1 fea of towers for dome c jl dournaux / jph amans gepi, pôle instrumental - paris observatory...
TRANSCRIPT
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FEA of Towers for Dome C
Means to increase tower’s stability Mechanical behaviour of steels at low
temperatures Description of the models used for
simulation Results on nominal solutions Purposed solutions to improve stability
of truss tower
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How to increase tower’s stability (Hammerschlag et al., 2006)
Active methods consume power and can generate heat
Some passive methods are: Eigenfrequencies of towers > 10 Hz
Energy in the wind variations decreases quickly between 1 and 10 Hz
Only plane motions of the platform parallel to the ground (i.e. no rotations x or y) Astronomical objects are far away
But Changes in tower’s design have to keep the centre
of the tower free to lift the telescope
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Aim of the study Preliminary FEA of 2 concept towers designed by JP
Amans (GEPI, Paris Observatory) Check the stability of these concept towers Improve performances of these 2 concept towers
Truss Tower “Amans” Tabouret Tower (ATT)
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Mechanical Behaviour of Steels at low temperatures
E increases slowly when T decreases
Small differences in E values between summer (-30°C) and winter (-80°C) For a C steel: 207 / 210 GPa For a stainless steel: 168 / 174 GPa
Ductility decreases strongly when T decreases
5 Stainless Steel / 6 C Steel
(Thermeau, 2004)
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Models Description Containers and platform are not modelled Boundary Conditions:
Tower’s feet are fixed Mass applied on the top of the tower: 100 t
No rotation between tubes (joints) No thermal gradients
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Dynamic behaviour of truss tower
Mode Fréquence Rx Ry Description du mode
N° (Hz) Fraction Fraction
1 5,16 / 5,20 47,7% 47,7% Flexion 1er ordre / <1 1 0>
2 5,16 / 5,20 47,7% 47,7% Flexion 1er ordre / <1 -1 0>
3 17,6 / 17,72 0,0% 0,0% Torsion / <0 0 1>
4 18,54 / 18,68 0,0% 0,0% Ouverture sommet
5 21,16 / 21,31 1,7% 1,7% Flexion 2e ordre / <1 -1 0>
6 21,16 / 21,31 1,7% 1,7% Flexion 2e ordre / <1 1 0>
7 21,57 / 21,73 0,0% 0,0% Traction Compression / < 0 0 1>
Tube 300x5, C steel Small differences of dynamic behaviour in summer
and in winter: frequencies variations < 0,1 Hz
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Dynamic behaviour of truss tower
Tube 300x5, stainless steel Small differences of dynamic behaviour in summer
and in winter: frequencies variations < 0,1 Hz
Mode Fréquence Rx Ry Description du mode
N° (Hz) Fraction Fraction
1 4,64 / 4,73 47,7% 47,7% Flexion 1er ordre / <1 1 0>
2 4,64 / 4,73 47,7% 47,7% Flexion 1er ordre / <1 -1 0>
3 15,85 / 16,13 0,0% 0,0% Torsion / <0 0 1>
4 16,70 / 16,99 0,0% 0,0% Ouverture sommet
5 19,05 / 19,39 1,7% 1,7% Flexion 2e ordre / <1 -1 0>
6 19,05 / 19,39 1,7% 1,7% Flexion 2e ordre / <1 1 0>
7 19,43 / 19,78 0,0% 0,0% Traction Compression / < 0 0 1>
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Dynamic behaviour of truss tower The following results are for a
Carbon steel @ -80°C The 1st modes @ 5,2 Hz harm
because they create a strong rotation of platform
Change tower’s design to increase these frequencies and reduce the rotation they produce
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Dynamic behaviour of truss tower Different kind of add-ons are tested The most efficient is obtained by reinforcing
the corners of the tower in all directions Reinforce only the 2 first floors allows to
increase the frequency @ 5.3 Hz. The rate of rotation is almost not affected
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5,1
5,2
5,3
5,4
5,5
0 1 2 3 4 5
Nb d'étages renforcés
Fré
qu
en
ce (
Hz)
85%
90%
95%
100%
0 1 2 3 4 5
Nb d'étages renforcés
ΣR
1 (
%)
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Dynamic behaviour of truss tower
Increase tube diameter of the 2 firsts floors allows to improve tower’s performancesDiamètre Epaisseur Section M (t) Modes 1+2
mm mm cm² Fréq moy (Hz) ΣRx (%) ΣRy (%)
300 5 23,4 19,8 5,31 93,4% 93,4%
508 3 23,9 19,9 5,42 93,1% 93,1%
508 5 39,7 22,2 6,31 90,9% 90,9%
1016 5 79,6 28,1 7,63 85,1% 85,1%
1016 8 127,2 34,0 8,31 79,8% 79,7%
5
6
7
8
9
0 50 100 150
Section des tubes des 2 premiers étages (cm²)
Fré
qu
en
ce (
Hz)
75%
80%
85%
90%
95%
100%
0 50 100 150
Section des tubes des 2 premiers étages (cm²)
ΣR
1 (
%)
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Dynamic behaviour of Amans Tabouret(Stool) Tower
Tubes 1016x4 & 291x3 Modes 1/2 & 4/5 harm Eigenfrequencies are lower
than for truss tower but the platform is more stable
Mode Fréquence Tx Ty Tz Rx Ry Rz
N° (Hz) Fraction Fraction Fraction Fraction Fraction Fraction
1 3,80 0,8% 52,3% 0,0% 59,0% 0,9% 0,0%
2 3,80 52,3% 0,8% 0,0% 0,9% 59,0% 0,0%
3 6,41 0,0% 0,0% 0,0% 0,0% 0,0% 67,0%
4 6,51 25,7% 0,1% 0,0% 0,1% 16,4% 0,0%
5 6,51 0,1% 25,7% 0,0% 16,4% 0,1% 0,0%
6 9,38 0,0% 0,0% 0,0% 0,0% 0,0% 2,3%
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Dynamic behaviour of ATT Tower’s performances seem to be less
sensitive to tube diameter than Truss Tower
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200 250
Section des tubes des 2 premiers étages (cm²)
Fré
qu
en
ce (
Hz)
Modes 1+2 Modes 4+5
Ǿ Ep. SectionM (t)
Modes 1+2 Modes 4+5
mm mm cm² f moy ΣRx (%) ΣRy (%) f moy ΣRx ΣRy
1016 4 63,7 32,4 3,80 60,0% 60,0% 6,51 16,4% 16,4%
1016 8 127,2 62,6 3,68 61,3% 61,3% 6,30 14,0% 14,0%
1524 8 191,1 93,1 4,56 70,1% 70,1% 8,21 7,3% 7,3%
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Conclusions Results:
Add appropriate add-ons and increase diameters of vertical tubes of first floors may allow to obtain 1st modes of truss tower beyond 10 Hz
Platform’s rotations are weaker for ATT but eigenfrequencies too
Next steps: Test other concept tower(s) Master student (Calculate transfer function to precisely
determine wind effects by FEM, implement methods for vibration control, define a prototype…) in collaboration with Pr André Preumont (ULB/INSA Lyon)