T1300414 Faraday Isolator Blade Creep
6/17/13
acceleration of gravity, m/s^2
Faraday Isolator upper blade spring
E correction factor (see p. 4)
new modulus of elasticity, Pa
modulus of elasticity, psi
Weight suspended
OFI without balance wts, lb
variable balance wt, lbs
design weight, lbs
suspended mass, kg
yield stress of C-250 steel, Pa
yield stress of C-250 steel, psi
factor of safety (see p. 4)
working stress of C-250 steel, Pa
working stress of C-250
steel, psi
number of springs
mass supported by each
blade spring, kg
load on blade spring, N
arc of blade spring, rad
blade arc angle, deg
horizontal distance of suspension point from blade spring mount, in
mounting location of blade spring
left of center, m
radius of blade spring, m
radius of blade spring, in
length of blade spring, m
length of blade spring, in
design width, in
Calculate thickness
thickness of blade spring, in
incremental weight change
with δt inch increase
in thickness, lbs
maximum stress, Pa
maximum stress, psi
factor of safety
Vertical Bounce Frequency
vertical height of suspension
from blade spring mount, m
vertical height of suspension
from blade spring mount, in
unloaded height of blade spring, m
vertical distance blade moves, m
vertical distance blade moves, in
vertical resonant frequency based on blade depression, Hz
effective spring constant, N/m
effective spring constant, N/m
incremental force for
0.25 lb weight change, N
height change with 0.25 lb
added weight, m
volume of suspended OFI, in^3
volume of suspended OFI, m^3
density of air, kg/m^3
effective reduction in mass during
pumpdown, kg
height change due to change in
effective mass, m
height change vs temperature
Modulus variation with temperature, Pa/degC
(ref: Lisa Bates, et al; p.9 Vol 18, #1 Journal of Undergraduate Researach in Physics, and De Salvo P070095)
Effective spring constant variation with temp, N/m-degC
Effective height variation with temp, m/degC
Blade height change with long-term creep
ref: De Salvo P070095
blade spring elongation
under load, m
long-term creep elongation, m
effective balance weight loss
of blade due to initial creep aging, lbs
Pendulum Frequency
length of pendulum, m
pendulum frequency, Hz
CREEP RATE THEORY
Boltzmann's constant1.38*10^-23, J/K
Dislocation activation energy, J
Temperature of blade, deg C
vertical deflection of blade under load, m
maximum vertical creep, m
maximum creep strain, m/m
based on the DeSalvo-SURF data
probability of dislocation activation
time interval of applied load, day
activation rate constant, day^-1
total number of available dislocations
per unit vertical
activation rate of dislocations
number of dislocation events per unit vertical
deflection of blade after interval t
vertical deflection of blade per
dislocation event
integrated vertical creep of blade after time t, m
maximum vertical creep, m
maximum vertical creep strain, m/m
Then, integrated vertical creep of blade after time t, m
initial creep rate, m/day
Riccardo-SURF data (Ref: LIGO P070095-02-Z
initial blade deflection under load, m
maximum stress, Pa
SURF Creep data
least squares fit of activation energy, activation rate, maximum creep t o creep data
First Iteration
Guess activation energy, J
Guess activation rate constant, day^-1
Guess maximum creep, m
Creep theory, m
difference between data and theory at each data point
Second Iteration
Guess activation energy, J
Guess activation rate constant, day^-1
Guess maximum creep, m
activation energy, J
activation energy, eV
activation rate constant, day^-1
maximum creep, m
maximum vertical creep strain, m/m
Creep relaxation time, days
Riccardo-Surf Data compared with theory for each temperature run
VIRGO data
initial deflection of blade under load, m
maximum stress, N/mm^2
maximum stress, Pa
VIRGO Creep data
First Iteration
least squares
fit of activation energy,
activation rate, maximum creep t
o creep data
theoretical creep vs time, m/day
difference between data and theory at each data point
Guess activation energy, J
Guess activation rate constant, day^-1
Guess maximum creep, m
Second Iteration
Guess activation energy, J
Guess activation rate constant, day^-1
Guess maximum creep, m
activation energy, J
activation energy, eV
activation rate constant, day^-1
maximum creep, m
maximum vertical creep strain, m/m
VIRGO creep Data compared with theory for each temperature run
VIRGO Initial Creep Rate data
First Iteration
least squares
fit of activation energy and
activation ratet
o creep data
maximum creep, m
theoretical initial creep rate, m/day
difference between data and theory at each data point
Guess activation energy, J
Guess activation rate constant, day^-1
Second Iteration
Guess activation energy, J
Guess activation rate constant, day^-1
maximum strain, m/m
activation energy, J
activation energy, eV
activation rate constant, day^-1
inverse absolute temp, K^-1
Summary of SURF and VIRGO parameters
SLC Data
maximum stress, Pa
maximum stress, N/mm^2
loaded deflection of blade, m
creep parameters based on VIRGO Data
maximum strain, m/m
maximum creep, m
activation energy, J
activation rate constant, day^-1
theoretical creep vs time, m/day
use the VIRGO parameters
10 year time period, days
maximum creep @ 27 deg C for
10 years, m