Stability of Mechanical Systems S. Sharma and V. Ravindranath.
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Transcript of Stability of Mechanical Systems S. Sharma and V. Ravindranath.
Stability of Mechanical Systems
Stability:
• Thermal• Vibration
Systems:
• Girder-magnets assembly• Vacuum chambers (BPMs)• Stands for special BPMs
An NSLS-II Girder, Magnets, Vacuum Chamber Assembly
APS X-BPM Assembly with Support Stand
Tolerance Limits ΔX RMS Quads ΔY RMS Quads
Random magnet motion < 0.15 μm < 0.025 μm
Random girder motion <0.6 μm < 0.07 μm
Tolerances on Magnets’ Motion
ΔX Tolerance limits are easily achievable.
ΔY Tolerance limits:
Thermal: relative thermal displacement between magnets on the same girder: < 0.025 μm. (RMS thermal displacement of girders over a pentant (6 cells) < 0.1 μm)
Vibration: no magnification of ambient floor motion up to 50 Hz.
• Below 4 Hz girder motions are highly correlated• Above 50 Hz the rms floor motion is < 0.001 μm
Tolerances on BPMs
BPMs mounted on vacuum chambers: ± 0.2 μm (vertical)
User BPMs (upstream and downstream of IDs) : ± 0.1 μm (vertical)
X-BPMs: ± 0.1 μm (vertical)
BPMs in a Typical Cell
Fluctuations in the tunnel air and chamber water temperatures
Air Temperature
Chamber cooling water temperature
25
25.02
25.04
25.06
25.08
25.1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Time (hrs)
Tem
pera
ture
(Deg
C)
Stability of Tunnel Air and Cooling Water Temperatures
Tunnel air: ± 0.1 ºC Cooling water: ± 0.05 ºC
FE Thermal Analysis
The girder is insulated by 2” thick mineral wool insulation except on the top surface.
Stainless steel plates supporting the chamber are insulated with 1” thick insulation.
Max. ΔT in girder: ~0.01 ºCAvg. ΔT in SS plates : ~0.02 ºC
Thermal Deformations
Magnets:Relative displacement on a girder: 0.01 μm
Average displacement of girders over a pentant: 0.09 μm
Vacuum Chamber:Near fixed and flexible supports (SS plates): 0.2 μm
Maximum: 1.2 μm
• Chamber deformations near the supports are ~ 0.15 μm with Invar plates. • BPMs need to be located near the fixed or flexible supports.
25
25.004
25.008
25.012
25.016
25.02
25.024
25.028
0.00 0.10 0.20 0.30 0.40 0.50
Time (hrs)
Tem
per
atu
re (
Deg
C)
Sand
Steel
Insulation
Concrete
FE Thermal Analysis
Temperature rise in the thermally insulated, sand-filled steel stand is limited to 0.004 ºC
Thermal Deformations – Steel Support Stand
Maximum thermal deformation (expansion/contraction) is limited to 0.013 μm as compared to the tolerance of 0.1 μm.
Displacement PSDs at locations near the NSLS-II site(Source: N. Simos)
RMS Displacements at CFN
( 0.5-4) Hz : 200 nm (4-50) Hz : 20 nm(50-100) Hz : 0.4 nm
Ambient Floor Motion
Design Approach
Stiff girder-magnets assemblies 1st natural frequency > 50 Hz
Low profile girders mounted directly on the floor Simple alignment mechanisms for the girders and the magnets
Natural modes of vibration for the girder-magnets assembly: (a) rolling mode = 63 Hz, (b) twisting mode = 79 Hz
RMS (2-50) Hz Displacements:Floor: 20 nm
Magnets: 21 nm
(b)(a)
Mode Shapes of the Girder-Magnets Assembly
Summary and Conclusions
Specifications on temperature stability and ambient floor motion are reasonable and necessary.
Proposed designs of the girder, magnets and vacuum chamber assemblies will be able to meet the specifications on mechanical stability.
BPMs on the vacuum chambers need to be located near the fixed or flexible supports.
Thermally insulated, sand-filled steel stands will meet the mechanical stability requirements for the special BPMs.