Vehicle Dynamics starting points and design process

Hi everyone,

So after being soundly made to look stupid in my last few posts here I'm back with some more on how we're progressing!

Firstly, I would like to give some 'real' justification for front and rear beam axles beyond the fact that they significantly reduce frame complexity and weight. At the start of this thread I talked about the uselessness of the Avon tyre data and was advised by Claude to seek out access to the TTC, I did, and was told that it was not an option to fund the resource. The reasons why it was rejected is beyond this thread. However, given that the previously mentioned Avon data is for most purposes useless, how would it be possible to decide upon a front view virtual swing arm length for a double wishbone system? what exactly would have been the justification without tyre data? beyond the original optimumlap sim I ran? With this being the case the use of beams makes a lot of sense for this reason alone, there is no need to consider a FVSAL because there are no compromises in pitch or roll, the need for tyre data to establish this parameter is eliminated.

I appreciate that other factors to be decided remain unchanged such as ackermann geometry, anti-dive, etc but there's considerable literature available to support various points and depending on the method of constraining the beams certain parameters are almost fixed by structural needs. Whether you consider this to be a disadvantage of a beam is up to you but personally, I find it advantageous as there is no 'black art' aspect involved, the answers can be found through first principle generated numbers.

Furthermore, comparison of last years car (in CAD) and this years car shows a considerable drop in yaw inertia (the actual numbers I have forgotten but we were talking at least 5%) this is because there is a much lower proportion of chassis members outside of the wheelbase and the pedalbox is 10cm shorter than previously.

Initial studies on the front beam also show a camber compliance in the region of 0.5deg/g, sounds rather large, so maybe something will be done to reduce this. But, consider this, the beams have FVSAL = track/2 in roll therefore, 100% camber compensation in roll, compare this to a car with 50% camber compensation in roll and is a compliance of 0.5deg/g really that bad when after 1 degree of roll a car with 50% compensation has already lost 0.5deg due to geometry?

Moving on, the upright steer arms will be 100mm long, this is a practical limit due to both the wheel and the desired wheel/wheel ratio, I initially decided upon a bevel gearbox ratio of 2.5:1 however, discovering that no one in the local area makes these ratios (and that trying to calculate your own gears and then finding someone to cut them is actually rather tricky!) I found a local supplier who will supply 2:1 and 3:1 ratios. Personally, I believe the 2:1 ratio will result in steering which is too heavy so I have decided the 3:1 is the best compromise. I have put together a brief set of numbers which are included as an attachment, the second tab includes the formulas used for calculating the 2.5:1 ratios in case anyone is interested. One thing I have been able to use the Avon data for is approximating the maximum self aligning torque (~90Nm) and then assuming this is being 'fought' by the driver to give the necessary torque the bevel gearbox must carry. I think I may have made an oversight here but I'm interested in what others have to say. Using these numbers gave a crown gear torque of ~70Nm, using a 3:1 ratio this drops to ~25Nm at the steering wheel, this is directly at odds with this article (http://www.sae.org/students/cockpit_control_forces.pdf) which suggests the the system should be designed for a steering wheel input of 100Nm. This being based off data of peak torques generated by test subjects, now, my question is, is my assumption that the 90Nm aligning torque as a maximum is wrong? or is it that these tests are effectively assuming that said person is trying to resist the tyre striking something such as a kerb?

This brings me to the next part of this problem, selecting a 'correct' gearset. The gears will be sourced from Cross+Morse (who are pretty local to the University) the data sheets are shown here: http://www.cross-morse.co.uk/pdf/Bevel%20GearsEN.pdf . After some testing (using a gaming wheel) we concluded that it's reasonable to expect the wheel to be turned at approximately 60rpm, following from this, the transferred power (assuming crown gear is made to withstand 100Nm) is 0.628kW. Looking at the data sheet (and assuming a moderate shock and light impulse modifier of 1.5) this suggests that gear set M501545 is appropriate but this gear set is enormous and heavy! with a crown gear of diametrical pitch of 225mm and a pinion dp of 75mm, this is unacceptably large and heavy (8.4kg!!!!), now, it makes sense that at higher rpm these gears can withstand higher powers as less torque is transferred however, I don't believe it right to just assume the rpm is twice as much to end up with a reasonable gear size.

But onto the rest of the car!

The front beam has been redesigned to be a leading arm with peg and slot lateral restraint, the reasons for this were discussed previously and have allowed the front roll hoop to move rearward by 200mm, this has also condensed more frame mass towards the CofG whilst retaining very similar chassis masses (difference of -0.2kg). One interesting thing is that with the rearward balljoint and the 'peg' placed on the chassis and on an axis parallel to the ground plane axle roll steer is reduced to zero throughout the range of travel WRT the body since this axis is fixed on the chassis. There was also the added advantage of removing any interference issues between the steering arms and the damper units. A few pictures are shown below:

http://i1296.photobucket.com/albums/...ps389f4e60.png

http://i1296.photobucket.com/albums/...ps72fd9f13.png

I imagine most will note that the arms do not converge at the balljoint and hence put the lower link in bending, this is a further concern since in braking this link is also in compression, yes there is a buckling concern however, if the links converged at the balljoint housing then the driver would be sitting through the links! I'd also assume that it's noticed that the links actually pass through the frame, my understand is that this is fine providing they are shielded by a solid material (at least, that's what the rules say) thus, the floor will sweep over these links which will also form the leg support for the driver. In order to fit the beam in the car it will be welded up as shown in a jig before the upper links are cut out, sleeved and then bolted back into the beam, all this will be done in a jig to prevent any alignment changes.

The rear went from a folded construction to a bent tube back to a folded construction again. This was because the requirements changed, initially we were going to run rear uprights however, weighing up the benefits of the reduced complexity and weight versus the lack of adjustable toe we decided that integrating the hubs into the rear beam was a more worthwhile endeavor. Again the beam will be made up within a jig to minimize any resultant toe angles from construction. Please excuse the poor quality of the CAD, it was drawn up in somewhat of a rush.

http://i1296.photobucket.com/albums/...pse893c9e2.png

Since there are no longer rear uprights and hence there is no longer a 'steer axis' my thoughts were that the center of the hub bearings have now effectively become the steer axis, as such, in order to minimize scrub radius and hence tyre advantage the beam has been pushed out as far as possible into the wheel, this has resulted in a scrub radius of ~50mm. The shock position results in a motion ratio of 0.5, yes this is digressive as the system will move similar to a scissor jack but it is yet to be determined whether this is a problem or not. The rear roll center works out to be 90mm, resulting in 1/3rd of the weight transfer being kinematically transferred. In contrast to the front 0.8 degrees of axle roll oversteer is present, this may be too much? but it is thought that this will help to turn the car into corners and reduce understeer common of FSAE cars, so passive steer effectively.

From a personal point of view tensions between myself and the 'management' have calmed somewhat but some issues remain. When a third year mechanical engineering student doesn't understand basic gear principle you know something is wrong...

Likewise, when lazy members try to take credit for my and the chassis guys work we can't help but get somewhat annoyed.

There's more I've forgotten I'm sure but that will be sufficient for now I'm sure, as always, feel free to throw stones/ask questions/etc.

Thanks,

Christian

EDIT: Oh and I've started investigations with one of the faculty advisors into the future development of an un-sprung undertray for this year or at minimum next.

EDIT EDIT: The front beam is not complete! so don't blast me for the peg and slot having no side support or the use of a single gusset for the shock support, the shock support will be boxed and the peg and slot will have side supports I just haven't drawn them in on the CAD yet because it's time I can better spend doing other things!

Don't forget to add the Moments from the trail and offset to the self aligning torque of the tyre.

I think there might be some confusion between max design strength, and expected steering forces. 100Nm sounds like a reasonable value for the highest loads a person could exert, but is miles too high to steer the car.

Pete

Christian,

Looking good. Just brief note for now ('cos Xmas-Chaos!!!).

Quick look at your gear charts, and I would pick either M251545, or maybe even M201545. The power ratings given (though I didn't look closely) are probably VERY conservative. The M25 or M20 gearsets can be lightened a lot by machining away much of the heavy bosses.These are made extra big so that customers have plenty to work with. Choose slightly bigger gears now, then next iteration you can go smaller and lighter and use the company's induction hardening services.

As theoretical check of your required gear tooth size just calculate what load at the steering-wheel rim is required to shear one tooth off its base, assuming tooth made of mild-steel. If this load is much bigger than, say, 100 kg, then unlikely the driver can do it. Plus you have the safety factor of the tooth being better-than-MS. And maybe add another SF = 2+?

The overall arrangement is really looking good. Track width looks quite wide though?

For the Model-T-front-beam I still suggest the tapered torque arms as suggested on page 12. This is also the way Ford, and countless others since, have done it. All round simpler, lighter, lower-CG, stronger, easier, +++. I will post another sketch on a slight variation to lateral location for this type of beam soon, but silly-season now...

Also good idea to build at least two of each beam, both front and rear. A "lightweight" one for initial testing (ie. to check compliances and ultimate strength) and a significantly stronger one for "just in case". So if the lightweight one fails just before comp, fit the heavier one, take the 5 kg (?) hit, and go on to complete all Dynamic Events. Note how UQ at Oz-14 had to significantly (!) brace their lightweight rear-beam just before comp, even though initial testing showed it to be OK. More testing = faster drivers = higher loads everywhere!!!

Z

Christian, seems you have made some solid steps since the beginning of this thread, keep it up! Adding to Pete's comment, think that you most probably need some camber/toe adjustment, as those are important factors to vehicle setup (actually near the top of the list together with springs/LLTD and tire pressures). Hint: Take a look at Z's adjustment method proposed on "Suspension Design" thread, where he talks about swing axles (cannot find the link right now)

Wow. What a great thread! I've got some reading to catch up on here...
Nice work Christian.
OK. Digressive rate at rear. Therefore with weight transfer to rear (under accel) the ratio of F:R roll stiffness becomes more forward biased compared to linear rate. Therefore lateral loads taken more on front end than with a linear rate rear. Therefore less weight transfer across rear axle than with a linear rate rear. Therefore better grip under accel???
Does that make sense?

Pete, Ahh yes, thanks for reminding me! I had realised I was missing the mechanical trail x lateral force and the scrub x longitudinal force torques but at the time of writing I had forgotten that the initial investigation failed to consider these. Rather silly considering I talked about the scrub radius and resultant tyre advantage at the rear! You're correct that there is some confusion, from personal experience with torque wrenches, karts, etc, I was thinking that around 20Nm max for a 'normal' steering load but my argument is that if it only takes 20Nm or so to turn the wheels dry (and steering torque reduces at speed) then why is it necessary to design to 100Nm? It seems pointless to me because it is not physically possible to exert this torque and have the tyre react it unless the tyre is somehow bolted rigidly to the ground. You'll end up with a system somehow capable of transmitting ~300Nm to the wheels, also, I remember doing up flywheel bolts to 110Nm and I was using all my strength on a 0.5m+ long bar. Given this, I see 100Nm as a totally unreasonable load to expect the steering to withstand.

Z, the gear 'size' you have selected tallies closer to my original estimates when running through the ANSI document to size my custom gears, this would have resulted in a pinion capable of reacting approx 40Nm of torque. I will perform the shearing calcs to test the smaller gear set though and also contact the company to see what their specs really are. I agree that the gears can probably lose much of their weight through some 'lightening' holes and reduction of the bosses so I'll look into that.

The track width is 1200mm, from a rough drawing of the car inclined at 60 degrees we were unhappy with how close the CofG was to going 'over' the outside tyre pivot so when considering transient maneuvers and the early talks of lifting inside wheels I decided to bring it up to 1200, it can always be reduced next year if we think it necessary.

With regards to the tapered torque beams you're going to have to show a sketch or picture as I'm having difficulty understanding where you're coming from, I looked at model T beams and they appear similar to the one I've drawn albeit missing the upper links. This isn't exactly possible in our configuration unless the beam was inside the car. One option is to 'split' the pivots so that there is a pickup on either side of the car for each side arm pair, whilst this makes the structural issues easier and lowers the loads, since the convergence point of all 4 is now 'imaginary' axle roll steer is back to changing over the travel and the beam must also now be torsionally flexible otherwise it's over constrained. I suppose this is easy enough to do by cutting holes in the front view of the beam and might even be helpful for feeding air to an undertray?

The plan is to have two beams as suggested, one as the 'design' and the other as the heavy weight with double thickness of all sections.

Mech, thanks :) I see where you're coming from but I honestly believe we will benefit more from jigging something to spec at the rear and just driving what we end up with, any issues can be fixed next year. The front will however have both toe and camber adjustment, toe through the threaded arms and camber by having different housings slotted into the ends of the beam. Hopefully we don't have to use the second but it's possible if necessary.

Geoff, firstly, it takes a strong person to accept they were/are wrong so a big thumbs up for the UWA thread although I don't believe that you should be held to account in isolation but that is for another thread. Elsewise, thanks :) and yes that makes sense to me! Via a similar logic though front springs stiffening relative to the rear will give understeer on corner exit?

More to come soon, busy with Christmas!

Thanks,

Christian

Christian,

Another short note...

Track width =1200 = good. Much more = too wide = too slow through the slaloms. Much less = too risky for roll-over, given unknown CG height and cornering grip levels.

For the tapered torque arms see this SLT-Swing-Arms post. Try to make sense of the structure of the arms there, from the image and any words describing it (also more words in some later posts I think). Otherwise I can post another sketch later. It is all straightforward blacksmithery, and very useful stuff to learn for projects like FS.

For Front-Camber&Castor-Adjustment I suggest an adjustable, or replaceable, bracket between the beam and "upright", either at the upper or lower BJs (only one needs to be adjusted). (Edit: Angle-grinder and welder also good for adjustments here!) Toe is easiest adjusted via the toe-links (ie. conventionally).

For Rear-Camber&Toe-Adjustment you can use something similar to above Swing-Arm link.
BUT (1) if you can do a stiff, accurate, and UN-adjustable zero-camber&toe-angle beam, then that would be good enough. That is ECU's approach.
BUT (2) I also have another suggestion. Do the ends of an unadjustable beam with short horizontal-lateral-axis tubes at the ends that act as the bearing-carriers. Make these tubes with ID about 10 mm larger than the OD of your bearings. Then fit a sleeve inside these tubes that carries the bearings, and is clamped in place by the outer tube. Importantly, machine inner-surfaces of this sleeve so they are NOT parallel with OD. Say 1 degree out of parallel. Then, by rotating the sleeve you can get camber = +/- 1 degree, or same from toe, or a combination inbetween... Or replace sleeve with another one for bigger/smaller adjustments of camber&toe.

The "split pivots" twist-beam, with connection to chassis at each side, is a good idea. BUT (!!!) it requires considerably more structural know-how than the simpler Model-T style. Maybe for next time...

In side-view the Model-T apex-BJ only has to be about 0.4 - 0.6 metres behind front-axle-line. Not sure where yours is, but in plan-view an "X-shaped" floor brace, fitted between the V-shaped SIS tubes and the FRH, could carry the apex-BJ at its crux. (Edit: This structure would work very well for torsional stiffness. Think about the "load paths". Though tor-stiff NOT very important...)

Must now go a-visiting...

Z

Christian,

The ECU beam has shims to adjust camber and toe. Enough to be zero for accel, and a couple of degrees for skidpan. A shim in for toe adjustment, just to account for welding deformation. Nothing fancy, just thin shims inbetween a bearing carrier and the beam. The goal was to make it non-adjustable in the future once testing showed what camber was best to run. Not so sure anymore as the adjustment was very useful.

There are nicer ways of doing this. Z suggested machining the bearing carrier off axis to allow a few different angles depending on orientation.

Love the work by the way. Some nice simplifications and shouldn't be too hard to pull off.

Kev

Z - Yes that was the idea on the track, as much as was necessary to be 'stable' but no more :) maybe 1150 or less next year...

I have looked at the post you mentioned, I can see where they're going but if you look at the front beam and consider if you were to place one beam in the place of the two links. It would be around midway between them, trying this ends up with the arms intersecting the chassis quite catastrophically so the only way to do it would be to remove the upper link entirely and replace the lower link with a much thicker one. It would probably be necessary to fabricate some gusseting between this and the upper attachment point too, I will try this although initial attempts have not been promising! I'm just concerned I'd be placing a considerable bending load (pretty much the entire braking torque) on the attachment between the beam and the arm.

Front camber is adjustable by the method you mentioned already, those open box ends will have billets which connect to the upright, these will be removable and hence provide 'adjustment' probably only +-2 degrees of caster but easily enough camber (2,3 maybe even 5+ possible!).

I like the idea for the rear, although I don't understand how such a mechanism would be restrained, what happens if the housing spins? and if it is a press fit then it's not exactly easy to adjust anymore?

The pivot point is 640mm behind the axle line, I will show more pictures tomorrow so you can see more of what is happening underneath the car.

Kevin, thanks for your input, I was hoping I'd hear your thoughts on this at some point! :) Interesting to know how much adjustment you had given the similar rear setups, did you have any issues with movement of the shims? Thanks for the compliment though, hopefully it will all come together well.

I was hoping to have all my design work done by Christmas but it looks like I'll be overrunning slightly unless I can get all of this sorted over the next few days which is doubtful.

Christian

Z's link was the one I was talking about a couple of posts earlier. Consider that camber adjustment method would be better to be done by replacing something solid (i.e. shims) rather than using some sort of slider, as loads are high and you want to avoid compliances as much as possible. Kev I had a short talk to some of the team at UK which mentioned that camber and caster are shim adjustable. How you guys cope with mounting holes/bots misalignment though? Slightly overbore holes and call it a day?