lcgt 防振系 真空槽 a) 直径 2m 、高さ 3.1m+2.2m(cryostat): fm1 、 fm2 、 em1 、 em2 b)...

LCGTLCGT 防振系防振系真空槽真空槽

A) A) 直径直径 2m2m 、高さ、高さ 3.1m+2.2m3.1m+2.2m(cryostat):(cryostat): FM1FM1 、、 FM2FM2 、、 EM1EM1 、、 EM2EM2B) B) 直径直径 2m2m 、高さ、高さ 4.5m:4.5m: BS BS 、、 PRMPRM 、、 SEMSEM 、、 MC2FMC2F 、、 MC2EMC2EC1) C1) 直径直径 2m2m 、高さ、高さ 3m:3m: MC1F MC1FC2) C2) 直径直径 1m1m 、高さ、高さ 2m:2m: MC1EMC1E 、、 MMTMMT 、、 PDPD

防振系防振系A) SAS(GASF 3A) SAS(GASF 3 段段 )+)+ 低温懸架低温懸架 :: FM1 FM1 、、 FM2FM2 、、 EM1EM1 、、 EM2EM2B) SAS(GASF 2B) SAS(GASF 2 段段 )+)+ 常温懸架常温懸架 :: BSBS 、、 PRMPRM 、、 SEMSEM 、、 MC2FMC2F 、、 MC2EMC2EC) STACK+C) STACK+ ２段振り子２段振り子 :: MC1F MC1F 、、 MC1EMC1E 、、 MMTMMT 、、 PDPD

R. Takahashi2010.6.15 LCGT f2f Meeting

Type-A

Type-B

Modeling of LCGT-SASModeling of LCGT-SAS

m Q f0 C[kg] [Hz] [kg・Hz]

Filter0 120 1 0.07 -Filter1 120 100 0.56 -Filter2 120 100 0.56PF 120 100 0.5 -IM 60 1000 0.7 530MB 60 1000 0.7 530TM 30 1000 0.8 -RM 30 6 0.8 -

xg

x1

x2

x3

x5 x4

x0 m0

m1

m2

m3

m5

m6

m4

m7

C

x6 x7

Filter0

Filter1

Filter2

PF

IM

TM RM

MB

Equation of motion of 8 material points model

8 ｘ 8 stiffness matrix Refer parameters of TAMA-SAS Calculated by MATLAB

Type-A

Material Point Model of LCGT-SAS (Type-A)Material Point Model of LCGT-SAS (Type-A)

GAS フィルターが 3 段入っているので 1Hz 付近では水平よりも防振比が高い。最終段 (TM) は 1.8mmφ のサファイア・ファイバー 4 本でかなり固く、垂直方向の共振周波数は約 100Hz になる。PF へアンカーする 0.01Hz のヒートリンクで 1% カップリングだと5Hz の要求を満たす。 0.03Hz だとNG だがこれでも実質 OK 。 (vertical)

Modeling of LCGT-SASModeling of LCGT-SAS

m Q f0 C[kg] [Hz] [kg・Hz]

Filter0 60 1 0.07 -Filter1 60 100 0.56 -PF 60 100 0.5 -IM 30 1000 0.7 265MB 30 1000 0.7 265TM 16 1000 0.8 -RM 16 6 0.8 -

xg

x1

x2

x3

x5 x4

x0 m0

m1

m2

m3

m5

m6

m4

m7

C

x6 x7

Filter0

Filter1

Filter2

PF

IM

TM RM

MB

Equation of motion of 7 material points model

7 ｘ 7 stiffness matrix Masses are about a half of Type-A’s Calculated by MATLAB

Type-B

Modeling of LCGT-SASModeling of LCGT-SAS

m Q f0 C[kg] [Hz] [kg・Hz]

Stage0 200 3 5 -Stage1 200 3 4.5 -Stage2 200 3 4 -IM 1 1000 1 12.5MB 1 1000 3 12.5TM 1 1000 1 -

Equation of motion of 6 material points model

6 ｘ 6 stiffness matrix Model for Stack is simplified Calculated by MATLAB

Type-C xg

x1

x2

x4 x3

x0 m0

m1

m2

m4

m5

m3

C

x5

Stage0

Stage1

Stage2

IM

TM

MB

Summary of RMSSummary of RMS

Type-A,B vs. C0.1 → 2 [m] x200.1 → 2 [m/s] x20

Integration 0.01-4Hz(Integration 0.1-4Hz)

Type-A Type-B Type-C[μ m] 1.0 1.0 1.0

(0.006) (0.006) (0.1)[μ m/ s] 0.08 0.08 0.2

(0.008) (0.008) (0.2)[μ m] 0.7 0.7 2.0

(0.10) (0.09) (1.9)[μ m/ s] 0.12 0.11 2.3

(0.11) (0.10) (2.3)

Mic

rose

ism

sno

rmal

larg

e

低周波防振が無いと個々のミラーの RMS は非常に大きくなる。

Model vs. Measurement in TAMA-SASModel vs. Measurement in TAMA-SAS

10-2

10-1

100

101

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

Frequency [Hz]

Dis

plac

emen

t [m

/rtH

z]

GroundTestmassRMS [m]RMS [m/ s]

Model Measurement

Disp. [m] Vel. [m/s]61.1 5.4 (0.01-10Hz)0.3 →0.8 0.8 (0.1-10Hz)

平均値 1.9m/s

PHD 信号と透過光量から算出

共振器維持状態のフィードバック信号から算出和泉氏の修論より

Rigid body Model of LCGT-SASRigid body Model of LCGT-SAS

OctopusOctopus is a non-official Virgo tool. The modeling will be used for AdV, but it is n

ot the only model that can be used. It provides (once completed): I) Point-by-point 6x6 matrixes of Force/displacement TFs or displacement ratios. II) Designing tool: several configurations or parameter tuning, within a given conf

iguration can be explored. III) Some add-ons as fitting a dataset of experimental TF and extracting a fit whi

ch can be used to extract actual mechanical parameters (…).

SimMechanicsSimMechanics™ extends Simscape™ with tools for modeling three-dimensional

mechanical systems within the Simulink® environment. Instead of deriving and programming equations, you can use this multibody simulation tool to build a model composed of bodies, joints, constraints, and force elements that reflects the structure of the system. An automatically generated 3-D animation lets you visualize the system dynamics. You can import models complete with mass, inertia, constraint, and 3-D geometry from several CAD systems.

wireswires F1F1 F2F2 PFPF MBMB IMIM RMRM TMTM

materialmaterial MARAMARA MARAMARA MARAMARA WW WW WW SASA

lengthlength 0.80.8 0.80.8 1.01.0 0.50.5 0.50.5 0.40.4 0.40.4

numbernumber 11 11 11 44 4*4* 44 44

diameterdiameter 3.5e-33.5e-3 3.1e-33.1e-3 2.7e-32.7e-3 0.6e-30.6e-3 0.61e-30.61e-3 0.72e-30.72e-3 1.8e-31.8e-3

Y CM-dist upY CM-dist up 00 00 00 0.50/20.50/2 0.25/20.25/2 0.34/20.34/2 0.25/20.25/2

X CM-dist upX CM-dist up 00 00 00 0.39/20.39/2 0.15/20.15/2 0.03/20.03/2 0.03/20.03/2

Z-CM-dist upZ-CM-dist up 00 00 00 00 00 00 00

Z-CM-dist dwZ-CM-dist dw 00 00 00 00 00 00 00

rotationrotation F1F1 F2F2 PFPF MBMB IMIM RMRM TMTM

IyyIyy 1111 1111 3.803.80 1.601.60 0.610.61 0.550.55 0.170.17

IzzIzz 2020 1818 7.207.20 3.503.50 1.301.30 0.550.55 0.170.17

IxxIxx 1111 1111 3.803.80 2.202.20 1.001.00 0.680.68 0.230.23

(All MKS)*(or 2 for a development study)

ParametersParameters

VerticalVertical F1F1 F2F2 PFPF MBMB IMIM RMRM TMTM

MM 120120 120120 120120 6060 6060 3030 3030

fo (vertical)fo (vertical) 0.20.2 0.20.2 0.2*0.2* 0.840.84 2.72.7 34.434.4 100100

fo (pitch)fo (pitch) 0.20.2 0.20.2 0.70.7 11 22 3.83.8 2020

*(for payload)

This presentation/practical cases.- Often it is useful to show longitudinal/pitch and transversal/yaw sub-matrixes - In the case of LCGT, the Vertical might be more crucial and should be included.

Example of outputs of OctopusX Y Z Tx Ty Tz

Fx

Fy

Fz

Ftx

Fty

Ftz

Model on SimMechanicsModel on SimMechanics

Under construction

Sensors and ActuatorsSensors and ActuatorsFilter0Filter0 Filter1Filter1 Filter2Filter2 PFPF IM-MBIM-MB TM-RMTM-RM

SensorSensor ACC(H) x3ACC(H) x3

ACC(V) x1ACC(V) x1

LVDT(H) x3LVDT(H) x3

LVDT(V) x1LVDT(V) x1

LVDT(V) x1LVDT(V) x1 LVDT(V) x1LVDT(V) x1

OL x1OL x1

PS(H) x3PS(H) x3

PS(V) x3PS(V) x3

OL x1OL x1

PS(H) x3PS(H) x3

PS(V) x3PS(V) x3

OL x1OL x1

ActuatorActuator MC(H) x3MC(H) x3

MC(V) x1MC(V) x1

MC(Y) x1MC(Y) x1 MC(H) x3MC(H) x3

MC(V) x3MC(V) x3

MC(H) x3MC(H) x3

MC(V) x3MC(V) x3

MC(H) x2MC(H) x2

MC(V) x2MC(V) x2

MotorMotor STEP(H) x3STEP(H) x3

STEP(V) x1STEP(V) x1

PICO(Y) x1PICO(Y) x1 STEP(H) x2STEP(H) x2

STEP(V) x2STEP(V) x2

ACC: accelerometer, LVDT: linear variable differential transformer PS: position sensor, OL: optical lever, MC: magnet-coil, STEP: stepping motor, PICO: picomotor

For cryogenicStepping motor: tested in Rome, 4.8K ok!Position sensor: shadow sensor base?

Test of AML motor

当面の目標当面の目標

剛体モデルの構築剛体モデルの構築 制御のシミュレーション制御のシミュレーション センサ、アクチュエータの仕様決定センサ、アクチュエータの仕様決定 プロトタイプ（プロトタイプ（ payloadpayload ）の構築）の構築