Vibrations of Machine Foundations

Vibrations of 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. 2. 3. 4. 5.

High fidelity FE models were created Relative mirror motions from zenith to horizon pointing: about 400 μm in translation and 60 μrad in rotation. Natural frequency changes by 2 Hz as height changes by 10m. Wind buffeting effects caused by dynamic portion (fluctuation) of wind Modal responses sensitive to stiffness of bearings and drive disks

6. Soil characteristics were the dominant influences in modal (dynamic) behavior of the telescopes. 7. 8. 9.

Fundamental Frequency (for a lowest soil stiffness): OSS=20.5hz; OSS+base=9.9hz; SS+base+Coude+soil=6.3hz A seismic analysis was made with a sample PSD 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 Fundamentals-Modeling-Properties-Performance

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Topics for Today

Fundamentals Modeling Properties Performance

Alapok Modellezés Tulajdonságok Gyakorlati Alkalmazás

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Foundation Movement Alapok Mozgáslehetőségei Z Y

θ

φ X

ψ


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Design Questions (1/4) Tervezés How Does It Fail?

Static Settlement Dynamic Motion Too Large (0.02 mm) Settlements Caused By Dynamic Motion Liquefaction What Are Maximum Values of Failure? (Acceleration, Velocity, Displacement)

Hogy rongálódik/megy tönkre?

Statikus süllyedés Dinamikus mozgás túl nagy (0,02 mm) Süllyedés dinamikus mozgás következtében Megfolyósodás Rongálódás maximális értékei (gyorsulás, sebesség, eltolódás)

Fundamentals-Modeling-Properties-Design-Performance

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Velocity Requirements Sebesség Követelmények

0,40

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


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300

800


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Design Questions (2/4) Tervezés

What Are Relations Between Loads And Failure Quantities?

Loads -Harmonic, Periodic, Random Load→ Structure → Foundation → Soil → Neighboring Structures Model: Deterministic or Probabilistic

Mi a kapcsolat terhelési és törési mennyiségek között? Terhelések- Harmónikus, Periódikus, Véletlenszerü Terhelés → Épület → Alapozás → Talaj → Közeli Épületek Model: Determinisztikus és probabilisztikus


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Harmónikus

Periódikus

Véletlenszerű

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Design Questions (3/4) Tervezés

Hogy határozzuk meg a tervezéshez szükséges paramétereket? (How do we measure what is necessary?)

Teljes méretarányú teszt (Full scale Test) Prototípus teszt (Prototype Test) Kis méretű teszt (Small Scale Tests (Centrifuge)) Laboratóriumi teszt (Laboratory Tests (Specific Parameters)) Számítógépes program (Computer Model)


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Design Questions (4/4)

Milyen biztonsági tényezőt használjunk? (What Factor of Safety Do We Use? )

Van a biztonsági tényezőnek értelme? (Does FOS Have Meaning) Mi történik törés után (What Happens After There Is Failure)

Életvesztés (Loss of Life) Tulajdonvesztéd (Loss of Property) Gyártás kihagyás (Loss of Production)

Mi a munka célja, tervezett élettartalma, értéke (Purpose of Project, Design Life, Value)


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r -2

r -2 r -0.5 +

-

+

Rayleigh wave Vertical Horizontal component component

+

Nyíró hullám

+

Relative amplitude

-

r -1

+

+ Shear window Nyíró ablak

r

r -1 Compresszió hullám Waves


Wave Type Hullám típus

Összes energia százaléka

Rayleigh

67

Shear

26

Compression

7

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Alapok Modellezése

(Modeling Foundations) Egyesített Tömb (m,c,k)Lumped Parameter (m,c,k) Block System

Ellenállási Függvények Impedance Functions

Function of Frequency (ω), Layers

Peremérték Feladatok Boundary Elements (BEM)

Parameters Constant, Layers, Special

Infinite Boundary, Interactions, Layers

Véges Elemes (Finite Element/Hybrid (FEM, FEM-BEM))

Complex Geometry, Non-linear Soil Fundamentals-Modeling-Properties-Performance

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Lumped Parameter (Egyesített tömb) P = Po sin(ω t )

r

m

Gνρ

m c

k

m &z& + c z& + kz = P0 sin( ω t )


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Egy szabadságfokú (Single Degree of Freedom)

mz &z& + c z z& + k z z = 0 ⎛ m ⎞ mz &z& = Inertia Force ( kg )⎜ or ( N ) c 2 ⎟ ⎝ sec ⎠ Tehetetlenségi erő ⎛ N − sec ⎞⎛ m ⎞ c z z& = Damping Force ⎜ ⎟⎜ ⎟ or ( N ) ⎝ m ⎠⎝ sec ⎠

z m k

Csillapító Erő

⎛N⎞ k z z = Spring Force ⎜ ⎟(m) or ( N ) ⎝m⎠ Rugó erő

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Egy szabadságfokú Single Degree of Freedom megoldás

mz &z& + c z z& + k z z = 0

állandó

solution will take form z = α e .......α = constant

where (ms 2 + cs + k )α e st = 0 ahol k st 2 divide by mα e and set ωn = m osztás c 2 2 then s + s + ωn = 0 m tehát solution for s depends on c s megoldása c-től függ

st

c=0…Undamped Nem csillapított

c=2mω…Critically Damped c<2mω…Underdamped Alul csillapított USC USC

Single Degree of Freedom

c 2 s + s + ωn = 0 undamped...s = ±iωn m iω n t − iω n t z (t ) = α1e + α 2 e where α1 , α 2 = f (init. cond .) 2

Euler ' s identity e iωnt = cos(ωnt ) + i sin(ωnt ) z (t ) = A sin(ωnt ) + B cos(ω t ) A, B = f (initial condition) z (0) = B and z& (0) = Aωn

Kiinduló feltétel

⎛ z& (0) ⎞ ⎟⎟ sin(ωnt ) + z (0) cos(ωnt ) z (t ) = ⎜⎜ z& (0) ⎝ ωn ⎠ z(0)

t USC USC

Single Degree of Freedom

c 2 s + s + ωn = 0 if damping present m 2

2

c ⎛ c ⎞ 2 then s = − ± ⎜ ⎟ − ωn 2m ⎝ 2m ⎠

critical

c if = 0 then c = ccrit = 2mωn and s = − = −ωn 2m −ω n t z (t ) = (α1 + α 2t )e where α1 , α 2 = f (init. cond .) z& (0) z(0)

z (t ) = [z (0)(1 + ωnt ) + z& (0)t ]e −ωnt t

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Single Degree of Freedom if c < 2mωn then suppose D =

c ccrit

then s = − Dωn ±

< 0 underdampe d

= damping ratio and ω D = ωn 1 − D 2

(Dωn ) − ωn 2

2

= − Dωn ± iω D

(

z (t ) = α1e − Dωnt +iω Dt + α 2 e − Dωnt −iω Dt = e − Dωnt α1eiω Dt + α 2 e −iω Dt z (t ) = e

− Dω n t

z (t ) = e

− Dω n t

( A sin(ω D t ) + B cos(ω D t ) ⎡ z& (0) + z (0) Dωn ⎤ sin(ω D t ) + z (0) cos(ω D t )⎥ ⎢ ωD ⎣ ⎦ See Chart

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)

Single Degree of Freedom mz &z& + c z z& + k z z = P0 sin(ω P t ) z=e +

( −ωn Dt )

{A sin(ωDt ) + B cos(ωDt )} P0

(k − mω ) + c ω 2 2

P

cω P tan φ = 2 k − mω P

k ωn = m

P = Po sin(ω P t )

2

2

m

sin (ω P t − φ ) c

k

P

ω ⎛ ⎞ P 2 D⎜ ⎟ ω n⎠ ⎝ = 2 ω ⎛ 1 − ⎜ P ⎞⎟ ⎝ ωn ⎠

ω D = ωn 1 − D 2

D=

c ccrit

ccrit = 2 km USC USC

SDOF Átmenti és Állandó Transient and Steady-State

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z (t ) =

P0

(k − mω ) + c ω 2 2

P

z max

P0 = k

z max = z static

2

2

sin (ω P t − φ )

P

1 ⎡ ⎛ω ⎞ ⎢1 − ⎜⎜ P ⎟⎟ ⎢⎣ ⎝ ωn ⎠

2

2

⎤ ⎡ ω ⎤2 ⎥ + ⎢2 D P ⎥ ωn ⎦ ⎥⎦ ⎣

1 ⎡ ⎛ω ⎞ ⎢1 − ⎜⎜ P ⎟⎟ ⎢⎣ ⎝ ωn ⎠

2

2

⎤ ⎡ ω ⎤2 ⎥ + ⎢2 D P ⎥ ωn ⎦ ⎥⎦ ⎣ USC USC

Dynamic Magnification (Logarithmic) 100 D=0.02 D=0.05 D=0.10 D=0.20 D=0.50

Magnification

10

1

0.1 0.1

1 Frequency Ratio (ωP/ωn)


10

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Lumped Parameter System Z

mz &z& + c z z& + k z z = P0 sin(ω P t )

Cz

Kz

Iψ

m

ψ

Kx X Cx

Cψ/2

Kψ

Cψ/2


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Rendszer paraméterek Lumped Parameter Values Mode

Vertical z

Horizontal x

Rocking ψ

Torsion θ

Stiffness k

4Gr 1 −ν

8Gr 2 −ν

8Gr 3 3(1 − ν )

16Gr 3 3

Mass Ratio m ˆ m

m(1 − ν ) 4 ρr 3

m( 2 − ν ) 8 ρr 3

3Iψ (1 − ν ) 8 ρr 5

Iθ ρr 5

Damping Ratio, D

0.425 mˆ 1 / 2

0.288 mˆ 1/ 2

0.15 (1 + mˆ )mˆ 1/ 2

0.50 1 + 2mˆ

D=c/ccr G=Shear Modulus ν=Poisson's Ratio r=Radius ρ=Mass Density Iψ,Iθ=Mass Moment of Inertia Fundamentals-Modeling-Properties-Performance

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Design Example 1 (Példa) VERTICAL COMPRESSOR Unbalanced Forces (kiegyensúlyozatlan erők) •Vertical = 45 kN függőleges •Horizontal Primary = 0,5 kN vízszintes •Operating Speed = 450 rpm üzemelő seb. •Wt Machine + Motor = 5 000 kg Gép+motor súlya DESIGN CRITERION: Tervezési feltétel Talaj jellemzők Soil Properties Smooth Operation At Speed Nyíró hullám Shear Wave Velocity Vs = 250 m/sec Velocity <0,10 in/sec Density, ρ = 1600 kg/m3 Displacement < 0,002 in <0,05mm Shear Modulus, G = 1,0e8 Pa Poisson's Ratio, ν = 0,33 Jump to Chart


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4Gr 4 × 1,0 ×108 × r k= = (1 −ν ) 0,667 Q0 (1 −ν )Q0 0,667(45 000)1000 = = 0,05mm = kz 4Gr 4 ×1,0 ×108 × r 0.075 r= = 1.5m 0.05 tömbalaptest Try a 3 x 2,5 x 1 foundation block, r = 1,55 m

Z static =

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

m(1 −ν ) mˆ = 4 ρr 3

mˆ =

(1 −ν ) m 0,67 × 23 000 = = 0,65 3 3 4r ρ 4 ×1600(1,55)

0,425 ⎛ 1 ⎞ = 0,53 M z ≈ 1,0 ⎜ D= ⎟ mˆ ⎝ 2D ⎠ Z dynamic = Z static = 0,05mm Fundamentals-Modeling-Properties-Performance

Jump to Figure

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Design Example - Table Top

5m

Q0=1800 N

10m 4m

Iψ=1,0 x 107 N-m-sec2 DESIGN CRITERION

X

5m

Emelt (asztal) alap m=250 000 kg

ψ

Soil Properties Shear Wave Velocity Vs = 200 m/sec Shear Modulus, G = 6,80x107 Pa Density, γ = 1700 kg/m3 Poisson's Ratio, ν = 0,33

5.0 mm/sec Horizontal Motion at Machine Centerline X = 0,04 mm from combined rocking and sliding együttes rocking, csúszás Speed = 320 rpm sebesség Slower speeds, X can be larger Kisebb sebességnél, x megnőhet


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Horizontal Translation Only Equivanlent D=

r=

lw

π

=

10 × 5

π

0,288 = 0,41 ∴ Mag x ≈ 1,2 1/ 2 mˆ

csak vízszintes mozgás 2 −ν m = 0,49 3 8 ρr Q 1800 2 − 0,33 −3 = 0 = = 1 , 3 × 10 mm 7 kx 8 6,8 ×10 × 3,99

= 3,99m mˆ = X static

Rocking About Point "O"

Ax = 40x10-3 mm

3 3 lw × 10 5 ω = 320 rpm = 33,5 rad / sec Equivalent r = 4 =4 = 3,39m 3π 3π 8Gr 3 8 × 6,80 × 107 × 3,393 kψ = = = 1,054 ×1010 N / rad 3(1 −ν ) 3(1 − 0,33)

ωn =

kψ Iψ

1,054 ×1010 = 32,4 rad / sec = 1,0 ×10 7

3(1 −ν ) Iψ 3(0,67) 1,0 ×10 7 mˆ ψ = = = 3,29 5 5 ρr 8 8 1700(3,39) 0,15 0,15 Dψ = = = 0,019 ∴ Magψ = 25,0 (1 + mˆ ψ ) mˆ ψ (1 + 3,29) 3,29


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Static Moment About Base = M 0 = 1800 × 5 = 9000 N − m Static Angular Deflection = ψ s =

Mo 9000 −7 = = 8 . 54 × 10 rad 10 kψ 1.054 ×10

Horizontal Motion = X ψ = ψ s × h = 8.54 ×10 −7 × 4 = 3,4 ×10 −3 mm At Resonance = 25,0(3,4 ×10 −3 ) = 85,0 ×10 −3 mm

X = 40x10-3 mm

Dynamic Magnification (Linear)

X

30

0,02

ψ

Magnification

25

0,05

20 15

0,1

10

0,2

5

0,5

0 0,0

0,5

1,0 1,5 Frequency Ratio (ω P /ω n)


2,0

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Impedance Methods Ellenállási függvények

Based on Elasto-Dynamic Solutions Compute Frequency-Dependent Impedance Frekvenciától függő Values (Complex-Valued) ellenállási értékek Solved By Boundary Integral Methods Peremérték integrál módszer Require Uniform, Single Layer or Special Soil Property Distribution Egyenletes, egy réteg, speciális talajérték eloszlás szükséges Solved For Many Foundation Types Többfajta alap típusra megoldott Fundamentals-Modeling-Properties-Performance

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Impedance Functions P = Poeiωt = Po (cos(ω t ) + i sin(ω t ) )

Sz ⎛ ⎞ Rz 2K = K + iω C = (K STATIC × k (ω ) ) + iω ⎜⎜ C + Sz = DSOIL ⎟⎟ ω Az ⎝ ⎠ Radiation Damping

Energia csillapítás

Jump Wave


Soil Damping Talaj csillapítás USC USC

Impedance Functions a0 = ω r

ρ G

=

ωr Vs

ψ Luco and Westmann (1970)


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Impedance Functions

ψ


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Boundary Element Peremérték feladatok

Stehmeyer and Rizos, 2006 Fundamentals-Modeling-Properties-Performance

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B-Spline Impulse Response Approach


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[M ]{u&&}+ [K ]{u} = {p}e

i ωt

{u} = {U}eiωt then 2 {[K ] − ω [M ]}{U} = {p}


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u1

u7 G1,ρ1,ν1

u2

u8

[K1 ] = fn(G1 , ρ1 ,ν 1 ) [m1 ] = fn( ρ1 ) ui = ai x + bi y + cxy + d

⎧ k1,1 ⎪k ⎪⎪ 2,1 ⎨ ⎪k ⎪ 7 ,1 ⎪⎩k8,1

k1, 2

k1, 7

k 2, 2

k 2, 7

k7 , 2

k7 , 7

k8 , 2

k8 , 7

ε = linear k1,8 ⎫⎧u1 ⎫ σ = linear

k 2,8 ⎪⎪⎪u2 ⎪ ⎪⎪⎪ ⎪⎪ ⎬⎨ ⎬ k7 ,8 ⎪⎪u7 ⎪ ⎪⎪ ⎪ k8,8 ⎪⎭⎪⎩u8 ⎪⎭


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[M ]{u&&}+ [K ]{u} = {p}eiωt ⎡m1 ⎢ m2 ⎢ ⎢ ⎢ ⎢ ⎢⎣

m3 m4

⎤ ⎧u&&1 ⎫ ⎡ k1,1 k1, 2 ⎥ ⎪u&& ⎪ ⎢k k ⎥ ⎪⎪ 2 ⎪⎪ ⎢ 2,1 2, 2 ⎥ ⎨u&&3 ⎬ + ⎢k3,1 k3, 2 ⎥⎪ ⎪ ⎢ k 4, 2 ⎥ ⎪u&&4 ⎪ ⎢ m5 ⎥⎦ ⎪⎩u&&5 ⎪⎭ ⎢⎣

k1,3 k 2,3

k 2, 4

k3,3 k3, 4 k 4,3 k 4, 4 k5, 3

k5, 4

⎤ ⎧u1 ⎫ ⎧ p1 ⎫ ⎥⎪ ⎪ ⎪ ⎪ ⎥ ⎪⎪u2 ⎪⎪ ⎪⎪ p2 ⎪⎪ k3,5 ⎥ ⎨u3 ⎬ = ⎨ p3 ⎬eiωt ⎥ k4,5 ⎥ ⎪u4 ⎪ ⎪ p4 ⎪ ⎪ ⎪ ⎪ ⎪ k5,5 ⎥⎦ ⎪⎩u5 ⎪⎭ ⎪⎩ p5 ⎪⎭

if {z} = {Z}eiωt then {&z&} = −ω 2 {Z}e iωt and

{[K ] − ω [M ]}{Z} = {p} given ω , solve for {Z} 2

[K ], {Z} are complex − valued

(

G* = G 1 − 2 D 2 + 2iD 1 − D 2

) USC USC

Dynamic p-y Curves

Tahghighi and Tonagi 2007


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Soil Properties

Shear Modulus, G and Damping Ratio, D

Talaj jellemzők

Soil Type Talajtípus Confining Stress Void Ratio Hézagtényező Strain Level Nyúlás szint

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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Oscilloscope

Crosshole Testing ASTM D 4428 Pump

Δt Shear Wave Velocity: Vs = Δx/Δt Downhole Hammer (Source) Test Depth

Δx

packer Note: Verticality of casing must be established by slope inclinometers to correct distances Δx with depth.

Slope Inclinometer

PVC-cased Borehole

Velocity Transducer (Geophone Receiver) Slope

Inclinometer

PVC-cased Borehole

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Resonant Column Test

G, D for Different γ Fundamentals-Modeling-Properties-Performance

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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


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Steam Turbine-Generator (Moreschi and Farzam, 2003)


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Machine Foundation Design Criteria

Deflection criteria: maintain turbine-generator alignment during machine operating conditions El/kihajlási kritérium: a turbina-generátor szintben maradjon működése alatt

Dynamic criteria: ensure that no resonance condition is encountered during machine operating conditions Jump to Resonance

Dinamikus feltétel: nincs rezonancia a gép működése alatt

Strength criteria: reinforced concrete design Erősségi feltétel: előfeszített beton tervezés


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STG Pedestal Structure


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Vibration Properties Evaluation Identification of the foundation natural frequencies for the dominant modes Az alap saját frekvenciáinak meghatározása a domináns lengésekre/módokra Frequency exclusion zones for the natural frequencies of the foundation system and individual structural members (±20%) Kihagyási frekvencia zónák a természetes frekvenciákra Eigenvalue analysis: natural frequencies, mode shapes, and mass participation Eigenérték elemzés:természetes frekvenciák, factors lengésmódnál alakok, tömeg együttdolgozása


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Finite Element Model Structure and Base

Z Y

X


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Low Frequency Modes 1st mode 6.5 Hz 95 % m.p.f.

2nd mode 7.2 Hz 76 % m.p.f Fundamentals-Modeling-Properties-Performance

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High Frequency Modes

28th mode 46.3 Hz 0.3% m.p.f

42nd mode 64.6 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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Assumptions in FE analyses

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=3.1×1010 N/m2, ν=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) Fundamentals-Modeling-Properties-Performance

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Frequency vs Soil Stiffness Stiffness units = SI, frequency mode (hz) Stiffness Kx Ky Kz Krx Kry Krz

MODE 1 2 3 4 5 6

min 1.19E+10 1.19E+10 1.48E+10 1.34E+12 1.34E+12 1.74E+12

1.83E+10 1.83E+10 2.45E+10 2.21E+12 2.21E+12 2.61E+12

2.48E+10 2.48E+10 3.41E+10 3.09E+12 3.09E+12 3.49E+12

max 3.12E+10 3.12E+10 4.38E+10 3.96E+12 3.96E+12 4.36E+12

6.3 6.4 9.4 9.4 10.4 11.2

7.0 7.1 9.7 10.3 11.9 13.0

7.4 7.5 9.9 11.1 12.6 13.6

7.5 7.7 10 11.8 13.3 13.7

m in+33.3% m in+66.6%

• 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 Fundamentals-Modeling-Properties-Performance

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Summary and Conclusions (Cho, 2005) 1. 2. 3. 4. 5.

6. 7. 8. 9.

High fidelity FE models were created Relative mirror motions from zenith to horizon pointing: about 400 μm in translation and 60 μrad in rotation. Natural frequency changes by 2 hz as height changes by 10m. Wind buffeting effects caused by dynamic portion (fluctuation) of wind Modal responses sensitive to stiffness of bearings and drive disks

Soil characteristics were the dominant influences in modal behavior of the telescopes. Fundamental Frequency (for a lowest soil stiffness): OSS=20.5hz; OSS+base=9.9hz; SS+base+Coude+soil=6.3hz A seismic analysis was made with a sample PSD 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 Fundamentals-Modeling-Properties-Performance

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Free-Field Analytical Solutions uz

ur

⎛ ω L0V ⎞ 2⎛ ωr ⎞ ⎟⎟ u z (r ,θ ,0) = −i ⎜⎜ 3 ⎟⎟ RV (a0 ) H 0 ⎜⎜ ⎝ 2β ρ ⎠ ⎝ CR ⎠ ⎛ ω M 0V ur (r ,θ ,0) = i ⎜⎜ 3 β ρ 2 ⎝

⎞ 2⎛ ωr ⎞ ⎟⎟ ⎟⎟ RV (a0 ) H1 ⎜⎜ ⎠ ⎝ CR ⎠


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Trench Isolation

Karlstrom and Bostrom 2007 Fundamentals-Modeling-Properties-Performance

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Chehab and Nagger 2003 Fundamentals-Modeling-Properties-Performance

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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 +

-

+

Rayleigh wave Vertical Horizontal component component

+

Shear wave

+

Relative amplitude

-

r -1

+ Shear window

r -1

+ r Wave Type

Percentage of Total Energy

Rayleigh

67

Shear

26

Compression

7 USC USC

Waves Compression, P Primary Shear,S Secondary

Rayleigh, R Surface

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Machine Performance Chart Performance Zones A=No Faults, New B=Minor Faults, Good Condition C = Faulty, Correct In 10 Days To Save $$

0.002

D = Failure Is Near, Correct In 2 Days E = Stop Now

450

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Vibrations of Machine Foundations

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