Re: [ATM] ball bearings for triangles

["Jeff Anderson-Lee" <jonah@eecs.berkeley.edu>]

Arjan te Marvelde wrote:

>>But the more I think about what mirror cells are supposed to do, the less
>>sense having to counterbalance triangles makes to me. If you think about a
>>mirror cell from the wrong direction, instead of supporting 1/27 of the
>>mirror but supporting 1/3 of itself at a time, it HAS to balance. Even if
>>    
>>
>That depends on the weight of the triangle. If it is only a fraction of the
>supported portion of the mirror, the induced error will be small. The
>tolerance for the location of the bearing/supports might be more important.
>Balance of the triangle does not guarantee this.
>
I did an analysis on 18 point mirror cells with Monte Carlo simulation 
of balance and placement errors. Cumulative small errors in fabrication 
can cause large changes in performance.

http://elib.cs.berkeley.edu/~jonah/18plus/p18.html

"To compare the effects of the various factors, [I looked at] the ratio 
of difference between the design RMS error and the average RMS error of 
the Monte Carlo runs in Table 8. From this we see that the variation in 
balance (2.77) contributes most to the overall performance change 
(2.92). Positioning errors contribute far less (1.64), and most of that 
is due simply to positioning errors in the outer radii (1.53), even 
after we factor out the skew component. Of the balance errors, the 
radial (2.05) and skew (2.00) components contribute almost all of the 
error, while the bar balance (1.14) contributes far less, and the axial 
balance error (1.00) practically nothing at all.

"Thus it appears that accurate construction of the triangles is 
essential to good performance, especially with regard to locating the 
support and balance points. After that, it is most important to properly 
locate the outer two support points of each triangle at the proper radius.

"The average cumulative change in performance for this error model was a 
factor of 2.92 and the maximum error for the worst case found was a 
factor of 8.22. Keep in mind that all of these effects are caused by 
multiple variations of 1 to 2-millimeters or less in positioning! What 
this seems to indicate is that accurate positioning and/or 
over-engineering are key to building a successful cell. Otherwise, your 
1/120th wavelength / 1/60th wave-front cell design can become a 1/15th 
wavelength / 1/7th wave-front implementation, or worse! Not only that, 
but measuring the mirror for design and centering the mirror on the cell 
afterwards may also need to be done to sub-millimeter precision if you 
chose a design that is close to the design limit."

And regarding construction:

"Likewise, it seems apparent that small errors in fabrication of parts 
on the order of one or two millimeters can have dramatic effects on the 
performance of a cell. The effects were considerably minimized when all 
of the parts had equal errors leading to systemic changes in the cell. 
This suggests that in making the parts, a “jig” should be used, so that 
all parts are as symmetrical and as close to identical as possible."

Jeff




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