Design and Test of TunedMass Damper for LIGOMEPI Isolator

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Design and Test of Tuned-Mass Damper for
LIGO/MEPI Isolator

• Lei Zuo
• Samir Nayfeh
• Richard Mittleman
• April 30, 2003

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• This report documents the design and test of a
  TMD for MEPI system
• It includes the design formulas and a practical
  design procedure.

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LIGO/MEPI Y-Mode TF

• 0.5
• Q100

Magnitude
Phase, deg
Frequency, Hz
A mode at 51Hz limits the gain of Y-mode control
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Vibration Mode at 51 Hz
bending of the stiffening beam and gull wing
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Damp the 51 Hz Mode

• Tuned mass damper (TMD)
• Piezoelectric Damping
• a) Resistor shunt same result as viscoelestic
  damping
• b) Resistor-inductor shunt similar to TMD
• Constraint-Layer Damping (viscoelestic)

• The effects of piezoelectric damping and
  constrained-layer damping are dependent on the
  distribution of strain-energy.
• The effect of a TMD depends on the motion
  magnitude at mounting point.

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Tuned Mass Damper
md
kd
cd
Ms
F
Primary System Ms, ?s, ?s Absorber System
md, ?d, ?d.
Frequency ?/?s

• Tuning rule (for small ?s) for a given mass
  ratio ?md/Ms
• Tuning frequency
• Damping ratio

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Concept of Equivalent Mass

• To design the TMD, we need to know the Equivalent
  Mass Ratio of the 51 Hz mode seen from the TMD
  location
• Suppose v1, v2, vn are the mode shapes, we can
  obtain the equivalent mass of this mode
  at the point r base on the relation of total
  kinetic energy
• TMD should be located in the place where the
  motion magnitude is large (Meq is small)

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Measurement of Equivalent Mass

• Method of adding mass
• add a small mass at the location where the TMD
  will be located, and measure the frequency shift

m
Ms
Ms

• Ms690kg, seen from the middle of front
  stiffening beam
• Ms 770kg, seen from the middle of back beam

Magnitude
Frequency (Hz)
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Parameter Design and Tuning

• Putting an absorber md14 kg on the middle of
  front cross beam, then ?md/Ms 14/690,
• kd1.42x106 N/m, cd 6.29x102 Ns/m
• ?d50.7 Hz, ?d7.05
• If we use viscoelastic damping in this TMD, the
  desired loss factor
• ?d ? 2 ?d 0.141
• Stiffness, damping, and fine tuning

absorber weight
Viscoelastic EAR-C1002 Steel
Adjust the supporting length
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Design for kd and ?d
Stiffness kd, N/m
Loss factor ?d
Length L, mm
Note 1, Loss factor should be designed a little
larger than the desired value, since non-perfect
binding Note 2, Stiffness tuning is more
important than loss factor tuning.
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Hardware Construction
Beam with constrained-layer damping
md
kd(1 j?d)
Assembly
Pre-test
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Installation
md
kd(1 j ?d)
Ms
Fine tuning
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Result Y-mode (Zoom)
A factor of 5
Magnitude
Phase, deg
51 Hz mode is damped well.
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Result Y-Mode
Magnitude
Phase, deg
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Result Rotation about Y
Magnitude
Phase, deg
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Collocated Transfer Function
Magnitude
Phase, deg
It might be better to install another TMD on the
back beam, to keep symmetry. But asymmetry is ok,
since the TMD will not have much effect on other
mode.
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Clamp TMD to the Crossing Beam
Slotted holes
OR
10-32 screw
stiffening beam
Constrained-layer beam
Slotted holes
OR
Note slotted holes are made so that the
stiffness can be fine tuned
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Conclusions

• A tuned mass damper (TMD) has been designed and
  tested to damp the mode at 51Hz of LIGO MEPI
  system.
• Very effective to damp a single mode 5x
  reduction achieved
• Its design procedure is very simple and
  practical. Its construction is easy a mass and a
  spring with proper stiffness and loss factor.