Behavior of an inverted Behavior of an inverted pendulum in the Kamioka pendulum in the Kamioka

mine mine R. TakahashiR. Takahashi (NAOJ), A. Takamori (ERI), E. (NAOJ), A. Takamori (ERI), E.

Majorana (INFN)Majorana (INFN)

GWADW2010

We are investigating behavior of an inverted pendulum (IP) in the Kamioka mine where is the site of LCGT.

IP is employed as pre-isolator of the seismic attenuation system (SAS) for LCGT.

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IP

Seismic Attenuation System (SAS) for Seismic Attenuation System (SAS) for LCGTLCGT

ContentsContents

1.1. Unsealed IP Unsealed IP with a geophonewith a geophonea.a. Setup of apparatusSetup of apparatusb.b. GeophoneGeophonec.c. ResultsResultsd.d. Ground tiltGround tilt

2.2. Sealed IP Sealed IP with a small with a small accelerometeraccelerometer

a.a. Setup of apparatusSetup of apparatusb.b. AccelerometerAccelerometerc.c. ResultsResultsd.d. Vertical ground vibrationVertical ground vibration

3.3. SummarySummary

1. Unsealed IP with a geophone1. Unsealed IP with a geophone

Aug. 19-20, 2009 @CLIO site

One-leg IPGeophones (Horizontal 2, Vertical 2)

1-a. Setup of apparatus1-a. Setup of apparatus

Load (50mHz)Geophone(horizontal)

Geophone(vertical)

“Roughly” enclosed to avoid air flow

Flex joint

1. Unsealed IP

1-b. Geophone1-b. Geophone

Vertical

Velocity response of 1Hz geophone (L-4C)

Ground 1

Ground 2

Differential

Sensitivity limit by CMR ： 5x10-11m/Hz1/2 @1HzIt is possible to sense the level less than 1/10 of ground vibration in 0.2-2Hz.

1. Unsealed IP

1-c. Results (1)1-c. Results (1)

Ground

IP

Noise limit

Horizontal

1. Unsealed IP

The displacement of IP reached the sensitivity limit at 3Hz.The displacement of IP was larger than ground vibration around 0.2Hz.

1-c. Results (2)1-c. Results (2)

Ground

IP 1st

IP 2nd

IP 3rd

Ring down of IP

Q~35

Prediction

settled

unchanged

The excess around 0.2Hz is not due to harmonics of fundamental mode.

The excess around 0.2Hz is not due to harmonics of fundamental mode.

1. Unsealed IP

What is this gap?What is this gap?

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We supposed that the excess is due to ground tilt.

IP is very sensitive to ground tilt. IP with natural frequency of 50mHz corresponds to 100m pendulum.

Actually Virgo group pointed out ground tilt is dominant source of the IP displacement in the SA at frequencies less than 0.1Hz.

1-d. Ground tilt (1)1-d. Ground tilt (1)1. Unsealed IP

Blue line ： Ground tilt supposing that displacement of IP is due to ground tiltRed line ： Ground tilt estimated by differential signal between two vertical geophones 　

The excess around 0.2Hz in IP spectrum is not due to ground tilt.

The excess is due to residual air flow?

1-d. Ground tilt (2)1-d. Ground tilt (2)1. Unsealed IP

Jan. 28-29 & Feb. 24-25, 20102. Sealed IP with a small accelerometer2. Sealed IP with a small accelerometer

Smallaccelerometer

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2-a. Setup of apparatus2-a. Setup of apparatus2. Sealed IP

0.1 1 10 1000.01

0.1

1

10

100

Frequency [Hz]

Open-loop G

ain

0.1 1 10 100180

120

60

0

60

120

180

Frequency [Hz]

Phase

[deg]

f0=1.98Hz

Q=2060mm

65mm

Folded pendulumMaker UFTMaterial A7075Size 60 x 30 x 65Hinge 20m

2-b. Accelerometer (1)2-b. Accelerometer (1)

A servo type accelerometer consist of this pendulum and a position sensor.

2. Sealed IP

2-b. Accelerometer (2)2-b. Accelerometer (2)

Commercial photo sensor

2. Sealed IP

0.01 0.1 1 10110 11

110 10

110 9

110 8

110 7

110 6

110 5

110 4

110 3

Frequency [Hz]

Dis

pla

cem

ent

[m/r

Hz]

2-c. Results2-c. Results

0.01 0.1 1 10110 11

110 10

110 9

110 8

110 7

110 6

110 5

110 4

110 3

Frequency [Hz]

Dis

pla

cem

ent

[m/r

Hz]

GroundIP

Though measured displacement was close to sensitivity limit, displacement of IP was still larger than ground vibration around 0.2Hz.

Natural frequency of IP was tuned to 70mHz.

0.01 0.1 1 10110 11

110 10

110 9

110 8

110 7

110 6

110 5

110 4

110 3

Frequency [Hz]

Dis

pla

cem

ent

[m/r

Hz]

GroundIP

2. Sealed IP

Prediction(Q=69)

GroundIP

Notch at 2Hz is due to the resonance of the folded pendulum.

2-d. Vertical ground motion2-d. Vertical ground motion

Vertical ground vibration had not correlation with IP displacement.IP resonance is excited by vertical vibration? (out of sensitive zone)

2. Sealed IP

Sensitive zone for both sensor

3. 3. SummarySummary

We investigated behavior of an IP in the Kamioka We investigated behavior of an IP in the Kamioka mine.mine.

The displacement of IP was larger than ground The displacement of IP was larger than ground vibration around 0.2Hz.vibration around 0.2Hz.

The excess is not harmonics of fundamental mode of The excess is not harmonics of fundamental mode of the IP.the IP.

The excess is not due to ground tilt.The excess is not due to ground tilt. The excess is not due to vertical vibration directly.The excess is not due to vertical vibration directly. Though we could not specify the origin, it might be Though we could not specify the origin, it might be

non-linear vertical coupling.non-linear vertical coupling. We need more investigations.We need more investigations.

Long term stabilityLong term stability

X Y Z( ) X Y Z( )

2/24 16:22 – 2/25 7:53

IP was stable without glitch for 15.5 hours.

IP tilt meterIP tilt meter

The drift of ~0.5rad was observed for 15.5 hours.The application of IP to tilt meter may be useful.

Since 70mHz IP corresponds to 50m pendulum.Ground tilt→Displacement of IP→Tilt of accelerometer→DC signal of accelerometer

Measured transfer function of IPMeasured transfer function of IP

Measured transfer function from force to displacement of the SAS in TAMA

Measured isolation ratio of the SAS prototype(IP was tuned to 220mHz.)

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Displacement of IP in TAMADisplacement of IP in TAMA•Controlled by LVDT with different band width•Measured by ACC

Broad band: following the ground motionNarrow band: free at > natural frequency (~0.05Hz)IP motion > ground motion at 0.16Hz