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If one has a specified allowed X length and Y height, into which a fillet can be placed to reduce stress concentrations, is there an equation which can be used to determine the optimal shape of the fillet?

I have looked into Baud Fillets and Thum-Bautz fillets, but I find that although these fillets work fantastically for a desired y height OR a desired x height, these don't work well when one has constraints on both of these dimensions. Furthermore, it seems scaling the fillet shape along the axis does not work well, in many cases ending up worse than a circular fillet.

If it is relevant, this is for fillets that are to be placed on the ID or OD of steps in tubing.

I know one option is various shape optimization algorithms, but I was hoping that there was some kind of out of the box solution that I could use to hopefully avoid this.

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I'm not an expert in this area, but what you might do is constrain just x, see what the resulting FEA stress is, and compare that to just constraining y. That would at least get you the best out of those formulas.

Here is a good fillet research paper I skimmed. Looks like the grodzinski filet shape might be something to look into.

Image source (might be a good paper but you have to buy it) enter image description here

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  • $\begingroup$ I have actually looked into this fillet design in the past. I actually found that it can be more efficient to have a chamfer with a fillet on the chamfer edge than this technique. Although, that does require extra playing around, and in many cases that might not be worthwhile for the marginal benefit that it allows. $\endgroup$ – user1814893 Oct 31 '17 at 21:28
  • $\begingroup$ Are you using FEA to evaluate? What software? Have you validated the model with real world tests? What sizes are we dealing with here? Has tool tolerance and surface quality been accounted for? Again, not an expert on this, but that might bring up some good discussion. Its important that you are solving the real problem and not just tricking the simulation. Posting some of your attempts and respective stress heat maps to your question would be helpful. $\endgroup$ – ericnutsch Oct 31 '17 at 21:39
  • $\begingroup$ I have been using the FEA built within SolidWorks. I have not validated the model with real world tests, and no I have not been accounting for surface quality or tolerancing here, but for my case, with the quality of machining that I would be using, I do not believe these factors to be relevant. While I cannot share the parts that are used in this simulation, I can show images, which I have included here. In terms of loading and FEA setup, the part is elastically supported on one end, sliced into sixteenths, and a force of about 38000 pounds is placed on the other $\endgroup$ – user1814893 Nov 1 '17 at 17:22
  • $\begingroup$ end, representing a total force of just over 600,000 pounds. In terms of the mesh, it is made more fine around the location of the fillet, and an image of that is shown in my above link. $\endgroup$ – user1814893 Nov 1 '17 at 17:23
  • $\begingroup$ In terms of tricking the simulation, I am not too concerned with this, as the procedure that I have used is how we analyze all of our parts, historically it has performed well, so I very much hope that it is at least somewhat accurate. $\endgroup$ – user1814893 Nov 1 '17 at 17:29

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