# Help with Finite Element Analysis

I don’t know if this belongs in GQ or not…

I have a reasonably simple plastic (HDPE) part - basically, a cylinder with an internal snap-ring groove. I want to determine how much stress the plastic is under when the snap-ring is loaded with 40 lbs.

There are some open-source FEA programs (notably Aurora Z88) that I’m sure could do this, but I don’t have the time or inclination to learn how to model the part and use the software.

Is there anyone here who knows how to do this, and would be willing to help me out with this problem?

If all you are looking for is a close order of magnitude estimate on the stress applied by the constrained deformation of the snap ring to the internal boss, you don’t need to run a finite element analysis. That can be determined by a relatively simple hand calculation using the principle of virtual work. See Shigley & Mischke, Hartog, et cetera for methods thereof. The difference in energy between the constrained state and the undeformed state can be applied as a uniform strain around the circumference of the bore, which gives a good approximation of the preload notwithstanding frictional differences.

I don’t know Aurora Z88, but to run this kind of problem in a structural FEA code requires defining contact conditions. This is certainly within the capability of many modern codes such as Ansys, Abaqus, and the various flavors of NASTRAN, but is not necessarily a trivial problem to set up and run, and may be outside the capability of many open source FEA codes to run with assurance.

May I ask why you are concerned about the stress in an internal snap ring? The stress in the “parent” part is typically negligible given the difference between the effective deflection of the snap ring and the housing. While I’ve done analysis of preloads for a number of conditions involving preloaded fasteners and external clamp bands, I can’t think of a single scenario where I would be bothered to calculate the compressive load developed by an internal snap ring unless there was some kind of notch or stress riser in the housing. I would be more concerned about stress and restraining forces in the snap ring itself to assure that it cannot be forced out of the groove.

Stranger

Sorry, I guess I wasn’t very clear.

What I am interested in is determining the stress on the plastic cylinder “above” the snap-ring groove, that is exerted by the spring-loaded snap-ring. I am concerned that the groove weakens the wall of the plastic enough that when the spring is installed, the snap-ring will exert enough force to eventually cause the upper lip of the groove to deform enough to let the snap-ring slip out (the snap-ring groove is pretty close to the end of the cylinder - there’s not much plastic “above” the snap-ring).

I’ve had one of these assemblies sitting for over a year, and it seems OK, but I’d like to get a less empirical answer than that.

I have drawings, if that will help…

When you say “spring loaded snap ring” do you mean that the retaining ring is a wave-type ring (not flat), or the ring is being used to retain a spring which then bears against this upper lip, or what?

Stranger

The latter.
The snap-ring acts as a spring retainer. The spring is compressed to around 40lbs.

Here’s my very quick and sloppy drawing of a cut-away:
http://cl.ly/image/220V1Y2n3i0r

I can provide actual dimensions later.

Well, the simple case is just to assume that the 40 lbf load is evenly distributed about the inner edge of the upper flange of the groove. With that axisymmetric condition you can just treat it as a canilever beam in bending and shear, and use the simple Ml/I plus shear to calcuate the stress at the inside fillet where stress will be highest. That can give you both the margin to yielding of the HDPE cyclinder and the deflection of the flange. (The deflection will be slightly overstated because out of plane stresses will help stiffen the flange against bending, so if you want an exact answer you can dig into Roark’s but for this purpose the constribution will be negligible.)

Whether the snap ring can escape is a little more complex of a question, for which you would have to look at the combined deflection of the snap ring and parent part, and then compare the geometry. However, if you’ve followed the manufacturer’s guidelines for the depth and width of the interenal groove, you should have to lose almost the entire flange before the snap ring would be sufficiently free to rotate about its circumference such that it will pop out of the groove. Almost invariably when you see snap ring retaining failures, whether they are internal or external, you find that the groove was not correctly sized.

Stranger

I found this guide on the web.
Based on their formula, and some guessing, I calculate that the maximum safe load (with a 2x safety factor) is 51 lbs. This tells me what I already suspected - that the current design is marginal, and we should increase the edge margin for the snap ring groove, and make the cylinder wall a little thicker, too.