Transcript Slides - Agenda INFN

aLIGO Monolithic stage
Giles Hammond, University of Glasgow
for the Advanced LIGO Suspensions Team
aLIGO/aVirgo Workshop Pisa, Italy 23rd-24th February 2012
LIGO-G1200109-v1
Overview
•
Overview of the Monolithic suspension design for Advanced LIGO
•
Monolithic suspension fabrication (LIGO Hanford)
•
Bend points and modal frequencies
•
Thermal noise of the upper stages (Mathematica code)
•
Thermal noise of the final stage (Finite Element Modelling)
•
Comparison of FEA with measured violin modes
•
Summary
aLIGO Quadruple Suspension
• Seismic isolation: use quadruple pendulum with 3
stages
of
maraging
horizontal/vertical isolation
steel
blades
for
• Thermal noise reduction: monolithic fused silica
suspension as final stage
four stages
• Control noise minimisation: use quiet reaction
pendulum for global control of test mass position
• Actuation: Coil/magnet actuation at top 3 stages,
electrostatic drive at test mass
40kg silica
test mass
parallel reaction
chain for control
aLIGO Monolithic Stage
Steel wires
Penultimate mass
Ear
Ear
Steel wire break-off prism
Horn
Stock
Weld
Silica fibres
Neck
Fibre
End/input test mass
Ear
Monolithic Suspension at LIGO Hanford
•
Hydroxide catalysis bonding of the ears
•
•
Fibre profiling for importing into Finite
Element Analysis
A. Cumming et al, Rev Sci Inst 82, 044502 (2011)
A. Heptonstall et al, Rev Sci Inst 82, 011301 (2011)
Fibre pulling with CO2 laser
Monolithic Suspension at LIGO Hanford
•
•
PUM and ITMy installation with ERGO arm
Alignment was performed with:
– autocollimator
– scale/auto leveller
•
•
•
Perform 8 welds to PUM and ITMy
De-stress welds (to set pitch angle)
Hang
Modal frequencies
•
The modal frequencies of interest are:
– For the test mass
• Pendulum (longitudinal and transverse)
• Pitch
• Yaw
• Roll
• Bounce or vertical
– For the fibres
• Violin mode(s) of each fibre
Autocollimator
Shadow sensor (violin modes)
Optical lever
Overview of the Modal Frequencies
*
Mode
Predicted (Hz)
Measured (Hz)
Method
Longitudinal
0.65
0.65
AC front
Transverse
0.65
0.65
OL side
Pitch
1.07
1.12
AC front
Yaw
1.10
1.09
AC front/OL side
Bounce*
6.50
6.75
OL ear
with the PUM free, this will correspond to a lowest
vertical
suspension
mode
frequency
of
approximately 9.2 Hz
AC: Auto Collimator
OL: Optical Lever
Violin Modes
• FEA predicted frequency of 1st violin mode is 511Hz
• Measured spread of 512Hz±3Hz (=> uniform fibre dimension and fibre tension)
Analysis of Bend Points
•
Prior to welding each fibre is profiled using a
camera and edge finding software to produce a
cross-sectional profile along its length
•
Transferred to ANSYS to determine how the fibre
bends under loading
•
The bend point is set through fibre profiling and
knowledge of material consumed during welding
CoM
3200
Effective
bending
point
2800
diameter of fibre (microns)
2400
10.8mm
2000
1600
Attachment point
•
The region where bending takes place is
designed to be close to 800m diameter to
reduce thermoelastic noise
•
•
d=10±1mm gives: fpendulum=0.653±0.002Hz
fpitch
=1.07±0.02Hz
1200
Effective bend point
CoM
800
400
0
575
580
585
590
595
600
distance along fibre (mm)
605
610
615
Thermal Noise Modeling
•
Upper stages:
•
•
Mathematica based model (M. Barton, T020205-02, http://www.ligo.caltech.edu/~e2e/
SUSmodels/).
•
•
•
•
•
rigid bodies with up to 6 DoF
wires with longitudinal/transverse/torsional elasticity
springs described by a 6x6 matrix of elastic constants
arbitrary damping function (e.g. structural, viscous)
thermal noise/transfer function estimate
•
Monolithic stage:
•
ANSYS Finite Element Analysis.
•
•
•
•
•
realistic fibre geometries and dilution
fibre, weld, horn and bond loss included
pendulum and vertical thermal noise estimate
violin mode loss (Q) and thermal noise estimate
thermal noise due to laser beam
Upper stages
Lower stage
11
Mathematica Model and the PPP Model
•
The Mathematica model describes the same physics as the modelling tools for the VIRGO
pendulum (PPP effect)
•
A simple model of the VIRGO+ suspension was used to predict the thermal noise
performance (m1=101kg, m2=61kg, m3=20kg). Viscous damping and thermoelastic loss
were added to the Marionetta and reaction mass. The silica stage included thermoelastic
and surface loss.
•
Results identical within factor of 2
Mathematica
VIR-0015E-09
12
Mathematica Model and the PPP Model
Mathematica
Mode
f (Hz)
Vertical (GAS)
0.31
Pendulum
0.41
Pendulum
0.60
Pendulum
0.91
Bounce 1
6.06
Bounce 2
14.68
VIR-0639E-09
13
A. Cumming - "Aspects of mirrors and suspensions for advanced
gravitational wave detectors“, PhD thesis, Glasgow, 2008.
R. Kumar - "Finite element analysis of suspension elements for
gravitational wave detectors“, PhD thesis, Glasgow, 2008.
Dissipation Dilution from FEA
•
Use ANSYS to predict dilution of real fibre geometries
•
A variety of different geometries were analysed including fibres/ribbons, 2-wire and 4-wire
(GEO/aLIGO) pendulums with/without necks.
DFEA 
m
Eelastic
Ekinetic
Theory
ANSYS
1405
1396
 pendulum   fibre
D
kgravity
kfibre
kfibre
kgravity
2 Eelastic / x 2 Eelastic


2 Ekinetic / x 2 Ekinetic
14
Dissipation Dilution from FEA
•
ANSYS used to predict energy stored in the suspension elements (elastic and kinetic)
•
Model accepts real fibre data from profiler in order to calculate accurate dilution values
•
A. Cumming et al., Class. Quantum Grav., 215012, 2009
aLIGO pendulum dilution 91 (energy in fibre
necks is important for realistic estimation)
15
M. Barton et al, T080091, 2008
A. Gretarsson and G.M. Harry, Rev. Sci. Instrum., 70, 4081–7, 1999
S.D. Penn et al., Phys. Lett. A, 352, 3–6, 2006
G. Cagnoli and P. Willems, Phys. Rev. B, 65, 174111, 2002
A. Cumming et al, Class. Quantum Grav., 26, 215012, 2009
Final Stage Thermal Noise Model
•
Use the following loss terms to model the bond, weld region and silica fibres
bond  0.11
weld  5.8 107
bulk  1.2 10 11 f 0.77
surface  8hs / d
YT 

thermoelastic 
   o 
C 
Y
•
•
2
  


2 


1




The FEA model calculates the energy stored in each section of the lower silica stage
which results in Eelastic  E1  E2  ...  En (where the sum extends over the bonds, horns,
welds and fibre).
 fibre  surface  thermoelastic  bulk
The total loss (undiluted) is given by:
total    
bond
Ei
Eelastic
bond,i  
horn
•
Ei
Eelastic
horn,i  
weld
Ei
Eelastic
weld ,i  
fibre
 fibre  surface  thermoelastic  bulk
Ei
Eelastic
 fibre,i
the thermoelastic time constant () is modified
depending on whether fibres or horns are modelled 16
Energy Stored in the Fibre
•
It is important to model all sources of loss (e.g. fibre, weld, horn and bond)
Elastic energy (arbitrary units)
fibre
1000
800
600
400
200
400m fibre
0
0
horn
100
200
300
400
500
Element number
600
700
800
17
900
horn
Weld regions
•
•
For the aLIGO pendulum mode 91.5% of energy in the fibre, 6.3% of energy in the weld,
remainder in horns
For aLIGO violin modes, more energy stored in neck/horn/weld as frequency increases
=> violin mode Q decreases with higher frequency
Energy Stored in the Fibre
•
ANSYS was used to predict energy ratio in different parts of the lower stage
•
The largest energy ratio is in the fibre. The majority of the energy ideally resides in the
800m thermoelastic cancellation region
•
Although the bond has high loss, there is very little energy stored in that region and thus
the effect on the diluted loss is 1%
Item
Energy ratio Loss
Diluted loss
Upper bonds 8.3410-9
9.1810-10
1.1110-11
Lower bonds 2.5010-9
2.7510-10
3.3310-12
Ears
6.9010-3
1.8210-11
2.2010-13
Fibres
9.9310-1
1.1910-7
1.4410-9
Overview of Thermal Noise Terms
Mode
Bond
loss
Horn
loss
Weld
Loss
Surface
loss
Thermoelastic loss
Dilution
Pendulum
YES
YES
YES
YES
YES
Eelastic
Ekinetic
Vertical
YES
YES
YES
YES
(surf /2)
NO
NONE
YES
Eelastic
Ekinetic
Violin
YES
YES
YES
YES
P. Willems et al., Physics Letters A 319 (2003) 8–12
Bond Thermal Noise due to Laser Beam
•
The previous treatment of bond thermal noise determines the loss associated with
energy stored due in the pendulum mode (i.e. treating it as part of the fibre)
•
The loss associated with thermal noise from the Gaussian laser beam is also included
using the model of Levin
2
xLaserBeam

2k BT Wdiss
 2 f 2 F02
Wdiss  2f
 dV
body
•
The strain energy, , in the material is evaluated at each node of the FE model and
summed to find Wdiss
•
The total thermal noise is then
2
2
2
2
xTOT  xPendulum
 xVertical
 xViolinMode
 xLaserBeam
20
aLIGO Final Stage Displacement Noise
thermal displacement noise for single test mass
1E-12
1E-13
Vertical
1E-14
Fundamental violin mode
1E-15
Total
Horizontal
rms displacement (m Hz-1/2)
•
2nd Violin mode
1E-16
Bonds and ears
1E-17
1E-18
1E-19
1E-20
1E-21
1E-22
1E-23
0
5
10
15
20
25
30
Frequency Hz
A. Cumming, Class. Quantum Grav. 29 (2012) 035003
21
Violin Mode Quality Factors (LASTI)
•
1st/2nd violin modes (n=1, n=2) measured on LASTI monolithic.
22
aLIGO Violin Modes (LASTI)
• The measured and modelled frequencies tie up well indicating a good accuracy of model
geometry compared to the real suspension
• For V1 the projected Q from FEA is to within 7% of measured value
• For V2 the projected Q from FEA is to within 19% of measured value
• As frequency increases the dilution reduces due to more energy in horn/weld/fibre neck
• Surface loss and weld loss have roughly equal contributions => important to model
Mode
ANSYS
frequency
(Hz)
Measured
frequency
(Hz)
FEA
dilution
ANSYS
Quality
factor
Measured
Quality
factor
V1 (n=1)
511
511,520
54
6.66108
6.11108
(average)
V2 (n=2)
1017
1020
51
5.71108
4.62108
23
Summary
•
aLIGO Monolithic suspensions now installed at LASTI, MIT and 2x LIGO Hanford
•
The suspension is well engineered and a robust procedure is in place to both build and
repair (LIGO Hanford suspensions performed by LIGO personnel)
•
A range of tools have been developed to model the suspension performance
(Mathematica and ANSYS). Mathematica model has been used to predict VIRGO+
sensitivity within a factor of 2.
•
The use of real fibre geometries are necessary for accurate dilution/mechanical
loss/thermal noise estimates
•
There is good agreement between measured/predicted modal frequencies and bending
points
•
The measured violin modes at LASTI show high values (Q=611M for n=1 and Q=462
for n=2)which agree well with FEA
•
Accurate thermal noise estimates and violin mode Q’s require accurate estimation of all
energy loss processes (i.e. loss in weld, horn, bond)
24