ANSYS: Axisymmetry - Modelling of holes

[Saladsamurai]

Hello all!

I am curious. Sometimes I would like to do a trade study on a mechanical component; so in the interest of time, I think I would use 2D analysis techniques so that a) I can save time on the front end in the CAD package and b) save time on the analysis side of things. But I want to improve my limited skills.

Imagine you have a body of revolution. Let's use a simple cylinder with a flange that has a uniform, equally spaced bolt pattern. For example, the image below (from web) which has a 2D cross-section looking (approximately) like the second image. The solid is not truly axisymmetric because of the hole, so I am wondering what kind of techniques, if any, we can use to try to simulate the hole?

Once person suggested that I try to adjust the element properties in the vicinity of where the hole would be in the 2D model. Any thoughts on how to do this or if there are better ways to do this?

Thanks,
KC

 

[AlephZero]

It depends what you want to get from the analysis. One approximate way is to pretend the hole is "smeared out" around the circumference, and just reduce Young's modulus and the material density in proportion to the amount of material that is missing. (Since this is approximate, there is no point in going into too much detail when doing it).

Otherwise, you could make a 3-D model of a sector of the ring containing just one hole. You can then impose restraints on the "cut faces" of the sector to model the axisymmetric behaviour of the complete structure. Or, you can do a Fourier analysis of arbitrary forces applied to the complete object, use the sector model constrained in the corresponding way for each Fourier coefficient, and sum up the results. If your FE package can do this automatically, the option is probably called "cyclic symmetry" or something similar.

This type of anaylsis is a standard way to model things like a turbine disk with a large number (e.g. > 100) of blades, each of which is a complicated 3D object. The model is just one blade and the coresponding pizza-slice of disk.

Actually, you can extend this even further, to model sectors that are similar but not identical (for example, in a real turbine the vibration frequencies of each blade have a probability distribution around their nominal value, because of manufaturing tolerances etc, or there may be reasons why they are intentionally not made "as identical as possible"). But that is closer to "research" than than what is in commercial FE packages.

 

[Saladsamurai]

Thanks for that AlephZero

It depends what you want to get from the analysis. One approximate way is to pretend the hole is "smeared out" around the circumference, and just reduce Young's modulus and the material density in proportion to the amount of material that is missing. (Since this is approximate, there is no point in going into too much detail when doing it).

I think this it what my colleague was suggesting. Basically using different material properties in the vicinity of the hole. Actually, looking again at your response, I am not sure if that is what you are saying. I think you might be suggest reducing Young's modulus and density for the entire cross-section correct? Something like:

E_{reduced} = \left(\frac{A_{XSECT} - A_{HOLE}}{A_{XSECT}}\right)E

where I was thinking of using the original, unreduced E everywhere but the hole. At the hole I would use

E_{HOLE} = \left(\frac{A_{HOLE}}{A_{XSECT}}\right)E .

I am not sure that my way captures it any better or worse though. It migh be interesting to compare results from the two methods. And then compare those to the 3D model. I have an old copy of ANSYS student around. Perhaps an experiment is in order.

Otherwise, you could make a 3-D model of a sector of the ring containing just one hole. You can then impose restraints on the "cut faces" of the sector to model the axisymmetric behaviour of the complete structure.

This will be my next 'thing to learn.' Sectors make a lot of sense for the geometry that I am dealing with (i.e. turbofans). I hear a lot of '1-cup, 2-cup' talk and so I am interested to learn.

Or, you can do a Fourier analysis of arbitrary forces applied to the complete object, use the sector model constrained in the corresponding way for each Fourier coefficient, and sum up the results. If your FE package can do this automatically, the option is probably called "cyclic symmetry" or something similar.

This type of anaylsis is a standard way to model things like a turbine disk with a large number (e.g. > 100) of blades, each of which is a complicated 3D object. The model is just one blade and the coresponding pizza-slice of disk.

Actually, you can extend this even further, to model sectors that are similar but not identical (for example, in a real turbine the vibration frequencies of each blade have a probability distribution around their nominal value, because of manufaturing tolerances etc, or there may be reasons why they are intentionally not made "as identical as possible"). But that is closer to "research" than than what is in commercial FE packages.

This I will have to come back to as it is beyond by understanding at the moment. I'll tuck it away for when it starts to make sense.

 

[AlephZero]

Everywhere except at the hole, you don't change E. Over the area of the hole, reduce it in proportion to the reduced amount of material, i.e. a factor of something like $$1 - \frac{n_h d_h}{2 \pi r}$$ where $n_h$ is the number of holes, $d_h$ is the hole diameter, and $2 \pi r$ is the circumference of the part at that radius. That's probably conservative because it sort of assumes the holes are square not round, but the whole thing is very approximate anyway.

Sectors make a lot of sense for the geometry that I am dealing with (i.e. turbofans).

I would think that is the "standard" method now. The other approximations were useful when computers were less powerful though.