[ATM] Re: RTV, You Will Comply

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

I wrote:

> F = EA(dh)/H  or E = FH/A(dh)
>
> (7.2 lb) *  (0.125 in)  / (0.82^2/4/pi in^2) / 0.004 in  = 427 lb/in^2 
> 27131.14
>
> That makes a *big* difference on the viability of RTV on a stiff plate 
> backing.  I'm a little tired tonight, so perhaps another time.

Can't get to sleep so...

Back of the (Excel) envelope calculations for a 0.25 in steel backplate 
and a 16 x 1+5/8 inch f/4 pyrex mirror:

Assuming 9 RTV pads 3/16 inch thick by 3/4in diameter each place along 
the flex contour lines of the backplate when supporting the backplate by 
three collimation points.  The P-V for the backplate is 6.35e-4 mm, so 
assuming that we can reduce that difference by a factor of five by 
following the contour lines, we have a displacement threshold of 1.27e-4 
mm.  Using an elasticity of 450 psi, a 1.27e-4 mm displacement of the 
RTV means a relative force difference of  0.135 lbf.  Since the average 
force on each mirror support point is 0.929 lbf, that works out to less 
than a 15% variance in forces.  However, the 9 point support pattern 
should tolerate up to a 25% force difference, so we are within spec.

Thus, a 1/4 inch steel backplate should be stiff enough to support a 16 
inch mirror on 9 RTV blobs, with no wiffle tree. Then again, a 9 point 
cell is easy enough to make with just RTV, so why bother?

Jeff Anderson-Lee

--
;Plop file for 9 point mirror support:
;9 point support for use with steel backplate
var r_inner  0.351279
var r_outer  0.727273
diameter 406.4
thickness 41.275
density 2.23e-06
modulus 6400
poisson 0.2
f-ratio 4
n-mesh-rings 12
rel-support-radii r_inner r_outer r_outer
num-support 3 3 3
support-angle 0 30 90
basis-ring-size 3
basis-ring-min 0
obstruction-diam 0
optimize r_inner 0.01
optimize r_outer 0.01


;Plop file for steel backplate
;9 point mirror support on 0.25in steel backplate w/ 3 collimation points
var r_inner  71.3344
var r_outer  147.782
var r_supp  122
var r_supp0  109.1
diameter 321
hole-diameter 50.8
thickness 6.35
density 8.03e-06
modulus 193100
poisson 0.29
sagitta 0
n-mesh-rings 20
support-radii r_inner r_outer r_outer r_supp
rel-force -0.929 -0.929 -0.929 5.41115
num-support 3 3 3 3
support-angle 0 30 90 0
basis-ring-size 3
basis-ring-min 0
obstruction-diam 0