Seismic Noise & Vibration Isolation Systems AIGO Summer Workshop School of Physics, UWA Feb. 28 - Mar. 2, 2010
Seismic noise Ground noise: X =α/f 2 ( m/ Hz) α: 10-6 ~ 10-9 @ f = 10 Hz, x = 1 0-11 m GW detector requirement: 10-18 m @ 10 Hz Vibration isolation essential Ground displacement noise m/sqrt(hz) 10-10 10-12 10-14 10-16 10-18 Quiet site 10-9 /f 2 10-1 10 0 10 1 10 2 10 3 10 4 Frequency Hz
Vibration isolation basic ideas Mechanical low pass filter Below resonant f << f 0 x = x 0 follow excitation At resonant f = f 0 x > x 0 motion amplified Above resonant f >> f 0 x > x 0, vibration isolation
Vibration Isolators horizontal and vertical components Vertical Spring/Mass system y0 + y Horizontal Pendulum x0 x * Transfer function Input output TF output TF = = input x x 0
Transfer Function single stage 10 4 10 2 10 0 X/X 0 TF= 10-2 10-4 (f 0 /f) 2 10-6 10-8 10-1 10 0 10 1 10 2 10 3 10 4 Frequency Hz
Some numbers 1 Hz isolator, TF@10Hz~(1/10) 2 =0.01 @10 Hz, seismic x 0 =10-11 m x=x 0 TF=10-14 m Not good enough Multiple stages: TF=TF1 TF2 TF3 TF N @ high frequency Input TF1 TF2 TF3 output
Multi-stage isolator k 1 l 1 m 1 Vertical isolator spr ing/mass system k 2 m 2 k i m i x i + m i m 2 l i m 1 Integrated 3-D isolator l 2 θ i Horizontal isolator pe ndulums k n l n x i m n m n Roll off slope (f 0 /f )2( f 1 /f) 2( f 2 /f) 2.(f n /f )2 If f 0 =f 1 =f 2 =.., then slope (f 0 /f )2n
Transfer function multi-stage 5 stage 1 Hz pendulum 10 2 10 0 Single 1Hz pendulum slope 10-2 10-4 x/x 0 10-6 10-8 10-10 10-12 10-14 10-16 Now @10Hz TF=(1/10) 2 5 X=x0 TF=10-21 m Wonderful 10-18 0.1 0.2 0.5 1 2 5 10. 20. 50. 100. Frequency Hz
Some facts Coupled system: the total transfer function is not simply multiplication At high frequency, TF=TF1xTF2xTF3 Near resonant frequencies, the peaks spilt Corner frequency highest resonant peak Spring mass system with identical stages: fc~2f 0 Pendulum system with identical stages: fc~2f 0 N
At low frequencies. Vibration isolation mechanical low pass filter High resonant peaks at low frequency amplitude Q-factor of the isolation components Hard for interferometer cavity locking control Needs damping to reduce the peaks height Or.
Pre-isolation stages Have an Ultra-low frequency (ULF) pre-isolation stage in front of the isolation chain with f 0 ~0.1 Hz. Then the peaks of the chain will fall on the slope of the this preisolator. Trnasfer function 50 0-50 -100-150 -200 0.01 0.1 1 10 frequency
A single ultra ultra low f stage? 50 0 Trnasfer function -50-100 Not as simple as that! -150-200 0.01 0.1 1 10 frequency
Internal frequencies Any structure will have internal resonances. Chladni figures are the results of the internal resonates of the plate
Example: cantilever Mode 1 Mode f 1. 163.26 2. 1016.7 3. 1030.7 4. 1498.1 5. 2835.7 6. 3215.2 7. 5521.9 8. 5743.3 Mode 2 Mode 5
Pre-isolation stage working range Low frequency pre-isolation is usually large structures with low internal f Usually the first internal frequency is roughly 10~100 times of f 0. It roll off does not goes on forever Needs to combined with low f isolation chain. 0.001 0.01 0.1 1
Remarks Due to the cross coupling between the vertical and horizontal direction ~10-3 (nothing is perfect), it is important to have good vertical isolation system. It is relatively easy to create horizontal low frequency isolation system pendulums Vertical low frequency isolation system is not so straight forward (coil spring, cantilever ) Needs to support heavy load spring creeping Low frequency larger structure lower internal modes
Pre- isolation First stage of seismic noise reduction Very low frequency Two approaches Active, stiff system Passive, soft system
Stiff system Basic Idea: Sensing the seismic motion, then move the stiff system accordingly to hold it still seismometer Stiff system Require very sensitive commercial seismometer Large forces on rigid system LIGO system is stiff system
Requirements for Active systems Complicated servo control Needs very good seismometer to sense the motion of m. Noise in seismometer would be taken as displacement signal and fedback Remark: the passive isolation chain is actually a very good seismometer Usually the a isolation system is a combination of both but more active-like or more passive-like
LIGO isolation system Active isolation platform + quadruple pendulum hydraulic external pre-isolator (HEPI) active isolation platform quadruple pendulum
Basic idea: Soft system Spring-mass system (or equivalent) Transfer function falls as (f 0 /f) 2 at f 0 >>f i, seismic will be reduced Soft system is a very good seismometer itself Small control force mainly for alignment and damping VIRGO, TAMA, ACIGA adopted the soft system
Pre-isolation Linkages Anti-springs Example: Inverted pendulum (wobbly table) Gravity acted as anti-spring
Inverse Pendulum 1 st horizontal ULF Pre-isolation ~100mHz
Lacoste Linkage Vertical ULF preisolation stage ~100mHz
Zero length spring ka 2 =bw f=0
Robert linkage 2 nd ULF horizontal Pre-isolation stage ~100mHz Key feature Two stages allow super-spring implementation
Robert s Linkage Suspension point P moving in a shallow potential well
Key feature Passive critical damping Self-Damped pendulums (3 Stages) ~
Self Damped Pendulum thin fibre pendulum link simple wire pivot 2-d gimbal pivot Eddy current viscous coupling magnets copper to next stage Eddy current damped rocker vertical Euler springs Couple pendulum motion with very low frequency rocking motion use eddy current damping between these two motions
Vertical Euler Springs (3 Stages) Euler spring with anti-spring is near critically damped Tuned near pendulum frequency
Euler Spring mass load motion l clamped end Low stored energy means low mass high internal mode frequency superior to blade springs
UWA Vibration Isolation and Suspension System Inverse Pendulum (Horizontal) 0.05 Hz Roberts Linkage (Horizontal) 0.05 Hz LaCoste (Vertical) 0.5Hz 4 horizontal Self-damped pendulum stages (~0.6Hz) 4 Vertical Euler Springs stage (~0.6Hz) Test mass
Newtonian Noise fundamental limit Gravity Gradient Noise Local gravitational field fluctuation: masses (people, vehicles, kangaroos) moving ground density change due to land wave.. (go underground) Environment is coupled to test masses by a equivalent spring with typical frequency G f 7 10 5 grav 2 π ρ Hz