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 ?

Why a hollow sphere ?

• 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

MachiningMachining

22 mm

“Hollowing” the sphere

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