Design of Accelerator Girder System for Vibration Suppression

S. Sharma 

Ambient Ground Motion 

NSRRC/July 21, 2005 

Design of Accelerator Girder System for Vibration Suppression 

by 

Sushil Sharma 

Contributors: B. Rusthoven, V. Ravindranath and C. Doose 

Mechanical Engineering Group 

Accelerator Systems Division

Outline 

S. Sharma 



An overview of some storage ring girder systems 

Ambient ground motion 

Transmissibility and damping 

Girder design (materials, geometry and alignment) 

Conclusion 



Girder vs. Table 

A girder is used for several purposes: 

1. Provides common platform (strongback) to 

precisely mount several components. 

2. Raises components to nominal beam height 

(acts as a spacer). 

3. Simplifies installation and alignment of the 

components in the accelerator ring. 

4. Expedites realignment (e.g. to compensate for 

floor settlement). 

The girder, however, adds another structural element to the system. This 

adversely impacts beam stability due to amplification of floor motion and thermal 

deformations. 

S. Sharma 




Accelerator Systems Division 

Girder 

Pedestal 

APS Storage Ring 

Table 

APS Linac Bunch Compressor

APS Girder System 

First natural frequency is ~ 10 Hz 

(Rocking with high center of mass) 

Higher frequencies (>23 Hz) � quads motion 

Vibration amplification (rms 4-50 Hz): 

no damping: 9 

damping with viscoelastic pads: 3 

damping with pads and shims: 1.5 (~ 35 nm) 

S. Sharma 





Wedge Jack 

Doose, Sharma [MEDSI 2002]

SPring-8 Girder System 

High first natural frequency. 

Stiff alignment mechanism. 

Six support points. 

Vibration amplification: 1.9 (48 nm) * 

Vibration of chambers (not magnets) 

dominates orbit fluctuations. Nakazato et al. 

[MEDSI 2002] 

* Sharma et al., [GMV 2000] 

S. Sharma 



Mode ω n 

1(H) 18.9 

2(H) 21.3 

3(V) 25.6 

4(V) 29.5 

5(H) 29.6 

Vertical Alignment 



http://epaper.kek.jp/p01/PAPERS/TPAH117.PDF [2001]

ESRF Girder System 

The girder system has several low natural 

frequencies. 

Vibration amplification 

without damping: 2.2 

with viscoelastic damping link: 1.3 (40 nm) 

S. Sharma 





Sharma et al. [GMV 2000] 

Mode Test 

(Hz) 

1 8.68 

2 11.74 

3 13.63 

4 22.33 

5 26.29 

http://www.esrf.fr/machine/reports/sassenage02/ 

presentations/zhang.pdf

NSRRC Girder System 

First natural frequency – horizontal rolling: ~ 15 Hz. 

Simple alignment hardware (threaded rods). 

Cross-talk of flow-induced vibrations in magnets and 

vacuum chamber. 

Vibration amplification: 

S. Sharma 



no damping: 1.8 

damping with viscoelastic pads: 1.3 (92 nm) 



Courtesy, D.J Wang, May 2005 

Sharma et al. [GMV 2000]

SLS Girder System 

Diamond and Boomerang girders are of 

similar design. 

Magnets are clamped to precisely machined 

girder’s surface. 

The magnet support (girder) shows a number 

of resonances in 15 Hz to 50 Hz frequency 

range. 

Without cam movers, the calculated 

frequencies can be quite high (f1 = 60 Hz for 

Diamond girder, N. Hammond, MEDSI 2002 ). 

Vibration amplification (rms above 4 Hz): 10 

S. Sharma 





Cam Mover (SLS) 

Machined Top Plate 

http://slsbd.psi.ch/pub/varia/dynal_iwbs04.pdf 

S. Redaelli et al., EPAC 2004 THPK011

LCLS Girder System 

Cam movers are used for beam-based alignment. 

Cams are attached to the upper girder flange to 

minimize thermal deformations and to lower center 

of mass. 

Mode-1 (67.9 Hz) Mode-2 (76.9 Hz) Mode-3 (79.8 Hz) 

S. Sharma 



The first four modes correspond to girder deformations 

(flexure, torsion, flexure, and flexure). 

Modes 5 corresponds to undulator torsion. 



Mode-4 (99.0 Hz) 

Mode-5 (128.8 Hz)

Ground Motion Characteristics 

Seryi [2003] 

http://www.desy.de/~njwalker/uspas/coursemat/pp/unit_8.ppt#10 

S. Sharma 





Sharma et al. [GMV 2000] 

Ground motion amplitude drops sharply at higher frequencies. The first natural 

frequency of the support system (girder/magnets + alignment mechanism) 

should be as high as possible (preferably, f 1 >20 Hz).

Transmissibility 

n = ω 

ξ = 

2 

c 

k 

mk 

m 

Transmissibility 

S. Sharma 



= fraction of critical damping 

= 

Y 

X 

= 

4ξ 

2( 

ω / ω 2 

n) 

+ 1 

[ 1−( 

ω / ω ) 2] 

2 4 2( 

/ ) 2 

n + ξ ω ωn 

For vibration isolation: 

• Systems on soft supports (ω/ω n > √2) � no damping. 

• Systems on very stiff supports (ω/ω1

Systems on Soft Supports 

Seismic Isolation and Suspension 

Systems for Advanced LIGO 

http://www.ligo.org/pdf_public/techpapers_robertson.pdf 

[2003] 

S. Sharma 



� Limited to comparatively low mass. 



http://www.minusk.com/

Damping 

ξ = fraction of 

η = loss 

Q = quality 

factor 

factor 

S. Sharma 



critical 

damping 

1 ω 2 −ω 

1 

2ξ 

= = = η 

Q ω 

System Viscous Damping, ξ 

Metals in elastic range < 0.01 

Steel 0.001 – 0.002 

Continuous Metal Structures 0.02 – 0.04 

Metal Structures with Joints 0.03 – 0.04 

Reinforced Concrete Structures 0.04 – 0.07 m&y 

& + k( 

1+ 

iη)( 

y − x) 

= 0 

H. Bachmann et al., Vibration Problems in Structures, Birkhauser Verlag, 

Berlin, 1995. 

V. Adams and A Asknazi, Building Better Products with Finite Element 

Analysis, OnWord Press, Sata Fe, N.M., 1999. 



n 

Amplitude 

ymax 

y 

max 

2 

ω 1 

ω n 

ω 2 

Frequency 

m&y 

& + c( 

y& 

− x& 

) + k( 

y − x) 

= 0 

y max

Girder Design - Material Properties 

Misc. Sources 

Flexural Vibration: 

π ⎡ EI ⎤ 

f1 

≈ ⎢ 3 ⎥ 

2 ⎣ L ( M + M b) 

⎦ 

S. Sharma 



1/ 

2 

* Bowden [SLAC-TN-05-028, 2002] 



Comparison (for same I and L) 

Al Steel Anocast Gr. Epoxy 

Frequency (M>>Mb) � E 1/2 8.3 14 6 8 

Thermal Bending � α/k * 0.13 0.23 0.70 0.2 

Thermal Expansion � α 23.4 12 16.9 2.7

Deflection/Force (in/lbf) 

Girder Design - Anocast Polymer Composite 

Seconds 

Anocast damps vibrations more 

rapidly than aluminum, cast iron, or 

granite, by a factor of 45, 10 and 4, 

respectively. 

S. Sharma 



Seconds 



Seconds 

Seconds 

http://www.rockwellautomation.com/anorad/downloads/ 

pdf/Anocast.pdf 

http://www-project.slac.stanford.edu/lc/local/notes/tset/Mover/ 

mover_notes_oct12_post.pdf

Girder Design - External Viscoelastic Damping 

Materials with high structural (internal) damping 

may have lower thermal performance: 

L (0.5m) α (20μm/m.ºC) ΔT(0.1ºC) = 1μm 

Viscoelastic polymers have high loss factor. 

Viscoelastic films absorb vibrational energy 

by high cyclic shear deformations. 

Many viscoelastic materials are creep and 

radiation resistant. 

Viscoelastic damping pads (or damping links) 

are simple in design and can reduce rms 

vibration amplification to ~ 1.2 

S. Sharma 



APS Damping Pad and Shim 



Temperature 

http://casl.ucsd.edu/data_analysis/nomograms/isd112.htm 

ESRF Damping Link 

3M – ISD112 

Frequency

Girder Design – Geometry and Supports 

• A box-type cross section is preferable for high stiffness in flexure (both directions) 

and torsion. 

• Full-length welds, gussets and plate stiffeners can significantly increase the 

overall stiffness. 

SPring-8 Boomerang Diamond 

CLS APS 

• Unsupported length of the girder should be kept as small as possible 

(SPring–8 girders are supported at six points). 

Supports at Airy Points 3–Point Support 

CLS Boomerang 

S. Sharma 





Girder Design - Alignment Mechanisms 

Threaded Rod 

Six-Strut System 

S. Sharma 



Threaded Rod with 

Lateral Adjustments 

(APS) 

Cartridge Adjuster 

(CEBAF) * 

Wedge Jack (APS) 

Motorized Jack (ESRF) 

* Other Concepts [1994] http://www-group.slac.stanford.edu/met/IWAA/TOC_S/Papers/RRula95a.pdf 



http://wwwgroup.slac.stanford.edu/met/IWAA/TOC_S/ 

PAPERS/KTsum02.pdf 

SPring-8 Alignment 

http://accelconf.web.cern.ch/AccelConf/ 

e00/PAPERS/WEP4A17.pdf 

Cam Mover (SLS)

Conclusion 

Viscoelastic 

Film 

S. Sharma 



Low center-of-mass to reduce vibrations (and thermal deformations). 

- Why a beam-height of 1.4 m? 

Compromise between high stiffness and ease-of-alignment: 

- Simple alignment mechanism. 

- Fasten magnets directly on precisely machined girder’s surface. 

Reduce flow-induced vibrations and cross-talk by viscoelastic damping. 

Vibration mitigation should not be at the expense of thermal stability. 

Belleville Washers 

A Support Concept 

Graphite-Epoxy 

Locating Slot 



No Girder ! 

CLS 

SPring-8

Design of Accelerator Girder System for Vibration Suppression

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