Cage Study

[osborni]

Had an hour or two at work today to kill. I've been playing with this study idea for a while and wanted to get-r-done.

It is a comparative look at relative stiffness of different cage designs. I took the base measurements off my Coupe (sorry M3 guys). I fixed 4 of the six points and applied an upward force to simulate a torsional flex of a chassis at the lower front left corner and back right corner. I did not examine any impacts to the cage. The results are in displacement and are not absolutely correct, and should be take as directional/comparative only.

Material is mild steel
Tubes are 1.5" diameter and 0.12" thick.

Base, minimum required cage per IP rules.
Case 1:


Altered driver's door X for more access and added triangles to the rear down bars as well as gusset at the driver's head and roof bar >> A-pillar gussets.

Case 2:


Added Triangle to the A Pillar and gusseted to the roof bar and a roof cross bar.
Case 3:


Added gussets to the dash bar and a gusset to the passenger a-pillar/roof corner. Deflection improved at the passenger front, lower A-pillar location marginally.

Case 4:


Executive summary:
The change in deflection from each case represents an improvement in stiffness when subjected to the same load. This is directional only and doesn't represent an actual cage deflection in the real world. (Anybody have a shell model of a e36/e46 chassis that can be imported to Pro/E?)

Max deflection for each case:
Case 1: 0.00028190 in (edit from .00026 - oops)
Case 2: 0.000110 in
Case 3: 0.000078 in
Case 4: 0.000069 in

% Improvement:
1 > 2 = 61%
2 > 3 = 30%
3 > 4 = 11%

1 > 3 = 72%
1 > 4 = 76%

So case number 4 is 76% stiffer then Case 1 and is 11% stiffer then Case 3.

What is cool is how much stiffness improvement you get out of a few simple gussets. Also how floppy the base IP cage is compared to one with a minimum of extra tubes.

I haven't done the mass properties yet (forgot and don't feel like cranking up Pro/E right now...)

BTW, did this on Pro/E with Mechanica as the backend. Spline curves and section sweeps based on measurements taken from my Coupe. No, I'm not going to do an e36 study.

Disclaimer: If anybody takes this work as gospel and puts it, verbatim, in a car, particularly against the advice of your builder - you are an idiot and I take no responsibility for what happens.

[osborni]

There are some geometry simplifications that I made for convenience that shouldn't impact the results. i.e., the gusset by the driver's head isn't shaped for clearance, the dash bar doesn't follow the firewall, etc. Stuff like that typically won't impact the stiffness of a tube enough to matter though.

I also didn't do any DOEs or optimizations for tube placement, Each run takes about 15 minutes, and a full DOE would take several days with all the possible combinations.

[clopez95m3]

BTW, did this on Pro/E with Mechanica as the backend. Spline curves and section sweeps based on measurements taken from my Coupe. No, I'm not going to do an e36 study.

Hey what if I send you a .stp file, would you consider it then? I mean you don't want to be bored at work or anything.

We could do a 'typical' IP cage (not minimum required tubes) to a full on 'teh Jaffscage' with every tube the Jaffster suggests and then quantify the change in stiffness. No?

Cheers,
Carlos.

[JamesM3M5]

Very nice work. It's no surprise that the 3rd iteration showed a marked improvement, but you added 3 bars at once. I'd like to see what it looks like without the upper bar over the roof plane. Also, if you want to run a roof bar, you typically run it from the front passenger side over to the roll hoop over/near the driver's head.

I thought a lot about doing a bar over the roof plane. But when I thought about it more, I figured that once the cage is tied into a full structural chassis with a top of its own (i.e. not a convertible), you end up duplicating the steel roof structure with a very heavy, very high tube. 1.75x0.095" tubing weighs in at 1.68lb/foot, 1.5x.120" is 1.77lb/foot.

Also would like to see what happens with a 1.75x0.095" tubing cage. You of course can't model the joint stiffness very easily, but since all the welds cover a 17% greater circumference, you get joints with a lot better stiffness in bending.

[RacerX]

Very nice work. It's no surprise that the 3rd iteration showed a marked improvement, but you added 3 bars at once. I'd like to see what it looks like without the upper bar over the roof plane. Also, if you want to run a roof bar, you typically run it from the front passenger side over to the roll hoop over/near the driver's head.

I thought a lot about doing a bar over the roof plane. But when I thought about it more, I figured that once the cage is tied into a full structural chassis with a top of its own (i.e. not a convertible), you end up duplicating the steel roof structure with a very heavy, very high tube. 1.75x0.095" tubing weighs in at 1.68lb/foot, 1.5x.120" is 1.77lb/foot.

Also would like to see what happens with a 1.75x0.095" tubing cage. You of course can't model the joint stiffness very easily, but since all the welds cover a 17% greater circumference, you get joints with a lot better stiffness in bending.

We will be using thinner walled tubing for some of the non required bars in order to save weight in places like this. I have some data from someone (not sure if it's meant to be public knowledge) and it shows several tube iterations. One of the best improvements by way of roof tubing is a diamond, same for the windscreen (a la Trans AM). I'm still hoping I can find some time to do a bit of optimization like this for my cage.

Nice work to the OP!

[txse46m3]

Hey, that's really cool. Thank you for sharing it!

How much force was applied?

[Steve J.]

Where is teh jaffscage?

Do a quick mass calc on each case and do a relative stiffness per weight. I guarantee you'll fine even an extra 15-20lbs of tubing can yield 75-100%+ stiffness. Well worth the weight.

And of course gussets are your friend

[osborni]

Very nice work. It's no surprise that the 3rd iteration showed a marked improvement, but you added 3 bars at once. I'd like to see what it looks like without the upper bar over the roof plane. Also, if you want to run a roof bar, you typically run it from the front passenger side over to the roll hoop over/near the driver's head.

I thought a lot about doing a bar over the roof plane. But when I thought about it more, I figured that once the cage is tied into a full structural chassis with a top of its own (i.e. not a convertible), you end up duplicating the steel roof structure with a very heavy, very high tube. 1.75x0.095" tubing weighs in at 1.68lb/foot, 1.5x.120" is 1.77lb/foot.

Also would like to see what happens with a 1.75x0.095" tubing cage. You of course can't model the joint stiffness very easily, but since all the welds cover a 17% greater circumference, you get joints with a lot better stiffness in bending.

Good feedback. I'll see what I have time for over the next few days. Mr Mom duty this weekend.

I took some educated guesses at what are the logical steps different cages take in sophistication. As I'm not a cage builder, I'm not an expert in that.

I ran the roof bar that way since head space is at a premium inside a M Coupe and if I can ever afford to build up a racecar, that's how I would probably have it run to keep it away from my head as much as possible. I'll try it the other way, just the same. Now that most of the model is built, it will be easier to delete parts and see what happens.

From a gross deflection analysis, the joint modeling works just fine. It just fall apart when you are doing stress analysis at the joints.

[osborni]

Hey, that's really cool. Thank you for sharing it!

How much force was applied?

Thanks! 500lbs at the left front and at the right rear in the vertical direction. Crude, but simulates torsional bending of the cage.

[osborni]

We will be using thinner walled tubing for some of the non required bars in order to save weight in places like this. I have some data from someone (not sure if it's meant to be public knowledge) and it shows several tube iterations. One of the best improvements by way of roof tubing is a diamond, same for the windscreen (a la Trans AM). I'm still hoping I can find some time to do a bit of optimization like this for my cage.

Nice work to the OP!

I thought about doing that at the roof to see what happens. It needs to carry a lot of the load as the door area is worthless since it needs to be relatively open for driver access. Most of the cage is parametric so moving stuff is a few clicks at most.

[patavakian]

Your timing couldn't be any better Osborni :-))) ... keep the iterations coming, I am about two week away from building the cage.

Thanks!!!

Patrick

[Chris@RRT]

Oddly, or maybe not so much, this reminds me of building balsa wood models of roll cages several years ago with Barry Battle and James Clay. While not very accurate, they still predicted the same high strain areas, in particular the bend where the a-pillar meets the roof. Fun and interesting stuff, picking cage design elements from photos of cars on the internet and trying them out.

It's great to see work like this posted to the forum: It's definitely very educational.

[Steve J.]

I would be interested to see how your comparative modeling results from support that goes to the front strut tower.

Some small "taco" sheet metal gussets or even tubes in the X bracing off the A pillar.

I bet a couple very small changes could yield a very high % gain in overall stiffness.

This also shows how important it is for the Apillar to be fully tied into the chassis on mod cars.

Did you get any deflection numbers off that 500/500lb loading?

We have model specific torsional rigidity numbers and you could plug them in to see how they compare, in terms of your deflection and load limits you set.

[osborni]

I thought about the front shock tower, but since the tubes are so closely coupled to the chassis structure, and I don't have the chassis modeled, it wouldn't tell me much. A pyramid from the shock tower to the foot of the A pillar and the dash height of the A pillar with a 3rd bar to the center of the dash bar seams to be pretty standard and pretty stiff, particularly when tied into multiple locations of the firewall, wheel well, motor support area, A-pillar and tranny tunnel.

I picked the 500lb loads arbitrarily. I thought about using a forced deflection and measuring stress, but stress is so localized as to be useless. Applying a load was the simplest way to get a comparative analysis.

As for the sheet metal stuff, thought about that too, and perhaps I'll add some tacos in there, but my overall goal was to show show simple additions to a cage can have dramatic impacts on overall stiffness - particularly for an IP cage. For mod, with the full ties to the chassis, it just gets better for relatively little weight penalty - but without having a full chassis model - impossible to estimate accurately.

If you have data on flex angle or distance at specific chassis boundary conditions, I can match the analysis and look at restoring forces, etc.

[B.Watts]

I'd love to see a comparison between 4-5 different driver door bar setups. I can provide pictures/examples of 4-5 different setups if needed.

[osborni]

I'd love to see a comparison between 4-5 different driver door bar setups. I can provide pictures/examples of 4-5 different setups if needed.

That would be cool if you have pics. I sorta copied yours actually - but without the tacos.

I was thinking of doing Nascar bars as well.

[B.Watts]

I would start with your basic cage in example #2 above and compare these options for the driver side:

1) Standard X

2) A 3D X:


3) Standard X with the down bar from the top of the A-pillar

4) This:


5) A 2-bar "NASCAR" setup:

[Massive Lee]

Here's a cage I am building with friends. Car is a no-sunroof e46. Cage follows FIA standards to North American requirements. Nothing fancy in the cage but a lot of work. No Nascar door bars.

[txse46m3]

5) A 2-bar "NASCAR" setup:

Take that setup but make the lower bar unbent. That's what I'm running on the driver's side, as are a few other guys who have had cages done at Lucas Racing. Sure makes getting in and out nice and easy. The upper bar just barely makes contact with the skin of the door. Would definitely be interested in seeing how it came out.

edit:

[Greg S]

How about a 3 bar Nascar setup?

[PEI330Ci]

Here's a cage I am building with friends. Car is a no-sunroof e46. Cage follows FIA standards to North American requirements. Nothing fancy in the cage but a lot of work. No Nascar door bars.

Very cool!

Thanks for the pics.

[Massive Lee]

This weekend we are removing the engine, finish the front cage to the shock towers and will finish welding all the gussetting between the cage and the shell. We are running in Mod.

[osborni]

Did more runs today - to late to post them though.... Though I did notice that a rear X at the down tubes didn't do much. Roof bars did help though. Lines up with intuition. Rear area is already pretty stiff, the roof less so and improves more with more bracing.

[Steve J.]

How about an iteration with an "X" in the main hoop (with cross horizontal harness bar), with the door xbracing going to that center horizontal harness bar (instead of lower as in the examples above...large node). Also place a gusset tube from the dash bar to the apillar, and you can do the case#3 A pillar support bar tied into the Xbrace and Apillar vertical tubing. This should help triangulate that are and reduce the deflection that translates through to the opposite side.

As for the rear, as you said its pretty stiff. A single tube from the rear bulkhead attachment point to the base of the bpillar should help though, as that will create a large triangulation in an area that is basically a big trapezoid (trapa no good).

[osborni]

How about an iteration with an "X" in the main hoop (with cross horizontal harness bar), with the door xbracing going to that center horizontal harness bar (instead of lower as in the examples above...large node). Also place a gusset tube from the dash bar to the apillar, and you can do the case#3 A pillar support bar tied into the Xbrace and Apillar vertical tubing. This should help triangulate that are and reduce the deflection that translates through to the opposite side.

As for the rear, as you said its pretty stiff. A single tube from the rear bulkhead attachment point to the base of the bpillar should help though, as that will create a large triangulation in an area that is basically a big trapezoid (trapa no good).

Good points, though I built the cage geometry off the internal structure of an M Coupe. There is a big box section just behind the seats and the B pillar/door structure basically requires that the side X is a bit lower then the harness bar and I can't run a bar from the rear shock tower to the bottom of the main hoop like you can on a e36 cage. I could triangulate from the rear shock tower to the harness bar though. Ran out of time yesterday to do it.

From a torsional rigidity perspective, I'm not sure there will be enough of a difference with what you suggest as there is really not that much load going through those points in torsion. From a front impact, yes, it makes more sense. But if this was a mod cage, that location would be well tied into the structure anyway. I suppose I could "shape" the X to clear where my theoretical elbow would go though.