Stability of Mechanical Systems

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

2. Stability of Mechanical Systems • Stability: • Thermal • Vibration An NSLS-II Girder, Magnets, Vacuum Chamber Assembly • Systems: • Girder-magnets assembly • Vacuum chambers (BPMs) • Stands for special BPMs APS X-BPM Assembly with Support Stand

3. 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. Air Temperature Chamber cooling water temperature Fluctuations in the tunnel air and chamber water temperatures 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) Ambient Floor Motion RMS Displacements at CFN ( 0.5-4) Hz : 200 nm (4-50) Hz : 20 nm (50-100) Hz : 0.4 nm

12. 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

13. (b) (a) 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 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.