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