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Some Curved Vane Spider Design Ideas

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#1 bigbangbaby

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Posted 19 September 2021 - 12:34 PM

Actual testing is the best way to prove out a design, and Oberon has tested numerous spider designs in his excellent Spiders on Trial thread. Highly recommended.

 

Second best is finite element analysis, which was used to assess a couple unconventional curved vane spiders. I compared these to a conventional three-vane spider. The criteria are deflection and first modal frequency. Low deflection is key to maintaining collimation. First mode is the first natural frequency at which a structure vibrates. There are also a number of harmonics, but the first mode is generally considered most important. The stiffer the structure, the higher its first mode. In the case of a spider, stiff is good. All analyses assume the scope is pointed at the horizon (Altitude = 0 degrees), worst case for deflection. Some of the analyses use actual geometry for the secondary and holder. Others employ a point mass offset from the spider and connected to the hub. The combined weight of the secondary mirror and holder is assumed to be 0.3 lb. All vanes are steel; Hubs are either wood or steel, depending on the design.

 

First up, an un-tensioned three-vane spider with .007 in. thick x 1.5 in. wide steel vanes fit into a 15 in. I.D UTA. The hub is wood. The larger cylinders at the three adjustment studs are bushings fixed to the UTA. The studs are free to slide in the bushing bores. A displacement constraint is placed on the stud ends. The constraint is used to stretch the spider vanes radially outward as would happen when tightening the tensioning nuts. For this un-tensioned case, displacement is held at zero inches. Gravity is vertical down in the images. One of the three vanes is aligned vertically with gravity.

3-vane_untensioned.jpg

Vertical deflection at the mirror (in the direction 90 degrees to the optical axis) is about .002 in.

First mode = 30 Hz torsional about the optical axis

 

Next, the vanes are stretched .001 in. radially. This results in a 43 lb tension. For a 1/4-20 stud, that's about 1.6-2.0 lb-in. of torque on the tensioning nut.

3_vane_tensioned.jpg

Vertical deflection at the mirror is less than .001 in.

First mode = 100 Hz torsional about the optical axis

 

Doubling stretch to .002 in. doubles the tension and torque and raises first mode to 135 Hz. Mirror deflection is just slightly less than at .001 in. stretch. This shows that first mode is not linear with tension. Also, there is likely diminishing returns for further tensioning, which would require an increasingly stouter (heavier) UTA structure.

 

Now, compare this to a conventional curved vane design. Again, vanes are .007 in. x 1.5 in. wide. Hub is steel hex. No tension, of course. Ends are fixed to the UTA I.D. A point mass simulates a 0.3 lb secondary and holder offset 1.5 in. from the hub.

c1_1.jpg

Vertical deflection at the hub is .004 in.

First mode = 51 Hz rocking in plane

 

In this case, the curved vane spider deflects more than an un-tensioned three-vane spider of the same thickness and width. It also helps to explain why curved vanes must be made relatively thicker.

 

The first alternative curved vane design is a single loop .010 in. thick. I thought I had come up with something novel, but later discovered another CN member thought of it earlier and successfully built and used one. The hub is made of wood and employs a 4-screw adjustment. This departs from the single-loop spider posted on Stellafane that has no angular adjustment and must be bent into alignment.

alt1_1.jpg

Vertical deflection at the mirror is less than .001 in.

First mode = 114 Hz rocking in plane

 

Two concerns with this design: the wide vane must be perfectly aligned with the optical axis or it will optically appear much thicker. Also, off-axis incoming light may be diffracted more than from a less wide vane.

 

The second alternative curved vane design adds material where moment loads are highest. This stiffens the structure, raising first mode and lowering deflection. The added material resides outside the primary mirror O.D. and shouldn't impact diffraction, I think. The vanes are .007 in. thick x 1.5 in. wide with 4.0 in. wide ends. The assembly uses a steel hex hub and, as in the previous case, a .3 lb secondary offset 1.5 in.

alt2_1.jpg

alt2_2.jpg

Vertical deflection at the hub is less than .001 in.

First mode = 106 Hz rocking in plane

 

I'm encouraged with the results. Deflection and modal frequency are about that of a tensioned three-vane spider of the same thickness.

 

Keep in mind, these analyses assume idealized attachments. In reality, deflections may be slightly higher than calculated. That said, it helps identify trends and inform design direction.


Edited by bigbangbaby, 19 September 2021 - 05:39 PM.

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#2 bokemon

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Posted 19 September 2021 - 02:00 PM

Vertical deflection is obviously not the mode with the lowest frequency.  It's tilting of the mirror.


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#3 bigbangbaby

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Posted 19 September 2021 - 02:08 PM

Actually, torsion about the optical axis or in-plane rocking is the first mode in all the designs analyzed. To be clear, the posted images show vertical deflection only. The modal response is dynamic and can't be fully captured by a still frame.


Edited by bigbangbaby, 19 September 2021 - 02:15 PM.


#4 Oberon

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Posted 19 September 2021 - 05:25 PM

I found vertical deflection to be a non issue. Curved vane spiders could very clearly perform very well vertically along the axis of the hub. What they do very poorly at is resisting tip/tilt of an unbalanced hub and mirror, and at damping vibration. 

 



#5 bigbangbaby

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Posted 19 September 2021 - 05:36 PM

Vertical, in this case, is at right angles to the optical axis, i.e. tip tilt. By that measure, these analyses show the alternative curved vanes perform on par with a tensioned 3-vane spider. Damping is another issue. There are ways to damp vibrations, though without active damping, none of the designs analyzed will have a damping coefficient greater than 0.1 or so, I'm guessing.


Edited by bigbangbaby, 19 September 2021 - 05:36 PM.


#6 MitchAlsup

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Posted 19 September 2021 - 07:43 PM

I enjoy your FEM analysis.

 

But let us turn our attention to the more classical 4-vane in the >-< configuration. the - part should be 85% the width of the secondary minor axis.

 

Second widen the vane at the attachment point from 1" to 2.5" (for the scope you used) and narrow the UTA attachment end to 0.25".

 

Also note that the vanes should be at 45º to the focuser orientation so the - part can be tucked up under the secondary itself, minimizing cantilevered forces.

 

Something more along the lines of::

 

13Secondary01.JPG


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#7 Jon Isaacs

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Posted 19 September 2021 - 08:08 PM

Vertical, in this case, is at right angles to the optical axis, i.e. tip tilt. By that measure, these analyses show the alternative curved vanes perform on par with a tensioned 3-vane spider. Damping is another issue. There are ways to damp vibrations, though without active damping, none of the designs analyzed will have a damping coefficient greater than 0.1 or so, I'm guessing.

 

Why are you using three vane spiders? 

 

Standard spiders are typically 4 vane and Mitch's 4 vane design is probably what Jonathan was thinking of for comparison. 

 

This is a worthwhile thread if you haven't seen it:

 

https://www.cloudyni...ves/?hl= spider

 

Jon



#8 bigbangbaby

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Posted 19 September 2021 - 08:38 PM

I'm using a conventional three-vane spider because one of the alternative curved spiders I looked at is also three vane. It's a more valid comparison than to a four vane. There is no single vane conventional spider, so there is nothing to compare it with. Yes, I mention Oberon's spider thread at the beginning of this one.  The point of this thread is, curved spiders are often maligned because the current designs aren't as stable as conventional tensioned spiders. The alternative designs in theory fix these shortcomings. If I were to use a conventional spider -- should one of the alternative curved spiders not work as predicted -- I'd build the thinnest possible three-vane spider (like .003-.004 in. thick), not a four-vane. I strongly dislike diffraction spikes, and those from a four-vane spider I find the most objectionable.



#9 bigbangbaby

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Posted 19 September 2021 - 09:27 PM

MitchAlsup, that's a clean design. And if I didn't dislike diffraction spikes as much as I do, I'd seriously consider going that direction. A curved spider is actually plan B for me. Plan A is a window.


Edited by bigbangbaby, 19 September 2021 - 09:27 PM.


#10 jg3

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Posted 19 September 2021 - 10:39 PM

Bigbangbaby, I appreciate your sticking you neck out with that analysis, with the expected hard but worthy comments.  As for "why not this?", "why not that?", the asker bears the burden of proof, not you, although I'm not alone in being curious about various alternatives, not limited to those Oberon analyzed empirically.  Definitely make a priority of adding tip-tilt deflection to the report (since that's the major part of losing collimation), and indicate whether axial rotation is among the vibration modes.  And try to analyze some of the same cases as Oberon's experiments - comparison would validate (or call into question) both.



#11 Oberon

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Posted 20 September 2021 - 03:59 AM

Vertical, in this case, is at right angles to the optical axis, i.e. tip tilt. By that measure, these analyses show the alternative curved vanes perform on par with a tensioned 3-vane spider.

In that case see my first comment. Something is wrong with the analysis. I don’t know enough about FA to point out where you might be going wrong, but I do know enough about spider designs to be convinced you’re mistaken. Perhaps explore what about your curved spider you think is special, what unique features make it extra stiff etc.
 
This conclusion cannot be true…
 

I'm encouraged with the results. Deflection and modal frequency are about that of a tensioned three-vane spider of the same thickness.


So far as 3 v 4 vanes, I’m content that 3 vanes can be for all practical purposes as stiff as a similarly constructed 4 vaned spider (all vanes point to center), and provided the hubs are maximum diameter sufficiently stiff for good performance (although >-< is most rigid of all). But thats OT really, my point is that no curved spider even closely compares with a reasonably well made straight spider held in tension until the vanes are very thick.

Question - how does your model account for tension and the UTA?

Edited by Oberon, 20 September 2021 - 04:03 AM.

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#12 Oberon

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Posted 20 September 2021 - 04:06 AM

PS. btw I love the fact that you’re modeling spiders, so big thumbs up there! waytogo.gif 

Just need to get the models modeling reality! wink.gif



#13 bigbangbaby

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Posted 20 September 2021 - 07:22 AM

Bigbangbaby, I appreciate your sticking you neck out with that analysis, with the expected hard but worthy comments.  As for "why not this?", "why not that?", the asker bears the burden of proof, not you, although I'm not alone in being curious about various alternatives, not limited to those Oberon analyzed empirically.  Definitely make a priority of adding tip-tilt deflection to the report (since that's the major part of losing collimation), and indicate whether axial rotation is among the vibration modes.  And try to analyze some of the same cases as Oberon's experiments - comparison would validate (or call into question) both.

I don't consider it sticking my neck out, just sharing of ideas. I'm confident that what I presented is correct or I wouldn't post it.

 

To be clear, all the deflections I report are tip-tilt! Quoting from my post: "All analyses assume the scope is pointed at the horizon (Altitude = 0 degrees), worst case for deflection. Gravity is vertical down in the images." I could have reported total deflection, but deflection in the direction of gravity -- when the scope is pointed horizontal -- most affects collimation. It is the limiting case and bounds the problem.

 

I also indicate which direction the first mode vibration occurs. Rocking in plane, in these examples, means shaking back and forth in and out of the page. "Torsional about the optical axis" is self-explanatory.

 

Lastly, I'm not trying validate or invalidate any spider design. I looked at a couple curved spider designs, one that happens to be three vane. The comparison of it to a conventional three-vane spider is to show that a curved spider can be made to perform as well as a conventional one. Is it exhaustive? No. Does it perfectly replicate real hardware? It does not. As I posted above,  "Keep in mind, these analyses assume idealized attachments. In reality, deflections may be slightly higher than calculated. That said, it helps identify trends and inform design direction." In other words, it provides a compass to steer a design in the right direction. Clearly, most curved vane spiders as they exist today are mechanically inferior to their tensioned counterparts. However, with a few tweaks, curved vanes can be made to perform as well as a similarly dimensioned conventional spider. At least on paper.


Edited by bigbangbaby, 20 September 2021 - 07:56 AM.


#14 bigbangbaby

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Posted 20 September 2021 - 07:55 AM

In that case see my first comment. Something is wrong with the analysis. I don’t know enough about FA to point out where you might be going wrong, but I do know enough about spider designs to be convinced you’re mistaken. Perhaps explore what about your curved spider you think is special, what unique features make it extra stiff etc.
 
This conclusion cannot be true…
 

So far as 3 v 4 vanes, I’m content that 3 vanes can be for all practical purposes as stiff as a similarly constructed 4 vaned spider (all vanes point to center), and provided the hubs are maximum diameter sufficiently stiff for good performance (although >-< is most rigid of all). But thats OT really, my point is that no curved spider even closely compares with a reasonably well made straight spider held in tension until the vanes are very thick.

Question - how does your model account for tension and the UTA?

To your first point. From my post: "The second alternative curved vane design adds material where moment loads are highest. This stiffens the structure, raising first mode and lowering deflection. The added material resides outside the primary mirror O.D. and shouldn't impact diffraction, I think."  This added material is the only difference between the two curved three-vane spiders analyzed. First mode frequency doubles and deflections are reduced by nearly an order of magnitude. Curved vanes are basically beams with a fixed-fixed boundary condition. Moments are elevated at the attachment points, in this case, at the UTA and center hub. Adding material at these locations boosts stiffness compared with vanes of constant cross section, which most if not all curved vanes currently are.

 

moment.JPG .

 

The single loop also adds material where bending moments are highest and puts the mirror CG near the center of the structure, so there is little to no overhanging load.

 

To your second point. From my post: "Keep in mind, these analyses assume idealized attachments. In reality, deflections may be slightly higher than calculated. That said, it helps identify trends and inform design direction."  Including the UTA would add a spring in series with the spider attachments, which would certainly lower the first mode and increase deflection. All the models assume rigid attachments, so all of the models are equally unrealistic in that regard. As such, the models do accurately capture differences among them, notably deflection and stiffness.


Edited by bigbangbaby, 20 September 2021 - 08:22 AM.


#15 MitchAlsup

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Posted 20 September 2021 - 11:22 AM

I'm using a conventional three-vane spider because one of the alternative curved spiders I looked at is also three vane.

secondaryrocking.jpg

 

A 4-vane spider with the vanes pointing at the center of the secondary is not stiff in the rotation of the secondary

whereas a 4-vane spider in the >-< orientation is stiff to rotation.

 

No 3-vane spider can be stiff to rotational moments of the secondary.

Curved 3-vane spiders are even less stiff to rotation of the secondary than illustrated above.



#16 bigbangbaby

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Posted 20 September 2021 - 11:43 AM

MitchAlsup, I concur, four-vane spiders are mechanically more stable than three-vane. The intention of this thread is not to debate the merits of conventional spiders, three or four vane. It's to identify the shortcomings of existing curved spiders and possible enhancements to make them more usable. By that measure, I have identified two design enhancements that, in theory, improve curved-vane spider mechanical stability, perhaps to the level of a conventional three-vane spider. It's always good to have a reference from which to compare, which is why I included a conventional three-vane spider in this discussion.


Edited by bigbangbaby, 20 September 2021 - 11:47 AM.


#17 bokemon

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Posted 20 September 2021 - 11:53 AM

Vertical, in this case, is at right angles to the optical axis, i.e. tip tilt. 

So in this case, the flexure in this mode is "unrolling a curved piece of thin sheet metal", which is just about the softest mode there is.


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#18 thoughtwave

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Posted 20 September 2021 - 02:57 PM

Vertical, in this case, is at right angles to the optical axis, i.e. tip tilt. By that measure, these analyses show the alternative curved vanes perform on par with a tensioned 3-vane spider. Damping is another issue. There are ways to damp vibrations, though without active damping, none of the designs analyzed will have a damping coefficient greater than 0.1 or so, I'm guessing.

Tip/tilt are angles, so we'd want to know the change in angle of the secondary mirror normal vector under load, in degrees (or radians), not inches. Vertical deflection of the hub or mirror isn't necesarily proportional to the resulting tip/tilt of the mirror.

 

For your last design you only look at the deflection of the hub, since the mirror is a point mass and not part of the mesh, where as you look at the deflection of the mirror in the straight vane case, so it's not exactly apples to apples. Also, is the mesh mirror exactly 0.3lbs? 

 

Finally, modeling the mirror as a point mass leaves out something crucial: moment of inertia. This is probably why you don't see the rotational mode as the lowest frequency mode in the last design. 

 

Just some suggestions. Really cool that you're doing this analysis!


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#19 duck

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Posted 20 September 2021 - 04:56 PM

how is a rotational mode about the optical axis excited?



#20 John Miele

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Posted 20 September 2021 - 05:06 PM

how is a rotational mode about the optical axis excited?

I was wondering that myself. It seems that would be the least important axis to worry about stiffness...or not?



#21 MitchAlsup

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Posted 20 September 2021 - 05:15 PM

how is a rotational mode about the optical axis excited?

Any miscentering of forces results in rotational moment excitation.

 

For example if the spider is centered n the tube/UTA and the secondary moved away from the focuser and towards the primary, places the secondary CoM away from the center of forces the spider can carry.

 

Alternately, if the secondary remains centered on the spider, and the spider offset, 2 vanes are longer than the other two vanes, enabling excitation of the rocking couple.

 

A tap on the focuser can result in the excitation of the rocking couple.

 

The real question is how do you PREVENT the excitation of the rocking couple if the spider is not stiff wrt rotation !!


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#22 bigbangbaby

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Posted 20 September 2021 - 05:53 PM

Gravity aligned with z axis and pointing down. Curved vane first mode with actual mirror model, not point mass, is 48 Hz side to side rocking. Torsional mode about the optical axis is the third harmonic at 148 Hz.

 

You can do the trig for the tip/tilt. Distance between mirror surface at center and vane center is 2.25 in. Z axis deflections shown at those locations. As you can see, the mirror assembly doesn't tilt much. The whole structure more or less sags in plane.

 

c1_2.JPG

 

Curved vane first mode with added material with actual mirror, not point mass is 95 Hz side to side rocking. Torsional mode about the optical axis is third harmonic at 231 Hz.

 

alt2_w_mirror.JPG

 

Distance between mirror surface at center and vane center is 2.25 in. Z axis deflections shown at those locations.


Edited by bigbangbaby, 20 September 2021 - 07:12 PM.


#23 Oberon

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Posted 20 September 2021 - 07:04 PM

To your first point. From my post: "The second alternative curved vane design adds material where moment loads are highest. This stiffens the structure, raising first mode and lowering deflection. The added material resides outside the primary mirror O.D. and shouldn't impact diffraction, I think."  This added material is the only difference between the two curved three-vane spiders analyzed. First mode frequency doubles and deflections are reduced by nearly an order of magnitude. Curved vanes are basically beams with a fixed-fixed boundary condition. Moments are elevated at the attachment points, in this case, at the UTA and center hub. Adding material at these locations boosts stiffness compared with vanes of constant cross section, which most if not all curved vanes currently are.

 

attachicon.gifmoment.JPG.

 

The single loop also adds material where bending moments are highest and puts the mirror CG near the center of the structure, so there is little to no overhanging load.

 

To your second point. From my post: "Keep in mind, these analyses assume idealized attachments. In reality, deflections may be slightly higher than calculated. That said, it helps identify trends and inform design direction."  Including the UTA would add a spring in series with the spider attachments, which would certainly lower the first mode and increase deflection. All the models assume rigid attachments, so all of the models are equally unrealistic in that regard. As such, the models do accurately capture differences among them, notably deflection and stiffness.

The weakest point in a curved spider - the point that would most benefit from beefing up - is not the ends, it is the center of the vanes half way between the tube and the mirror, fair in the beam. This is trivial to demonstrate with a simple strip of metal, cardboard, plastic, a stick, a pipe, virtually anything at all, they all fold fail and buckle midway. Your curved spider is no different, it will bend most in the middle of the vane when subjected to a force.



#24 bigbangbaby

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Posted 20 September 2021 - 07:17 PM

Sorry, but I respectfully disagree, Oberon. Adding material at the attachments does help boost stiffness as evidenced by the FE models, and confirmed by first principles (moment diagram). Think of it this way. You have a beam supported at each end by rubber bands. The beam sags vertically under the weight and has a low first modal frequency. If the end attachments were made stiffer, say out of hard rubber, sag would be less and first mode would go up. This is, in principle, what's going on with this design.


Edited by bigbangbaby, 20 September 2021 - 07:29 PM.


#25 thoughtwave

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Posted 20 September 2021 - 09:12 PM

I have a question about the FEA model. I'm not an expert on FEA by any means, but I do have a BS in mechanical engineering. It seems to me that to correctly model the way the curved vanes bend, you would need them to be multiple elements thick. A beam in bending has one side under tension and the other under compression, but if the vanes are only one element thick, they can only be entirely tension or entirely compression. Of course, maybe the software models moments between elements as well. It might be interesting to see a simulation with just a single horizontal beam of the same 0.007" thickness, with a point mass in the middle, and compare the deflection with the theoretical deflection for a beam fixed at both ends. This would be an easy sanity check to the FEA results.

 

zkxivq1.png?1




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