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Entry  Sun May 2 13:04:51 2010, Koji, Summary, SUS, Coil Actuator Balancing and Spot Position coil_balance.png
    Reply  Sun May 2 15:38:12 2010, rana, Summary, SUS, Coil Actuator Balancing and Spot Position 
       Reply  Sun May 2 16:52:44 2010, Koji, Summary, SUS, Coil Actuator Balancing and Spot Position 
Message ID: 2863     Entry time: Sun May 2 13:04:51 2010     Reply to this: 2865
Author: Koji 
Type: Summary 
Category: SUS 
Subject: Coil Actuator Balancing and Spot Position 

I liked to know quantitatively where the spot is on a mirror.

With an interferometer and A2L scripts, one can make the balance of the coil actuators
so that the angle actuation does not couple to the longitudinal motion.
i.e. node of the rotation is on the spot

Suppose you have actuator balancing (1+α) f and (1-α) f.

=> d = 0.016 x α [m]

Full Imbalance   α = 1      -> d = 15 [mm]
10% Imbalance α = 0.1   -> d = 1.5 [mm]
1% Imbalance   α = 0.01 -> d = 0.15 [mm]


Eq of Motion:

I ω2 θ =  2 R f 
(correction) - I ω2 θ =  D f cos(arctan(L/2/D))
(re-correction on Sep 26, 2017) - I ω2 θ =  D f

m ω2 x = 2 α f ,
(correction) - m ω2 x = 2 α f ,

where R is the radius of the mirror, and D is the distance of the magnets. (kinda D=sqrt(2) R)

d, position of the node distant from the center, is given by

d = x/θ = α I / (m R) = 2 α β / D,

where β is the ratio of I and m. Putting R=37.5 [mm], L=25 [mm], β = 4.04 10-4 [m2], D~R Sqrt(2)

i.e. d = 0.015 α [m]

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