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A Fractal Flexural Mirror Support

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#101 clivemilne

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Posted 29 December 2019 - 10:03 PM

Like this: 

 

torsion cell1

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#102 figurate

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Posted 29 December 2019 - 10:59 PM

Very nicely done, and does seem more logical from the standpoint of balanced torsional forces (that sharp angle is what I didn't understand about the design). And an edge-cantilevered version of this might be the way to go.  



#103 figurate

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Posted 30 December 2019 - 12:25 AM

A simplified version would make it easier to fabricate; the 60/120 degree branching defines the hexagonal geometry and from then on it is all right angles and torsional balances. The dotted-line extensions inside here could either form three inner supports (for 21 total), connect to a fan shroud, or be eliminated in favor of grounding mirror support to the outside.

 

And the fractal aspect can be utilized here as well. Every end point can sprout another series of tees, ad infinitum.

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#104 brave_ulysses

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Posted 30 December 2019 - 01:22 AM

next iteration

 

 

 

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#105 Benach

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Posted 30 December 2019 - 04:49 AM

Please do not include the support in the deformation plot.

#106 polaraligned

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Posted 30 December 2019 - 08:46 AM

next iteration

With all due respect, getting meaningful and accurate results for a problem like this is way, way beyond the beginner level. 

 

Meshing is just one aspect of a proper setup that will give good predictable results.  Starting with a course mesh for a first pass is fine, thought it may not produce accurate results, what it does is allow you to confirm your constraints are proper (more below).  You can converge the mesh once you have everything else in order.  As for the mesh, you need to not only look at the density of your mesh- which will depend on the type of elements you use-, but the aspect ratio of the elements.  Keeping the aspect ratio as close to 1 as possible is ideal, going over 2 is not the best practice.  That would be near cubes for HEXA elements and near equal sides for TET elements. 

 

The hardest part -by far- is defining your constraints.  Some issues to think about:

 

-How is the mirror constrained? You need to grab a node near the center of the mirror and prevent x-y translation and rotation around z, but allow freedom of translation in z and rotation about x and y.  The mirror cannot be constrained to the cell, but it does need to be constrained as outlined above.  

 

- How are the mirror to cell contacts defined?  These need to be defined as non-linear sliding contacts.  This will put the solver into time stepping mode and the model will settle into minimum energy condition.  The elements need to touch but allow sliding.  You also need to define the friction between these contact points. 

 

-Using point constraints puts a lot of stress in localized regions and should be used carefully.   There are elements such as RBE3's that constrain lots of points to a single location and allow an averaging as to how the nodes will deform.

 

- The best way  to verify the support of the optic is to produce a polynomial surface based on the mirror surface nodes and then load that into a ray tracing package. 

 

I have probably spent 200+ hours working with NASTRAN and I certainly consider myself a rookie.  There is an awful lot to know to get meaningful results.  Start with small simple models and work your way up as you get meaningful results.   This is why people get Masters degrees in FEA modeling, there is a lot to know to get results that are accurate. 


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#107 brave_ulysses

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Posted 30 December 2019 - 04:28 PM

thanks for the comments. i'll continue to work on this...maybe others will join in



#108 bcarter1234

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Posted 30 December 2019 - 05:48 PM

The only way I can see to do something like this Dale, would be with a series of

small Load Cells so that one could see several point loads at the same time...

 

Your thought on any other ways to verify the actual forces being applied to the

contact spots on the back of the mirrors surface?

 

Best Regards,

 

Preston

Please keep in mind I have no idea what I'm talking about. Could individual water columns be used to measure the loads at each point? It may be too insensitive by orders of magnitude for all I know but maybe it will inspire someone else to think great thoughts.

 

Take care,

Brent
 



#109 Benach

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Posted 30 December 2019 - 07:40 PM

thanks for the comments. i'll continue to work on this...maybe others will join in

I am already.

 

polaraligned: I already meshed a model for brave_ulysses with TET4's. But although the geometry cleanup and meshing was fairly straightforward, I deliberately left the BCs out of the story because I wanted brave_ulysses to make up his mind for this.

Apart from that, you know know the problems with TET4's I guess.



#110 polaraligned

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Posted 30 December 2019 - 08:13 PM

thanks for the comments. i'll continue to work on this...maybe others will join in

2 more of my cents. 

 

-I would start out with something simple, like a beam with an object sitting on it to simulate a mirror point load.  Once that is worked out and the results seem reasonable, add arms to that beam and maybe do a 3 point cell.  Work up from there. 

 

- At this point you will run into the problem of refining the flexures so that they all produce the proper reaction at each point on the back of the mirror.  This leads to the problem of how stiff the bars need to be so that focus is not altered significantly moving in altitude, yet still apply the proper reaction force.  On fast f/3.5 optics, the critical focus zone is a mere 5 microns- that requires a very stiff cell- and one which might not flex enough to provide proper support at all points in a real world cell. 

 

- You can measure the reaction force in FEA at each pad and confirm it is close to what PLOP predicts, rather than looking for distortion in the mirror that sits on top. 

 

- If you obtain satisfactory results with the model -that up until this point has been "ideal"-, then you need to see how a non-ideal, real world cell would perform.  The back of the mirror is not perfect and the cell could never be constructed perfect, so these flexures will start twisting slightly as soon as the mirror loads them.  The idea is then to find tolerances that work for the cell.

 

- Then you run into the solder/braze vs weld.  Welds can be modeled in FEA.  If the weld has 100% penetration you don't need to do anything special.  Solder/braze need to be modeled as such.

 

 

I will hold my comments going forward so as to not steer this thread off course. 


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#111 polaraligned

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Posted 30 December 2019 - 08:17 PM


Apart from that, you know know the problems with TET4's I guess.

They are over stiff and can produce garbage.  crazy.gif



#112 brave_ulysses

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Posted 30 December 2019 - 10:16 PM

hi benach,

 

thank you for the mesh. none of the tools i have can do anything with it. the issue may be behind the keyboard...

 

to clarify "maybe others will join in" - it would be great if those with experience would use free tools to create and simulate a model. fusion360 and freecad are available to anyone who wants to use them; i fall on the linux side and that guides my choices.  a comparison with professional sw would be icing on the cake. seems like a worthy goal to make correctly done fea more widespread for the atmers

 

if oberon is agreeable, i'll continue to whittle away at the issues and post any results

 

 

I am already.

 

polaraligned: I already meshed a model for brave_ulysses with TET4's. But although the geometry cleanup and meshing was fairly straightforward, I deliberately left the BCs out of the story because I wanted brave_ulysses to make up his mind for this.

Apart from that, you know know the problems with TET4's I guess.



#113 Oberon

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Posted 31 December 2019 - 01:56 AM

Always agreeable! waytogo.gif



#114 Oberon

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Posted 31 December 2019 - 06:41 AM

Jon,

 

I believe the cell will work better if you keep all rotational moments orthogonal to the long axis of each torsion member.

Perhaps. But a transition from hexagonal to right angle must occur somewhere.



#115 Oberon

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Posted 31 December 2019 - 06:48 AM

Please keep in mind I have no idea what I'm talking about. Could individual water columns be used to measure the loads at each point? It may be too insensitive by orders of magnitude for all I know but maybe it will inspire someone else to think great thoughts.

 

Take care,

Brent
 

Actual loads don't matter; relative loads do. A mirror cell's function is to distribute support evenly. So we don't care too much about loads per se, but we do care a lot about differences.



#116 Oberon

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Posted 01 January 2020 - 05:58 AM

Some more design options and examples...

1. Type 7 - as per Clive Milne's suggestion in post #101

 

2. Type 8 - similar to type 7 but modified to minimise dimensions (note reduced dimensional circles required to define the design). This design minimises the angle of joints that do not enjoy the optimum angle of 90 degrees at the expense of increasing the number of sub-optimal joints

 

3. Type 9 - same as type 7 but showing a likely connection to the outside world. This is the sort of thing that most designs would do.

gallery_217007_7148_260205.png


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#117 mark cowan

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Posted 01 January 2020 - 09:03 AM

Leaving aside various permutations, and referring to the earliest layout, it occurs to me that this whole thing is perhaps overly complicated.  The areas outlined in ovals indicate all the parts that need to execute a flex motion, SFAIK, in order to produce the cell motion, for two triangles.  The rest can be made of anything that doesn't bend much.  Is this not true?  If so they can be optimized more easily if separated out of the overall structure.

 

 Clipboard02.jpg

 

 

 

 


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#118 Oberon

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Posted 01 January 2020 - 01:05 PM

Certainly it is true that not all elements need to flex. However I’m pretty sure you need to duplicate your blue markers onto the left side of the lower group to give a total of 5 markers for the group and allow both triangles freedom to move.

 

Hmmm...its a good question that will keep me awake for hours.


Edited by Oberon, 01 January 2020 - 01:19 PM.

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#119 Dale Eason

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Posted 01 January 2020 - 05:36 PM

I just realized that in order for there to be equal forces when balanced and no load on the cell the orange lever arms times the weight of the arm must be equal.  Otherwise it will add unequal forces to the back of the mirror.  In this case it is due to gravity acting on the cell.

 

Same probably is true when loaded and the spring constant of each and the lever distance needs to be similar.  However one arm has two points holding the mirror and the other has only one. In this case it is a difference in spring constants and lever arm lengths. 

 

 That may complicate things a bit.

 

 

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#120 Oberon

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Posted 01 January 2020 - 10:00 PM

I think you’ll find it is, or very close to it. In any case the structure is intrinsically lightweight, and far less exposed than most cells to the risk of out-of-balance rocker forces being imposed on the mirror as the mirror tilts in altitude.



#121 mark cowan

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Posted 01 January 2020 - 10:13 PM

Certainly it is true that not all elements need to flex. However I’m pretty sure you need to duplicate your blue markers onto the left side of the lower group to give a total of 5 markers for the group and allow both triangles freedom to move.

 

Hmmm...its a good question that will keep me awake for hours.

Yes, that occurred to me as well but I knew you'd work it out.

 

The flexes could be ordinary bearings in tubes or similar.  What I'm considering is that it might yield a more compact sort of deployment without static forces but I'm not quite there yet. ;)



#122 Oberon

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Posted 02 January 2020 - 12:06 AM

I can see how you’re thinking. waytogo.gif   My driver objective was to deliver a low profile whiffletree that functioned on a single plane, ie, a flat single layer. A flexure seemed the obvious choice, but until now a satisfactory method had eluded me. Really happy then that this “fractal T” design also opens a fruitful path to a single plane whiffletree utilising bearings.



#123 figurate

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Posted 02 January 2020 - 11:17 AM

Several short points. I like the arrangements shown above (types 7 thru 9) by Oberon as contrasted with the original scheme, illustrated in Dale Eason's posts, where the straight crossbar holding each T winds up aimed at one support (minor point, I assume that would limit the effect of that torsion member on that particular support). I had angled crossbars in my drawing, based on Clive's suggestion, for the convenience and the more or less tangential orientation it provided at the joint with the tee (falling naturally out of the geometry) and resulting radial orientation of any flexure there. Again, maybe not a big deal, but that was the reasoning. As Oberon said, there has to be transition somewhere, and I put it at the front.

 

My own needs are less stringent. I plan on building an open triangular cell framework to save appreciable weight, with the exact location of that framework relative to the mirror back yet to be determined, so this is purely an enjoyable speculative exercise. I may plan for being able to use either system, conventional triangles or flexures, although the tiny scale of these support trees might be a problem with 10" of diameter.

 

Relative loads: it occurred to me that a crude but effective method might be utilized to verify relative behavior under a load in the analog domain (and by all means feel free to wad this up and throw it in the metaphorical waste bin if you want). Buy a sufficient number of the kind of modeling clay that comes in standard-sized blocks, set the support frame upside-down on the malleable clay with a sufficient weight on top. After some time, examine the depressions left in the clay; the component corresponding to the deepest indentations is too stiff and the most shallow one is too compliant.                      

 

And here's hoping for relief from the fire risk for all our Australian commenters here on CN. 


Edited by figurate, 02 January 2020 - 05:54 PM.

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#124 Oberon

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Posted 17 January 2020 - 05:29 PM

That’s not a saw!

 

THIS is a saw!

 

69BB5A36-E868-4198-AD3D-F68FB40E0F82.jpeg

 

 


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