[ATM] Re: Second Thoughts on Mirror Support

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

Michael Lindner wrote:

>On Wednesday 04 February 2004 09:01 pm, Jeff Anderson-Lee wrote:
>  
>
>>Out of curiosity, what's the formula used to derive 0.007" from the
>>dimensions and the Compressive Yield Strength?
>>    
>>
>
>FL/EA where F is force, L is length of column (in this case thickness of pad) 
>E is modulus of elasticity and A is surface area of pad, The formula is in 
>Kreige/Berry's book "The Dobsonian Telescope", although it isn't applied to 
>RTV pads in there. ;-)
>
http://www.matweb.com/search/SpecificMaterial.asp?bassnum=PDOWC03
Dow Corning 733 Glass & Metal Sealant  (335 psi)
http://www.matweb.com/search/SpecificMaterial.asp?bassnum=PDOWC12
Dow Corning 832 Multi-Surface Adhesive/Sealant  (350 psi)

If we use 350 psi  with a 1in diameter 0.125 inch thick pad and 0.67 lb, 
we get a compression of 3.1e-4 in or 7.8e-3 mm.  If we narrow the pad to 
3/4 inch and thicken it to 3/16, we end up with 8.2e-4 in or 2.1e-2 mm.  
Both are (just) above the expected back plate deformation of 6.8e-3mm or 
2.7e-4 inches which is good news.  What it means is that the sagging of 
the 1/8th inch plate will introduce a (barely) tolerable difference in 
forces.  Thus, we would probably do well to increase the plate thickness 
from 1/8 to 3/16 or 1/4 inch, but even the 1/8th in plate might suffice.

>FWIW I find nothing wrong with RTVing a mirror to supports, and have made all 
>my scopes this way. However, 9 pads are not the same as 9 floating points. 
>The whole purpose of a flotation cell is so that the forces are evenly 
>distributed among the support points, even if the cell sags or warps. RTV 
>pads may compress, but they will still transmit force through to the mirror.
>  
>
True, however, even the best made cell does not entirely distribute the 
forces evenly.  There may be construction errors that offset the balance 
points slightly or stiction that prevents equalization.  Thus cell 
designs must (and generally do) tolerate some unevenness of forces.  
Plop with its ability to specify variable forces on points gives us a 
chance to evaluate the effect of those uneven forces on the mirror to 
see if it makes a significant difference.  The preceding analysis 
suggests that the sagging of the plate under its own weight plus the 
weight of the mirror, would introduce a P-V error (on the plate) that 
would still be within limits of inducing a relative force differential 
on the mirror which is within the constraints of the cell design.

>The difference might be negligible from pad to pad on a bar or triangle (or 
>near zero if they're the same distance from the single support point, so it 
>sags the same at each mirror attachment point), but across the entire length 
>of the cell, itself supported at only 3 points (for collimation), uneven 
>sagging may transmit enough force to be detrimental. Also, unlike fine 
>annealed glass, metal may distort over time enough to create uneven force on 
>the back of the mirror.
>  
>
The expected sagging due to forces has been calculated using Plop and 
found to be within tolerance, if just barely for the sample case.  
However, sound engineering principles suggest that overbuilding by some 
factor (2 or 5 for instance) gives a margin for error, and hence a 
thicker plate will most certainly do.

Yes, it might distort over time, but I'd like to quantify that aspect 
too, rather than just worrying with no validation of concern.

Both theory (with Plop) and practice (with Don's Discovery scope)  show 
that using more than 3 support points on a single back support canbe 
made to work.  Now I'd like to work out the details so that those of us 
who might want to try it can move forward with reasoned expectations.

Jeff Anderson-Lee
Sacramento, CA