torsional stiffness

[Karam El Hady]

Hi everyone i'd like to know how is torsional stiffness is good for chassis and how is it related to suspension force and what is the optimum valve of torsion stiffness for space tubular frame
and when i know that the valve of torsional stiffness enough to resist the suspension forces ?

[Claude Rouelle]

Karam,

Based on what I have seen in many years and many competitions for a tubular chassis 2000 Nm/deg from hub to hub (what is the point to have a stiff chassis if you have uprights and wishbones in chewing gum- a stiff spring in series with a soft spring is still a soft spring) and less than 25 kg would be a good target.

For a composite monocoque 8000 Nm/deg and under 15 kg is a good target

Just to give you an idea an LMP1 is now over 100KNm/deg. Bigger than F1. Because LMP1 cars rear bulkhead is much lager (bigger m^4) and it has a roof.

Make sure you calculate and you measure everything. Most of the time FEA is too optimistic. See picture. Without validation you won't impress any design judges.

Some students measure the chassis torsion stiffness from the front to the rear bulkhead. OK, it is a number but it is not relevant. Chassis torsion comes from a different roll torque front and rear. The forces comes from the tires to the chassis via the suspension and the inboard pick up points. That is why hub to hub measurements make sense. Be aware you still miss the compliance of the rim and the inevitable compliance of the tire.

Make sure you calculate and measure the chassis torsion stiffness distribution: you can have a first half of the chassis stiff and the second part stiff or vice versa and still have a total chassis torsion stiffness the same. But the car behavior will be different. A stiffer front part of the chassis will have the same effect as a stiffer front ARB (qualitatively, not quantitatively). When you change the Total Lateral Load Transfer Distribution (TLLTD) - what I call a magic number, there will be a "sweet spot, within a few 1/10 of one percent- that will give you a good balance performance - you change the Yaw moment. On a Go Kart there isn't front or rear ARB or springs either but they change the TLLTD by adding (bolting) or removing a front of a rear chassis brace

If I was you I would measure the chassis torsion in at least five different planes along the X axis. Usually the cockpit area is the weakest.

To know what chassis torsion stiffness does on your car behavior you will need to simulate it. You need a tire model and a good vehicle dynamics model to do so.

If you want to make simulate in transient you will need the chassis torsion damping. I let you find out how to do that...

[Claude Rouelle]

A cheap, alternative solution for chassis torsion stiffness measurement

Make sure the car has dummy – rigid – dampers.

Put shims of aluminum (lets' say 200 x 200 x 1 mm) between the front wheels (or, better, the setup – rigid -wheels) and the setup pad scales.
For example, 10 sheets of 1 mm under each of the LF and RF tires

Jack the car up. Remove 1 sheet from the RF and put it under the LF wheel. You now have 11 mm of shims under the LF wheel and 9 mm under the RF wheel. Put the car down the scales and make a note of all 4 corner weights. Continue like this until the LR load is zero or very close to zero.
Let's say that this happen when you have 17 mm of shims (+7) under the LF and 3 mm (-7) under the RF wheel. The torsion angle is ATAN (7+7)/1200 = 0.668 deg.

Measure the LF and RF corner weight. Calculate the LF and RF corner weight variation. Let’s say it is + 5 Kg on the LF and – 5 Kg under the RF.
Multiply the sum of the LF and RF corner weight variation by the track; you will have a front input torque. Let's say the front track is 1.2 meter, so the torque is (5+5)*9.81*1.2 = 117.7 Nm

Calculate the rear torque which is the opposite sign of the front one. With all the rear load on the RR, the rear torque is, with a rear track of 1.1 m; - (55 + 55)* 9.81* 1.1 = - 1187.0 Nm

Make the difference between the 2 torques, front and rear: 117.7 – (-1187.0) = 1304.7 Nm

The chassis torsion stiffness is 1304.7 Nm/0.668 = 1952.0 Nm/deg.

Worth to also do the same with real tire and dummy dampers or real springs and dummy wheels of real tires and real springs

[Claude Rouelle]

Spreadsheet attached

[BillCobb]

Instead of just dealing with a trivial "chassis torsional stiffness", do a normal modes analysis in FEA and also on the actual car so that chassis, motor and steering parts don't get fastened to spongy locations.

If your stacked (all parts assembled) model is any good, so will be you car. Otherwise, this will be just sandbox play.

https://www.youtube.com/watch?v=xXCeYg969o0


The Matlab CFE looks useful, too.

https://www.youtube.com/watch?v=iWzG8Uqu_dY

[FrederikWe]

Dear Claude,
Where do you have those numbers from? Are there teams out there that really combine a stiffness of 8000 Nm/° and weight of 15 kg? I mean you would surely know and I don’t want to say that I don’t believe you. And if it is also a hub-to-hub stiffness, it would mean that the monocoque is even stiffer?

Realizing weights around and below 15 kg you need a small monocoque. If your skin aera is to big you reach a point where bigger panel heights can't be compensated by thinner ply thicknesses and your mono gets heavier. But small monocoques usually feature a lower polar moment of inertia between the hubs which doesn’t help the torsional stiffness. Even if you go for UHM fibres and maximize the amount of fibres in the 45° degrees directions, I find it hard to believe that you can archieve values like that from what i know.

-Freddy

[dr. ill]

"For a composite monocoque 8000 Nm/deg and under 15 kg is a good target". Those may be good 'targets' but not many teams are achieving those numbers. More realistic numbers are ~3000-4000 Nm/deg and 22-27 Kg include hoops.

[Claude Rouelle]

That is what a few teams have told me. ETS is an example. I did not weight or measure the torsional stiffness myself so I have to trust them. That being said, compared with the large numbers of different cars I know, these numbers seem logical and possible.
Western Australia 10 years ago was in the 6000 Nm/deg region if I remember. If I am wrong any team is welcome to give more information.

Karam asked for some numbers, I gave what I have.

What I am more interested in is the effect of the chassis weight and hub-to-hub torsional stiffness and even more torsional stiffness and damping distribution on the car performance: criteria such as lap time obviously but more simply and probably more useful, response of yaw velocity, lateral acceleration response time (LART), yaw velocity damping, etc to step steer and chirp of steering input (same amplitude but different frequencies)

That is what will help you to make a decision on the compromise weight Vs torsional stiffness Vs time and $

[Claude Rouelle]

Freddy,

"Realizing weights around and below 15 kg you need a small monocoque." Well do you think that the goal of a Formula Student team is to create big cars?

After over 15 years of judging cars in many different competitions I can tell you that what was mission impossible for many teams at year X becomes possible at year X+2 or X+3. You have now cars that are in the 130 KG range but 5 years ago many teams in many FS paddocks told me it was impossible. It is often a question of believing and daring more than anything else.

Claude

[Claude Rouelle]

If you are in the "~3000-4000 Nm/deg and 22-27 Kg include hoops" region I am not sure why you would want an expensive composite material chassis: lots of expense for not such a big difference. You may want to use your time, focus, energy and money somewhere else. Like testing more.

[dr. ill]

Breaking down a 15 Kg monocoque
FRH ~ 1 kg
MRH + bracing +fasteners ~ 4 kg
Hardpoints ~2 kg
AL AI plate ~1 kg

That leaves ~ 7 kg for the carbon, core, and glue sheet.

My rough hand calcs say the minimum surface area for a small monocoque is ~3 m^2. Aerial mass for Toray T800 is ~.325 kg/m^2. Aerial mass for glue sheet is .15 kg/m^2. Aerial mass for 3/4" thick 3.1 lb/ft^3 Al honeycomb core is .95 kg/m^2

So for a 3 m^2 monocoque
Core mass = .95 kg^2 * 3m^2 = 2.85 kg
Glue sheet mass = .15 kg/m^2 * 3m^2 *2 (need glue sheet on top and bottom of core) = .9 kg
Carbon mass = 7kg - 2.85kg - .9 kg = 3.25 kg

How many layers of carbon is that? 1/(.325 kg/m^2 * 3 m^2 / 3.25 kg) = 3.33 layers.

3.33 layers is not possible. That is saying your layup is 1.3c2. This layup would not pass the SES nor give a torsional stiffness of 6000Nm/deg.

A global 4c4 layup (8 layers total) is on the light side with the current SES (average for different zones). Using the same calcs from above, a 4c4 layup would equal 7.8 kg in carbon and would result in a total chassis mass of 19.55 kg.

Again, thats assuming a team is using the minimum surface area chassis. Most teams are not (for various reasons), and are probably using heavier core and layups thus leading to the 22-27 kg range.

Its possible that teams are telling you the bare chassis mass only. IIRC when the design spec sheet asks for chassis mass it does not say if that includes the roll hoops or AI plate (a 6kg difference).

[DougMilliken]

... i'd like to know how is torsional stiffness is good for chassis and how is it related to suspension force...
Study this paper, http://papers.sae.org/2002-01-3300/ Then study it some more, and read it several times through. Once you understand the paper you can start to do your own thinking and develop targets for *your* car. Keep notes so you can describe your design process at competition.

[Z]

Breaking down a 15 Kg monocoque
FRH ~ 1 kg
MRH + bracing +fasteners ~ 4 kg
...
My rough hand calcs say the minimum surface area for a small monocoque is ~3 m^2. Aerial mass for Toray T800 is ~.325 kg/m^2. Aerial mass for glue sheet is .15 kg/m^2. Aerial mass for 3/4" thick 3.1 lb/ft^3 Al honeycomb core is .95 kg/m^2
...
A global 4c4 layup (8 layers total) is on the light side with the current SES (average for different zones). Using the same calcs from above, a 4c4 layup would equal 7.8 kg in carbon and would result in a total chassis mass of 19.55 kg.
...

dr. ill,

Thank you for your objective analysis. NUMBERS ARE GOOD!!! :)

For rough calcs I usually start with a pessimistic/realistic ~7+ kg for the mandatory two-hoops + bracing. I guess you have given optimistic numbers to see if Claude's "15 kg" figure is achievable. I doubt that it is, and such a mass is not really a "logical" goal given that reliability is so important for success. (And note that reliability is more about strength than stiffness.)

However, one way in which your mass-numbers can be reduced, and/or chassis-strength increased, is by realising that ... "MONOCOQUE" DOES NOT MEAN "HONEYCOMB"!

The typical "honeycomb-sandwich" construction used by most FSAE teams for their "tubs" is, for the most part, completely UNNECESSARY. This applies to both the AL-AL and CF-AL (or CF-Nomex) honeycomb versions of such tubs. By the very meaning of the word, a "monocoque" (= "one shell") structure carries the majority of its imposed loads via stresses that lie IN THE PLANE of the shell. Such shell-like structures need very little bending-stiffness of the shell-material itself.

Put simply, the 1.25 kg/m^2 you quoted for the Al-core+2*glue-sheet, is DEAD-WEIGHT. It is an utter waste of mass (and time, money, sticky-fingers++) because it contributes almost nothing to the REAL strength or stiffness of the monocoque.

So a combined "4c4" CF-honeycomb mass of 3.85 kg/m^2 can be reduced by ~33%, down to 2.6 kg/m^2 of "solid" CF-shell, which would be about 2 to 3 mm thick. So the complete tub (less hoops, etc.) drops from ~12 kg down to ~8 kg. Or the tub stays at ~12 kg (with more plies of CF), but is 50% stronger and stiffer.

At this stage there are legions of FSAEers crying "The gibbering old-fart has lost it again! IT'LL NEVER WORK" This, despite the fact that they all drive around in just such "monocoque" structures, albeit with skin thicknesses of less than 0.5 mm! Ahhh..., will they ever open their eyes?

Anyway, local reinforcement of point loads applied normal to the shell (eg. wishbone mounts) can be done with CF-"top hat" sections, either incorporated in the middle of the ~8 plies, or glued inside or outside the shell. The sides of the cockpit (ie. the "SIS") can be similarly reinforced. I would do a cockpit-upper-side "P"-section that is designed (and tested!) to carry all side-impact load. As such, this strengthening of the cockpit-rim would greatly improve overall torsional stiffness and strength.

As I have suggested many times before, similar "true monocoques" can be done in Aluminium (using 1 to 3 mm thick Al-sheet, as used on many small boats), Steel (I would use mostly the super-cheap 0.6 mm thick "zincalume" used for roof-flashing here in Oz), or Plywood (2 to 10 mm thick marine or aircraft-ply). All these would be much quicker and cheaper to do than anything with a honeycomb-core, and have at least as good performance.

To repeat, the shell-material of a true monocoque DOES NOT NEED A SQUASHY CORE! Using such is blindly following the flock. It surely ain't engineering! :)
~o0o~

Last teeny-weeny rant. Having a target torsional stiffness of ~8 kN.m/deg (or more?) is highly ILLOGICAL. I am not sure if Doug's linked ~15+ year old paper covers it, but this issue has been discussed on this forum for ages.

In short, aim for,
Chassis-torsional-stiffness = N x Suspension-torsional-stiffness.

Choose "N" such that small tuning adjustments to the suspension (ie. to TLLTD) are NOT swamped by chassis "floppiness". N = 10 is a good enough round number to start with. Note that the softer the suspension, then the more torsionally flexible the chassis can be, while still being "tuneable".

Z

[DougMilliken]

... I am not sure if Doug's linked ~15+ year old paper covers it, but this issue has been discussed on this forum for ages.

Yep, the paper I referenced talks about that and more. Here's another one that's a bit older, http://papers.sae.org/2000-01-3554/
Follow the links to read the abstracts. If you really like reading posts, search this forum with the paper numbers, plenty of hits.

[oebakkom]

dr. ill,
The typical "honeycomb-sandwich" construction used by most FSAE teams for their "tubs" is, for the most part, completely UNNECESSARY. This applies to both the AL-AL and CF-AL (or CF-Nomex) honeycomb versions of such tubs. By the very meaning of the word, a "monocoque" (= "one shell") structure carries the majority of its imposed loads via stresses that lie IN THE PLANE of the shell. Such shell-like structures need very little bending-stiffness of the shell-material itself.

I fully agree. The monocoques are full of stuff not adding anything.
The SES must take a lot of blame for poor creativity in this area. You very quickly run into problems if you try to be clever.
Your design is perfectly reasonable, and you could maybe reach the targets set by Claude, but I think the hardest part would be to make it compliant with the SES.
Everything is based on out of plane bending tests, and the only recognized failure mode is tensile. Which means an automatic advantage to sandwich structure with relatively thin and dense cores.

[Marshall Grice]

The typical "honeycomb-sandwich" construction used by most FSAE teams for their "tubs" is, for the most part, completely UNNECESSARY. This applies to both the AL-AL and CF-AL (or CF-Nomex) honeycomb versions of such tubs. By the very meaning of the word, a "monocoque" (= "one shell") structure carries the majority of its imposed loads via stresses that lie IN THE PLANE of the shell. Such shell-like structures need very little bending-stiffness of the shell-material itself.
{snip}
Anyway, local reinforcement of point loads applied normal to the shell (eg. wishbone mounts) can be done with CF-"top hat" sections, either incorporated in the middle of the ~8 plies, or glued inside or outside the shell. The sides of the cockpit (ie. the "SIS") can be similarly reinforced. I would do a cockpit-upper-side "P"-section that is designed (and tested!) to carry all side-impact load. As such, this strengthening of the cockpit-rim would greatly improve overall torsional stiffness and strength.

As I have suggested many times before, similar "true monocoques" can be done in Aluminium (using 1 to 3 mm thick Al-sheet, as used on many small boats), Steel (I would use mostly the super-cheap 0.6 mm thick "zincalume" used for roof-flashing here in Oz), or Plywood (2 to 10 mm thick marine or aircraft-ply). All these would be much quicker and cheaper to do than anything with a honeycomb-core, and have at least as good performance.

To repeat, the shell-material of a true monocoque DOES NOT NEED A SQUASHY CORE! Using such is blindly following the flock. It surely ain't engineering! :)
~o0o~

Z

You mean build a racecar monocoque the same way they have been building airplane monocoques for decades? BLASPHEME!