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A Fractal Flexural Mirror Support

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#26 mark cowan

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Posted 14 December 2019 - 11:42 PM

Tom, I'm primarily interested in supporting a 16" mirror on 18 points (a pair of actually), so all my design work will reflect that. However I see no reason why as a matter of principle (execution being a practical constraint) that the design principles don't naturally follow for larger structures with more support points, exactly as our more conventional whiffle-trees already do.

 

Yeah, to my eye it looks good for at least one more step to 54 points, which pretty much will support any mirror done by amateurs.  My WAG was 50% on this crude illustration, by PLOP it works out closer to 60%.  But there looks to be plenty of room to scale it up, with appropriate considerations of course. wink.gif

 

I think the basic principle is sound, having played with a stainless ruler clamped in a vise (no weights just fingers) but the devil may well lie in the details as usual.  Good idea, Jonathon. :waytogo:

 

 

 Clipboard01.jpg


Edited by mark cowan, 14 December 2019 - 11:48 PM.

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#27 Oberon

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Posted 15 December 2019 - 03:57 AM

I'm not a good FEA person or even much of a mechanical engineer.  I'm an electrical engineer. Took statics and dynamic force classes too long ago.  It seems to me that it might not provide an even force at each point of contact to the mirror.  Which a correctly made whiffel-tree does.  That is because now the torsion spring nature of the bars start to work instead of just a gravity load by the mirror.  

 

Fusion360 can do FEA and it is free to people like us.  However there is a learning curve that some may not want to tackle.  Me included.  I use it to make 3D printed parts but have never tried the FEA feature.

 

Dale

The object is to provide an even force within a few grams, within the tolerances of positioning the mirror. Having illustrated how trivial it is to twist an SS rule significantly more than is required, I’m confident that the method can produce that level of performance in principle. OTOH I’m always mindful of gotcha’s arising in fabrication that obstruct high performance in practice, so until I’ve built and can demonstrate I will remain cautious and tentative. However the principle is sound.



#28 Benach

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Posted 15 December 2019 - 06:17 AM

Oberon: Well, I may have professional FEA software at my disposal in a few weeks from now for an astronomical project I am not allowed to clarify yet. Being a professional FEA analyst for three years, I can check out a design if you're interested. But spending time on really refining it to the level that you'll get it production ready will take a lot of time.

Alternatively and preferably you can try to make the analysis yourself and I will check yours and give feedback on it.

#29 hamishbarker

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Posted 15 December 2019 - 03:44 PM

Watch out for Lateral torsional buckling when attempting to use beams with a very large ratio of stiffnesses. The critical load ( beyond which the beam will buckle sideways) is fairly straightforward to calculate.
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#30 figurate

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Posted 17 December 2019 - 02:26 PM

I would think that, if the proportions were indeed as extreme as those of the steel rule, not only buckling but the tendency to flex sideways could be an issue, on the principle that if it conceivably can happen, it will.

 

Though an earlier sketch here showed a very different kind of conceptualization, my first thought upon seeing this thread was along different lines, and actually more like what is depicted here. I tend to design my own stuff based on materials I have at hand and the tools and methods at my disposal (and I don't have large-mirror issues or 3D printing capability anyway) but more to the point, I've been needing a different and lighter cell for my 10" f6 Zambuto mirror that someone transplanted into a 1960s style newtonian tube assembly. The idea of using cantilevered flexural supports in a fractal arrangement immediately suggested a solution to my problem, although the validity of the idea remains to be demonstrated, and there are lots of difficulties to work out in this particular realization.

 

Here I show 3/32" thick aluminum cantilevers using a three-branch fractal pattern in a riveted support tree assembly, solidly attached to hard points on a triangular frame (which will mate with external lugs via three slots in the tube). Each tree replaces one conventional triangle and creates nine points of support rather than three. I decided to concentrate some degree of compliance primarily at the supporting tips (and not allowing for much in the way twisting) and I show this in the profile view; I am only assuming small edge-on deflections in order to accommodate any irregularities in the flat bottom surface of the mirror, and this degree of springiness could be tuned by removing material at the support fingers. Too much and the fingers could bend or deflect and the mirror position shift, too little would not equalize the load on the supports. In addition to that issue, fabricating the assemblies (18 of the smaller pieces needing to be made) and keeping the required alignment along the top edges wouldn't be trivial jobs, though one possibility is adding raised plastic tips and making those plane (the sketch shows layers of tape added to form support pads as an simple expedient).                   

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Edited by figurate, 17 December 2019 - 09:24 PM.


#31 MitchAlsup

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Posted 17 December 2019 - 09:56 PM

This is just an idea for now. But its perfectly serious. And infinitely scaleable.

So how does it work?

Essentially it exploits the ease with which a flat plane can twist, yet support a load edge on. 

gallery_217007_7148_208309.png

What I see and understand is the bending of the flat plane when intersecting at 90º

What I don't see/understand is what kind of secondary forces manifest themselves when one plane intersects at an angle other than 90º !?! as seen in your figure where the 3 point triangles are picked up by the double loaded beam.

 

For example, consider a 12-point cell I am making for my 20" F/3::

 

Skew.jpg

 

Now, consider aligning the pivot axis to the beam axis::

 

Askew.jpg

 

In this second case, the center beam is transferring forces from the left and right beams, but it is ALSO moving non-perpendicularly moving the pivot points of the other two beams.

 

I wonder if the non perpendicular attachments in your drawing would cause a similar effect.



#32 brave_ulysses

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Posted 18 December 2019 - 05:13 PM

working through an fea simulation in freecad/calculix

 

 

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#33 figurate

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Posted 18 December 2019 - 08:52 PM

Just want to point out that, ideally, all support cantilevers should be of equal length, at least in my case where an equatorial mounting was assumed and therefore any inclination is possible (my rendering has that kind of symmetry). Also the above test case could have mirrored the hub symmetry at the tip branchings unreversed to provide three equally cantilevered points, or alternatively insert a middle 'digit' in each arm to make three equal load-path points, which would duplicate the nine point mirror supports commonly in use (and I'm not completely sure about which are the supports in the illustration). Otherwise, looking forward to the results.                   

                                                                                                                                                                   



#34 brave_ulysses

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Posted 18 December 2019 - 09:10 PM

this is mostly an exercise for me to see it i can get a reasonable fea result with an oberon-ish support. initially, no attempt to optimise the structure

 

the red crosses are fixed surfaces that extend 1mm below the beams. the 6 cylinders at the extremities extend 1mm above the beams and support the mirror. the beams will be simulated as 6061 and the mirror as generic glass

 

this is largely uncharted territory for me, so i'm up for pointers/etc...

 

once the simulation runs, i'll post the results and file(s)

 

thanks,

 

clay


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#35 Oberon

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Posted 18 December 2019 - 11:16 PM

Hi Clay, note that my design is based on PLOP points and whiffle tree principles. In principle the defined PLOP points remain in play at all levels of the whiffle tree, caveat being that its functionally more subtle that a bearing.



#36 Oberon

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Posted 18 December 2019 - 11:25 PM

Oberon: Well, I may have professional FEA software at my disposal in a few weeks from now for an astronomical project I am not allowed to clarify yet. Being a professional FEA analyst for three years, I can check out a design if you're interested. But spending time on really refining it to the level that you'll get it production ready will take a lot of time.

Alternatively and preferably you can try to make the analysis yourself and I will check yours and give feedback on it.

Thank you Benach that sounds like an offer too good to refuse. In the meantime I will continue making analysis myself, but I’m pretty sure some FEA would be helpful for defining relationships.



#37 Oberon

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Posted 18 December 2019 - 11:45 PM

Just want to point out that, ideally, all support cantilevers should be of equal length, at least in my case where an equatorial mounting was assumed and therefore any inclination is possible (my rendering has that kind of symmetry). Also the above test case could have mirrored the hub symmetry at the tip branchings unreversed to provide three equally cantilevered points, or alternatively insert a middle 'digit' in each arm to make three equal load-path points, which would duplicate the nine point mirror supports commonly in use (and I'm not completely sure about which are the supports in the illustration). Otherwise, looking forward to the results.                   

Equal length superficially implies equal stiffness, but if that is a concern then perhaps our structure isn’t stiff enough in the direction we want it to be stiff. Also note that your supports don’t support the mirror optimally according to PLOP; that is, you’ve made the cantilevers equal but the support points aren’t equally loaded, which in turn means that the mirror will be unequally supported.

Stepping back, in a hypothetically perfect mirror support system axial support will be infinitely stiff, and co-planar adjustments will encounter zero resistance, permitting pure predictable evenly weighted support points ah la PLOP.

The flexure design proposed in the OP is intended to get very close to this. Errors in a superbly built and optimised support may prove be less than a gram, which is utterly trivial and insignificant. Even if errors are as high as say 10 grams in a lesser build they will be trivial and insignificant. Exactly what tolerances are acceptable I haven’t worked out yet (and here FEA analysis would be very helpful).



#38 Dale Eason

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Posted 19 December 2019 - 02:24 AM

I don't know how to do it but I would do a FEA test to see if each support point of the mirror support produces an equal force on the back of the mirror when one or all are slightly at different heights above the cross members.  That would simulate a slightly rough back surface of the mirror.  That is what a whiffle-tree would do.

 

Years ago when I was playing with different back supports on a thin 3/8 inch thick meniscus mirror and watching it deform using the interferometer adding about 1/32 inch shim under a mirror support changed the shape of the mirror drastically when not on a whiffle-tree support.  That of course was a very thin mirror.

 

Dale



#39 Oberon

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Posted 19 December 2019 - 06:53 AM

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?

 

I’ve already proven here that single components of this system will do better than a gram. If that performance is replicated for each section, then being a whiffle tree the entire support system will equalise to better than a single gram. Even if, say, some shorter sections were less flexible than longer sections and you ended up with a mixed bag of errors, some errors as high as 10g, well the system is still delivering equal support to 10g. 

 

So the question is not whether or not the system can deliver equal support, but to quantify our tolerances, and then perhaps use FEA to determine the stiffest strongest flexure that can meet those tolerances. 



#40 Oberon

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Posted 19 December 2019 - 07:05 AM

What I see and understand is the bending of the flat plane when intersecting at 90º

What I don't see/understand is what kind of secondary forces manifest themselves when one plane intersects at an angle other than 90º !?! as seen in your figure where the 3 point triangles are picked up by the double loaded beam.

 

For example, consider a 12-point cell I am making for my 20" F/3::

 

attachicon.gifSkew.jpg

 

Now, consider aligning the pivot axis to the beam axis::

 

attachicon.gifAskew.jpg

 

In this second case, the center beam is transferring forces from the left and right beams, but it is ALSO moving non-perpendicularly moving the pivot points of the other two beams.

 

I wonder if the non perpendicular attachments in your drawing would cause a similar effect.

Mitch, obviously I worried about those non perpendicular joints for a while too, but in the end dismissed the concerns for two reasons.

 

1. the motions are so minute the angles won’t have any real life impact

 

2. and even if they did, any distortion would easily be taken up by a twist flexure in the next section, rending the distortion of no effect.

 

Point #2 is where this design is importantly different to the examples you gave of a standard rocker. The standard rocker is stiff in all directions, and so a non perpendicular bearing will impose a significant constraining force on any significant motion. But the flexure support can both twist and bend sideways should it need to, and thus is able to manage non perpendicular forces also.



#41 Dale Eason

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Posted 19 December 2019 - 05:45 PM

Yes, I thought it was obvious there would be some appropriate tolerance.  I don't know what that is other than to say it should not be exceeded.  So still that is what needs to be measured.  It seems to me that it will be a larger force difference than the usual wiffle-tree version.  Is it too much different?  I don't know.

 

Dale



#42 Oberon

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Posted 19 December 2019 - 09:14 PM

I expect the force required will be way less than the usual whiffle tree because a flexure has no stiction.



#43 mark cowan

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Posted 19 December 2019 - 09:44 PM

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



#44 Earthbound1

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Posted 20 December 2019 - 12:39 AM

Not to take away from the design, but my floor buffer pad support has practically infinite points of contact yet only one in essence and permits ease of ducted air flow...extremely easy and especially cheap! It was the next step up from astroturf and though no testing of the figure DPAC or otherwise has been done, it pleases my inexperienced eyes very well. Sometimes simpler is better. Over engineering isn't necessarily a bad thing though... airless "run flat" tires that are based on geometric figures bode well for military and civilian vehicles. Regular tires work well too. Just not as well as when projectiles are beig hurled at them for the purpose of deflating them... Is the prey any MORE dead when shot by a plasma rifle than the lowly bow and arrow? Regardless, keep up the excellent work and documentation Jon! Active inquisitive minds propel innovation forwards!

Edited by Earthbound1, 20 December 2019 - 12:53 AM.


#45 figurate

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Posted 20 December 2019 - 02:00 PM

I'll add that I probably failed to fully see the logic in the (transverse) flexural nature of Jonathan's design initially; I was primarily concerned about any inherent unpredictability in the relative positioning of the parts over time in earlier remarks. It is a very interesting concept  and I just haven't been keeping up with developments in this area lately.

 

My own take on the idea, in the context of smaller diameters and more traditional mirror proportions (perhaps slightly off-topic here), centered on the fractal branching aspect, and as he noted earlier I did not have a completely satisfactory solution; it was just a first stab at it anyway. The great thing about a network of supports is the ease of tweaking the proportions to give some desired set of properties, by varying cantilever length, cross sectional dimensions or the branching angles and number. I plugged in one particular geometry, roughly hexagonal, three-fold, or snowflake symmetry ('tis the season), primarily to give equal spacing to the support points, and in hindsight I would reduce the stiffness of the radial component by one or more of those methods and certainly be open to any other tweaks required to obtain equal loading. The possible variations on the general theme are almost endless, but there are likely to be a few particular candidates that are a best fit for my particular need.                    


Edited by figurate, 20 December 2019 - 10:54 PM.

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#46 jtsenghas

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Posted 20 December 2019 - 11:55 PM

I'm on Cloudy Nights for the first time in a week because I've been visiting relatives near Seattle on my vacation, so I'm just catching up. 

 

I like the thought process indeed! 

 

I have a thought which I'd like you to consider for execution which may help significantly both in placing the pads on location and may eliminate the concern of the straps bending laterally in use. 

 

Since the centerline of each strap sees no torsion and is expected not to move except trivially under loading vertically,  fine wires in the plane of those strap centerlines attaching straps across intersections to triangulate should have no detrimental effects that I can see. They would essentially be what we call zero load trusses and their function would be simply to maintain shape.  Piano wires could be used and could manage the trivial compressive and tensile loads from actual variation from design.

 

For construction tiny holes could be drilled in the straps and the wires passed through them with bends as needed at each hole.  Wires could extend at least a few millimeters through each strap and be bent and epoxied to the opposite side of the strap,  or continue to terminate through yet another strap. 

 

The point of this design suggestion is that any method of attaching straps to each other along the centerlines of the straps should have no impact on the intended design and may go a long way towards maintaining and establishing shape. 

 

Good thinking,  Jonathan,  and I hope you are safe from the voracious fires that have been consuming NSW.  Many in the west coast of the states can sympathize with the plight of your region. 


Edited by jtsenghas, 20 December 2019 - 11:57 PM.

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#47 mark cowan

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Posted 21 December 2019 - 01:18 AM

That sounds pretty useful.  But I'd like to suggest just a simple build of one triangle cell followed by manual (or instrumented) testing to see exactly how/if it works.  This kind of thing has saved me from going down many unproductive paths in pursuit of practical ideas...


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#48 Oberon

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Posted 21 December 2019 - 07:11 AM

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

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? 



#49 Oberon

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Posted 21 December 2019 - 08:09 AM

I'm on Cloudy Nights for the first time in a week because I've been visiting relatives near Seattle on my vacation, so I'm just catching up. 

 

I like the thought process indeed! 

 

I have a thought which I'd like you to consider for execution which may help significantly both in placing the pads on location and may eliminate the concern of the straps bending laterally in use. 

 

Since the centerline of each strap sees no torsion and is expected not to move except trivially under loading vertically,  fine wires in the plane of those strap centerlines attaching straps across intersections to triangulate should have no detrimental effects that I can see. They would essentially be what we call zero load trusses and their function would be simply to maintain shape.  Piano wires could be used and could manage the trivial compressive and tensile loads from actual variation from design.

 

For construction tiny holes could be drilled in the straps and the wires passed through them with bends as needed at each hole.  Wires could extend at least a few millimeters through each strap and be bent and epoxied to the opposite side of the strap,  or continue to terminate through yet another strap. 

 

The point of this design suggestion is that any method of attaching straps to each other along the centerlines of the straps should have no impact on the intended design and may go a long way towards maintaining and establishing shape. 

 

Good thinking,  Jonathan,  and I hope you are safe from the voracious fires that have been consuming NSW.  Many in the west coast of the states can sympathize with the plight of your region. 

Hi JT, the fires mean very smoky days and very smoky nights, but fortunately for us no more immediate threat. Tragedies elsewhere sadly, not to mention the environmental waste.

My initial thoughts is that wires might get a bit fiddly compared to, say, gluing in pieces of rubbery foam cut to shape for the job. I briefly even considered potting the entire thing in silicone, but to be honest I'm doubtful its even going to be an issue.

The thing is, the flexure part works just as well using angle, and even with slotted RHS tube, so there are many options out there to avoid buckling. And just like the curved spiders, the critical thing is the thickness of the vane material itself. A 3mm thick aluminium vane is many times stiffer than 1.3mm angle, and ditto for 1.2mm RHS tube (with one side slotted so its technically no longer a tube).

Here are the materials I've tried so far...

 

med_gallery_217007_7148_146950.jpg

 

Of these, the order of flexibility is as displayed with the stiffest at the top right (50x3mm Aluminium) and the most flexible at the bottom left (25x0.7mm Steel Rule). Fair in the middle is the 25x25x1.2mm aluminium tube with a slot cut down one side.

 

Notes:

 

As you would expect, the 50x3mm flat was exactly 2.5 time stiffer than the 20x3mm flat.

 

Also, in each case flexure was linear with the weight applied, whether flat, angle or slotted tube. 

My initial impressions are that these two simple and direct relationships continue irrespective of whether the material is flat, angled or slotted tube (so long as the latter are not constrained at their ends). That may not be news to ME's living in the world of unconstrained beams, but I was a little surprised to see that emerging and will look at it more closely when I get the chance.

Obviously anyone with access to FEA could confirm or dispel that very quickly. 

Caveat: we're talking about the flexibility to twist along the length here, not the ability to bend in any other way.


Edited by Oberon, 21 December 2019 - 08:29 AM.


#50 Oberon

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Posted 21 December 2019 - 09:16 AM

My initial impressions are that these two simple and direct relationships continue irrespective of whether the material is flat, angled or slotted tube (so long as the latter are not constrained at their ends). That may not be news to ME's living in the world of unconstrained beams, but I was a little surprised to see that emerging and will look at it more closely when I get the chance.

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.




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