FEA Model versus Actual Results 4

[rpm63]

I have modeled several simple metal cantilever beams in Algor and have compared the results to actual Instron pull (push) test data. I have applied a small displacement at one end. The models calculated force is always 30 – 50% higher than actuals. The FEA results agree with the hand calculated force using formulas from the Machinists Handbook. Any suggestions?

 

[pbeng]

Another source of error may be the small strain assumption used in linear FEA. ALGOR had an excellent demonstration of this effect on one of their webcasts - on the same cantilever beam example. The differences are pretty dramatic. It may be true that the displacements are relatively small, but the rotations may be large.

 

[brad]

pbeng--
I think you actually mean "nonlinear geometry" or "finite rotation", which has already been ruled out. If finite rotation is an issue, then it should not be behaving with a linear response. The poster has already stated that the initial response is linear.

rpm63--as suggested above, please follow-up with additional information. These types of problems are really fun, and are what help to make better FEA engineers out of all of us.

Regards,
Brad

 

[rpm63]

It is good to here that rpstress thinks E values should be close to published values. It kind of defeats the advantages of FEA if I had to pay (to outsource) to get E values for every material. I work with many different materials.

Yes analysis should linear with reasons stated before.

I verified my measurement instrument. I was using Instron pull tester. I re-measured using a completely different piece of equipment and got similar results.

Here are some numbers. Cantilever beam 1.08 inches long x 0.75 wide x .032 thick. C260 brass ½ hard, E=16,000,000 psi. At deflection (d) = 0.040 F (measured) = 2.4lbs. FEA results yield F= 3.1 lbs when applying a -0.040 inch displacement to the end. Therefore, 30% off.
Hand calculation equation matches FEA exactly: I=bd^3/12, d=FL^3/3EI.
Stress stain curve is linear until 0.071 inches.

 

[EnglishMuffin]

rpm63: But did you ever do one with a simply supported steel specimen ? You did mention you had done or were going to do that - the point being that it should eliminate any doubt about the E-value and the boundary conditions. And if you have done this, is it also 30% off ?

 

[EnglishMuffin]

I am also somewhat surprised that the hand calculation can match the FEA "exactly", since you said you were using a point load, not a line load, and the beam formula you have given is for a line load. (I actually make it .043" for 3.1 lbf). Just out of interest, how much transverse deflection do you see across the plate when you load it, if any? (Unfortunately I can't find this case in Roark in the plate section - maybe I'm missing it).

 

[rpm63]

The simply supported beam FEA results for force were 60% higher than the measured results. I have tried multiple materials with different geometries, 4 cantilevers and 1 simply supported and they all range from 30 – 60% off.

I shouldn’t have used the term exactly. The hand calculations were 7% different. I was only using 2 significant figures and converting from metric to English, close enough for me. I would be extremely happy to be within 10%.

 

[EnglishMuffin]

Jeez -- there has got to be something obvious here that we are all missing. Even the seven percent difference doesn't make sense - the FEA stiffness should come out lower than the hand calculation because the calculation ignores the transverse deflection, so the error is in the wrong direction.

 

[rpm63]

I have redone my numbers with 3 significant figures, it is 2.6% different. I am sure I could get closer if I spent more time being more precise.

 

[EnglishMuffin]

But, as I keep trying to point out, the FEA and hand calculation should not come out the same if you are using a point load - the FEA result should predict a lower load for the same deflection.

 

[dpadler1]

A lot of good discussion here, a few points to consider.

The force measurement could easily be in error depending what you are using to measure it. A typical load cell might have 0.1% accuracy, so a 5000 lb capacity load cell is only accurate to +/- 5lb. What are the specs on the Instron?

You mentioned measuring with other equipment, like what? For something like this dead weights and a dial indicator would be a good sanity check. If it matches the bending I agree with the others, do a pull test on your Instron for E.

EnglishMuffin, though it doesn't sound like a modeling issue please explain the bit about point load vs line load. Are you talking local deflection at that node? I wouldn't expect it to matter much here due to the low force. But if you take the average deflection of the end nodes line and point results should match, right? But it's an important point in general that deflection at the node of applied force is higher than reality.

 

[RPstress]

I've done some checks to confirm the analysis. For the brass plate described, I get about 3.2 lbf, for both linear and non-linear analysis. With constraints that permit poissons deformation (as opposed to ones which enforce cylindrical bending at the fixed end) the force drops to about 2-3/4 lbf. Simple bending hand calcs give 3.1 lbf.

I have started some checks on modelling some blocks for clamping the plate, assuming just 0.108" of plate being clamped, and brass blocks 1/4" thick. So far the force has dropped to 3.0 lbf...

rpm63: how exactly is the plate clamped?? Also, can you tell us the geometry and forces for the simply supported test you did?? That might eliminate some uncertainty to do with clamping.

I'm not familiar with a "pull tester." Is there a machine ID so we can look at an example on the Instron website??

Finally, I agree with dpadler1 about a sanity check with a couple of weights and a rule or dial gauge. What was the other machine (the "completely different" one) you checked??

Sorry to lump in so many queries at once.

 

[RPstress]

I forgot to mention: shear deformation appears negligible.

 

[EnglishMuffin]

dpadler 1
What I meant is this :
If you apply a point load to a plate at the center of the overhung edge, the edges of the plate do not deflect as much as the center. The wider the plate is, the greater the effect will be. If it is very wide (say with a 100:1 aspect ratio), the majority of the plate will deflect hardly at all and all the deformation will be in a small region close to the load. The simple beam calculation assumes a line load evenly distributed along the edge, so from the principle of virtual work, it follows that the deflection predicted by a hand calculation should be exceeded at the point of application of the load by both the true deflection and the FEA prediction. Now it is possible that this may not remain true for a plate of about 1:1 aspect ratio, so I might have to take my statement back, although intuitively it would seem to me that it would still be true. I wish I had access to an FEA program (which at this moment I don't).

 

[jetmaker]

rpm63,

From what you have described here, it sounds like a discrepancy between your testing methods and your FEA. dpadler sounds like he is on the right track with the instrument tolerances. Typical rule in testing is that you should be operating within 20-80% of the load cell range to get the specified accuracy of the load cell. Therefore, you should have at most a 10# load cell on your Instron, or at least have the gain set to limit the output range of the load aquisition equipment, with the first option being prefereable.

Check your load cell accuracy and capability, and the gain level of the acquisition equipment, then determine if this produces acceptable tolerances. If the load cell were to be above 100# capacity... I'd strongly recommend doing a basic high school test in which a known weight is added to the end of the beam and deflections measured using a dial gauge. It is too easy to get caught up in technology and loose sight of the limitations which it carries.

Sometimes simpler is better. Hope this helps.

jetmaker

 

[rpm63]

Sorry for late reply, been traveling a lot. I’ll try to answer all questions.
The accuracy of the load cell was in the 20-80% scale range. I also did an accuracy/sanity check with dead weights and it checked out.

Unfortunately do not have the capability to find E with my pull tester other than an indirect method of working backward with a hand calculation for a cantilever. I would have to go out of house for testing and budgets are very tight. Multiple people mentioned previously that published E values should be close. However, I have not totally ruled out this possibility.

Thanks Rpstress for checking my FEA model with your model. I figured it would be good because is very close to hand calculations.

The part was clamped between two blocks.

The completely different method of testing is the following. I strapped a hand held digital force gage to a CNC mill with a manual z-axis. Even though it was a very crude set up, it was not far off from the Instron data. This appears to verify the equipment accuracy. I will also try a dial force gage.

The Instron model is 5544.

 

[EnglishMuffin]

rpm63: I say again - a quick way to settle the E value question is to do it with steel - there should be no question about the E value of steel (at least within a few percent).

 

[rpm63]

Yes I did it with steel, It was about 50% off.

 

[brad]

I would recommend trying to include the blocks in your FEA model, then rerun to see how much of an effect this makes on your results. This will introduce compliance in your model, which is directionally consistent with what is needed to correct the error. That's my best guess--these are not rigid relative to your part.

Alternately, fix your physical test without bolting anything down, such that it is consistent with only translational constraints and no rotational constraints. Compare this physical test with the equivalent numerical/FEA results. If these are closer in agreement, then this definitely suggests that there is a divergence in the fixturing assumptions vs. the physical fixture.

This is a tough nut to crack.
Brad

 

[dpadler1]

Agree with Brad, clamping is often the weak link, but I think someone above modeled with little effect. Also doesn't explain the simply supported results. However there are some potential issues in the simply supported results depeding how its done.

At this point these seem the likely suspects:

Interpretation of force vs. deflection - I've seen people read force and deflection straight off the test results, without subtracting out the take-up compliance. You have to project down the linear part of the curve to establish zero deflection. This is important with manual checks as well, you have to get 3 points to make sure you are really in a linear range and project zero, subract that from your deflections. "Zeroing" the equipment does not mean you don't have to do this.

Yield during clamping on cantilever test- if the clamping force is enough to yield the sample you'll get higher deflections when loaded.

Warping during simply supported test - if you used the same size sample you can only get about 0.010" deflection before yield (assuming 50 ksi yield); could easily have .005" warpage in this size sample. Not a problem - if you project zero deflection as above. Effect is reduced with a longer thinner sample, and deflections higher so easier to measure accurately.

Yielding during testing - copper doesn't have a sharp yield point; depending on whether they gave you the right material and your sample size you could be getting into yield, which goes back to ensuring linearity.

The fact steel is also lower than predicted indicates some sort of testing issue or combination of issues. Unless there's something we're all missing about bending of work hardened materials not behaving as linear elastic. 50% is just too far off.

 

[rpm63]

I again verified the Instron pull tester with a dial force gauge (beam type) – Instron tensile/compression tester sanity check OK.

I did subtract out take up compliance. The measured curves are always linear.

I believe my original simply supported fixturing had some problems. I chose a thick piece of steel and consequently had high forces with very small deflections. I may have had some inaccuracies due to slippage in the fixturing. The difference between measured (Instron) vs. FEA for 2 different simply supported materials ranged from 8-17%. An improvement from the

I changed my clamping method to a vise that has a much higher clamping force. This appeared to help. Cantilever results Instron vs. FEA went from 30% to 19% difference. FEA force is always higher.

8-19% difference between FEA and measured results is much closer than 20 – 50% I originally reported.