A Arm Load Calculations

[maxhouck]

Hello all,

I am from the University of Missouri's FSAE team and am working on the suspension for this year. I'm at a roadblock on trying to size the a arms.

I have already calculated the expected tire forces, and used our suspension geometry to do a 'truss analysis' of the system. From here we can see the expected tensile and compressive loads for all of our different cases (accel, cornering, braking, bump, and combined cases). From here I did some basic buckling calculations using the Euler formula to find the critical load. The consensus here was that we can run 1/2" 0.035 tubes for pretty much everything and we would have plenty of room for safety. However, the euler formula assumes perfectly concentric loading, which is never going to be true. We can estimate some error for manufacturing tolerances and calculate the eccentric loading case, and this still gives us a plenty of room for safety under realistic manufacturing tolerances.

I know from past experience that realistically if all of our a-arms were this small (1/2 inch 0.035) they would likely deflect a lot and possibly break. It seems that the error comes from the fact that our suspension links are not all 2 force members like we assume when we did our load calculations. The fact that the ends are welded together at the outboard spherical means they can exert a moment, and introduce bending into the situation. This is where I am stuck - I don't think it is possible to look at it like a basic statics problem if you make them "welded" joints. Short of running extensive FEA using our load cases on each corner, are there any calculations that can be done in order to estimate the amount of eccentric loading/bending that will be put into the arms? It seems that this will be of greater magnitude than any perfect tension/compression forces that we can calculate using basic static analysis.

Hate to be that guy that just posts to ask everyone to do the work for him - but I'm just curious if there is anything that can be done here short of "just overbuild them and test the car" or doing all the FEA, which it seems we are going to have to do. If you'd like to see specifics on what I have done so far I'd be happy to share.

[BillCobb]

1) Do the FEA. Why is this such a hard task.

2) Make up a plastic model and do some fringe pattern analysis (old school).

3) Build a real to print arm and fixture it. Apply loads, strain gauge the pockets.

4) Build a real arm into a Kart or a lawn mower even. Curb impact (head on) and curb push-away ( side load while parking).

See if it lives. Then acid etch the arm(s) and retest a few times. They will talk to you.

[DougMilliken]

Special loading cases for autocross cars -- cone strike and cone drag.

[Mikey Antonakakis]

In addition to what Bill and Doug mentioned, rather than taking a "will it break" approach, figure out how much deflection you can live with. I'm definitely no expert here, but think in terms of camber and toe (and??) compliance. If you get that down to an "acceptable" level, strength probably won't be a problem. As they suggested, use FEA, you already have figured out the loads so it's only marginally more work to run the simulation.

[jd74914]

Structures experts I know suggest always keeping buckling factor of safety > 8-10 to account for unknowns.

Like suggested above, do the FEA and see what it says. I'm surprised your hand calcs show 1/2-0.035" is OK. Perhaps they work as pure two force members (no push/pull rod loading). We built a past car with that size lowers, and sure enough yielded them (someone did the hand calc with the wrong loads-done again it showed they were very close to yield at pushrod attachment point).

[Claude Rouelle]

Buckling factor of safety > 8 ????????

[Claude Rouelle]

To accounts for "unknowns"?????????

[onemaniac]

Buckling factor of safety > 8 ????????

No need for such big surprise. I witnessed a similar number for "rule-of-thumb FOS" from my experience working at an engineering consulting firm. It's one of those "We don't have time for this, just size it up" decisions that are often made by the project managers or senior engineers.
For racecar design it might sound absurd but the assembly weight is often at the bottom of the priority list in big machineries.

[maxhouck]

Yes, the issue with the current calculations is that they assume everything is going to be a two force member. This is why the calculations say we can get away with such a small tube, while in reality because they are welded together and the pushrod puts a significant bending load into the lowers, they are unrealistic. The reason I was hesitant to do FEA was because I and our team are pretty inexperienced with it, but I guess its time to dig in and learn how to run it and analyze results properly. Just wanted to get some discussion going to see if there were any other methods, because we have heard from design judges before "dont waste your time doing FEA on every single part, because you're probably doing it wrong".

And yes, at the end of the day, I know many will say "just make it X OD and Y wall thickness and move on", but I feel that we are at the point where we can be taking these things one step further in order to make a lighter car. The weight difference between the 5/8" .065 a-arms (~9.3 lbs total) we had on our 2017 car and the 1/2" .049 a-arms (~5.7 lbs total) we had on the 2016 car is a pretty signficant amount of weight to save (or not to save).

[Claude Rouelle]

Not all the judges are right. Some of them would need an OptimumG seminar. In any case it is up to you to defend your opinion with the most objective and well quantified analysis
. Only fools will reject any good rational analysis.