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Stability of Mechanical Systems S. Sharma and V. Ravindranath.

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Presentation on theme: "Stability of Mechanical Systems S. Sharma and V. Ravindranath."— Presentation transcript:

1 Stability of Mechanical Systems S. Sharma and V. Ravindranath

2 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

3 Tolerance LimitsΔX RMS QuadsΔY 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

4 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

5 Fluctuations in the tunnel air and chamber water temperatures Air Temperature Chamber cooling water temperature Stability of Tunnel Air and Cooling Water Temperatures Tunnel air: ± 0.1 ºC Cooling water: ± 0.05 ºC

6 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 ºC Avg. ΔT in SS plates : ~0.02 ºC

7 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.

8 Thermal Deformations in the Support Stands for Special BPMs Thermally Insulated Steel Stand

9 FE Thermal Analysis Temperature rise in the thermally insulated, sand-filled steel stand is limited to 0.004 ºC

10 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.

11 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

12 Design Approach Stiff girder-magnets assemblies  1 st natural frequency > 50 Hz  Low profile girders mounted directly on the floor  Simple alignment mechanisms for the girders and the magnets

13 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

14 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.


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