advanced ligo lateral tilt mechanical coupling study
Skip this Video
Download Presentation
Advanced LIGO Lateral/Tilt Mechanical Coupling Study

Loading in 2 Seconds...

play fullscreen
1 / 9

Advanced LIGO Lateral/Tilt Mechanical Coupling Study - PowerPoint PPT Presentation

  • Uploaded on

Advanced LIGO Lateral/Tilt Mechanical Coupling Study. Ken Smith January 8, 2004 Ref: 20008299-A. Overview.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Advanced LIGO Lateral/Tilt Mechanical Coupling Study' - leroy

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
advanced ligo lateral tilt mechanical coupling study

Advanced LIGOLateral/Tilt Mechanical Coupling Study

Ken Smith

January 8, 2004

Ref: 20008299-A

  • ASI’s understanding is that many of the LIGO design requirements are related to a desire to fully decouple the in-plane (lateral and torsion) and out-of-plane (vertical and tilt) stiffness of the mechanical system
    • The issues relate to tilt/horizontal confusion of the lateral seismometers, and the effect on low frequency control; thus the primary concern is with stiffness purity, and less so with coincidence of stage cg’s
    • Related requirements:
      • Coincidence of the actuator plane and the lower LZMP plane to 1 mm
      • Flatness of the spring blades
      • Other alignment requirements
  • Joe Giaime is in process of restating these requirements in terms of off-diagonal terms of the system stiffness matrix (or flexibility matrix)
  • These requirements have a direct effect on the design of the springs and flexures, so ASI has been investigating system performance in this regard
overview 2
Overview (2)
  • During our investigation, the following were observed:
    • Even the “ideal” isolation system, with perfect alignment of actuators and LZMP, has some coupling between lateral translation and tilt rotation due to gravity-related terms in the stiffness matrix
    • This coupling, though small, is not avoidable in the current design paradigm
    • The amount of coupling due to gravity is approximately 40 times larger than the coupling caused by 1 mm error in aligning the actuator plane with the LZMP plane
      • Misalignment error of 1 mm results in a virtual pivot point ~800m from the LZMP plane, in the absence of the gravity-induced coupling
      • The gravity-induced coupling results in a virtual pivot point ~20m from the LZMP plane
  • These observations prompted ASI to elevate the issue to the LIGO project
analysis approaches
Analysis Approaches
  • Three complementary analysis methods independently give evidence that the gravity-induced coupling effect is real
    • Free-body diagrams
    • Comprehensive closed-form solution of the flexure rod stiffness
    • NASTRAN finite element analysis with preload stiffening included
  • Each approach is described in more detail on the following pages
approach 1 free body diagrams
Approach 1: Free-Body Diagrams
  • Assume the flexure rods are rigid pin-ended links between the UZMP and LZMP; apply a lateral force V to stage 2 at the LZMP, and an opposite force to stage 1 at the LZMP (as the actuators will do)
  • Stage 2: applied forces are V and P2 (gravity load); reaction provided by stage 1 at UZMP. Note that moment balance implies P2d = Vh.
  • Stage 1: applied forces are V and P2 (from stage 2) and -V from actuator; reaction provided by stage 0. Moment balance implies thatstage 0 must provide a moment reaction Vh (= P2d)
  • The moment from stage 0 implies that the system will tilt



Stage 2

Stage 1









Actions shown in red

Reactions shown in green











approach 2 closed form flexure rod solution
Approach 2: Closed-Form Flexure Rod Solution
  • See ASI technical note 20007235-B, “Analysis of LIGO Flexure Rods”
  • Lateral/tilt stiffness matrix of a single flexure rod:

This term shows that a moment is

reacted to the supporting stage from

a shear through the LZMP (the first

column of the stiffness matrix gives

the forces/moments to induce a

unit translation with zero rotation)

  • Lateral displacements v and tilt
  • rotations q at LZMP
  • subscript 3 = suspended stage
  • subscript 5 = supporting stage
  • Shear forces V and moments M at LZMP
  • subscript 3 = suspended stage
  • subscript 5 = supporting stage
approach 3 nastran finite element model
Approach 3: NASTRAN Finite Element Model
  • Developed a simplified model of the idealized system
    • Stage 0 is ground
    • Stages 1 and 2 are rigid bodies, with mass properties similar to ETF
    • Leaf springs idealized as vertical-only spring elements, rigid in other directions
    • Flexure rods modeled as bar elements, with preload-induced stiffening
    • Stage cg’s and actuation planes perfectly located at LZMP of flexure rods
nastran model

Stage 0: GROUND

Stage 0/1 springs and flexures

r = 25 in

Stage 1: 1914 lb

RTOR = 22.3 in, RTILT = 16.4 in

Stage 1/2 springs and flexures

r = 25 in

Stage 2: 3470 lb

RTOR = 19.5 in, RTILT = 18.7 in

Model shown “stretched”; stages are actually coincident under 1g

model results
Model Results
  • Stage displacements from 1 lb force applied to stage 2 and reacted at stage 1 (in plane of LZMP) in the X direction at the stage centers
  • Ratio of translational displacement to tilt rotation is approximately 675”
  • Effect of 0.04” misalignment is approximately 1/40th as severe

Case 1: Perfect alignment of forces with LZMP

Case 2: Forces applied 0.04” above the LZMP

Case 3: Forces applied 0.04” below the LZMP

Stage 1 tilt unaffected by misalignment

Stage 2 tilt slightly affected by misalignment,

but misalignment effects are much smaller

than the bias seen in the “perfect” case 1