expo machines vibrating.pdf

8/12/2019 expo machines vibrating.pdf

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Vibrationsof

Machine Foundations

Richard P. Ray, Ph.D., P.E.Civil and Environmental Engineering

University of South Carolina


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ATST Telescope and FE Model

Fundamentals-Modeling-Properties-Performance


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Summary and Conclusions (Cho, 2005)1.

High fidelity FE models were created

2.

Relative mirror motions from zenith to horizon pointing: about 400 m intranslation 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 influencesin modal (dynamic) behavior of the telescopes.7.

Fundamental Frequency (for a lowest soil stiffness):

OSS=20.5hz; OSS+base=9.9hz; SS+base+Coude+soil=6.3hz8.

A seismic analysis was made with a sample PSD

9. ATST structure assembly is adequately designed:1.

Capable of supporting the OSS2.

Dynamically stiff enough to hold the optics stable

3.

Not significantly vulnerable to wind loadings



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Topics for Today

Fundamentals Modeling

Properties Performance

Alapok Modellezs

Tulajdonsgok Gyakorlati

Alkalmazs


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Foundation Movement

Alapok Mozgslehetsgei

X

Z

Y



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Design Questions (1/4) Tervezs

How Does It Fail? Static Settlement

Dynamic Motion TooLarge (0.02 mm)

Settlements Caused By

Dynamic Motion Liquefaction

What Are Maximum

Values of Failure?(Acceleration,Velocity,

Displacement)

Hogy rongldik/megytnkre?

Statikus sllyeds Dinamikus mozgs tl

nagy (0,02 mm)

Sllyeds dinamikusmozgs kvetkeztben

Megfolysods

Ronglds maximlisrtkei (gyorsuls,sebessg, eltolds)

Fundamentals-Modeling-Properties-Design-Performance


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Velocity Requirements Sebessg Kvetelmnyek

Massarch

(2004) "Mitigation of Traffic-Induced Ground Vibrations"


0,40


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300 800


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What Are RelationsBetween Loads AndFailure Quantities?

Loads -Harmonic,Periodic, Random

Load Structure

Foundation Soil Neighboring Structures

Model: Deterministic or

Probabilistic

Mi a kapcsolat terhelsis trsi mennyisgekkztt?

Terhelsek- Harmnikus,Peridikus, Vletlenszer

Terhels pletAlapozs Talaj Kzeli

pletek Model: Determinisztikus s

probabilisztikus



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Harmnikus

Peridikus

Vletlenszer


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Hogy hatrozzuk meg a tervezshez szksgesparamtereket? (How do we measure what isnecessary?)

Teljes mretarny teszt (Full scale Test) Prototpus teszt (Prototype Test) Kis mretteszt (Small Scale Tests (Centrifuge))

Laboratriumi teszt (Laboratory Tests (SpecificParameters)) Szmtgpes program (Computer Model)



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Design Questions (4/4) Milyen biztonsgi tnyezt hasznljunk? (What

Factor of Safety Do We Use? ) Van a biztonsgi tnyeznek rtelme? (Does FOS Have

Meaning) Mi trtnik trs utn (What Happens After There Is

Failure) letveszts (Loss of Life) Tulajdonvesztd (Loss of Property)

Gyrts kihagys (Loss of Production) Mi a munka clja, tervezett lettartalma, rtke (Purpose of

Project, Design Life, Value)



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r -2 r -2 r -0.5

r-1

r -1

r

Nyrhullm

Verticalcomponent

Horizontalcomponent

Shearwindow

Rayleigh wave

Relativeamplitude+

+

+

+

- -

+

+

Wave TypeHullm tpus

sszes energiaszzalka

Rayleigh 67

Shear 26Compression 7

Waves


Compresszi

hullmNyrablak


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Alapok Modellezse (Modeling Foundations)

Egyestett Tmb (m,c,k)Lumped Parameter (m,c,k) BlockSystem

Parameters Constant, Layers, Special Ellenllsi Fggvnyek Impedance Functions

Function of Frequency (), Layers Peremrtk Feladatok Boundary Elements (BEM)

Infinite Boundary, Interactions, Layers Vges Elemes (Finite Element/Hybrid (FEM, FEM-BEM))

Complex Geometry, Non-linear Soil



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Lumped Parameter (Egyestett tmb))sin( tPP o =

m

G

k

m

c

)sin(0 tPkzzczm =++ &&&

r



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Egy szabadsgfok (Single Degree ofFreedom)

)()(

)(

)()(

0

2

Norm

m

NForceSpringzk

Nor

sec

m

m

secNForceDampingzc

Nor

sec

mkgForceInertiazm

zkzczm

z

z

z

zzz

=

=

=

=++

&

&&

&&&

k

m

c

z

Tehetetlensgi er

Rug er

Csillapt Er


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Egy szabadsgfokSingle Degree of Freedom

condependssforsolution

sm

csthen

m

k

setandembydivide

ekcsmswhere

constantezformtakewillsolution

zkzczm

n

n

st

st

st

zzz

0

0)(

.......

0

22

2

2

=++

=

=++

==

=++

&&&

c=0Undamped

c=2mCriticallyDamped

c


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Single Degree of Freedom

)cos()0()sin(

)0(

)(

)0()0(

)(,)cos()sin()()sin()cos('

.).(,)(...0

2121

22

tzt

z

tz

AzandBz

conditioninitialfBAtBtAtz

titeidentitysEuler

condinitfwhereeetz

issm

c

s

nnn

n

n

nnti

titi

nn

n

nn

+

=

==

=+=+=

=+===++

&

&

undamped

)0(z&

z(0)

t

Kiindul felttel


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[ ] tn

t

nncrit

n

n

n

n

etztztz

condinitfwhereettz

m

c

sandmccthenif

m

c

m

c

sthen

presentdampingifsm

c

s

++=

=+======

=

=++

)0()1)(0()(

.).(,)()(220

22

0

2121

22

22

&

critical


z(0)

)0(z&

t


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( )

( )

+

+=

+=+=+=

==

===


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)sin(0 tPzkzczm Pzzz =++ &&&

k

m

c

)sin( tPP Po =( ) ( ){ }

( )( )

22

2222

0

1

2tan

sin

cos)sin(

==

+

+

+=

n

P

n

P

P

P

P

PP

DD

Dt

D

mk

c

t

cmk

P

tBtAez n

critc

c

D=

m

kn= 21 DnD = kmc

crit 2=


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SDOF tmenti s lland Transient

and Steady-State


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( ) ( )

222

0max

2222

0

21

1

sin)(

+

=

+=

n

P

n

P

P

PP

D

k

P

z

tcmk

P

tz

222

21

1

+

=

n

P

n

P

staticmax

D

zz


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Dynamic Magnification (Logarithmic)

0.1

1

10

100

0.1 1 10

Frequency Ratio (P/

n)

M

agnification

D=0.02D=0.05

D=0.10

D=0.20

D=0.50


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Lumped Parameter System

Kx

Z

KzCz

Cx

K

C

/2 C

/2

X

)sin(0 tPzkzczm Pzzz =++ &&&

mI



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Rendszer paramterek Lumped Parameter Values

Mode Verticalz

Horizontalx

Rocking

Torsion

Stiffness

k

Mass Ratio

mDampingRatio, D

1

4Gr

2

8Gr

)1(3

8 3

Gr

3

16 3Gr

5r

I

3

8

)2(

r

m

34

)1(

r

m

2/1425.0

m2/1

288.0

m2/1)1(

15.0

mm+ m21

50.0

+

m

D=c/ccr

G=Shear Modulus =Poisson's Ratio r=Radius

=Mass Density I

,I

=Mass Moment of Inertia

5

8

)1(3

r

I



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Design Example 1 (Plda)VERTICAL COMPRESSORUnbalanced Forces

(kiegyenslyozatlan erk)

Vertical = 45 kN

Horizontal Primary = 0,5 kNOperating Speed= 450 rpm

Wt Machine + Motor = 5 000 kg

Soil Properties

Shear Wave Velocity Vs

= 250 m/sec

Density,

= 1600 kg/m3

Shear Modulus, G = 1,0e8 Pa

Poisson's Ratio,

= 0,33

DESIGN CRITERION:Smooth Operation At Speed

Velocity


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rGr

Qmm

k

QZ

z

static =

===

800

100,14

1000)00045(667,0

4

)1(05,0

mr 5.105.0

075.0==

( )

mmZZ

DM

mD

m

rm

staticdynamic

z

05,0

2

10,153,0

425,0

65,055,116004

0002367,0

4

)1(

33

==

==

=

=

=

Try a 3 x 2,5 x 1 foundation block, r = 1,55 m

Mass = 18 000 kg Total Mass = 18 000 + 5 000 = 23 000 kg

Jump to Figure


667,0

100,14

)1(

4 8 rGrk

==

34

)1(

r

mm

=

tmeg

tmbalaptest


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Horizontal Translation Only

mmk

QXMag

mD

r

mmm

lwrtEquivanlen

x

staticx

37

02/1

3

103,199,3108,6

33,02

8

18002,141,0

288,0

49,0

8

299,3

510

=

====

===

==

Rocking About Point "O"

0,25019,0

29,3)29,31(

15,0

)1(

15,0

29,3)39,3(1700

100,1

8

)67,0(3

8

)1(3

/4,32100,1

10054,1

/10054,1)33,01(3 39,31080,68)1(38

/5,3332039,33

510

3

5

7

5

7

10

10

373

4

3

4

3

==

+

=

+

=

=

==

=

==

= ==

===

==

Mag

mm

D

r

Im

secradI

k

radNGrk

secradrpmmlw

rEquivalent

n


Ax = 40x10-3

mm

csak vzszintes mozgs


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mmResonanceAt

mmhXMotionHorizontal

rad

k

MDeflectionAngularStatic

mNMBaseAboutMomentStatic

s

os

33

37

710

0

100,85)104,3(0,25

104,341054.8

1054.8

10054.1

9000

900051800

==

====

=

===

===


X

X = 40x10-3

mm

Dynamic Magnification (Linear)

0

5

10

15

20

25

30

0,0 0,5 1,0 1,5 2,0Frequency Ratio ( P/ n)

Magnification

0,02

0,05

0,1

0,2

0,5


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Impedance Methods

Based on Elasto-Dynamic Solutions

Compute Frequency-Dependent ImpedanceValues (Complex-Valued)

Solved By Boundary Integral Methods Require Uniform, Single Layer or Special Soil

Property Distribution Solved For Many Foundation Types


Ellenllsi fggvnyek

Frekvencitl fggellenllsi rtkek

Peremrtk integrl mdszer

Egyenletes, egy rteg, specilistalajrtk eloszls szksges

Tbbfajta alap tpusra megoldott


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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


Energia csillaptsTalaj csillapts


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Impedance Functions

Luco

and Westmann

(1970)

sVr

Gra ==0



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Impedance Functions



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Boundary Element

Stehmeyer

and Rizos, 2006


Peremrtk feladatok


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B-Spline Impulse Response Approach



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[ ]{ } [ ]{ } { } tie puKuM =+&&


{ } { }

[ ] [ ]{ }{ } { }pUMK

Uu

=

=

2

thene ti


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G1

,1

,1

u1

u2

u7

u8

[ ] ),,(1111

GfnK =

8

7

2

1

8,87,82,81,8

8,77,72,71,7

8,27,22,21,2

8,17,12,11,1

u

u

u

u

kkkk

kkkk

kkkk

kkkk

[ ] )( 11 fnm =

linear

linear

dcxyybxau iii

==

+++=


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[ ]{ } [ ]{ } { } tie puKuM =+&&

tie

p

p

p

pp

u

u

u

uu

kkk

kkkk

kkkkk

kkkkkkk

u

u

u

uu

m

m

m

mm

=

+

5

4

3

2

1

5

4

3

2

1

5,54,53,5

5,44,43,42,4

5,34,33,32,31,3

4,23,22,21,2

3,12,11,1

5

4

3

2

1

5

4

3

2

1

&&

&&

&&

&&&&

{ } { } { } { }[ ] [ ]{ }{ } { } { }

[ ]{ } valuedcomplexare

forsolvegiven

andethenezif titi

===

ZK

ZpZMKZzZ

,

,22

&&

22 1221* DiDDGG +=


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C h l T tiOscilloscope


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Crosshole TestingOscilloscope

PVC-casedBorehole

PVC-casedBorehole

Downhole

Hammer

(Source) VelocityTransducer

(GeophoneReceiver)

t

x

Shear Wave Velocity:Vs

= x/t

Test

Depth

ASTM D 4428

Pump

packer

Note: Verticality of casingmust be established byslope inclinometers to correct

distances x with depth.

Slope

Inclinometer

Slope

Inclinometer

R C l T


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Resonant Column Test

G, D for Different



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Torsional

Shear Test

Schematic Stress-Strain



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Hollow Cylinder RC-TOSS



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TOSS Test Results


Steam Turbine-Generator


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Steam Turbine-Generator (Moreschi

and Farzam, 2003)



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Machine Foundation Design Criteria

Deflection criteria: maintain turbine-generatoralignment during machine operating conditions

Dynamic criteria: ensure that no resonancecondition is encountered during machineoperating conditions

Strength criteria: reinforced concrete design


Jump to Resonance

El/kihajlsi kritrium: a turbina-genertor szintben maradjon mkdse alatt

Dinamikus felttel: nincs rezonancia a gp mkdse alatt

Erssgi felttel: elfesztett beton tervezs


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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 andindividual structural members (20%)

Eigenvalue analysis: natural frequencies,mode shapes, and mass participationfactors


Az alap sajt frekvenciinak meghatrozsa a dominns lengsekre/mdokra

Kihagysi frekvencia znk a termszetes frekvencikra

Eigenrtk

elemzs:termszetes frekvencik,

lengsmdnl alakok, tmeg egyttdolgozsa


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XY

Z

XY

Z

Finite Element Model

Structure and Base



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Low Frequency Modes

1st mode6.5 Hz95 % m.p.f.

2nd

mode

7.2 Hz76 % m.p.f



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High Frequency Modes

28th mode46.3 Hz0.3% m.p.f

42nd mode64.6 Hz0.03% m.p.f

Excitation frequency: 50-60 HzFundamentals-Modeling-Properties-Performance


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Local Vibration Modes

Identification of naturalfrequencies for individual

structural members

Quantification of changeson vibration properties due

to foundation modifications



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Assumptions in FE analyses


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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 & ONeils

formula based on the site test data (Shear

modulus:30~75ksi, Poissons ratio:0.35~0.45)

Assumptions in FE analyses



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Soil property range: Shear modulus (30~75ksi), Poissons 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 m i n m in +33.3% m in +66.6% m ax

Kx 1.19E+10 1.83E+10 2.48E+10 3.12E+10

Ky 1.19E+10 1.83E+10 2.48E+10 3.12E+10

Kz 1.48E+10 2.45E+10 3.41E+10 4.38E+10Krx 1.34E+12 2.21E+12 3.09E+12 3.96E+12

Kry 1.34E+12 2.21E+12 3.09E+12 3.96E+12

Krz 1.74E+12 2.61E+12 3.49E+12 4.36E+12

6.3 7.0 7.4 7.5

6.4 7.1 7.5 7.7

9.4 9.7 9.9 10

9.4 10.3 11.1 11.8

10.4 11.9 12.6 13.3

11.2 13.0 13.6 13.7

4

5

6

MODE

1

2

3

Stiffness units = SI, frequency mode (hz)


d l i ( h )


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Summary and Conclusions (Cho, 2005)

1.

High fidelity FE models were created

2.

Relative mirror motions from zenith to horizon pointing: about 400 m intranslation 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=6.3hz8.

A seismic analysis was made with a sample PSD

9.

ATST structure assembly is adequately designed:

1.

Capable of supporting the OSS

2.

Dynamically stiff enough to hold the optics stable

3.

Not significantly vulnerable to wind loadings


F Fi ld A l ti l S l ti


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Free-Field Analytical Solutions

=

R

VzCrHaRVLiru

2003

0 )(2

)0,,(

=

RVr C

rHaR

VMiru

2

103

0 )(2

)0,,(

uruz



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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?

2 2 0 5


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r -2 r -2 r -0.5

r -1

r -1

r

Shearwave

Verticalcomponent

Horizontalcomponent

Shearwindow

Rayleigh wave

Relativeamplitude+

+

+

+

- -

+

+

Wave Type Percentage ofTotal Energy

Rayleigh 67

Shear 26

Compression 7

Waves


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Waves

Rayleigh, R

Surface

Shear,S Secondary

Compression, PPrimary

Machine Performance Chart


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Machine Performance Chart

Performance ZonesA=No Faults, New

B=Minor Faults,

Good Condition

C = Faulty, CorrectIn 10 Days To Save

$$D = Failure Is Near,Correct In 2 Days

E = Stop Now

0.002

expo machines vibrating.pdf

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Transcript of expo machines vibrating.pdf