vibrations of machine foundations
DESCRIPTION
Vibrations of Machine Foundations. Richard P. Ray, Ph.D., P.E. Civil and Environmental Engineering University of South Carolina. Thanks To: Prof. Richard D. Woods, Notre Dame Univ. Prof. F.E. Richart, Jr. Topics for Today. Fundamentals Modeling Properties Performance. - PowerPoint PPT PresentationTRANSCRIPT
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Vibrations of
Machine Foundations
Richard P. Ray, Ph.D., P.E.Civil and Environmental Engineering
University of South Carolina
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Thanks To:Prof. Richard D. Woods, Notre Dame Univ.
Prof. F.E. Richart, Jr.
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Topics for Today
Fundamentals Modeling Properties Performance
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Foundation Movement
X
Z
Y
θ
ψ
φ
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How Does It Fail? Static Settlement Dynamic Motion Too Large (0.02 mm is large) Settlements Caused By Dynamic Motion Liquefaction What Are Maximum Values of Failure?
(Acceleration, Velocity, Displacement)
Design Questions (1/4)
Fundamentals-Modeling-Properties-Design-Performance
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Velocity Requirements
Massarch (2004) "Mitigation of Traffic-Induced Ground Vibrations"
Fundamentals-Modeling-Properties-Performance
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Design Questions (2/4)
What Are Relations Between Loads And Failure Quantities Loading -Machine (Periodic), Impluse, Natural Relations Between Load, Structure, Foundation,
Soil, Neighboring Structures Generate Model: Deterministic or Probabilistic
Fundamentals-Modeling-Properties-Performance
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Design Questions (3/4)
How Do We Measure What Is Necessary? Full Scale Tests Prototype Tests Small Scale Tests (Centrifuge) Laboratory Tests (Specific Parameters) Numerical Simulation
Fundamentals-Modeling-Properties-Performance
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Design Questions (4/4)
What Factor of Safety Do We Use? Does FOS Have Meaning What Happens After There Is Failure
Loss of Life Loss of Property Loss of Production
Purpose of Project, Design Life, Value
Fundamentals-Modeling-Properties-Performance
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r -2 r -2 r -0.5
r -1
r -1
r
Shear wave
Vertical component
Horizontal component
Shear window
Rayleigh wave
Relative amplitude+
+
+
+
- -
+
+
Wave Type Percentage of
Total Energy
Rayleigh 67
Shear 26
Compression 7
Waves
Fundamentals-Modeling-Properties-Performance
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Modeling Foundations Lumped Parameter (m,c,k) Block System
Parameters Constant, Layer, Special Impedance Functions
Function of Frequency (ω), Layers Boundary Elements (BEM)
Infinite Boundary, Interactions, Layers Finite Element/Hybrid (FEM, FEM-BEM)
Complex Geometry, Non-linear Soil
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Lumped Parameter)sin( tPP o
m
Gk
m
cν ρ
)sin(0 tPkzzczm
r
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SDOF
222
21
1
nn
D
static
dynamic
A
AMag
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Lumped Parameter System
Kx
Z
ψ
KzCz
Cx
Kψ
Cψ/2 Cψ/2
X
)sin(0 tPzkzczm zzz
mkcccD crcr 2
m
kn
mIψ
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Lumped Parameter Values
Mode Vertical Horizontal Rocking Torsion
Stiffness k
Mass Ratio m
Damping Ratio, D Fictitious
Mass
1
4Gr
2
8Gr)1(3
8 3
Gr
3
16 3Gr
5r
I
38
)2(
r
m
34
)1(
r
m
2/1ˆ425.0
m 2/1ˆ288.0
m2/1ˆ)ˆ1(
15.0
mm m̂21
50.0
m
mˆ
27.0m
mˆ
095.0
m
I x
ˆ24.0
m
I z
ˆ24.0
m̂
D=c/ccr G=Shear Modulus ν=Poisson's Ratio r=Radius ρ=Mass Density Iψ,Iθ=Mass Moment of Inertia
58
)1(3
r
I
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Mass Ratio
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Design Example 1VERTICAL COMPRESSOR
Unbalanced Forces
•Vertical Primanry = 7720 lb
•Vertical Secondary = 1886 lb
•Horzontal Primary = 104 lb
•Horizontal Secondary = 0 lb
Operating Speed = 450 rpm
Wt Machine + Motor = 10 900 lb Soil Properties
Shear Wave Velocity Vs = 680 ft/sec
Shear Modulus, G = 11 000 psi
Density, γ = 110 lb/ft3
Poisson's Ratio, ν = 0.33
DESIGN CRITERION:
Smooth Operation At Speed
Velocity <0.10 in/sec
Displacement < 0.002 in
Jump to Chart
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rGr
Q
k
QA
zzs
000114
)18857720(667.0
4
)1("002.0 00
'07.6"8.72 r
"002.0
2
10.166.0
ˆ
425.0
42.018.61104
9006467.0
4
)1(ˆ
33
staticzdynamicz
z
AA
DM
mD
g
g
W
rm
Try a 15 x 8 x 3 foundation block, Area = 120 ft2 and r = 6.18 ft
Weight = 54,000 lb Total Weight = 54 000 + 10 900 = 64 900
Jump to Figure
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Design Example - Table Top18'
34'
18'11'
Q0=400 lb
ψ
W=550 000 lb
Iψ=2.88 x 106 ft-lb-sec2
Soil Properties
Shear Wave Velocity Vs = 770 ft/sec
Shear Modulus, G = 14 000 psi
Density, γ = 110 lb/ft3
Poisson's Ratio, ν = 0.33
DESIGN CRITERION
0.20 in/sec Horizontal Motion at Machine Centerline
Ax = 0.0015 in. from combined rocking and sliding
Speed = 160 rpm
Slower speeds, Ax can be larger
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Horizontal Translation Only
inGr
Q
k
QAMag
mD
r
mmft
cdrtEquivanlen
xstaticxx
5002/1
3
100.32
80.1465.0
ˆ288.0
38.08
2ˆ96.13
341844
Rocking About Point "O"
.7200184006.509.0ˆ)ˆ1(
15.0
83.0)04.12(
2.32110
1088.2
8
)67.0(3
8
)1(3ˆ
/101088.2
1090.2/1090.2
33.02
04.12)14400014(8
2
8
/5.121200.123
91716
3
16
5
6
5
6
88
4
3
4
3
lbsftMMomentStaticMagmm
D
r
Im
secradI
kftlb
Grk
secradrpmftcd
rEquivalent
o
n
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.106.5)100.1(6.5
100.1)1218(10
50.0
10
50.0
109.2
)67.0(37200
44
46
68
inResonanceAt
inhAMotionHorizontal
radk
MDeflectionAngularStatic
sxs
os
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Impedance Methods
Based on Elasto-Dynamic Solutions Compute Frequency-Dependent Impedance
Values (Complex-Valued) Solved By Boundary Integral Methods Require Uniform, Single Layer or Special Soil
Property Distribution Solved For Many Foundation Types
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Impedance Functions
)sin()cos( titPePP oti
o
SOILSTATIC
z
zz D
KCikKCiK
A
RS
2
)(
Radiation DampingSoil Damping
Jump Wave
Sz
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Impedance Functions
Luco and Westmann (1970)
sV
r
Gra
0
Fundamentals-Modeling-Properties-Performance
ψ
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Layer Effects
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Impedance Functions
Fundamentals-Modeling-Properties-Performance
ψ
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Boundary Element
Stehmeyer and Rizos, 2006
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B-Spline Impulse Response Approach
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Finite/Hybrid Model
tie pzKzM
22 1221* iGG
pZMK
Zz
2
thene ti
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Dynamic p-y Curves
Tahghighi and Tonagi 2007
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Soil Properties Shear Modulus, G and Damping Ratio, D
Soil Type Confining Stress Void Ratio Strain Level
Field: Cross-Hole, Down-Hole, Surface Analysis of Seismic Waves SASW
Laboratory: Resonant Column, Torsional Simple Shear, Bender Elements
Fundamentals-Modeling-Properties-Performance
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Crosshole TestingOscilloscope
PVC-cased Borehole
PVC-cased Borehole
DownholeHammer (Source) Velocity
Transducer (GeophoneReceiver)
t
x
Shear Wave Velocity:Vs = x/t
TestDepth
ASTM D 4428
Pump
packer
Note: Verticality of casingmust be established by
slope inclinometers to correctdistances x with depth.
SlopeInclinometer
SlopeInclinometer
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Resonant Column Test
G, D for Different γ
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Torsional Shear Test
Schematic Stress-Strain
Fundamentals-Modeling-Properties-Performance
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Hollow Cylinder RC-TOSS
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TOSS Test Results
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Steam Turbine-Generator(Moreschi and Farzam, 2003)
Fundamentals-Modeling-Properties-Performance
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Machine Foundation Design Criteria
Deflection criteria: maintain turbine-generator alignment during machine operating conditions
Dynamic criteria: ensure that no resonance condition is encountered during machine operating conditions
Strength criteria: reinforced concrete design
Fundamentals-Modeling-Properties-Performance
Jump to Resonance
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STG Pedestal Structure
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Vibration Properties Evaluation
Identification of the foundation natural frequencies for the dominant modes
Frequency exclusion zones for the natural frequencies of the foundation system and individual structural members (±20%)
Eigenvalue analysis: natural frequencies, mode shapes, and mass participation factors
Fundamentals-Modeling-Properties-Performance
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XYZ
XYZ
Finite Element Model Structure and Base
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Low Frequency Modes
1st mode6.5 Hz
95 % m.p.f.
2nd mode7.2 Hz
76 % m.p.f
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High Frequency Modes
28th mode46.3 Hz
0.3% m.p.f
42nd mode64.6 Hz
0.03% m.p.f
Excitation frequency: 50-60 Hz
Fundamentals-Modeling-Properties-Performance
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Local Vibration Modes
Identification of natural frequencies for individual structural members
Quantification of changes on vibration properties due to foundation modifications
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ATST Telescope and FE Model
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Optics Lab mass/Instrument weight = 228 tons Wind mean force = 75 N, RMS = 89 N Ground base excitation PSD = 0.004 g2/hz Concrete Pier
High Strength Concrete (E=3.11010 N/m2, =0.15)
Soil Stiffness, k Four different values using Arya & O’Neil’s
formula based on the site test data (Shear modulus:30~75ksi, Poisson’s ratio:0.35~0.45)
Assumptions in FE analyses
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• Soil property range: Shear modulus (30~75ksi), Poisson’s ratio (0.35~0.45)
• Pier Footing: Diameter (23.3m)
• “min” for shear modulus of 30 ksi; “max” for 75 ksi
Frequency vs Soil Stiffness
Stiffness min min+33.3% min+66.6% maxKx 1.19E+10 1.83E+10 2.48E+10 3.12E+10Ky 1.19E+10 1.83E+10 2.48E+10 3.12E+10Kz 1.48E+10 2.45E+10 3.41E+10 4.38E+10Krx 1.34E+12 2.21E+12 3.09E+12 3.96E+12Kry 1.34E+12 2.21E+12 3.09E+12 3.96E+12Krz 1.74E+12 2.61E+12 3.49E+12 4.36E+12
6.3 7.0 7.4 7.56.4 7.1 7.5 7.79.4 9.7 9.9 109.4 10.3 11.1 11.810.4 11.9 12.6 13.311.2 13.0 13.6 13.7
4
5
6
MODE1
2
3
Stiffness units = SI, frequency mode (hz)
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Summary and Conclusions (Cho, 2005)
1. High fidelity FE models were created2. Relative mirror motions from zenith to horizon pointing: about 400 m
in translation and 60 rad in rotation.3. Natural frequency changes by 2 hz as height changes by 10m.4. Wind buffeting effects caused by dynamic portion (fluctuation) of wind 5. Modal responses sensitive to stiffness of bearings and drive disks
6. Soil characteristics were the dominant influences in modal behavior of the telescopes.
7. Fundamental Frequency (for a lowest soil stiffness): OSS=20.5hz; OSS+base=9.9hz; SS+base+Coude+soil=6.3hz
8. A seismic analysis was made with a sample PSD9. ATST structure assembly is adequately designed:
1. Capable of supporting the OSS2. Dynamically stiff enough to hold the optics stable3. Not significantly vulnerable to wind loadings
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Free-Field Analytical Solutions
RVz C
rHaR
VLiru
2003
0 )(2
)0,,(
RVr C
rHaR
VMiru
2103
0 )(2
)0,,(
ur
uz
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Karlstrom and Bostrom 2007
Trench Isolation
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Chehab and Nagger 2003
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Celibi et al (in press)
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Thank-you
Questions?
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r -2 r -2 r -0.5
r -1
r -1
r
Shear wave
Vertical component
Horizontal component
Shear window
Rayleigh wave
Relative amplitude+
+
+
+
- -
+
+
Wave Type Percentage of
Total Energy
Rayleigh 67
Shear 26
Compression 7
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Waves
Rayleigh, R Surface
Shear,S Secondary
Compression, P Primary
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Machine Performance ChartPerformance Zones
A=No Faults, New
B=Minor Faults, Good Condition
C = Faulty, Correct In 10 Days To Save $$
D = Failure Is Near, Correct In 2 Days
E = Stop Now
0.002
450