Fwd: Re:[ATM] Primary Mirror Retainers

[mlbrown at everstrive.com (Matthew L. Brown)]

>
>Tom, et alia,
>I know it's been too many years since I studied mechanics and materials, 
>but I'm having a hard time visualizing the "compliant" aspect of this 
>mounting scheme.
>
>For the sake of discussion...  assume 10 inches between the inner and 
>outer rings, and a travel of 1/2 inch.  If we allow something to "pull" 
>the center ring back (not indicated in the drawings, but allows a best 
>case scenario), then we get + or- 1/4" of travel from a "center" 
>position.  With no deflection (0 deg) the Hypotinose is the adjacent side, 
>or exactly ten inches.  at full deflection the hypotinose stretches to 
>10.003125 inches.  This is a "best case" with a stretch of a bit over 
>three thousandths in the diaphram material.  So far everything I've run 
>through the numbers that will stretch that much and return to original 
>(which it would have to do consistantly for *lots* of cycles), would also 
>be at least an order of magnitude too stretchy to hold the rings even 
>within 1/4 degree. Obviously I'm missing something in the visualization 
>and number crunching on this one.  Help!
>
>Rocky


>There are 2 diaphragms, working in parallel.  The material will stretch, 
>as you say, in tension.  In fact there will be dramatically more force in 
>the material in tension than the micrometer exerts, due to the shallow 
>triangle.  In your case, 10.003125/0.25 =40.01 times the force exerted 
>laterally in the material than axially.


>Let's say it took 2 N of force from the micrometer to get that 0.25" 
>deflection.  This is shared by 2 diaphragms, so each one has 1 N axial 
>load.  Arguing in 2D, the lateral force would be 40 N in each side of the 
>diaphragm.  And this occurred in 0.003125 inches, giving a stiffness of 
>12800 N/in.  Now consider attempting to rotate the mirror off-axis, 
>resisted by 2 such diaphragms, spaced even 1 inch apart.  A quarter degree 
>over 1 inch is 0.0044 inch.  This would require a 55.9 N lateral force ( 
>0.0044 * 12800) at the diaphragm (a torque of 55.9 inch-N).


>The design looks to space them something like 3 in apart, tripling that 
>torque.  And the micrometer is likely pressing with 20N of force or more, 
>increasing the required torsion by a factor of 10 to something like 1675 
>in-N.  And 3D considerations, along with the fact that the ID and OD of 
>the diaphragms are constrained from local bending, increase the apparent 
>stiffness even more.  And there's not much to supply that torque -- the 
>weight of the mirror perhaps.



>To rotate this off axis,