Acoustic properties of a prototype for a hollow spherical gravitational antenna
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Transcript of Acoustic properties of a prototype for a hollow spherical gravitational antenna
Acoustic properties of a prototype for a hollow spherical gravitational
antenna
Acoustic properties of a prototype for a hollow spherical gravitational
antenna
(^) Laboratori Nazionali del Gran Sasso dell’INFN(*) Laboratori Nazionali di Frascati dell’INFN
M. Bassan, S. Giannì, Y. Minenkov^, R. Simonetti
Dip. Di Fisica, Università di Tor Vergata eINFN, sezione Roma Tor Vergata
With crucial help from L. Quintieri*, A. Rocchi,
ILIAS - London Oct 27th 2006
SummaryShperical Antenna
Bulk Sphere
Discussion
Hollow Sphere
• Advantages• Comparison bulk- hollow
•General features•Suspensions• Experimental results
• Realization of a cavity• Bonding methods• Fabrication of a hollow sphere• Experimental results
• Comparison of results: bulk-hollow• Conclusions
• People interested in making high Q resonators of VERY large size will have to deal with the issue of bonding.
• We have addressed here the problem of preserving mode shapes and Q factors in brazed metallic resonators.
Who cares about these tests ?
Advantages
• it is omnidirectional• it can determine the direction of incoming g.w. • it can determine the polarization state of the g.w.• it has a larger cross section of a bar at the same frequency• it has a wider bandwidth
Bulk Sphere
• it has the largest mass• its cross section for the 1st spheroidal quadrupole mode is larger• it is difficult to construct and cool• its bandwidth is still too narrow wrt interferometers
Hollow Sphere
• its cross section for 1st spheroidal quadrupole mode is somewhat smaller than the bulk sphere• it is an easier object to fabricate and cool• using both 1st and 2nd mode we can recover both bandwidth and overall cross section
Why a Spherical Antenna ?
• The cross section is smaller wrt bulk, but it can make up at the n=2 mode
bulk shell
Cross section for the 1st and 2nd modes
Why a hollow sphere ?
• Choice of thickness can be used for centering two bandwidths
• Larger surface/ volume => easier cooling
Why a hollow sphere ?
• Larger surface/ volume => easier cooling
•The cross section is smaller wrt bulk, but we can make up at the
n=2 mode
• Choice of thickness can be used for centering two bandwidths
(C) Effects of bonding on modes and Qs ? (C) Effects of bonding on modes and Qs ?
(A) How do we produce it ? (A) How do we produce it ?
• casting• fabricating from plates• welding two half-spheres
• Will elastic continuity be retained across the welding interface ?• Will the bonding affect Q ?
Need to practice and investigate on a small size sample Need to practice and investigate on a small size sample
(B) How do we suspend it ?(B) How do we suspend it ?
• Can’t suspend it from center of mass• Would surface suspension affect Qs ?
Problems with a Hollow Sphere
Bulk Sphere in CuAl6%(kindly provided by Minigrail) General FeaturesGeneral Features
Density = 8145 kg/m3
Diameter = 0.15 m
Mass M = 14.4 kg
Young Modulus Y = 121x109 N/m2
Poisson Ratio σ = 0.33
Sound Velocity vs = 3854 m/s
Expected Resonant frequency (n=1 l=2) f = 13313 Hz
Our Benchmark:
Effect of suspension on the Q of the quadrupolar modes of the bulk sphereEffect of suspension on the Q of the
quadrupolar modes of the bulk sphere
(A)Testing suspension : surface vs center of mass
T=300 KT=300 K T=300 K ÷ 4.2 KT=300 K ÷ 4.2 K
Excitation : PZT or mag. hammerReadOut : PZT or accelerometer
Excitation : PZT or mag. hammerReadOut : PZT or accelerometer
Measuring Apparatus
FrequenciesFrequencies
Quality factors QQuality factors Q
Tests: T=4.2 K, T=77.4 K, T=300 K
Bulk Sphere in CuAl6%
Experimental results
Electron Beam WeldingElectron Beam Welding
DiffusionDiffusion
Furnace BrazingFurnace Brazing
Tested by Minigrail people.Really bad results:• poor beam penetration• cracks• Uneven welding
Tested by Minigrail people.Really bad results:• poor beam penetration• cracks• Uneven welding
Test on a hollow cylinder CuAl6%: m=4.261Kg, L=0.228m, Φ=56mm, thick. 22mm, fo
sp=8312Hz, τ<1s
Results:• OK at T=300K• Degraded after thermal shock at T=77K
Test on a hollow cylinder CuAl6%: m=4.261Kg, L=0.228m, Φ=56mm, thick. 22mm, fo
sp=8312Hz, τ<1s
Results:• OK at T=300K• Degraded after thermal shock at T=77K
Satisfactory results:• OK a T=300K• OK thermal shock a T=77K
Satisfactory results:• OK a T=300K• OK thermal shock a T=77K
(B) Bonding methods:
General featuresGeneral features
Density = 8145 kg/m3
Inner diameter(thick.= 22 mm) = 0.106 m
Mass M = 9.3 kg
Young Modulus Y = 121x109 N/m2
Poisson Ratio σ = 0.33
Speed of sound vs = 3854 m/s
Expected resonant frequency: (n=1 l=2) f = 7537 Hz
Hollow sphere in CuAl6%
T=300 KT=300 K T=300 K ÷ 4.2 KT=300 K ÷ 4.2 K
Same experimental set-up as for the bulk sphereSame experimental set-up as for the bulk sphere
Hollow sphere in CuAl6%
FrequenciesFrequencies
Quality Factors QQuality Factors Q
Tests: T=4.2 K, T=77.4 K, T=300 KQ vs Temperature
T= 4.2 K ÷ 300 K
(C ) Hollow sphere in CuAl6%Experimental results
Splitting modo sferoidale Sfera Piena
12500
13000
13500
14000
1 2 3 4 5
N modi
f (H
z)
f teorica f ANSYS f sperimentale
BULK SPHERE
Frequenza(Hz)
f1= 12637.7 0.1
f2= 13126.5 0.1
f3= 13429.4 0.1
f4= 13943.1 0.1
f5= 14040.0 0.1
Frequenza(Hz)
f1= 7074.2 0.1
f2= 7456.9 0.1
f3= 7479.6 0.1
f4= 7542.4 0.1
f5= 7604.5 0.1
HOLLOW SPHERE
T=300 KT=300 K
Splitting modo sferoidale Sfera Cava
7000
7500
8000
8500
1 2 3 4 5
N modi
f (H
z)
f teorica f ANSYS f sperimentale
FrequenciesFrequencies
Mode location and splitting
f (Hz)
13313
7537
5025
Good Agreement with theory !fpiena=13313 Hz fcava=7537 Hz
Det (Ap)=0
Validating Lobo’s Calculations
Q Bulk 300 KQ Hollow 300 K
Q Bulk 77.4 K Q Hollow 77.4 K
Q Bulk 4.2 KQ Hollow 4.2 K
Comparing Hollow vs Bulk Sphere
• Good agreement with elastic theory: potential gravitational antenna
• Good results from furnace brazing: homogeneity is mantained and Q degradation is small
• For the future: additional tests on different brazing techniques and procedures.
• Investigation of alternate bonding methods: diffusion welding and electron beam welding.
CONCLUSIONS