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.

Thermal Deformations in the Support Stands for Special BPMs

Thermally Insulated Steel Stand

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.