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Message ID: 12316     Entry time: Wed Jul 20 14:03:01 2016
Author: ericq 
Type: Update 
Category: SUS 
Subject: Effect of thicker ruby standoffs 

The new ETMX ruby guide rods are slightly thicker than the old aluminum ones; specifically 1.27mm vs 1.0mm.

Since we did not change the guide rod location in response to this fact, the vertical position of the suspension point changes, which in turn changes the dynamics of the suspension. Specifically, since the standoff is placed below the guide rod, the suspension point is lowered, which makes the pitch mode softer. I crunched a few numbers and have determined that this effect should not be a problem.

Given the wiki's value of the ETMX pitch resonance frequency of 0.829 Hz, I predict a the new pitch resonance frequency of 0.800 Hz.

(wiki link: https://wiki-40m.ligo.caltech.edu/Suspensions/Mechanical_Resonances)

A useful document about the dynamics of our suspension can be found at T000134

From this document, one will find that the effect of changing the suspension point height over the optic center of mass,`b`, on the pitch resonance frequency (while keeping all other dimensions equal) to be:

\frac{\omega'_\theta}{\omega_\theta} \approx \sqrt{\frac{b'}{b}}

The top of the standoff is fixed by the guide rod, so let's say that b' is given by the position of the center of the Ruby standoff. This is then smaller than the previous b by the differences in the radii of the standoffs:

b' = b - \frac{\oslash_{\textrm{ruby}}-\oslash_{\textrm{Al}}}{2}

The nominal value of b is 0.985mm. Thus, the pitch resonance frequency is changed by factor of 0.965, i.e. 3.5% smaller. Then, taking the wiki value of 0.829 Hz results in 0.800Hz, a 30mHz decrease.

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