180° Cyclic Symmetry

Jonathan,

Another colleague of mine looked at it too and, like me, right away said this is not an application for cyclic symmetry (CS) - together we have about 45 years of FEA experience. The general issue is this is not a part/assembly that is a repeating section within a cylindrical system. I’d like to say that one major rule is the number of sections must be greater than or equal to 3, but I cannot find this written anywhere. Cyclic symmetry is intended for parts that are repeated rotationally. We are not able at this point to provide a mathematical reason, but I'll try to explain as best I can. (Maybe somebody else can chime-in with a good one)

First, I am unable to get Simulate to mesh the model. Cyclically symmetric models require the "low" and "high" sides of the symmetry planes to have exactly the same geometry - surface-for-surface, line-for-line, etc. Your model does not have surface areas that are identical. This will cause havoc with the mesher. In addition, there is an extremely small surface at one end of the roller that is likely also wreaking havoc with the mesher – I’m using Creo 2 (M050). Two times the mesher wouldn't even try and the third time it ran for almost 10 minutes without creating one element. I did get eventually get Simulate to mesh the part when I removed all the additional volume regions that help with the contact, but it never gave “low-high” regions that were identical on the roller’s cut surfaces. When I tried to have it solve, Simulate crashed Creo (not surprised here).

From a cyclic symmetry point of view, constraint equations are used to “link” the two cut planes together so they deform in exactly the same way. In a typical CS part, the angular spacing, of 120° or less, of the symmetry planes keeps the part from moving in the “radial” direction except for small displacements due to stiffness that allow identical movement on each plane. When the CS cut planes lie in the same plane in space, you will have issues with the general constraint of the part. My colleague and I agree the underlying issue is with stiffness and how it doesn’t work when it’s a 180° section. We also agreed that this should just be solved as a full model. You may be interested to know that ANSYS will not solve this as a cyclic symmetry model either.

As far as hand calcs go, I would look to Roark’s and the “general case of two bodies in contact” (chapter 13, case 4). BTW – having spent 13 years at Torrington (Needle Bearing Division), 15° skew is huge – I hope this just an exaggerated example, otherwise you’ll have issues with load distribution and skew-lock!

I hope this helps,

Chris