Vib ti St bilit Of NSLS II Gi dVibration Stability Of NSLS II Girder-Magnets Assembly
MEDSI June 10, 2008
V. Ravindranath
S. Sharma, A. Jain, P. He, L. Doom, F. Lincoln
N ti l S h t Li ht S IINational Synchrotron Light Source II Brookhaven National Laboratory
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Outline
f f• Introduction-tolerance specifications for stability and design approach for the NSLS-II girder.
• FEA modal analyses and experimental verificationFEA modal analyses and experimental verification
• Response of the girder system to ambient vibration
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Introduction
• NSLS-II beam stability requirement: 10% or better of theminimum electron beam size → ± 0 3 microns verticallyminimum electron beam size → ± 0.3 microns vertically.
• For assuring beam stability stability of storage ring• For assuring beam stability, stability of storage-ringcomponents such as magnets, chambers, BPMs, girder arecriticalcritical
ToleranceLimits
ΔX RMS(nm)
ΔY RMS(nm)
Uncorrelated magnet motionwill lead to a closed orbit
lifi ti f 12 t th ID( ) ( )
Uncorrelatedmagnetmotion
< 150 < 25 amplification of ~12 at the IDcenter
motionUncorrelatedgirder motion
< 600 < 70
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Girder Design Approach
100
1000
)
0.5-4 Hz-400 nm
1
10
cmen
t (nm
)
4 100 Hz
0.1
1
RM
S di
spla
c 4-100 Hz -15 nm
0.001
0.01
0 10 20 30 40 50 60 70 80 90 100
R
RMS displacement for NSLS-II:
0 10 20 30 40 50 60 70 80 90 100
Freq (Hz)
0.5-4 Hz = 400 nm4-100 Hz = 15 nmF 30 H d ti 1
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Frequency > 30 Hz, ground motion < 1 nm
Conceptual Design- Multipole Girder
• 1” thick1 thick stiffeners welded to the girder to
1.2 m
minimize torsion
5 m0.86 m
• Girder fabrication : Commercial plates 1-2” thick, welded• Internal ribs to enhance stiffness and minimize torsion
0.86 m
te a bs to e a ce st ess a d e to s o• Girder support : Eight locations, 2” diameter bolts• Girder design was optimized by carrying out FEA modal analysis
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Girder Prototype For Vibration Tests
• Goal:To verify and if needed calibrate the FEA model, so that it is applicable to all future analysesto all future analyses
• Location: Section 4 of the NSLS-IIstorage ring Girder weight ~7000 lbsstorage ring. Girder weight ~7000 lbsand supported magnets weight ~ 7000lbs
SECTION 2 SECTION 3SECTION 4 SECTION 5 SECTION 6
3.2 m2.9 m3.6 m5.0 m
3.6 m
One cell of the NSLS-II storage ring
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Vibration sensorGround motion 1.E+00
Accelerometer
1.E-01
ons)
Geophone
4-100 Hz
1.E-02cm
ent (
mic
ro
30 nm
1.E-03
RM
S di
spla
1.E-040 10 20 30 40 50 60 70 80 90 100
PCB accelerometers, Model# B393B04
Freq (Hz)
Vibration sensors : PCB accelerometers versus Geophone
Model# B393B04
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Geophone
Vibration Study-Sequence
DUMMY WEIGHTS3. GIRDER-
WEIGHTS
GIRDER 1. FREE
WEIGHTS
GIRDER 1. FREE GIRDER
2 SUPPORTEDSUPPORTS
2. SUPPORTED GIRDER
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Modal Analysis – FREE GIRDERy
1.00E+00
1.00E+01GROUND
Girder_left
Girder_right
First natural freq = 38 Hz
Second natural freq = 50 Hz
Bending mode 42 Hz
1.00E-02
1.00E-01
sqrt
(Hz)
) Twisting mode freq = 116 Hz
Second natural freq = 50 Hz
1 00E 04
1.00E-03PS
D (m
icro
n/s
Bending mode 58 Hz
1.00E-05
1.00E-04
1.00E-060 20 40 60 80 100 120 140 160 180 200
Freq (Hz)Twisting mode = 112 HzImpact testing: Horizontal impulse excitation provided byImpact testing: Horizontal impulse excitation provided by a soft-tipped hammer.Peaks in the PSD curve –natural frequenciesGood agreement between FEA and experiment
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Good agreement between FEA and experiment
Phase Correlation For The Free Girder
120140160180200
406080
100120
eg) 38 Hz phase = 0 Deg
-60-40-20
020
Phas
e (D
eBending mode-42 Hz
160-140-120-100-80-60Bending mode 42 Hz
-200-180-160
0 15 30 45 60 75 90 105 120 135 150
F (h )
116 Hz phase = 180 Deg
Freq (hz)
Twisting mode-112 Hz • Measured phase correlation agrees with the
mode shapes predicted by FEA
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Modal Analysis - Supported Girder
90
100
y (H
z)
70
80
Freq
uenc
y
40
50
60
1st M
odal
MODE I = 125 HZ 400 200 400 600 800 1000 1200 1400 1600 1800 2000
Torque (ft-lbs)
MODE I = 125 HZ
• Experimental observation: Natural frequency depends on the tightening torque on the threaded bolt supports
MODE I = 157 HZ
• First natural frequency increased from 40 Hz to 85 Hz, as the torque increased up to 1000 ft-lbs
• Beyond 1000 ft-lbs the effect is not very significant - 5
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MODE I = 157 HZ Beyond 1000 ft lbs the effect is not very significant 5 Hz at 2000 ft-lbs
FEA Model Calibration
Young’s modulus of the 2” bolt
• With the modification, the modal analysis
reduced by a factor of 10
ROCKING MODE yresults agree better with the measured natural frequency of the girder at 1000 ft-
ROCKING MODE
lbs
• FEA Rocking mode = 86 Hz (Measured →85 Hz)
• FEA Twisting mode = 110 Hz (Measured →120 Hz)TWISTING MODE
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120 Hz)TWISTING MODE
Girder - Weights
1.00E+00
1.00E+01Weight_LeftWeight_CenterWeight_Right
MODE 1 ~40 Hz
1 00E-02
1.00E-01
on/s
qrt(H
z)
Girder_LeftGirder_CenterGirder_Right
~40 Hz
1.00E-03
1.00E-02
PSD
,mic
ro
1.00E-05
1.00E-04
0 20 40 60 80 100 120 140 160 180 2000 20 40 60 80 100 120 140 160 180 200
Freq, Hz
• Modal analysis of the adjusted girder model with 5000 lbs weight5000 lbs weight
• FEA Rocking mode:45 Hz (Measured → 40 Hz)
• FEA Twisting mode:56 Hz (Measured → 60 Hz)
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Modal Analysis - Girder- Magnet Assemblyy g y
• The calibrated model was used to estimate the natural frequencies of the final girder-magnet system
• FEA Rocking mode = 34 HZ
• FEA Twisting mode = 51 HZ
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Vertical Power Density Spectra
1 00E+00
1.00E+01Dummy weight
Girder
1.00E-01
1.00E+00
qrt(H
z)
Ground
1.00E-03
1.00E-02
PSD
,mic
ron/
sq
RMS Displacement (4-100 Hz), nm
1.00E-04
Ground nm
Girder, nm (Amp.Fac)
Weight, nm (Amp. Fac)
1.00E-051 10 100
Freq, Hz
• * N i i t f th t t 79.0* 79.8 (~1) 83.3 (~1)• * Noisy environment for the test
• Expected ambient motion (4-100 Hz) for NSLS-II ~15 nm
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Horizontal Power Density Spectra
1.00E+00
1.00E+01Dummy Weight
Girder
G d
1.00E-01
/sqr
t(Hz)
Ground
1.00E-03
1.00E-02
PSD
,mic
ron/
1 00E 05
1.00E-04 RMS Displacement (4-100 Hz), nmGround Girder nm Weight nm1.00E-05
1 10 100Freq, Hz
Ground nm
Girder, nm (Amp.Fac)
Weight, nm (Amp. Fac)
40.3 46.0 (~1) 81 1 (~2)*• *Dummy weights not secured firmly on the ( ) 81.1 ( 2)girder
• Expect lower amplification for the magnets-bolted to the girder
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bolted to the girder
Conclusion
• For the final girder-magnet assembly first two natural frequencies are 34 Hz Tolerance
LimitsΔXRMS
ΔYRMS q
(Rocking mode) and 51 Hz (Twisting mode)
• Tolerance on the uncorrelated magnet
Limits RMS(nm)
RMS(nm)
Uncorrelatedmagnet
< 150 < 25Tolerance on the uncorrelated magnet motion can be easily met:
– Girder transmits ground motion without any amplification in 4-100 Hz (horizontally
magnetmotionUncorrelatedgirder motion
< 600 < 70any amplification in 4-100 Hz (horizontally and vertically)
– On top of the dummy weights, Amplification of the vertical ground
girder motion
RMS displacement for Amplification of the vertical ground motion ~1
– The anticipated ambient motion for NSLS-II in 4-100 Hz is 10 times smaller than the
pNSLS-II:
0.5-4 Hz = 400 nmhorizontal tolerance
– The tolerance requirements can be met
4-100 Hz = 15 nm
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Thank You !Thank You !
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