Machine Foundation Dr. Bhatia

Foundations for Industrial Machines

Understandi~g. Dynarni~s

of Machine

Found~

Design Considerations

-r~-F-L-s-m-i-d-th p-riv-a-te-L-im-i-te-d~DeSign~~l

L

-;:=========_

=

~

Bombay 4,5& 18th March 2010 JI

Hyderabad 12, 13 & 26th _{March 2010}

Training Program

by

Dr. K. G. Bhatia

D-CAD TECHNOLOGIES

158, Vardhman Grand Plaza, Mangalam Place, Rohini Sect -3, New Delhi 110085, India Tel: +91-11-27948306, +91-9873003427

Foundations for Industrial Machines

Understanding· Dynamics of Machine Foundation

Design Consideration

Training Program

by

Dr. K. G. Bhatia

B.Sc. Engg, ME, PhD

FIE. FfSET,FfASE, MfSWE, FIGI

Formerly

General Manager, BHEL

Member - Research Council, SERC -G (CSIR) President - Indian Society of Earthquake Technology

Chairman -Indian Society of Earthquake Technology, Delhi Chapter Expert Member - Group on Earthquake Preparedness of NCT of Delhi

Specialization:

Structural Dynamics, Earthquake, Wind, Shock, Impact, Stress, Vibration, Machine Foundation, Vibration Isolation

O-CAO TECHNOLOGIES

Center for Applied Dynamics

158, Vardhman Grand Plaza, Mangalam Place, Rohini Sect -3, New Delhi 110085, India

Tel: +91-11-27948306, +91-9873003427

Regd, Off: C-2/155, West Enclave Pitampura, New Delhi -110034, India Tel: +91-11-27027746, +91-9810013428

email: [email protected];[email protected] Visit www.machinefoundation.com; www.structuraldynamics.co.in

Foundations for Industrial

Machines

Dr. K G Bhatia

Understanding

Dynamics of Machine

Foundation

Design Considerations

• Machine

• Foundation

• Support System

Dynamic Force Machine Foundation

M/c

Foundation Design

END OBJECTIVE

~/

>-

Desired Performance

y

Minimum Vibration

Transmission

I

1>-

Structural Integrity

PH FAN - FAN-PED-TOP

-Vertical-( Speed 1000rpm=16.8Hz ) 20 30

orders

'"

1:]

,.

0 "-26 w E _{0.2 13} ~ 96 ~ E 168Hz E 0 41,5 83 101.04.2009 16:07:06 O/Ail 0.457 mmls rms 1000 RPM

- )

-

PH FAN -FAN-PED-TOP

-Horizon!a!-~

1:]

O~

r---;::;[

s=pe:::ed::;,o:::::oo=,p=m====::---c

=16.8Hz U~ 168 Hz ~ E ~ 0.2 E E

101:04.200916:06:44

O/AII 0.541

mm/s

rms

1000

RPM

PH FAN -FAN-PED-TOP -Axial·

30 or.ders 10 20 168 Hz O/A1I1.696mm/s rms 1000 RPM ill

1:]

"

0 "-

_1.2

96 _{[ Speed 1000 rpm} 26

1

=16.8Hz ~ 08 E 13 -"'. 06 E 04 E 02 101:04.2009 16:07:20

- )

Max Speed 800 rpm (13.33 Hz) Transient Resonance

@8,75 Hz PH FAN - FAN DE . Vertical-vel Spec 1$0Hz Cursor A 11,625 Hz

IflIi01-44_2009 18:29:48 O/A1I1.10e 01011. tmS

0,612 orders 0,696 mOlls OIAlll,109 01011.'m"

Operating Speed 945 rpm (15.7 Hz) "' "" "' "" 1"' I " "' "' "

PH FAN FANDE -Horizontal- Vel Spec 1000 Hz

30m

Top Deck

30mx10mx1.5mthk

Ht. above zero Level 10m

o l._--t-+--r-+----+---I--c=l---I--~--J

Pick~upLocations, :Pick-up Locations Top Deck Left Edge i"Vertical Amplitudes Top Deck Right Edge

:~/~-j

<::> 1· 1_·"·__1,,,,,,,,,·+,· 1,,,, -··!---i----···!·,·,,,,··+·---r--··---!---plck··up Locatiom Horizontal Amplitudes

"'[

" '----t---+----+-~---c--+---+_r_----' Pick_up Locatiorl!;

210 MW TG Foundation - Top-Deck Vibration Record

Top

Bottom

17_,

,

- - - :

Identical Foundations for

Identical Machines on different soil

c.

~

_.-o 2

Foundation on

Hard Rock

Identical (adjacent) Foundations

for Identical Machines on Identical Soil

Unit -I Unit -2 ::T

+

Top of Deck Base ~ --+--I : I I

--+----o

20 40 60 Vibration in microns

Vibration along column height

A uniform reduction of vibration amplitudes from top to bottom of bearing housing exhibits a healthy trend.

For one of the bearing housing, the trend was opposite. -Records are shown in Figure

o 20 40 60 I80I I100I Vibration In microns

Bearing

WARNING

MOTTO

There are many factors

Cost of Machine foundation InadequatelY constructed foundations Shutdown cost System Eccentricity Harmonics )r Sub harmonics '" Super harmonics Modes of Vibration Coupling of Modes Balance Grade Rotor Eccentricity Unbalance Force Short Circuit Torque Bearing failure Loads Thermal Loads Handling Loads Earthquake Loads Terminology Commonly Used in the Presentation

DOF

»

SDOF )r 2 DOF

»

MDOF Damping Equation of equilibrium Equation of Motion Resonance Response )r Transient )r Steady State Amplitude Mass& MMI Stiffness );> Linear

»

Rotational

Basic

Design Philosophy

Support

Equation of Motion

Free

Vibration

~

v

P v= _ ..

rad/s

.

m

Magnification Equation of Motion Forced Vibration \ Support ....

--

...

_.

I I I I I I I I I I

l

I

"

---

/ NOTOK Response OK Strength Design

Strength Analysis

&

Design

• Short Circuit Forces • Earthquake Forces

• Electro-magnetic Forces • Equivalent Dynamic Loads

• Thermal Loads

Springs attached @

Uncoupled

Six Natural Frequencies

Along Axis

P==~

About Axis

ff

e

Pe=

-M

_mx y "

edt-x

x , z Six DOr's 3 Dispalcements x,y, z

alongX, Y&Zaxes respectively and

3 Rotations

e,

ljI, ¢

about X, Y& Z axes respectively

. .

-

.

Motion in X-V Plane

y

A Rigid Block Supported by

Translational

&

Rotational Springs

Natural Frequencies Limiting Frequencies

FE

~

PIfI:::: -Mmoy

2

1

(2

2)

1

J(

2 2)'

2 2

PI =-2- Px+p¢! --2- Px+P¢ -4yzPxp¢ Yz Yz

2

1

(2

,)

1

1(--;

2)'

2 2

p, ~-2- p, +p¢ +-2-'1 p,+P¢ -4y, P,P¢ y, y, r = Mill: . Z Millo;' 2 kr 2 k¢ Px= - , P¢= -m Millo: • - • - P2 Pu or PLl eould either be Px or P¢ • PI2

-- - - Pl.l • - • - PI 3 Frequencies - - 7 Y3

Only One Frequency

p

=

(k

y ~; 2 Frequencies

y,~

k2

f

Y1H=l

v~

~

Y, Y, 1 - OOF System 2-DOF System y

PI2 =

/1;

v-;;

Motion is coupled k, P,&P2 - Pu • - P2

-• Pu • - • - PI

.

-Natural Frequencies Coupled Frequencies 2-DOF System Base Plate Tube Bundle DATA for Foundation Design :-- Equipment Data - Weight - Height of Centroid - Associated forces: - Seismic -Wind - Thermal

- Nozzle Reactio n Forces - Frictional Forces - Thermal Loads :-- Foundation Data :-- Soil Data

A Typical Mlc Foundation System DrIve MachIne Coupling Driven Machme Machine Data: • Mass of Stator • Mass of Rotor • Operating Speed • Gear ratio

• Unbalance Dynamic Forces • Excitation Frequencies • Number of Blades

• No. of Poles ( Electro magnetic forces)

• Type of Bearing ( Journal Bearing or Anti-friction Bearing)

• Permissible amplitudes

Foundation Data Soil data

• Dynamic Soil Parameters

•

Static Equipment Dynamic Machine

EQPT Deck Deck Frame or Block Columns Frame or Block Columns

Equipment Foundation

Displacement

Oy

=

mg

k

_y y

l

[m

g

I

Weight

T

J

k {

Soil+Col

~L

Math. Model m=mass of Equipment +Deck +Columns +Raft Static Analysis Equation of Equilibrium

Is

==

F

kyO y

=:

mg

Strain; Estatic; Stress

Shear Force& Bending Moment Structural Design (S Representing by an Un-Damped SDOF System y = { : : }x

{flJ

1 Mathematica I M:.;:;o""de"'I'--_-"J Response Columns

Equation of Motion

Response

System Property that Causes

Vibration Amplitude to Diminish

Steadily

For Machine foundation, we consider

Viscous Damping, where

RESISTING FORCE is proportional to

my

y

Free Body Diagram

k

_v (Soil+Col) Mass C_y (Soil+Col)

Y

~j

T

In

r

f

k Y

CyY y

Solution to equation of motion

[EqUation of Motion]

The damping value for which

the

radical

becomes

zero

is

termed as Critical Damping of

the system.

For Under-Damped System, Free Vibration

Response becomes:

Constants A & B are evaluated

using Initial Conditions

1.'5 ... 1.0 0.5

o

-0.5 -1.0 -1.5 tiT~~..--+

Free Vibration Response

Undamped SystemSy"0,Under-Damped~J'<I

!

Dynamic Force F(t) Mass m y

~v

(Soil+Col) C_y (Soil+Col)

Response

y= 1 f.J y

=

J(1-fJ:)'+(2fJ/;)

f.Jy

=

Dyn. Mag. Factor

Forced Vibration Equation

ofMotion

I

Equipment Foundation]

py=)~; f3y=~;;

Sy

=

damping constant

[ Machine Foundation]

Displacement

5=~

y

k

y

Response

y={~}xi~)

r---1

5j

I~~,o

fly

=

~(I-

13;)

+

(213

y

s

y

~

41

I .\

I

I

!

~,

0.1

fi

y = 1. fl. y =

(2

S

y)

~. , :; J

j

~

Resonance ! .j:' I =

2~

_'7f

For 2% dampingfly = 25

0 .~ u For5%dampingfly =10

'"

§, rn

For 10% dampingfI" = 5

;;: I

~

I 0 J'_n 0 0.5 1.5 2.0 2,5 3.0 Frequency Ratio~~

Points to Note

That in case of machine foundation design ... • Machines weigh several tons

• Foundation overall dimensions runs in multiple of meters

• Columns sizes are relatively large say 1m

x

1.5 m or so

• Beam sizes are also relatively large say 1m wide and 1.5 m to 2.0 m deep

• Dynamic Forces in several tons

-All those elements which contribute to

mass and lor stiffness must not be

ignored

All

the

assumptions

and

approximations

made

during

modeling must be duly validated

•

Natural Frequency

•

Excitation Forces

,---'"

,tfI"'---,

\

:8

+

~=8

: Response

y==t~}xl~)

I I Machine Support Foundation I \

Machine Mass - Point of Application

Machine Centroid

Actual

~

,"-o<:"tion

.~\

I \

Point of Contact with Soil Where Equation of Motion is Developed

Generated

Dynamic Force - Point of Application

???

Rotor Center Line

xl

_..

_·----.I~

? Dynamic Force@ 0

-Change is Significant

Excitation Forces

?

•

~ Unbalance

~ Oil Whirl in the Journal bearings

~ No. of Rollers in Antifriction Bearings

~ Misalignment

~ No. of impeller blades

~ No. of Poles in motors/generators @Engine Order -1x @Sub-harmonics 1/2x, 1/3x, etc @ higher harmonics @2x @nx @n_px/2

Unbalance Dynamic Force

Excitation Frequency

Balance Quality Grades

ISO 1940 (Applicable for Rigid Rotors) Balance grade is given as (Gr)

r

represents velocity in mm/s

(r/w) gives eccentricity in mm

~

Thus a balance grade G 6.3 for machine operating at 900 rpm corresponds to: 6.3 10-3 668 10-6 e=--x

=.

x m 94.25

"

i900rpm

_{L. .} ~

94,25

_{,,_,}

-rad/s:

_{,_,, _ _} F(t)

=

m,. xexo/ sinrV! = 66.8 microns N

Rotor Eccentricity

Rotor Balance Grade ... _ I . /

.. _---\=---+----

._----1

1\;35

600 '7 500 0 2 u ~ 400 ~, ~ 300 0 " u u 200

"'

B" 0

'"

lOO o-o I 250 I soo I 750 1000 1501940 1250 1500 Rotor Speed (rpm)

Rotor Eccentricity Vs. Rotor Speed for Rigid Rotors

F(t)

=

m_r xe x oi sinOJt N ...", Plane Normal10 / / Rotor Axis z Bearing J

~

Unbalance Force Bearing 2 /

0--""

?"

Rolor Axis (along Z-Axis) y F=m e,. (tJ2

--

.~""

"" J-""

X

;~:or

)

---'/

(a) Rotor Supp0l1 on Bearings (b) Unbalance Foret' acting in a plane normal to Rolor axis

\to\or'l

L

x -

Component of Unbalance Force 1800 _{out of phase}

IThese in turn generate Dynamic Moment about

Y

I

,.

Rotor 1

Y - Component of Unbalance Force 1800 _{out of phase}

Dynamic Forces

• The Dynamic Forces are to be applied at the bearing location points

• Many suppliers list dynamic forces at the point of contact of machinel bearing pedestals with the foundation

• They list only forces and not the moments • Such a practice is undesirable.

• This influence is seen to be more predominant in Block Foundations than Frame Foundations.

i) In - Phase ii) Out of Phase

NOT Recommended

Elastic Modulus of Concrete

Static or Dynamic

??

Block Foundation

Rigid Body - No Effect of

E

Columns

Frame FOlilncfation

Elastic System

-significan't Influen,ce ofE

Hence Ghange inFrequency and amplitudes

-At low Strain Levels there is hardly

any change in dynamic vs. Static

Elastic Modulus

It is therefore recommended to use

Static Elastic Modulus only for

structural stiffness computations

Center

of

Mass:

AU components of machine + foundation top deck that contribute to inertia must be included in computing combined CG i.e. Machine mass, mass of top deck slab, beams, projections openings, notches etc.

Center

of

Stiffness:

Stiffness of Frames in Transverse Direction with ref to a point same as that for center of Mass

Frame Foundation

Overall Eccentricity:

(]50/0

Distance between overall Center of Mass and Center of Stiffness of soil I.e. CG of Base Raft in contact with soil

Ceco~~ende~

Center

of

Mass:

All components of machine + foundation (top deck + Columns +Base Raft)

Over-tuned Foundations

P

y

>

_OJ

Under-tuned Foundations

P

y

<

_OJ

Frequency Margin

+

20

%

4 0,5 O,K 10 1.2 15 01""·""··.,. ."., o Frequency RatiofJ 2,0 2.5 ),0

Magnification Factor p vs. Frequency Ratio rl

Fr~!l1eFoul1d"tion,,~

Column

sizes

(as

marked

on the

layout

drawing)

are

generally

provided

by

the

customer/supplier.

More often than not, it has become the

practice by the designers to stick to these

dimensions

Such a practice is undesirable and must be

discouraged. Given sizes should be taken as

indicative only and the designer must assess

the validity of

keeping in view the

Top Deck Eccentricity

- - - '

Max Displacement 38~7mm

Columns Original

Max Displacement 28~8mm Columns Modified

l!!!.!Im

.

.

..

-Why do we need such thick sections

e:t

Rotor Catenary Like a rope

Differential Settlement along Length

Every Mode Shape and associated Frequency does convey a message that must be well understood by the designer.

• Shear Modulus • Coefficient of

Sub-grade Reactions • Soil damping

• Soil Mass participation

..

Pile stiffness Properties

• Single Pile - Load Test

o Vertical Stiffness o Lateral Stiffness o Damping • Pile Group-o Vertical Stiffness o Lateral Stiffness o Damping

I

Effect due to static streststevetl

Suffix 01 - Test Level

I--~~~~~~~~~~~....,r- Suffix 02 - Foundation Level Formation Levei

Foundation Level

• WHETHER SOIL BEHAVES LIKE AN ELASTIC BODY? • WHETHER IT OBEYS HOOK'S LAW?

Presumption:

Foundation undergoes elastic vibrations as long as the total pressure (including static & dynamic pressure) on the soil is lower than its elastic limit

Itis the Ratio of Pressure to Deformation y F_I,

... J ...

Uniform Compression Uniform Shear Non-uniform Compression Non·uniform Shear z Foundnlion Block

Soilund~r UnifonTI Compression

F_y

c

~!2~ A ~!2. " y y Ay

Force~vApplied to the Foundation Block Resting over the Soil

E 1 C ~1.l3~ /, u \l-v·IvA 4 Gro 1 -I-v A G= E 2(1+v) 2 A~Ifro

Coefficient of Non- Uniform Compression

Coefficient of Uniform Shear

Coefficient of Non- Uniform Shear

C .J..= 0.5 C_u C 1=1.5 C,

• Foundation Supported directly over Soil • Foundation Supported over Piles

Linear Springs F k =----'-=C xA x x T F k =---"'-=C xA_{y u} y F k = _ Z=C xA Z z T Rotational Springs ko=MO=CDxl f) v xx M¢ k. = - = C x l 'I' ¢ 'I' zz

Soil Mass participation oo==:;> No-Soil Mass participation

Embedment Effect

Soil damping

DO==:;> Results in increased Damping

DO==:;> 8 to 10 %

1. Understanding the dynamic behaviour of a single pile as well as group of piles - Definite gaps exists 2. Dynamic characteristics of piles - Complex Task

and suffers with many Associated Uncertainties 3. Dynamic Behaviour of Group of Piles - is still

considered to be in its Infancy

4. Reliability of dynamic characteristics? - Reliability computed dynamic response?

Vertical pile stiffness (k_{v )}

and Lateral pile stiffness (

k

h )

• Foundation: Length 'L', Width 'B' and Depth 'H' • Pile: Diameter'd' & Pile spacing's'

Piles are so placed that their spacing along length and width of the foundation remains same.

Influence Coefficient

( ) 0.65

aejf =0.212 ;

Effective vertical stiffness of each pile Effective lateral stiffness of each pile

{ Pil,S",,10'

(!..)}

PIle D,ameter d 033 ) 4 45 5 6 {_Coemcien"'ff_{tas Proposed}} 043 0.52 0.56 0.60 0.68

{co'm:':,

Aft"

BM"O}

Tablel-14 pp48

041 0.64 0.65

This empirical relationship provides a fairly good estimate of influence coefficient of a single pile

Case Studies

Whenever high vibrations are notice

on any machine

.

• In 9 out of 10 cases, the blame always goes to machine manufacturer

• In 50 % of the cases, the source of the problem may

not be machine alone and solution may lie

somewhere else

• Each and every associated segment tries to play safe and becomes defensive

• It results in -Delay in finding solution

It requires Right Attitude to tackle all failure problems with of course Right Team of Experts armed with

Right Instrumentation

• A uniform reduction of vibration amplitudes from top to bottom of bearing housing exhibits a healthy trend.

• For one of the bearing housing, the trend was opposite. _ Records are shown in Figure

Bearing 4 1325

~l

0

.J.1 .. :: "-

Ji

'\. , r "-"

/

"-11 " --I ! I I _·+-+-t--t-"1

o

20 40 60 80 100 Vibration In microns d·,..e:--+_.::l, Bearln!!

• The grout underneath the bearing seating

plate was totally carbonized perhaps due to

chemical reaction of the grout with spilled

oil

• It behaved

like

charcoal

powdery cake

having no strength and it was fully soaked

in oil.

• After re-grouting the pedestal the problem

disappeared

o Vibration pick up Location o o o -===='==:;::==~_0

LC

~\r-::-!~~-~~~~~1! SECTION o D o , _ Base i Compressor i Plate I I3ctlow o~_~ ,~--- ----I PLAN o

Vibration measurement records

at various pick-up locations

Longitudinal Transverse Vertical

Foundation 40

Base frame Channel 40 20 25

Base Plate 60/420 Motor 150 125 Tank

~

150 90 Compressor 500 300

~

NRV

I

1500

I

₁₁₀₀₀

I

100 Piping

_I

₂₆₀₀

I

I

800

I

• High base plate vibration indicated loosening of foundation bolts.

• Close examination· revealed broken welding of support lug to base frame.

• Repair of support lug and tightening foundation bolts brought down vibration level from 420 microns to 130 microns.

• This also brought down compressor vibration levels to 250 /300 /250 microns in XN /Z direction

• High piping vibration levels suggested need to isolate NRV.

• Isolation of NRV resulted in drastic reduction of vibration all through. NRV levels were still around 200 microns.

on a frame inside a plant • A reciprocating compressor

foundation was to be located building.

• Dynamic forces developed by compressor were extremely high

• Supporting the foundation over the soil results in excessive amplitudes of vibration

• The size of the base raft also can not be increased

because of restrictions imposed by other

structural foundation.

The only options were

i) either to strengthen the soil by whatsoever possible means,

ii) resort to pile supported foundations or

iii) use strong stiffness material underneath the base of the foundation so as to limit the amplitudes within permissible levels.

The decision by the company was to resort to isolation technique and design the foundation.

, - - - -

-Machine

1

[J

" .. I /

..

i,(_

~

'1[:':::_: ' ..

. t· , .

Detail· A

Isolation PadfCork Pad

Placement of Isolator In case of Frame Foundation

• A common raft was provided spanning across

width of the building

• Compressor foundation was placed over the raft with Cork as Isolation device so as to minimize transmission of forces from machine to the common foundation

• This system was designed by the author in 1974 • With this arrangement Machine was installed and

has run satisfactorily keeping the amplitudes within permissible limits

Cork thickness of 75 mm below the frame foundation was found to be adequate. Cork properties were tested at one of the national laboratory. Recommended values for computation are as under:

Compressive strength Elastic Modulus (Static) Elastic Modulus (Dynamic)

Coefficient of Uniform Compression

500 kN/m2

10 MPa 15 MPa 20 x 104kN/m 3

• The concept was used once again by the author, in 1979, for design of a Frame Foundation for a Gas Turbine.

• The need arose because of slip

during planning. While making the

layout, not adequate space was left

to accommodate the GT.

• Unlike previous case, the machine is a high rpm machine and it was rather easy to get the required frequency ratio for achieving desired isolation.

• The success has given improved

confidence level for such designs.

Dissimilar vibration behaviour of Two Identical Units on Identical Foundations placed next to each other • Machine was running with high vibrations since a

decade and a half.

• High column vibrations as well as high deck vibrations are reported in one unit whereas another identical unit just adjacent to it is reported running satisfactorily.

• Cracks at the column top below deck have also been observed. These are perhaps locations of construction joint of column with top deck.

26.0OJ

o I 2 3 45 6 7

'" -- - {9-- -

-e- ----

® ®® ® ® . -Bearing#

- - - '

A 210 MW T G Foundation (Typical) - Top Deck Plan Showing Column and Bearing Locations

Bearing Vibrations Horilonlal ~75 § ji'50 s .g ?25 0-E < 0j..LILL.lL..UIl...LJLL.lL..UIlJ 2 3 4 5 6 JOO 75

~

50

_n

25 0 2 Vertical Axial

Bearing Numbers Bcaring Numbers Bearing Nwnbers

III Unit 2

Bearing Level Amplitudes Turbo Generator Units! & 2

Top Deck Vibrations

~

i

~,-<---I

~

J:

j

/

~":d

Pick tiplocutions Top Deck Ll'fl edge

l'i~k.lipLtJCUliolls Top Dc"k Right edge

j'id .up L'lCations

H.pr;l,QI)1111(Jt11PJilUdcs

Uni!I-' [}Ilil;----·I

pick· up Location,

Column Vibrations M:1X Al11rli:lOdc Uuitl 55 21 107 41 j2

."

154 44 Unit 2

"

IS ]7 _2~ 16

"

20 24 Top

,

"-1

7 14 1

,

"

1 1 ~ 1 1 12 _{\ \}

,

_c \ \ ~ 10 \ ~ \ \ ~ \ \ ~ \ \ ~ 6 \ \ 1 \ 1 \ c \ ~ 1 '" I

."

2

iJ

, • BottOIlJ I)

+...

200 {I20U 200 0 200 ZOOI)cOO 200 I)200 200 (] ZOO 200 I)200 200I)In0200 o201)

rui,

"

0 C D (j II

Amplitude Variatiun in Columns Along Height Horizont<-ll Amplitudes

M,\x Ampilltl(lc lIni! I

"

Uni12 \0 lop·

r

~ 14

"

E 12 c c 10

I

~ i: c I ~ E

I

c ~_c

I

-In ~

L

Bottom "---.:.100(I zon Cols A 22 7(, 5'>

"

12 49 169 I(, \6

"

16 \0

"

2< I

,

-I

I

,

I

I

I \ \

I

\ \

I

\ I

I

\ \ I

I

\

L

\ \

j

,

\I I)200 -200 I) ·200 () 201l -2-00 I):100-200 0200-200 I)ZOO -200I)'201l B r: F II K L A~,i.r!J,Amp-lil\I!l~..lm,i~[,\lfl~.l

• Ratio of bearing amplitudes of two units is of the order of 3

• Ratio of top deck amplitudes is of the order of 2

• It is a wild guess and a question mark whether cracking of the columns at top (close to deck bottom (soffit of beam) is responsible for such a behaviour or such high vibrations have resulted in cracking of the column?

• Visual examination of the column vibration and plot of amplitudes indicate that 2nd mode frequency of some of the individual columns in transverse direction has tendency to be in resonance with operating speed. Similar behaviour is also noticed for some columns in axial direction.

FFT analysis of column vibrati.on

• FFT analysis of records confirm to the above observation.

• It is seen that the resonant frequency of some of the columns lie close to 50 Hz which is the machine running speed.

• Though the amplitude levels are low, the trend is not healthy.

• It is primarily because the analytical tools available about two decades back were not adequate to carry out such a detailed analysis and moreover the need was neither emphasized by the owner I

1JLi

'0 Unll I , , 1(0 10 F!'(\I\I",1<:y in CrM --'1 1 I i

I

.i

Col A 1,!llil1 Fr~'1l1en~yinrPM , 10 10 Frequency in C1'M ,

'"

-To be noted that scales are d,lfferent Ihthese , ,;dlagrams

-C<lt\llnll Alf,plilU(k~"ITfR~wrd UnitI&2

Vibration Isolation of FD Fan Foundation

MB---"Motor BC<lrlng FH1---+ Fan Bearing· I (, J' _ _.,~ <112 -"+ Fan llctlring - 2

l.~j

014 5[J

l

L

~

a

1~;1Vli2

fBIIgiiO

L

_~.

__

110_{.:..._---}r

-

12

(c)Pick up locations at Foundation to&.sides

Recorded amplitudes are: • Vertical amplitude

@ pick up # 1, 2, 7& 8 about 600 microns • Axial amplitudes

@pick up# 4 & 10 50 microns

• Transverse amplitudes

@ pick up# 5& 8 100 microns

• Vertical amplitudes

@Steel frame for motor, fan etc 600 microns

• High vertical vibration led to the conclusion that desired frequency ratio is not being achieved as designed.

• After a thorough examination, it emerged that the connection from fan to air outlet duct is rigid.

• It restrains motion of the fan and thereby motion of inertia block.

• The system is not able to achieve desired frequency ratio for isolation to be effective.

• After bellow was introduced between fan and the duct, vibration levels reduced drastically.

CONSTRUCTION

ASPECTS

• Construction Joints

• Embedded Parts

• Placing

I

Laying of Concrete

Common Problems Noticed In Machine Foundations • Honeycombing

• Porosity

• Out of plumb columns

• Improper bonding of embedded parts • Opening up of construction joints, etc

• Patchwork repair of concrete beams and columns with sole objective of hiding faults and shortcomings is a common sight practically at every industrial set up.

Reasons

• Lack of right infrastructure with the

executing agency

• Inadequate

supervision

during

construction

• Lack of clarity

in

communicating

intricacies

associated

with

each

shortcomings

• Whereas the executing

agency walks

away after carrying out the necessary

repairs, it is the machine which has to

live with the associated problems for its

entire life.

• It then becomes a starting point of debate

between

customer/owner

and

manufacturer for all associated problems

related to machine performance.

• Proper contact of seating plate with concrete bears more importance for turbo Generator sets. • During Start-up and cooling cycle, turbine casing

undergoes differential thermal expansion and contraction.

• Casing slides over seating plates and frictional force is transferred to the foundation through these seating plates.

• This basic process demands proper contact and bond between seating plates and concrete.

• Quality assurance plans must be drawn to

Construction Joints

• An improper construction joint leads to change in natural frequencies of the foundation and that in turn reflects on the performance of machine.

• It is the designer who must analyze the implications of misbehaviour of construction joint and take due care while designing these construction joints

• Its specific location, details of shear dowels and procedure of joining old concrete with fresh concrete must be clearly marked on the drawing.

Embedded Parts

• Embedded parts are used to support auxiliary components, instrumentation, piping etc.

• Invariably it is noticed that a structural angle with lugs provided at suitable interval I spacing is placed

at each corner of practically every column.

• More often than not, these lugs are welded to the reinforcing steel to hold these in position.

• Such a practice reflects non-engineered approach and in author's opinion must be discouraged.

Welding of lugs of embedded parts to

reinforcing steel

• Welding of lugs of embedded parts to reinforcing steel of beams, columns, deck it is highly

undesirable.

• Due to shrinkage associated with concrete this

process results in loss of contact between embedded parts and concrete

• Itbecomes a source of vibration especially when these embedded parts are machine seating plates.

• Proper contact of seating plate with concrete bears more importance for turbo Generator sets. • During Start-up and cooling cycle, turbine casing

undergoes differential thermal expansion and contraction.

• Casing slides over seating plates and frictional force is transferred to the foundation through these seating plates.

• This basic process demands proper contact and bond between seating plates and concrete.

• Quality assurance plans must be drawn to

Concrete Beam

Seating Plate

Concrete Beam

Dummy Concrete to be chipped off after removal of side shuttering

while concrete is green

Support lugs of Seating plate or Embedded Plate must not be welded with

Main Rlf of Beam

Sketch showing Dummy Concrete for proper embeddemenl of Seating Plate located abutting Beam Edge

Cold

Joints

All efforts must be made to avoid cold joints.

• While laying concrete in thick blocks like base raftI

top deck of a frame foundation, large size block foundations etc, limitation on thickness layer, time lapse between laying two successive layers of

concrete, must be specified (by concrete

technologists).

• In absence of any other recommendation by the designer, the concrete layer height should be limited to 400 mm and time gap between laying two layers of concrete should be restricted to 25 - 30 minutes.

Segregation

• Construction process for machine foundation, especially frame foundations, is a bit complex compared to normal building construction.

• Heights of columns, which are to be concreted in a single pour, are invariably larger than routine building construction jobs.

• Height of drop of concrete must explicitly be specified so as to avoid any segregation of concrete.

• This must also be specifically and clearly indicated in the design drawing.

Mass Concreting

Ambient temperature for laying concrete must be specified.

In case concrete is laid in hot climate, concept of employing chillers must also be specified

Grouting

• Various types of grouts are currently available to cover up shortcomings of concreting process.

• These are employed for filling honeycombs, cracks etc.

• These are also used for leveling under seating plates, filling up bolt pockets etc.

• Each grout compound has associated limitations that restrict its usage for all kind of environments.

• Specific Epoxy grouts show a significant variation of elastic modulus with temperature. Such grouts are not recommended for use in high temperature zones like area near HP turbine.

• Some grouts may show reaction with oil & chemical environments. These are unsuitable for grouting seating plates in zones where oils and chemicals are active.

Mathematical

'--_ _mod::..:e:..:..I_--J

c:::::::>

Assumptions

Approximations

Simplifications

compatible

with

prototype

Validation

Extent of complexity of

Mathematical Model

Columns A Typ. Fdn. FE Analysis Highly Complex Model Feasible Complexity vs. Reliability Results ??? 1 - OOF System

Deck Columns A Typ. Fdn. 2-DOF System Columns A Typ. Fdn.

•

Equivalent SOOF system

Kinetic Energy Equivalence

);>

A column supporting the mass

);>

A cantilever beam supporting the mass

);>

A simply supported beam supporting the mass

);>

A fixed beam supporting the mass

I

m+0.5me

I

m

I

m+0.33mel

I

For Static Analysis

I

Strain Energy Equivalence

Physical System

Kinetic Energy Equivalence

Cantilever

Beam

Simply

Supported

Beam

Fixed - Fixed

Beam

=0.23 x mass of beam =0.37x mass of beam

Block Foundations

• Solution feasible only either in X-Y

Plane or Y-Z Plane

-(V

axis being

vertical axis in both the cases)

• Formulations for motion in X-Y Plane

are not directly applicable in Y-Z

Plane

Frame Foundations

Limitations

• Single portal frame to represent 3D system

??

• The formulations cover only standard frames • Real life Frames do not fall under this category • Machine mass @ off-center location - often

encountered

• Longitudinal beams considered flexible enough to permit transverse frames vibrate independently

LIMITATIONS

• Haunches

• Machine mass at beam off center locations • Beams extension as cantilever

• Beams inclined in elevation

• No frame beam at column locations

• Higher order frame column vibration frequencies • Presence of solid thick deck within the frames • Depression/recess in the top deck

(C) Mathematical Model (8) Deflection Under unit Load

[ Portal Frame - mass at Beam Center

J

'----~-y 11/ Ab,lh

t

---l---~-O

:), i

"~-(l,l

u.

A

Dill

X epA,,, I" epA,,1,

r-

L---4

(A) Portal Frame

Portal Frame with Machine Massmat Beam Center - Deflection and Bending Moments - Vibmtion in Vertical Mode

Portal Frame - with off-center mass at Beam

(C) Mathematical Model (B) Deflection Under unit Load

Portal Frame with Machine Massmat Beam Center~ Deflection and Bending Moments - Vibration in Vertical Mode

The formulations for deflection0Yb &0"

• Most

commonly

accepted

analysis

tool

• Effective Pre

&

Post-processing

• Interpretation of results

• Modifications - convenient

Commercially Available Packages

• Every package is a Black Box

• Associated limitations both explicit /implicit

Validation is a must

for acceptance of RESULTS

Modeling - Conveniences

• Machine modeled along with the foundation

• Rigid Beam Elements used for modeling the machine

• Solid Elements are used for modeling the

Foundation

• Soil is represented by equivalent springs

I

Solid Model

A Typical Block Foundation

FE Mesh

Solid Model ATypical Fan Foundation (portion below GroundLevel not shown)

Folludatioll Block -Solid Model&FE Mesh

Solid Model FE Mesh

A TypiCli1 TopPeck View

Openings, notches, cutouts, pockets eft.

Frame FOillldation - Solid Element Model&Shell Beam Model

Solid Model

Geometric Model

(b) Shell& Beam Elements

FE Mesb

• For Advanced Modeling

~ Rotor and Stator to be modeled independently

~ Rotor represented by appropriate beam

elements

~ Stator modeled using Rigid Links ~ Stator mass lumped at centroid

Foundation:

• Solid Elements

»

8-noded Brick Elements

»

or 10-noded Tetrahedral Elements

• Element size is fairly subjective and problem dependent

Degree of Freedom

• Incompatibility·

• Solid Elements - 3 OOF per node

• Boundary Elements (springs) 6 OOF

per node.

OlidElem~~

3· OFPer Node

j

Beam Element

6OOFPer Node

Degree of Freedom - Incompatibility

( SOIL

I

Many ways of mathematical

representation of soil

Design Office Practice for FE Analysis & Design of Foundations.

);> Soil represented by a set of equivalent springs

Soil represented by a set of eql,jivalent springs. " , . . . • . . . ' • . . • _ . _ . . . . • . . . . • ' " . d • . . _. . . . • . , . • . . . • . . . _ _ • . . . • . . . . .

3 Translational Springs and 3 Rotational Springs attached at CG of the Base

»

Results in close agreement with field measurements

3 Translational Springs attached at each node at the Base of the Foundation, in contact with the soil.

»

Provides upper bound to overall rotational stiffness Soil represented as continuum

»

Wide variation in Results noticed

3Translational&3Rotational Springs attached atCGof Base Area

3Translational Springs Attached at each node of Base Area in contact with soil

Solid Model FE Mesh Block- Without Embedment

Soil Represented as Continuum

(Soil Domain - 5 times respective dimensions)

Solid Model (cut-view) Solid Model (Full-view) Block- With Embedment

Soil Represented as Continuum

3 Translational & 3 Rotational Springs attached at CG of Base Area

Mode 1 3,62 Hi' Mode4 IO.89Hz Mode:: 563 Hz Mode 5 15.39Hz Mode 3 9.44 Hz Mode6 l5044Hz

Frequencies & Mode Shapes

3 Translational Springs Attached at each node of Base Area in contact with soil

Mooe 4 10,99 Hz

Mom-2 4,91 H2 Mode 3 8.86Hz

Mode 6 15.21 Hz

Mode 6

Mode 5 6,99 Hz

Soil Represented as Continuum

Block- Without Embedment

[

RECO~~~NDED

)

Frequencies & Mode Shapes

Soil Represented as Continuum

Block- With Embedment

NOT RECOMMENDED

c+

f

mg y 1,4 k

[-J-

~-:-

T

j , :fj;J \ (l I x I ~--,-99CQ / - , , - • ~_~,o _

Wf ...•.,... /,::y DOI-IJK'HIIOIl t

,~

tritt'.)

(~~ R

lill, d> III lJh:k I\'MX:(],IIKI".',l \\i~

(~) Block wilh C.:nlroidC1 •Displw:cl1'IcntiltII

restrained

(el Displ<lccd Posilion

A Rigid Block Supported by Translational & Rotational Springs

Equations of Motion at Base Point

Thus

All parameters (masse, stiffness and dynamic

force~~nSlated

to Base Point

Invariably this is not done

Thus the computed response never matches with actual field response

• Free Vibration Response • Forced Vibration Response

1 g acceleration load in each X, Y and Z direction

In case free vibration results show a pattern that does not appear to be logical, it is an indication to precisely review the mathematical model and make necessary amendments and repeat steps as above

Transient Resonance

0.6 0.5

•

~ ~ _0.4 ~~ B~ 0.3 c

-..

g • 0.2 .c 0 c 0:

"

0.1 For 50 Hz Mlc,

0.503 Max unbalance force

is about

0.5 times the Rotor Weight

Rotor Eccentricity

50microns

a 10 20 30 40 50 50 40 30 20 10 a

Start-up Steady-state Shut-down

I ( )~_I

>I<

'I

(

Speed Hz

,

Unbalance Force during Start-up, Steady-state & Shut-down for Rotor eccentricity 50 microns - Max Machine speed 50 Hz

!Responsel

Half

~5Z'

1. Computed values· Half amplitudes 2. Measured amplitudes double amplitudes

3. Permissible amplitudes, are at machine bearing locations

4. Machines can withstand much higher amplitudes (3 to 5 times higher) than permissible without any damage 5. Similar machines· different vibration limits· in different

environment

static deflection under self weight

p=

[k

=~

kg

~;;;

mg

p-

rg

v;;;g;k

p=

[ i

v5:

Parameters influencing

Machine Foundation Response

• Machine related

• Installation related

• Construction related

• Design related

Rotor

Machine

A Typical Block Foundation Supported by Soil Dynamic Forces

r'x,

F,,,F, Rotor Centerline m=System Mass C=System Centroid

M""=MMI@Centroid about X

M",y=MMI@Centroid about Y

M"" = MMI@Centroid about Z

M"wx=MMI@point 0 about X

M",,,y=MMI@point 0 about Y

M",,,=MMI@point 0 about Z

s h .x y

t

/

z

A Typical Block Foundation Supported by Soil Mathematical Representation

3 Translational

&

3 Rotational Springs

attached at the CG of Base Area

L

Soil Treated as continuum

]

- - - '

EQUIVALENT SYSTEM

ROlol' Centerline

~_

..

For Academic

Interest

if Springs are

attached

@

Centroid

Instead of CG

of Base Area

_{Springs attached @}

Centroid

Uncoupled

Six Natural Frequencies

Along Axis About Axis

z v y

edf-,

x ,

ri-p -

---

m

if

'l/ P'I/=

M

my Six DOF's 3 Dispalcements x,y, z

alongX, Y&Zaxes respectively and

3 Rotations

e,

'1/, ¢

Real Life Systems

Un-coupled Modes

Motion in X-Y Plane

Natural Frequencies

~

_{p = -}

kY ~p

_'f

=~=-"k'f

_M Y m . moy· 2 1 ( 2 2) 1 ~{ 2 2\2 2 2 pz =2IPx+P¢

+2

\px+P¢} -4yzpxp¢ Yz Y. lv!/liZ Yz=-_·; MlllOz Px2=:!:L ',P¢=-~2 k¢ m M_maz 2 1 ( 2 Pt =~

_r,

Pz+ MlliX ; Mihal

parameters (mass,

and

dynamic force) must be translated to

Base Point only

Invariably this is not done

Uncoupled modes of Vibration

!Alon9 -¥

I

Coupled modes of Vibration - X-V Plane

Dynamic Force and Moment applied at DOF Location

All computed Amplitudes are at OOF Location

Dynamic Force and Moment applied at DOF Location

(J ~

(Me)

" k_e

Molion in Y·ZPI~Jl~

Mt>l,no in X·Yrlarl~

MotioninZ~XPlane Amplihldc ('nmp0ncnl, 111 Foundation Top

X

Jlmax) =

I(Xo- H¢oH(L/2)lfo

I

Yflma,)=

Iyo

I

+

I(L/2 )Bol

+

I(B/2

)¢oll

Zflmax) =IcZo +

HBoll+!(B/2)lful

• Amplitudes of vibration to be within the allowable values.

• If higher amplitudes reanalyze

Example,

Slide 1 of 4

Find Response of the system?

Machine on RCC Block Supported byRotational Spring and Translational

Spring attached at Base Center Point 0

k, =1,6X10' kN/m k¢ = 2.1XI 0' kNm/rad Example Slide 2 of4 Mass Machine

=

5000 kg

=

5.0 I Block

=

2 X 3x4 X 2.5

=

60 I Tolal 65 I Limiting Frequencies

_ {k; _

1.6xlO' Px -

f;;; -

65000 =49,6radI s _ _ _ _1_.5=1,654m 2.1X10' =28.35 261.283 rad/s 0.319

F,

=

5 kN F, =:-5x3.5=-17.5 kNm (Moment) Frequency Ratios fl,

=

3!.-

=

94.24

=

3.71; fl,

=

~

=

94,24

=

0.963 p, 25.38 p, 97.84 flx

=

~

=

94.24

=

1.899; fl.

=

~

=

94.24

=

3.32 Px 49.6 p. 28.35 x = Fx _{= 5000 3.125X10-}5 _m s/ k_x 1.6xl08 X o =33.65xlO-5_-53.05xlO-5_=-19.4xl0-5_m

[

(1-,0;)

mh

,0;

J

,po = ,psi

(1_

,01'Xl

-,oiJ

Xst Mmo,

(I

-,o?

Xl-

,oJ)

d. = M¢ = -17500 =-8 33 10-5 _d

rsr 8 ' X ra

k¢ 2.lx10

!Po

= (-23.2) x 10-5+15.2xlO-5 = -8.0xlO-5rad

Example,~__ Slide30f4

[

Example'

Design

a

Block

Foundation

for

a

Rotary Machine set consisting

of

a

Drive

machine

and

a

Non-Drive

Machine, coupled directly.

Foundation outline Machine-loading diagram Sectional elevation Machine parameters Foundation parameters Soil parameters