[ATM] Re: Second Thoughts on Mirror Support

[jonah at eecs.berkeley.edu (Jeff Anderson-Lee)]

Tom Krajci wrote:

>The plate doesn't simulate it -- the RTV does.  
>  
>
>
>I disagree.  Pivots allow the mirror or support plate to flex...and at
>the end of it all...the same support forces exist...assuming there is no
>stiction in the pivots.  With a single plate, RTV'd to the mirror...as
>the mirror or plate flexes...the forces at the support points change.  I
>don't like the sound of that.  With a relatively non-thin mirror that
>may work, but for thinner and thinner mirrors I think you are setting
>yourself up for trouble.
>  
>
There are two major issues involved in supporting a mirror: placement of 
supports and force at these locations.  A properly made wiffle tree (or 
other pivoting cell) with minimal stiction will, as you say, compensate 
for any flexing by pivoting to keep the forces as nearly equal as 
possible.  The reality is that we want to keep the mirror rigid to 
within a fraction of a wavelength and if the support points are in the 
right locations as per Plop, that's possible to do.  (Design tolerances 
are often better that 1/100 wavelength RMS for the cell.)   However, all 
cell implementations have some slop from the design.  If holes are 
drilled slightly off center, that can affect the balance which in turn 
affects the "equalization" of forces.  Since this typically does not 
seem to be a problem, even for hand-made cells, it seems that many cells 
are tolerant of slight unevenness in support point loading. (Quantified 
below.)

>>Make the plate thick 
>>enough that it doesn't bend significantly and the RTV can probably make
>>    
>>
>>up the difference: a compliant cell!
>>    
>>
>I don't argue that the cell is compliant...but I have problems with "
>the RTV can probably make up the difference"...especially the word
>"probably."  Again, with thicker/smaller mirrors you are not pushing the
>envelope.  Thinner/larger mirrors are probably outside the envelope for
>this support scheme.
>  
>
Yes, larger/thinner mirrors often need 18 or more support points.  I'm 
not sure I'd want to trust this system for those cases, but there may be 
a variety of mirrors that would normally require more than 3 but no more 
than 9 support points for which this may suffice.

>What other evidence is out there that this support scheme (single rigid
>plate, RTV'd to mirror) works for various size/thickness mirrors?
>
Tom, I know you like quantified results.  I don't have the numbers, but 
I do have an inkling of how to get some.

1) Determine the spring coefficient of a 1/8 to 3/16 inch (3 to 4 mm) 
thick by 3/4 to 1inch (18 to 25 mm) round pad of your favorite RTV.

2) Determine the tolerance of your mirror/support points to varying 
forces (e.g. using Plop.)

3) Determine the change in compression/expansion of the RTV pads to make 
up that difference in force.

4) Determine the elasticity of your backplate material.


	modulus 	poisson 	density
Aluminum 6061-T6 	73100 	0.3300 	2.70E-06
Steel AISI 304 	193100 	0.2900 	8.03E-06
Steel AISI C1020 	203400 	0.2900 	7.85E-06


5) Determine the deformation performance or the backplate under loading 
and compare to the compression/expansion allowance due to the RTV pads.

I suspect that the flexing of a suitable designed back support will 
result in such a minimal displacement that the elasticity of the RTV 
will be able to make up for the change with only minor changes in the 
relative forces, hence only a minor effect of the mirror.  Thus, in many 
cases, a simple 4 to 9 point cell may be created as a complient cell 
using a sufficiently stiff backplate plus RTV.

However, I too would like to have a better quantificiation of what is a 
"sufficently stiff backplate".

For instance, given a 16 inch by 1 5/8 inch thick f/4 pyrex mirror, a 
conventional 9 point cell will suffice.  Plop suggest that such a mirror 
will tolerate variable loadings ranging between 0.25 to 1 and 1.25 to 1 
for inner to outer force ratios.   This mirror will weigh about 11.9kg 
(26.3lb), and with a 25% difference in loading, the difference in force 
on the inner and outer points would be 0.306kg (0.674lb).  Determine how 
much compression the RTV pad would experience under that load, and you 
have a rough idea of how much flexure such a complient cell would tolerate.

Does anyone know how compute how much compression a 25mm round by 3mm 
thick RTV pad would experience under a 0.306kg load?

Jeff Anderson-Lee