posts above. But I'm very curious to know, how much time you spend on your sketches? I really think they are fantastic. Do you sketch in pencil first and make adjustments, or do you get it all right first time in ink? Your talent for drawing is quite indisputable.

[Jay Lawrence]

Z,

What are your thoughts on the possible compliance with the sliding joint at the front bulkhead? I imagine this to be something that would be difficult to get right in practice (perhaps why you've suggested rubber bushes instead?)

Also, given how critical it is to have a solid brake pedal I find it hard to believe that your system would create confidence for the driver. I would think that the "L"-shaped bracket would also want to be bolted/retained up close to the pedal pivot (less practical for adjustment, but I just can't picture a lightweight solution according to your concept)

[Z]

With Oz-14 comp and Xmas I missed some above posts...
~~~o0o~~~

Matt,

Thanks for the frame images. I have dozens of similar little spaceframe sketches floating around here. Unfortunately, all the good looking ones are ... illegal!

It seems that whenever I find a way of "connecting the dots" that works really well, there is at least one (stupid!) little Rule that gets in the way. For example, equilateral triangles work well in spaceframes, but one of the Rules has words to the effect of "... in side-view the FRH must be within 20 degrees of vertical". I want to put it at 30 degrees from vertical, for nice equilaterals...!

Another of my sketches has the MRH and FRH at 45 degrees in side-view, and meeting at their bottoms. So the MRH follows the driver's back, and the FRH follows the driver's thighs, for really good side impact protection and a neat and very stiff frame. But the above "20 degree FRH" Rule again makes this illegal. Probably also illegal by the SIS Rules. Aaarghhh...
~~~o0o~~~

Harry,

It looks quite close to ECU's current car, at least at the rear...
~~~o0o~~~

Ralph,

Sorry, no idea?
~~~o0o~~~

CWA,

... Do you sketch in pencil first and make adjustments, or do you get it all right first time in ink?

Very briefly, it is NEVER, EVER, right, even the umpteenth time. Which is why pencils have erasers, biros have white-out, FSAE students have angle-grinders, etc... (And yep, damnit!!! Missed one tube...)

Several other people have also asked, so here is the general process.

I start with "an idea", then flesh it out with a lot of roughly drawn freehand sketches. These are typically quite small and drawn in the margins of the TV times while I am watching some junk on telly. So lots of time to do these! The sketches are taken from whatever "view" makes the idea easier to see or understand.

When I decide to turn one of these "ideas" into a sketch for this Forum, I usually do a few more rough drafts on small post-it notes (ie. about credit-card sized). This way I get an idea of how much information I can put into the finished sketch. In a way, these "small pictures" clarify the amount of "Big-Picture" thinking that can go into the final sketch. This is a bit like writing a point-form summary of some big subject, or stepping back from whatever you are working on to get a better over-view of it.

For the more complicated sketches (like the last one), I then do a rough, freehand, draft-sketch on A4 paper. This gives me a better idea of how much detail, both drawings and text, I can fit into the final sketch. Next I stick the draft onto a drawing-board I have, and start the actual sketch, also on off-the-shelf A4 white paper.

The drawing-board makes the isometric drawings a bit easier (ie. these have a vertical Z axis, and X and Y at +/-60 degrees from vertical). However, the old fashioned straightedge with a built-in roller works just as well for these parallel lines. I also have an ellipse stencil for drawing "isometric circles" (eg. the wheels, etc.). This stencil is a piece of plastic with elliptical holes in it, which cost ~$1.00. I also use similar "round circle" and "french curve" stencils, which are easier than a compass for small circles, although I have a cracker of a homemade compass for accurate large radius curves.

For the drawing proper, first comes the border, in black medium-point biro (ie. "ballpoint" pen). Then a bunch of pencil "construction lines", mainly the ground level centrelines, verticals through wheelcentres, etc. Once there are enough pencil lines to give a good idea of where everything goes, I fill in the details with a standard biro. Thicker lines are simply multiple biro lines next to each other. Also used very often is the "aaarghh!" white-out (ie. aka correction-fluid/~white-paint).

Text comes last, usually on a normal table because the drawing-board is in an inconvenient corner where I can't lay it down flat, Then all pencil construction lines are rubbed out. And maybe a bit more white-out and touch-ups...

Next comes the hard part! I have a really old scanner (last century? ) that works well and has a reasonable editing program (ie. allows files to be easily touched up, compressed, saved in different formats, etc.). This is still perfectly functional, but is on an old computer with no USB ports. So I now have to use a new scanner (admittedly only ~$59), which is a right PITA! Aaaaarghhh!!! Editing options include "Try your luck"... Honestly!

I have recently downloaded "Gimp" for last minute touch-ups, but its "ergonomics" are, well, at the poor end of the FSAE scale. I use it so I don't have to go through the scanning process a second time. I prefer a purely "black & white .tif" file, but the current scanner insists on "greyscale", and between that and the Google upload procedure the background to the sketches gets a bluish shadow. I guess I could try more trial and error to fix this, but...

All up, the last sketch (at the high-content end of the scale) probably took less than four hours from blank paper to scanned image. The initial rough drafts a lot less, but these are done in "free time", and are the most enjoyable. But the touching-up in Gimp takes an almost arbitrary (bordering on infinite?) amount of time. The purely B&W images were much easier for this, but, honestly, the ergonomics of even simple tasks like erasing little blotches is TERRIBLE. Even navigating with Zoom and Pan is a right PITA.

However, the hardest part of all, is deciding what to put in, and what to leave out. Given that I use A4 paper, I am probably erring on the side of trying to fit too much in. More different sketches, each with a simpler, bolder, message, is probably better. But that would mean more scanning, gimping, and uploading, which I don't like...
~o0o~

Anyway, bottom line is that the above sketching process is quite similar to the design & build of a whole FSAE car.

1. Start with many, many, rough draft ideas.
2. Decide what to put in, and what to leave out, and proceed to flesh out the details.
3. Execute the details, turning them into reality via the long, slow, grind.

Finally, never be satisfied with the end product, but acknowledge that it must be delivered sometime...

Z

[Z]

Jay,

What are your thoughts on the possible compliance with the sliding joint at the front bulkhead?

NO problems at all. It is a joint like any other. I image an extremely poorly made one might have 0.5 mm of slop, but much less "compliance" (ie. flex). This slop gives a steer-change of the beam, over its ~800 mm "centreline-base", of 1/1600 or less than 0.04 degrees.

Compare that with the slop + compliance of most FSAE steer-arms, which are typically much less than 100 mm long, so with ~ten times the steer-change, or more. And then all the extra slop that comes from a conventional suspension's dozen or more BJs.
~o0o~

Also, given how critical it is to have a solid brake pedal I find it hard to believe that your system would create confidence for the driver. I would think that the "L"-shaped bracket would also want to be bolted/retained up close to the pedal pivot (less practical for adjustment, but I just can't picture a lightweight solution according to your concept).

Tsk, tsk, tsk...

I should have added as one of the advantages that it would give a MUCH STIFFER installation than many of the conventional pedal-trays and brake-linkages.

Think about where all the forces go. Do some FBDs! Here is a start...

1. FBD of Driver while braking.
Vertical: Gravity pulls down, Seat-base pushes up (~1kN each).
Horizontal: Left-side-seat-back pushes forward on Driver's-back (2kN ->). Brake-pedal pushes rearward on Driver's-left-foot (<- 2kN).

2. FBD of above Side-Mounted-Pull-Type-Brake-Pedal-Tray.
Vertical: Small gravity, etc.
Horizontal: Driver's-left-foot pushes forward on Brake-pedal (2kN ->). Double-shear-pin-at-left-side-FRH pushes rearward on Pedal-tray (<- 2kN).

3. FBD of Frame.
Vertical (...).
Horizontal: Driver's-back pushes rearward on Left-side-seat-back (<- 2kN). Pedal-tray pushes forward on Double-shear-pin-at-left-side-FRH (2kN ->).

This would be much easier with a simple sketching facility, but put simply,
ALL THESE FORCES TAKE THE MOST DIRECT PATHS POSSIBLE!!! All forces are in a straight(-ish) line from Left-side-seat-back to Brake-pedal!

For anyone who still can't see this, picture a rope (roughly equal to the brake pull-rods) tied to left-side-FRH and looped around driver's left-foot while he pushes it forward HARD!

Ahh... education system... groooaaann...

By comparison, some conventional pedal-trays use leverage to create much larger forces (ie. 3++ kN) that act vertically, trying to rip piddly little bolts out of a flimsy floor! (Do FBD of the "almost vertical M/Cs" that are quite common.)

Z

[Jay Lawrence]

Z,

Thanks. I guess with the slop I imagined a fairly short length of bush being subjected to that variety of forces would cause any slop it may have to 'catch an edge', which would be bad for nice suspension movement (kind of like a poorly designed wishbone fouling on a pickup or something). I'm probably just imagining problems because I haven't tried this solution myself, hence the question.

As for the brake system: I'm aware of where the forces go, it was more the mounting method that concerned me. Do you intend to hammer the locating pin in so it's a nice fit with zero compliance? Or am I missing something?

[MCoach]

Yep, can vouch for forces that could almost rip bolts out of the floor from "almost vertical MCs". However, 3/4 that hold our pedal assembly together are in compression. So it's no big deal.


One thing that may be more related that bothers me that is more related to suspension design that most people don't seem to take into account is lengths. I'm not talking about mechanical leverage, yes, that should be a given. But rather how much material is used to create these connections. For example, Z, your brake MC placement seems very logically sound, but if presented to me I'd ask the understudy to compare this design's compliance to the conventional pedal in bending (MCs at bottom) and the now "conventional" (oh crap, am I calling something very unconventional outside of FSAE, conventional???) near-vertical MCs.

I'll tie this back into beams and suspension in a just a minute...

The reason being that however sound your load paths may be, I'm concerned about the load lengths. A pedal with near vertical MCs, if designed correctly, can essentially render the main section of the brake pedal nearly loadless, loading mostly into the MCs, thus making the analysis of deflection relegated to the transferred forces to the floor which could be innumerable in material choices and design as well as brackets, so I'll leave it alone. I could go into the comparisons of the load paths further, but essentially it boils down to a comparison of the total deflection of the parts. Is it worse to have a 8" 1"x1" steel box tube pedal in bending (conventional design) or to have two 30" ~5/16" solid steel(?) rods that connect to the brake pedal at the same point (and the pedal is still in bending)? It would be beneficial for someone to check with their own braking forces to compare the three I'd be curious at the result and most likely your design judges will, too . If Claude is going to make sure you know the compliance from your brake pads, you better know the compliance from everything else up to that point, too.

So, back to suspension things. One more time with feeling. Our team used to be very big on titanium for everything, it's the material of race cars and mach 3 recon spy planes. It's awesome stuff, right? Oh, yeah it is. Our '09 car used titanium suspension links that saved us a lot of weight that were all designed for strength so that it would survive the suspension forces. However you could always tell if the car was driving in pictures because if the rear suspension was not positively cambered, you were obviously stopped when the picture was taken...and a cone killer...facing the wrong direction on track...like me :P . I did a study last year on how camber compliance from the suspension design and assembly may have affected our total camber gain. To summarize, things start to show their nasty side when you imagine that the rear links were about a meter long and weighed less than the 1/2" x 0.028" steel stuff people use now, so LOTS of compliance. It turns out that from our design, yes, we effectively had positive camber gain with the links contributing more than the wheel. It was geometrically sound, of course, but was basically held together with fishing line and long sections of it. It just didn't work the way the designer intended.

So, now the kicker. If you double the length of your part to "optimize" it's load path and reduce the resultant load by 20% or something arbitrary, if reduced at all, what has really been accomplished? One step forward, and two steps back...

[BillCobb]

Why aren't you evaluating your sketchers in F.E. analysis ? If you were working for me and swagged out a suspension, steering and body assembly for a vehicle without supporting documentation from first a stick and then a plate, tube, rod and rubber bushing element model, your next and last work endeavor would be in the Design Center cafeteria.

Your model had better be 90% to 110% of an alpha vehicle K&C compliance test result. And don't forget the wheel bearings and degrees of freedom they interact with. In my experience, the FE models are probably more accurate than the Mule vehicle results because of the approximations used to construct a mule from old stuff.

[Goost]

So, now the kicker. If you double the length of your part to "optimize" it's load path and reduce the resultant load by 20% or something arbitrary, if reduced at all, what has really been accomplished? One step forward, and two steps back...

What is often considered the seminal paper on structural optimization gives a fascinating introduction to how to think about these concepts.

A.G.M. Michell. The Limits of Economy of Material in Frame-structures. Philosophical Magazine Vol 8. 1904.

Attached an excerpt. I think this can be found on Google Books. Short story - make everything parallel/perpendicular between loads and constraints. Where curvature is needed to 'connect-the-dots', replace parallel/perpendicular with tangent/normal (in a circle or a logarithmic spiral).

Doesn't only apply to frames either - in many practical circumstances applying topological optimization to a 'smooth' shape (e.g. monocoque) will result in a frame-like 'optimal' anyway (e.g. space-frame-like strips of reinforcement within the monocoque wall).

So assuming you have access to water-jet, maybe the ideal beam axle looks something like this [attached] cantilever...