Chassis rigidity - FEA
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Author:  enderw88 [ July 2, 2007, 12:42 am ]
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THAWA wrote:
The thing I don't fully understand about FEA is how to convert the amount of displacement into ft-lbs/degree of twist.

I tried to use GRAPE and I could never get it to operate right for me.

Let's assume you have the rear spring perches fixed (you'll need need one perch fixed in position in all three dimensions, and the other fix in only two, otherwise you will get over constrained.) and you apply a vertical load to one of the front spring perches (the other will have to be constrained in the vertical direction to prevent the frame from rotating about the rear perches)

Run the analysis and you will find the displacement of the loaded perch. You want to take this displacement and estimate ft-lbs/degree of twist.

torque on chassis = applied load * distance between perches.

chassis twist = arctan (perch displacement/distance between perches)

divide chassis torque by twist and you get your result.

Make sure you use an arctan that yields degrees not radians.

Author:  THAWA [ July 3, 2007, 12:12 am ]
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Awesome, thanks.

So it would look as thoughI may have figured this out. And can get to more than 8000 ft-lbs/degree without a cage! With a cage, who knows. Although it would probably be very hard to weld some of the tubes, and near impossible to fit any engine without having a removable tube or two. With a more conventional design looks like around 6000 ft-lbs/degree is possible. Though with some cleanup of some of the tubes one could probably keep a good rigidity, and have fewer tubes, which would mean less weight. All this is without any stressed panels also. And I guess it's all relative. A stock book chassis came out to a little less than 1000 ft-lbs/degree with no stress panels, so take it for what it's worth. I'll clean it up and post some pics with the different designs.

Author:  Locost 5.0 [ July 3, 2007, 2:29 pm ]
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Looking forward to the pictures. I've looked at Whittlebeast's posts it will be nice to see some of yours.


Author:  d_dejohn81 [ July 5, 2007, 2:25 pm ]
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Hi everyone... I've been a longtime lurker but this is my first post on the forum. I'm a mechanical engineering grad student at Pitt with a lot of years (too many?) of Formula SAE experience, mostly focused on chassis design/fabrication.

Anywho, since I already knew the FEA process for a space frame I spent a few hours playing with the Locost frame in the ANSYS student edition. The results are similar to what you'll find elsewhere (i.e. Cymtrik's report), but one advantage is that the screen shots I have show the stress distribution through the frame... so you get an idea of the most critical load paths.

This analysis wasn't intended to be 100% accurate, but rather to give a relative comparison of stiffness and weight changes for the most common modifications. The dimensions aren't perfect, some modifications may interfere with other parts of the vehicle, your mileage may vary, weight loss results not typical, and all the other disclaimers apply.

The analysis details are:
X axis lateral, Y axis vertical, Z axis forward
Left rear shock mount constrained about X-Y-Z displacement
Right rear shock mount constrained about Y displacement
Left front shock mount displaced 0.200in along Y
Right front shock mount displaced -0.200in along Y
Beam elements for square section members, Pipe elements for round section

Since the shock mounts are 23.0in apart, this corresponds with one degree of twist. The program solves for the force (lbs) required at each front shock mount to generate this twist, so averaging the forces and multiplying by 23.0 gives the approximate stiffness in in-lbs/deg. Divide by 12 to get ft-lbs/deg

I'll summarize the results. Note that we want to see tubes "turn green" in the pics; this indicates they are loading up. Blue means they aren't carrying much load and red means they are carrying disproportionately high loads.

First Pic: Basic book frame
Note that the stresses in most of the frame are very low... this is because it takes very little torque to twist one degree! Stiffness is only 663 ft-lbs/deg, weight is 92 lbs as modeled here.

Second Pic: Similar to common "Aussie mods," but with an additional V from shock mounts down to aft crossmember (may interfere with crank pulley!)
The braces shown here are 0.75x0.065 round steel tubing. Stiffness roughly doubles to 1291 ft-lbs/deg for a five pound weight increase to 97 lbs.

Third pic: Engine bay crossmembers
Hre's the tricky part: if you want a stiff frame, you HAVE to find some way to get these tubes in the frame. If you leave these tubes out, improvements to the cockpit area will give little benefit since the engine bay flex will dominate (think softest spring in series). The closer they are to meeting at the center, the stiffer the frame, but obviously that is impossible due to interference with the engine. Note that the lateral crossmember (across the shock mounts) doesn't take any load, so this can be omitted.
Stiffness: 2072 ft-lbs/deg, weight 100 lbs.

Fourth pic: Diagonals in scuttle, floor, and trans tunnel
Since most builders panel in these areas anyway, it is up to you to decide if it is worth adding both the panelling AND the tubes. Attempting to model a bunch bonded and riveted aluminum panels accurately is beyond the scope of this analysis ;-) Regardless, this gives you an idea of the gains from stiffening these areas. Note that the diagonals in the trans tunnel yielded the largest improvement of this set of mods.
Stiffness: 2580 ft-lbs/deg, weight 117 lbs.

Fifth pic: Reinforcing the seat back plane and rear structure, "mirroring" the panhard brace
I recognize that the rear structure isn't modeled accurately here, but again, this gives an idea of the types of gains to expect by stiffening this area... which are suprisingly (at least to me) substantial.
Stiffness: 3462 ft-lbs/deg, weight 122 lbs.

Sixth pic: Adding "hoop style" diagonals under dash, moving engine bay diagonals
The change to the engine bay diagonals here is an attempt to make it more feasilbe to fit them around the engine... the nodes are shifted outboard 3in each and upward 6in. The dash hoops ADDED approx 200 ft-lbs/deg and shifting the engine braces REMOVED slightly more.
Stiffness: 3392 ft-lbs/deg, weight 129 lbs.

Seventh pic: Enlarge the "primary" framerails to 1.5x0.065 square tubing and enlarge the diagonals in the front suspension bay to 7/8 x 0.065 round tubing.
This was a quick way to analyze the sensitivity of increasing the tubing size (and thus bending stiffness) used for the upper and lower framerails.
Stiffnes: 4385 ft-lbs/deg, weight 140 lbs

Eighth pic: Remove the engine bay crossmembers
To illustrate the importance of the engine bay braces, I eliminated them while inluding MOST of the about changes (I sorta did this out of order). If you simply cannot fit these tubes, increasing the size of the primary framerails in the engine bay is a decent crutch fix.
Stiffness: 2852 ft-lbs/deg

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Author:  d_dejohn81 [ July 5, 2007, 2:45 pm ]
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Sorry for the extremely long first post guys...

I couldn't get the last two pics to post, so I'll try them here. Also, here's a pic of the "V" added behind/between the front shock mounts.

Sorry that this is all a bit cryptic... who knows how long it would've been if it wasn't!

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Author:  sodamninsane [ July 5, 2007, 3:12 pm ]
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Wow, first set of posts and he comes out swinging!!

Great work, if nothing else you have at least provided a theoretical correlation of mods to the original chassis. Have you studied roll cages at all?

Again, great work.

Author:  JonW [ July 5, 2007, 5:48 pm ]
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Nice contribution. Can that program model welded steel sheet paneling?

Author:  THAWA [ July 5, 2007, 8:23 pm ]
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Cool stuff.

Can I ask why you only used four restraints instead of the usual six? I understand it doesn't really matter for the sake of figuring out which mods provide the improvement, but I'm just curious. I did a couple of the same things you did, but mine looks messy compared to yours, and probably weighs a ton. :)

Author:  JackMcCornack [ July 5, 2007, 8:44 pm ]
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Nice contribution indeed. Good to have you aboard. What do the numbers associated with the colors mean, specifically?

Man, a couple hours, eh? Truly remarkable. It makes me feel quite old-fashioned, I'll tell ya.

Author:  THAWA [ July 5, 2007, 9:28 pm ]
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Here are my two contributions.

First is around 7000 ft-lbs/degree. I think this is probably better, since it's more realistic. I can't remember what setup gave around 6000 ft-lbs/degree though.

The next is the higher stiffness one at about 8500 ft-lbs/degree. This one is not very realistic, too many tubes, and a lot of them would have to be removable just to install the engine.

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Author:  mr.peabody.d [ July 6, 2007, 4:07 am ]
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Sorry I am at a lost all can say is WOW!

I wish we could run several old time space frames through FEA to compare. Maseratti Type 60 & 61 (birdcage), the Mercedes '57 300SL (gull wing), the Lister Jag (space frame), and the lotus 23 (mid-engine). Maybe even a terrapin or two.

(A crazy wish for a guy that has admired the hard work of guys that have done so much) You guys are awesome!!!!

Author:  d_dejohn81 [ July 6, 2007, 2:36 pm ]
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Sodamnninsane - no, I didn't look into roll cages yet as I don't (at least not yet) have any intention of using a full cage. But if there's a particular design you want analyzed, post a pic or draw it in Paint and I'll try to get to it.

JonW - yes, the program can do sheet paneling, but I was freezing the computer when I tried. Probably just user error ;-)

While it's probably not the most satisfying answer, I would expect a WELL-JOINED panel to give similar stiffness as adding a tube diagonal. A reasonable rule of thumb is that in a decent space frame, as long as the bay is "closed" to prevent lozenging (if you're not familiar with that term, just picture a rectangle distorting into a parallelogram) beefing/adding more diagonals or stiffeners won't give a large increase in stiffness. Or perhaps more appropriately, it'll add stiffness but at the expense of structural efficiency.

Regardless, I'll probably take another shot at modeling paneling in the near future.

THAWA, how did you set up your constraints? Technically my model has six since one rear corner is constrained about all three axes, but I'm not sure if that's what you mean.

JackMcCornack, in my plots the numbers and colors correlate with stress in PSI. For reference, the yield strength of carbon steel is about 50-55,000 psi. The values can be misleading here - the baseline frame shows less stress, but keep in mind that we've specified one degree of twist. The frame is so flexible that it doesn't take much load (about 340 lbs in opposite directions at the front shock mounts) to achieve this, therefore low stress. The stiffer frames take a lot of load (nearly 2300lbs at each front mount) to twist one degree.

In THAWA's plots, the colors correlate with deflection.

mr.peabody.d, I'd be interested in modeling some of those frames as well, but it may be a while before I get a chance. That birdcage Maserati has a lot of tubes! ;-)

Author:  chetcpo [ July 6, 2007, 11:16 pm ]
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I added some tubes to my frame in an attempt to add rigidity. (based only on gut instinct and not on science) The biggest addition is an extra tube that crosses right at the base of the scuttle and the idea is to shorten the length of the "open tub." I hate the way it looks and I'm wondering if I should just cut it off. If it stays It is going to get wrapped in roll bar padding and look a bit out of place.

I added the red lines on one of the diagrams posted earlier in this thread and was hoping that one of you folks could tell me having those tubes there on a mostly book chassis really helps and if so by how much. It sure would help the aesthetics if I could just cut that top red tube away. Obviously if the difference in rigidity is substantial I'll leave it.

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Author:  THAWA [ July 7, 2007, 2:13 am ]
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mr.peabody.d wrote:
Sorry I am at a lost all can say is WOW!

I wish we could run several old time space frames through FEA to compare. Maseratti Type 60 & 61 (birdcage), the Mercedes '57 300SL (gull wing), the Lister Jag (space frame), and the lotus 23 (mid-engine). Maybe even a terrapin or two.

(A crazy wish for a guy that has admired the hard work of guys that have done so much) You guys are awesome!!!!

From Cymtriks document:
Lotus 23 replica
The stiffness is 1449 ftlbs per degree of twist and the weight is 100 lbs.
This assumes round 1 inch dia 16 gauge tubes

John - My restraints are:
LR x,y, and z
RR y, and z
RF y

Force applied to LF.

chetcpo - I did something similar, though I'm not sure you can see it in the two pics. I put a horizontal tube above P, and had tubes connecting to the second set of H's, and the front k's on the tranny tunnel.

Here's the results from my analysis, again take it for what it's worth.

Stock - 881
Bottom diagonals only - 892
Bottom diag and top three - 900
All tubes - 912
Top and middle, no bottom - 907
top, no middle or bottom - 893

So like a maximum of 3.5% increase with all the tubes. However, you can see that the bottom diagonals add as much alone as the top tubes add alone. I'm willing to bet it would be worthwhile to integrate the front engine area into those tubes.

Actually, running two tubes, each from the outer front H tubes to the middle tubes in your pic brings the stiffness up to 1011, so that's 14.7% increase, slap two more tubes from the middle front H tubes to the middle tubes in your pic and you're at 1123, so now 27.4%. And so on.

Author:  sodamninsane [ July 7, 2007, 7:56 am ]
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one thing that no one is taking into account (and frankly I wouldn't bother trying) is the structural nature of the engine. you would have to expect rigidity to increase somewhat by adding the engine into the chassis as well as the trans too I would expect. While this is a case that is not easily modeled (Anyone have an accurate engine model? :-p) I think it's worth just a little thought and atleast reminding ourselves that this chassis isn't just a toothpick barely holding itself together.

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