summary of support tube r&d
DESCRIPTION
Nov. 11, ’04. Summary of Support tube R&D. KEK H. Yamaoka. Introduction. P1. P2. 4m. CFRP tube. Tungsten Tube (t=100). ・ Components at IR region Supported by Tungsten tubes, CFRP tube ・ For high luminosity Ground motion, culture Noise → Analyses, Excitation tests - PowerPoint PPT PresentationTRANSCRIPT
Summary of Support tube R&D
Nov. 11, ’04
KEK H. Yamaoka
・ Components at IR region Supported by Tungsten tubes, CFRP tube・ For high luminosity Ground motion, culture Noise
→ Analyses, Excitation tests
Study Items;
・ Consistency of analyses
・ How much is relative
amplitude?
|P1-P2| < 1nm(Criteria)・ Is necessary CFRP tube?→ How much thickness?
Introduction
4m
P1 P2
Tungsten Tube(t=100)
CFRP tube
(2) 20t x 100w x 1440L
(4) 20t x 100w x 695L 2.5t x 100w x 200L
(1) 20t x 100w x 695L
(3) 20t x 100w x 695L
Exciting Test
(5) φ80 x 10t x 200L(1/10 scale)
(6) φ80 x 10t (1/10 scale)t=3mm
Input exciting force(Excitation table or Impact hammer) ↓ Measurement: natural frequencies Mode shape ↓ Compare to the FEM results
20t x 100w x 695L 2.5t x 100w x 200L
t=3mm
2: 40Hz
3: 161Hz
1: 26Hz
2: 43Hz
3: 184Hz
1: 30HzMeasurement FEM
1
X
Y
Z
JUL 29 200318:01:57
DISPLACEMENT
STEP=1SUB =5FREQ=259.703DMX =38.732
1
X
Y
Z
JUL 29 200318:01:38
DISPLACEMENT
STEP=1SUB =3FREQ=75.762DMX =44.94
1: 76Hz
2: 256Hz
3: 489Hz
1
X
Y
Z
JUL 29 200318:06:24
DISPLACEMENT
STEP=1SUB =7FREQ=486.8DMX =42.803
1
2
34
56
7
8
910
1112
131415
1617
18
192021
(+Y): [ ] 521 右側 コン フ レ゚ ックス
: 1.0, : 振幅 ト ヴ ェル(g) X,Y,Z 方 向 遠
1
234
5678
9
101112
1314
1516
17
18 19
20
21
(+Y): [ ] 258 右側 コン フ レ゚ ックス
: 1.0, : 振幅 ト ヴ ェル(g) X,Y,Z 方 向 遠
123
456
7891011121314
151617
18
192021
(+Y): [ ] 77.5 右側 コン フ レ゚ ックス
: 1.0, : 振幅 ト ヴ ェル(g) X,Y,Z 方 向 遠
1: 78Hz
2: 258Hz
3: 522Hz
1st ~ 3rd mode: Good agreement with FEM Support structure should be modeled in FEM.
1 10 100 10001E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
Am
plit
ud
e(n
m)
Frequency(Hz)
1 10 100 10001E-6
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
Am
plit
ud
e(n
m)
Frequency(Hz)
Stiffness: 1:512
2.5mm thick plate
By connecting very weak structure, Deviation can be absorbed. Correlation can be given.Relative amplitude can be estimated.
1st: 99Hz2nd: 548Hz
1st: 106Hz2nd: 548Hz
1st: 88Hz
2nd: 126Hz
Case-1
20mm thick plate
Case-2
1
X
Y
Z
F0cos(t)=(m ・ a)sin(t)
QC-L: Tungsten(100mm) QC-R: Tungsten(100mm)
CFRP
0 – 1000HzCalculation of relative amplitude
1
X
Y
Z
JUN 23 200409:31:56
ELEMENTS
REAL NUM
U
2m3.85m
7m8m
QC-L QC-R
3mm 5mm 10mm0Hz1Hz3Hz5Hz
CFRP thick.
Difference of 1st mode of resonantfrequency between QC-R and QC-L.
Get relative amplitude (QC-R)-(QC-L)
(Model-A)
(Model-B) F0cos(t)
2m7m8m
P1 P2
Estimation of Input Acc.
Data: Vertical @ATF(17:00 Feb. 10, 2004)
(ロ グ周波数0.1 1 10
1E- 6
1E- 7
1E- 8
1E- 9
Linear Spectrum
2x10-7m/s2
Input Acc. = 2x10-7m/s2
Mass=90tons/9.8[m/s2]
Self weight
Input data
1
X
Y
Z
APR 7 200414:19:12
DISPLACEMENT
STEP=1SUB =1FREQ=73.152DMX =1.279
U
1st mode 2nd mode
Same phase Opposite phase
Relative amplitude: QC-R and QC-L
Amplitude: QC-R and QC-L
t100mm t100mmt5mm
In case of 100mm-5mm(CFRP)-100mm, f=0Hz
Relative amplitude between QC-R and QC-L
QC-R QC-RQC-LQC-L
Dif
fere
nc
e(n
m)
1e-4
1
1
X
Y
Z
JUN 23 200409:31:56
ELEMENTS
REAL NUM
U
QC-L QC-R
1
X
Y
Z
QC-L QC-R
Other calculations
Diff: Relative amplitude between QC-R and QC-L.
Tungsten Tungstenf Mode 3mm 5mm 10mm 100mm 3mm 5mm 10mm 100mm
Freq.(Hz) 75.8 76.0 76.0 49.2 17.583 17.7 17.9 16.3Diff.(nm) 0.098 0.055 0.016 9.09E-05 0.065 0.026 0.008 2.60E-04Freq.(Hz) 77.5 78.6 81.4 113.0 20.2 21.8 25.0 44.4Diff.(nm) 0.213 0.206 0.192 0.080 2.816 2.398 1.763 0.325Freq.(Hz) 75.2 75.3 75.5 49.0 17.0 17.1 17.3 16.0Diff.(nm) 0.129 0.080 0.035 1.10E-03 0.823 0.480 0.234 3.60E-02Freq.(Hz) 77.0 78.2 80.9 112.6 19.8 21.4 24.7 43.3Diff.(nm) 0.174 0.177 0.177 0.081 2.357 2.186 1.696 0.334Freq.(Hz) 73.4 73.7 74.2 48.5 15.6 15.9 16.3 15.3Diff.(nm) 0.173 0.133 0.076 3.26E-03 2.339 1.496 0.752 1.30E-01Freq.(Hz) 76.9 77.8 80.4 111.9 19.5 20.9 24.1 41.0Diff.(nm) 0.094 0.116 0.143 0.082 1.547 1.726 1.532 0.349Freq.(Hz) 71.5 72.0 72.7 48.1 13.9 14.4 15.1 14.4Diff.(nm) 0.204 0.172 0.113 5.62E-03 3.813 2.631 1.396 2.84E-01Freq.(Hz) 76.8 77.6 80.0 111.0 19.3 20.6 23.6 38.4Diff.(nm) 0.056 0.078 0.114 0.084 1.077 1.343 1.343 0.359Freq.(Hz) 75.6 17.4Amp(p-p) 0.224 3.869
CFRP CFRP3-Point fixed(Both end+3.85m) 2-Point fixed(Both end)
1stCanti
1st
2nd5Hz
1st
2nd3Hz
0Hz1st
2nd
1st1Hz
2nd
Results
1
X
Y
Z
JUN 23 200409:31:56
ELEMENTS
REAL NUM
U
P1 P2
1
X
Y
Z
P1 P2
Natural frequency: 76Hz, relative amp. : 0.1nm <1nmThis is ideal configuration.In case of no CFRP tube(Cantilever): Amplitude=0.2nm <1nm CFRP tube is not necessary because of less than 1nm. However, it is difficult to amount on a very stiff base stand. So actual natural frequency must be lower than this value.
Natural frequency: 17Hz, relative amp. : 2 ~ 3nmIn case of no CFRP tube(Cantilever): Amplitude= 4nm
⇒ CFRP tube: - No efficient to reduce amplitude. - Deviation of natural frequency between two tubes can be absorbed.
(Model-A)
(Model-B)
1
X
Y
Z
APR 7 200414:19:34
DISPLACEMENT
STEP=1SUB =3FREQ=79.927DMX =.986417
U
1
X
Y
Z
APR 7 200414:19:12
DISPLACEMENT
STEP=1SUB =1FREQ=73.152DMX =1.279
U
7m
8m
2m
Right side: 70Hz
LC
RCFRP: Changed!
Left side: 75Hz
L R
L
R
1st mode
2nd mode
70Hz75Hz
1
X
Y
Z
APR 7 200414:09:13
DISPLACEMENT
STEP=1SUB =3FREQ=71.63DMX =1.28
U
1
X
Y
Z
APR 7 200414:08:52
DISPLACEMENT
STEP=1SUB =5FREQ=75.798DMX =1.209
U
1st mode(CFRP: 1mm) 2nd modeLess than this thickness, correlation and opposite phase doesn't appear at 2nd mode.
Optimization of CFRP tube thickness
1st mode 2nd modeCFRP(mm) Freq(Hz) Freq(Hz)
20 73.6 85.210 72.9 80.15 75.5 78.43 72.0 76.51 71.5 75.7
At least, thickness of CFRP: >3mm
Configuration of support system
・ Both-ends supported structure with CFRP tube connection → Correlation is given to both-sides tubes in oscillating behavior. Tungsten tube: 100mm thick, CFRP: 5mm thick Support position: Both ends and 3.85m from I.P.
・ Active vibration isolation system is necessary → Relative amplitude will be above 1nm. CFRP tube is not efficient to reduce amplitude less than 1nm.
・ It is necessary to design the stiff support base as possible → Natural frequency becomes high. → Amplitude is decreased proportional to frequency.
Conclusion CFRP tube(5mm)
Tungsten masks(100mm)
A
EI
lf ii
2
2 1
2
Stiffness(CFRP tube)
EI: Bending stiffness E: Young’s modulus I : Moment of Inertia
64
44IO dd
I
EI
pl
3CFRP tube(t=5mm) E=150GPa I=π ・ (d1
4-d24)/64
=π ・ (8004-7904)/64 =9.9×108mm4
Tungsten(t=100mm) E=415GPa I=π ・ (d1
4-d24)/64
=π ・ (8004-6004)/64 =1.4×1010mm4
Ratio = CFRP:Tungsten = 1 : 39
CFRP Tube→Not efficient to increase natural frequency and decrease amplitude.
・ Natural frequency
・ Deformation
fF
fXfH
j
iij
FRF(Frequency Response Function)
Xi: Output Acc.Fj: Input force
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
- 100
- 50
0
50
100
Out
put
Acc
.(m/s
2 )
Time(sec.)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10- 5
0
5
10
15
20
25
30
35
40
45
50
Inpu
t Fo
rce(
N)
time(sec.)
10 100 1000
1E- 4
1E- 3
0.01
Fou
rier
Spe
ctru
m(N
)
Frequency(Hz)
10 100 1000
1E- 5
1E- 4
1E- 3
0.01
0.1
1
10
Fou
rier
Spe
ctru
m(m
/s2 )
Frequency(Hz)
Hz0.0 4E3
(
m/s
2̂ログ振幅
1
0.1
1E- 2
10
Hz0.0 4E3
(
m/s
2̂ログ振幅 1
0.1
10
100
Hz0.0 4E3
(
m/s
2̂ログ振幅 1
0.1
10
100
Hz0.0 4E3
(
m/s
2̂ログ振幅 1
0.1
10
100
Hz0.0 4E3
(
m/s
2̂ログ振幅 1
0.1
10
100
Hz0.0 4E3
(
m/s
2̂ログ振幅 1
0.1
10
100
Hz0.0 4E3
(
m/s
2̂ログ振幅 1
0.1
10
100
Hz0.0 4E3
(
m/s
2̂ログ振幅 1
0.1
10
100
Hz0.0 4E3
(
m/s
2̂ログ振幅 1
0.1
10
100
frf- frf- frf-
frf- frf- frf-
frf- frf- frf-
FFT
FFT
FRF
Input
Output
Input
Output
○ Tests(Hammering test)
FRF Table
10 100 1000
1
10
100
FR
F((
m/s
2 )/N
)
Frequency(Hz)
P1 P2 P3 P4 P5 P6 P7 P8 P9
12
34
56
78
9
(+Y): 56.2 Hz (283右 側
: 1.0, : 振幅 ト ヴ ェル(g) X,Y,Z 方 向 遠
A: 57Hz
○ Results
(Taper flange, 12-M6)
123
45
6
78
9
(+Y): 129 Hz (- 11右 側
: 1.0, : 振幅 ト ヴ ェル(g) X,Y,Z 方 向 遠
B: 129Hz
C: 585Hz
1
2
34
5
6
7
8
9
(+Y): 1.21E3 Hz (196右 側
: 1.0, : 振幅 ト ヴ ェル(g) X,Y,Z 方 向 遠
D: 1216Hz
1
2
3
4
5
6
78
9
(+Y): 1.69E3 Hz (153右 側
: 1.0, : 振幅 ト ヴ ェル(g) X,Y,Z 方 向 遠
E: 1690Hz
1
23
4
56
78
9
(+Y): 2.5E3 Hz (143右 側
: 1.0, : 振幅 ト ヴ ェル(g) X,Y,Z 方 向 遠
F: 2500Hz
A B
C DE F
123456789
G-sensor
Fixed
*
''
*
2*
'
' FEr
FEr
testr
testr
FEr
testr
rrMAC
MAC(Modal Assurance Criteria)
Modal assurance criteria quantitatively compare all the possible combinations of test and analysis mode shape pairs.
Mode Freq. Damping(%) 1 30.4Hz 1.68 2 188Hz 0.422 3 419Hz 0.303 4 584Hz 0.113 5 992Hz 8.02E-2
nf
ff
2
21
f2fnf1
2
Damping ratio
0.0 0.0
0.2 0.2
0.4 0.4
0.6 0.6
0.8 0.8
1.0 1.0
1
2
3
4
5
テスト
5
4
3
2
1
FEM
5th3rd2nd
4th
5th1 st4th3rd2nd1st
FEMTest
MAC=1: Mode shape pairs is exactly match MAC=0: pairs that are completely independent
1st: 31Hz
3rd: 457Hz
5th: 1022Hz
4th: 534Hz
FEM
2nd: 192Hz
Comparison with FEM
Test
3D : Ref [ ] 988 表示 コンフ レ゚ ッ ク ス
: 1.0, :振幅 ト ヴ ェル(g) X,Y,Z :方 向 遠 近
3D : Ref [ ] 32.5 表示 コン フ レ゚ ッ ク ス
: 1.0, :振幅 ト ヴ ェル(g) X,Y,Z :方 向 遠 近
3D : Ref [ ] 186 表示 コンフ レ゚ ッ ク ス
: 1.0, :振幅 ト ヴ ェル(g) X,Y,Z :方 向 遠 近
3D : Ref [ ] 417 表示 コン フ レ゚ ッ ク ス
: 1.0, :振幅 ト ヴ ェル(g) X,Y,Z :方 向 遠 近
1st: 30Hz
3rd: 419Hz
2nd: 188Hz
5th: 992Hz
3D : Ref [ ] 578 表示 コンフ レ゚ ッ ク ス
: 1.0, :振幅 ト ヴ ェル(g) X,Y,Z :方 向 遠 近
4th: 584Hz
1
X
Y
Z
F0sin(t)=(m ・ a)sin(t)
F0: Input force(F0=ma)X: AmplitudeXst: Static deformationζ: Damping ratio(2%)ωn: Resonant frequencyω: Frequency If =n, X/Xst=25
Harmonic analysis
F0sin(t): Excitation force0 – 1000Hz: Sweep frequency
tFkxxcxm sin0
222 21
1
nnstX
X
F0sin(t)
Model-1A Model1-B Model-2AModel-
2B
Deformation(mm) 1.6 - 0.09 -
Stress(MPa) 23 - 5 -
Natural frequency(Hz)
(Vertical)
1st mode 17 15 71 152nd Mode 81 38 179 543rd mode 173 105 202 93
Harmonic response(nm) @QC1 8.0 8.0 0.2 6.0
Spectrum analysis(nm)
@QC1
1st mode 6.5 2.0 4.3 2.72nd Mode -1.7 1.1 0.2 0.23rd mode -0.4 0.1 1.9 0.002
(Model-1A) (Model-1B)
(Model-2A) (Model-2B)
現実に考えられる固有振動数のずれについて
Young’s modulus の違い Aluminum の場合種類によって 6.9GPa – 7.3GPa の範囲がある。 → fi: 3% different If 70Hz: 2Hz, 17Hz: 16.5Hz
寸法の誤差 寸法が多少ずれても断面 2 次モーメント( I)に大きな差は生まれない。また、寸法を管理することができることから「寸法の誤差」による固有振動数のずれは小さいと考えられる。
組み立て及び設置誤差によるずれ ネジ締めのトルク管理、寸法測定等で管理できるが完全にはできない。 3%以内の誤差にできるのではないだろうか。(根拠はすこしあいまい)
全体では 5% ぐらいに抑えられるかもしれない。 → どのくらいの誤差に収められるか試験。
A
EI
lf ii
2
2 1
2
64
44IO dd
I