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A Fractal Flexural Mirror Support

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123 replies to this topic

#51 mark cowan

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Posted 21 December 2019 - 04:22 PM

That may be true for that moment. But what happens when a temperature change, or a distortion in the support frame occurs due to...just tipping to a different altitude? 

Something is screwed up with the quote function since it won't nest... I said

 

OTOH once the low-stiction whiffletree adjusts it exerts no unbalanced forces against the mirror.

That doesn't leave any force beyond the accommodation motion, which with low stiction is over and done.  The design you're suggesting retains the force of adjustment indefinitely in twist in the support.  It may be small but it seems to me it's always there.  So there is a difference. :shrug:


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#52 mark cowan

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Posted 21 December 2019 - 04:30 PM

As a rule of thumb, for a given material I think it is safe to say this is confirmed. After correcting for dimensional differences in the samples I used, the performance of the flats and the angle were the same, with the tube being a little stiffer, which I strongly suspect could be a result of the extrusion process, or a different alloy (or perhaps even the anodising?). 

 

Rule of thumb = angles, U shapes and slotted tubes flex in twist the same as a flat section of an equivalent material with equivalent total width and thickness. 

 

Example: a 25 x 25 x 3mm angle will twist the same as a 50 x 3mm flat.

Yes this has to be true.  Laying a flat section on its side (as opposed to vertical) doesn't change its resistance to twisting.  Putting two flat sections orthogonaly doubles the resistance to twisting.  And so on...


Edited by mark cowan, 21 December 2019 - 08:09 PM.

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#53 MitchAlsup

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Posted 21 December 2019 - 04:36 PM

Quantify equal force. If some equals are more equal than others, how much inequality can we tolerate in a support system and still call it equal?

 

My 16” is 11kg and carried on 18 points. Thats 611g each point (aside from any difference PLOP may appoint to ignore the central obstruction). What is my tolerance? How much difference can I ignore and still call it equal force?

 

20g?

 

10g?

 

5g?

 

1g?

 

 

With my 13" F/3 supported on 6 points, I made the balance beams so that they were dynamically balanced and ride on miniature ball bearings (1/8 ID × 1/4 OD). You can take a hair off your head and gently drape it on the end of a beam (while still in your hands) and the beans will adjust to this amount of weight. The mirror cell can be placed at any angle and still the beams have no preferred direction.

 

Overkill? probably. But to a large extent I was following the lead of mr. Lockwood who indicates that friction (in all forms) is the enemy, and to a large extent was trying to see if the whole lower end could be made as precise as a balance beam. I can darned near perfection, and the mount works well.

Would a mount with more friction be adequate? probably. But, this fell into the category of "it's my telescope".

The real question is how low a friction is "low enough"--which reverts to the question of "will the cell impart any forces on the back of the mirror that are not parallel with the gravitational vector?" 


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#54 Oberon

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Posted 21 December 2019 - 05:32 PM

Agree with all that. But its friction solved under no load conditions. 

 

What about stiction? What about a loaded system? What about the effects of time on a loaded bearing?

 

I think we’re all agreed we can make some wonderfully free systems that move easily under ideal conditions. But a flexure can be so sensitive it doesn’t just wobble in the wind, it wobbles as you walk past. Always and forever. Not that that matters either, really, but does illustrate the non-existence of friction. Zip, Zilch. Nowt.

 

So while its true, as Mark insists, that a flexure must always impose ‘some force’ even if vanishingly small, it is also true that any bearing has friction, and much more seriously, will have stiction, and that in time and under load the stiction that it intrinsic to the system is both indeterminate and very likely to be many times larger than that of a flexure.

 

The fundamental problem with stiction is the unknown bit. Basically we build it as best we can and hope for the best. A flexure on the other hand can be designed and built to perform in a determined way.

 

Anyway, all of this is a digression. This thread wasn’t intended to argue for flexures v bearings. That is to miss the point. In this thread the fundamental benefits and characteristics of a flexure are a given, and we are looking at the PLOP derivative design described in the OP for practical accessible ways to implement that design and similar structures. 


Edited by Oberon, 21 December 2019 - 06:44 PM.

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#55 jtsenghas

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Posted 21 December 2019 - 07:49 PM

As a rule of thumb, for a given material I think it is safe to say this is confirmed. After correcting for dimensional differences in the samples I used, the performance of the flats and the angle were the same, with the tube being a little stiffer, which I strongly suspect could be a result of the extrusion process, or a different alloy (or perhaps even the anodising?). 

 

Rule of thumb = angles, U shapes and slotted tubes flex in twist the same as a flat section of an equivalent material with equivalent total width and thickness. 

 

Example: a 25 x 25 x 3mm angle will twist the same as a 50 x 3mm flat.

 

I was thinking along these lines too before you posted this. Such profiles could help to keep assemblies shorter for height and better avoid sideways motion.

 

  If you wanted to be absolutely compulsive about members of different lengths having equivalent (perhaps negligibly small anyway) torsional resistance among members you could use thin walled tubes slit along their lengths with the slits not the full length of the tubes to "tune" them. 


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#56 mark cowan

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Posted 21 December 2019 - 08:18 PM

Agree with all that. But its friction solved under no load conditions. 

 

What about stiction? What about a loaded system? What about the effects of time on a loaded bearing?

 

For ball bearing or similar supports the working load from a well-supported mirror is so small (gms) compared to more normal usage (kgs) as to be almost trivial. shrug.gif

 

And of course you can easily test for stiction by loading the balanced mechanism and applying the same sort of small loads to measure it.  

 

What a low-stiction traditional sort of bearing will do that this "torsion cell" (see what I did there... wink.gif ) won't do is release any forces down to the level of its inherent stiction when in use.  So if it is built accurately enough and/or with conformation allowed somehow (silicon adhesive for instance) in that configuration it will act as a zero-stiction support if nothing else changes and it works as expected.

 

What nobody seems to know is how small these stiction forces can be to not interfere with support.  Knowing the extreme sensitivity of thin mirrors to support issues under tests I'm not overly optimistic that you can design unaccomodated forces into such a cell (i.e., relying on the torsion to do the final fitting) and get away with it for thin mirrors.  To test this you'd want to build the cell and then jimmy up the pad fitment until you started seeing distortion under test.  That would give you a number to divide by about 10 for actual construction.

 

Basically I'd like to see a simple model built as proof of principle.  Best hurry as I've got a spare hour or so and might fix one up....     OK I've got pieces of a hacksaw blade for the arms made to size, which seems a good material.  But I can't find my brazing rods at the moment so it'll have to wait a bit.


Edited by mark cowan, 21 December 2019 - 08:50 PM.

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#57 jtsenghas

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Posted 21 December 2019 - 09:35 PM

What a low-stiction traditional sort of bearing will do that this "torsion cell" (see what I did there... wink.gif

FracTorsion?


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#58 figurate

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Posted 21 December 2019 - 11:15 PM

I probably don't completely follow the logic and I suspect everything in the OP would require an equal tendency for flexure in either direction, but it would be straightforward to produce an induced torsion, in one preferred direction, simply by offsetting certain support points from the cantilever centerlines on tabs at right angles (that aluminum angle in the photo would work). By allowing for some extra size, the degree of torsion for a particular member could be tuned by adjusting pad location along that perpendicular without breaking a sweat or making any mess. Similar to the adjustable lever arm at the end of an anti sway bar, or the old Volkswagen and Porsche suspensions. Torsion bar suspension?


Edited by figurate, 22 December 2019 - 08:50 AM.


#59 brave_ulysses

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Posted 22 December 2019 - 02:49 AM

freecad/calculix simulation. support is "calculix steel" and mirror is "generic glass"

 

green 0 displacement, dark blue 87nm displacement

 

i need to add something flexible between the mirror back and support faces

 

 

oberon.png

 

 

freecad file - remove .zip extension

 

Attached File  oberon.FCStd.zip   94.44KB   0 downloads


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#60 brave_ulysses

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Posted 22 December 2019 - 02:51 AM

mirror front. abs of displacement

 

freecad packages here (linux, mac and windows)

https://www.freecadw...g/downloads.php

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  • Screenshot from 2019-12-22 01-50-55.png

Edited by brave_ulysses, 22 December 2019 - 02:53 AM.

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#61 Benach

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Posted 22 December 2019 - 04:17 AM

Brave_ulysses: can you please also upload the scale since colors say nothing in a FEM plot.

#62 brave_ulysses

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Posted 22 December 2019 - 08:38 AM

hi benach,

 

this is the output

 

 

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#63 brave_ulysses

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Posted 22 December 2019 - 08:46 AM

no scale for output

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#64 Oberon

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Posted 22 December 2019 - 06:13 PM

Nice work!

 

Next trick is to apply the PLOP generated dimensions to place the support points correctly; this will even up support and remove mirror distortion. 

 

Then apply the “T” based flexure system as per OP. This may highlight which elements are working harder than others and potentially help us to fine tune the structure to ensure equal forces are applied to each support.

 

Suggest start with a 6 point support for first pass.


Edited by Oberon, 22 December 2019 - 06:17 PM.


#65 brave_ulysses

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Posted 22 December 2019 - 07:03 PM

hi jonathon,

 

do you have dimensions from a plop simulation that i can start with? should the tees connect at the bases? where do the fixed constraints go? i'm uncertain how you intend for this to be setup...

 

thanks,

 

clay



#66 Oberon

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Posted 22 December 2019 - 07:08 PM

Can do, will send something later that assumes a 16” mirror but it all scales. Thx.



#67 Oberon

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Posted 23 December 2019 - 10:26 AM

Some dimensions to work with.

 

Notes:-

 

a. supports are all equivalent-distance apart on their respective rings, ie, 30 degrees on the outer ring and 60 degrees on the inner

 

b. dimensional circle diameters are in mm, and the red lines are 15 degrees apart

 

c. mirror is pyrex, 400 x 42

 

d. bold type indicates PLOP definition (this means "C" is not definitive for support function, which opens up other possibilities, more on that later)

 

gallery_217007_7148_94400.png


Edited by Oberon, 23 December 2019 - 10:28 AM.


#68 brave_ulysses

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Posted 24 December 2019 - 07:08 PM

hiding in the garage while my wife completes superfluous preparations for xmas...freecad/gmsh/calculix is giving me some trouble, will start looking at command line operation

 

merry xmas + happy holidays to all

 

 

 

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#69 Benach

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Posted 24 December 2019 - 10:53 PM

Brave_ulysses: this is not a good mesh. A good mesh should be small near contacts and the difference in element size of the flexures and the inner zones of the mirror is risky.

Apart from this: a minimum of two elements over thickness is highly recommended thus the element size over the thickness of the mirror as well as the element size over the thickness of the flexures is too big. Thickness is the smallest direction, it is not the same as element height.

All in all: make the elements of the mirror about half to one quarter of the size of the outer zones. Make sure that the elements of the flexures are small enough and make local refinements near the contacts.

#70 Oberon

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Posted 25 December 2019 - 09:21 PM

For completeness, here are 6 options for building this flexure:-
 

Type 1 - as per OP, flexures radiate in from outside, suits a cell with circular mount, such as mounted on a tube
Type 2 - as per model in previous posts, flexures radiate out from centre, best for illustrating basic principles
Type 3 - as Type 2 but with a stiff circular piece in the centre for mounting a fan
Type 4 - continues the T theme just because we can
Type 5 - as per Type 2 but with extended final flexures to improve flexibility
Type 6 - combines advantages of both Type 5 and Type 3

 

gallery_217007_7148_271272.png


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#71 brave_ulysses

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Posted 27 December 2019 - 02:24 PM

thanks, benach. that mesh was created by gmsh with default values. this mesh is created by netgen

 

the last analysis showed the average deviation was 379km  :0   more investigation is indicated...

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  • netgen.jpg


#72 Benach

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Posted 27 December 2019 - 02:49 PM

Still the element size in the supports is too big. There should be at least two elements over thickness. Also the local refinements are not matched.

#73 brave_ulysses

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Posted 27 December 2019 - 04:25 PM

the mesh programs i know about are tetgen, netgen and gmsh. do you know how to control any of these from the command line? the freecad interface to netgen and gmsh does not expose too much...

 

what do you use to create a mesh?

 

thanks



#74 Oberon

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Posted 27 December 2019 - 04:45 PM

Perhaps I’m missing something but its not obvious to me what is being tested here.



#75 Benach

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Posted 27 December 2019 - 05:18 PM

Oberon: nothing is tested, there is a problem here. The mesh is too coarse in the supports to get correct results. This will result in numerically undersampled results that are incorrect.
To approximate the displacement field properly, at least three integration points are necessary, or in layman's words: to properly approximate the deformations, you need at least two elements over thickness to be sure that you have enough information.

Normally a rule of thumb is that you should do at least a parabolic fit over a small displacement field. To read a bit more:
https://enterfea.com...ze-quick-guide/

Brave_ulysses: will be back from holiday tomorrow. Will then check out FreeCAD. Normally, I prefer professional software because of this. This allows me to tweak the mesh in any way I prefer. But these programs are ridiculously expensive and require much more time to master. To name a few that I know reasonably well: ANSYS, HyperWorks and Abaqus. But I am not sure if these are compatible with FreeCAD. Will check that out tomorrow.
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