Descripción: 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& 18
th
March 2010
JI
Hyderabad 12, 13 & 26 th 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
1
2
• Machine • Foundation • Support System
Dynamic Force
Machine
Foundation
3
M/c Foundation Design END OBJECTIVE
~/
>-
Desired Performance
y
Minimum Vibration Transmission
1>-
Structural Integrity
I
4
Columns
5
6
PH FAN -FAN-PED-TOP -Vertical-
1:]
,.'" 0
"-
26
( Speed 1000 rpm
=16.8Hz
)
w
E
0.2
~
13
96
~
E E
168Hz
0
41,5
83
20
-)
101.04.2009 16:07:06
O/Ail 0.457 mmls rms
~ 1:] O~
30
orders
1000 RPM
PH FAN -FAN-PED-TOP -Horizon!a!-
r--------;::;[s=pe:::ed::;,o:::::oo=,p=m====::---c =16.8Hz
U~
~
E ~
0.2
E E
168 Hz
101:04.200916:06:44
O/AII 0.541 mm/s rms
1000 RPM
7
PH FAN -FAN-PED-TOP -Axial· ill
" "0
~
E
-"'. E E
1:] 1.2 1
26
96
[ Speed 1000 rpm = 16.8Hz
08 13 06 04 02 10
30
20
168 Hz
-)
101:04.2009 16:07:20
Transient Resonance @ 8,75 Hz
or.ders
1000 RPM
O/A1I1.696 mm/s rms
PH FAN - FAN DE . Vertical-vel Spec 1$0 Hz Cursor A
11,625 Hz
0,612 orders
0,696 mOlls OIAlll,109 01011.
'm"
Max Speed 800 rpm (13.33 Hz)
IflIi 01-44_2009 18:29:48
O/A1I1.10e 01011. tmS
8
PH FAN FAN DE - Horizontal- Vel Spec 1000 Hz
Sub-harmonic@ 7.6 Hz
12.5
H~
m"
0665 OIA111.116
Operating Speed 945 rpm (15.7 Hz)
"' "" "'
"" "' I " "' "' " 1
9
30m
Top Deck 30mx10mx1.5mthk Ht. above zero Level 10m
[ A Typical TG Foundation)
10
o
l._--t-+- -r-+----+---I--c=l-----I--~--J
Pick~up Locations,
Top Deck Left Edge
:~/~-j
1·
1_·"·__1,,,,,,,,,·+,·
:Pick-up Locations
i"Vertical Amplitudes
1,,,, -··!----------i----·····!·,·,,,,··+·-------r--··------!-----
plck··up Locatiom
Top Deck Right Edge
"'[
"
'----t-----+----+-~---c--+---+_r_----' Pick_up Locatiorl!;
Horizontal Amplitudes
210 MW TG Foundation - Top-Deck Vibration Record
Top
17 , ,
Bottom
COLUMNS
11
----
-
:
Typical Column Vibration Modes
12
Identical Foundations for Identical Machines on different soil c. ~
Foundation on Hard Rock
_.-
o
2
Distance in meters along length from Turbine end
13
Identical (adjacent) Foundations for Identical Machines on Identical Soil Top of Deck
Unit -2
::T
Unit -I
+
~
Base
--+ --I
o
20
:
I
40
I
--+---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
Bearing
o
I
20
40
60
I
80
I
I
100
Vibration In microns
Amplitude along Bearing Height 200 MW TG Foundation
14
WARNING
MOTTO
There are many factors that significantly influence the response
15
Cost of Machine foundation
InadequatelY constructed foundations
Shutdown cost
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
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
16
Basic Design Philosophy
Equation of Motion Free Vibration
Pv = Support
.
_ .v rad/s
~ m
17
\
Equation of Motion Forced Vibration
Support
....
-- ......... _.
Magnification
I I I I I I I I I I
l "---------
NOTOK
Response
I /
OK Strength Design
18
Strength Analysis & Design •
Short Circuit Forces
•
Earthquake Forces
•
Electro-magnetic Forces
•
Equivalent Dynamic Loads
•
Thermal Loads
Springs attached @ Centroid
19
Uncoupled Six Natural Frequencies
y
"
edt-x
About Axis
Along Axis
z
Pe=
ff e Mmx
--
x
,
Six DOr's 3 Dispalcements x, y, z along X, Y & Z axes respectively and 3 Rotations
e,
ljI,
¢
about X, Y & Z axes respectively
P==~
... -
Motion in X-V Plane y
A Rigid Block Supported by Translational & Rotational Springs
20
Natural Frequencies Limiting Frequencies PIfI::::
2
(2
2)
1 Px+p¢! --21 PI =-2-
Yz
Yz
~
FE --
M moy
J(Px+P¢ 2 2)' -4yzPxp¢ 22 1(--;
2 1 (2 ,) 1 2)' 22 p, ~-2- p, +p¢ +-2-'1 p, +P¢ -4y, P,P¢ y,
r Z
--
• -
-
• -
2 k 2 k¢ Px = -r , P¢ = - -
= Mill: .
m
Millo;'
Millo:
P2
• PI2
Pu or PLl eould either be Px or P¢
-
• -
y,
-
Pl.l
• -
PI
3 Frequencies
--7
Y3
Only One Frequency 2 Frequencies
= (k
p y
~;
y,~ k
2
Y,
f
Y1H=l
Y,
v~
~ 1 - OOF
System
2-DOF
System y
Frequencies are coupled
21
PI2 =
/1;
v-;;
Motion is coupled
k,
2-DOF System
Natural Frequencies
.-
--
Coupled Frequencies
P,&P2 • -
P2
- Pu • Pu
• -
• -
PI
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
Base Plate
Fixed Tube Heat Exchanger
22
Machine Data:
Coupling
DrIve MachIne
• Mass of Stator • Mass of Rotor • Operating Speed Driven Machme
A Typical Mlc Foundation System
• 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
Frame or Block
Deck
Deck
Columns
Columns
Frame or Block
23
Equipment Foundation Static Analysis
y
l [mg JI
Equation of Equilibrium Weight
Is
T
k {
Soil + Col
~L Math. Model
== F kyO y =: mg
Displacement Oy = mg
ky
m= mass of Equipment +Deck + Columns + Raft
Strain; Estatic; Stress Shear Force & Bending Moment Structural Design
Representing by an Un-Damped SDOF System (S
Columns
Mathematica I M:.;:;o""de"'I'--_-"J
y = { ::} x
Response
{flJ
1
24
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 VELOCITY
25
my y Mass
Y
kv (Soil + Col)
Cy (Soil + Col)
In
~j
r
T
kyY
f CyY
Free Body Diagram
[EqUation of Motion]
Solution to equation of motion
The damping value for which the radical becomes zero is termed as Critical Damping of the system.
26
For Under-Damped System, Free Vibration Response becomes:
Constants A & B are evaluated using Initial Conditions
,,'--------------'/
27
1.'5 . .
1.0 0.5
o -0.5 -1.0
-1.5
Free Vibration Response Undamped System Sy" 0, Under-Damped ~J' < I
tiT
~~
..--+
Critically Damped
~y =
I & Over-Damped c"v > 1
28
y
!
Dynamic Force F(t)
m
~v (Soil + Col)
Response
Mass
y= Cy
1
(Soil + Col)
y
f.J f.J y
Forced Vibration Equation ofMotion
= J(1-fJ:)'+(2fJ/;) = Dyn. Mag. Factor
py=)~; f3y=~;; Sy = damping constant
I Equipment Foundation]
Displacement
5=~ y k
[ Machine Foundation]
Response
y
f.J y
y={~}xi~)
= Dyn. Mag. Factor
29
r---
I~~,o I .\
5j 41 ~.
:;
~
=
0
.~
u
'"§,
J
j Resonance
2~
I !~,
!
.j:'
;;: I
I 0
0.5
0
J'n
fi
0.1
= y
1
~(I- 13;) + (213y sy ~ = 1.,
fl.
y
I
=
(2 S y)
I
'7f
rn
fly
For 2% damping fly = 25 For5%dampingfly =10 For 10% damping fI" = 5
~ 2.0
1.5 Frequency Ratio
2,5
3.0
~~
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
30
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 • Excitation Frequencies
31
,tfI"'-------, \
:8
Machine
+
: Response
~=8
y==t~}xl~)
I I Foundation
I \
Support
,-------'"
32
Machine Mass - Point of Application
Excitation Forces - Point of Application
33
Machine Centroid
~
Actual ,"-o OJ
Py < OJ
Frequency Margin + 20 %
4
01""·""··.,. 0,5 o
."., O,K
10
1.2
15
2,0
2.5
),0
Frequency Ratio fJ
Magnification Factor p vs. Frequency Ratio rl ± 20% Frequency Margin Region
44
Fr~!l1e
Foul1d"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
38~7
Columns Original
mm
Max Displacement
28~8
mm
Columns Modified
45
.. l!!!.!Im .
---
e:t
Why do we need such thick sections for Frame Foundation? •
46
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.
47
&
48
.. • 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 Groupo Vertical Stiffness o Lateral Stiffness o Damping
49
IEffect due to static streststevetl I--~~~~~~~~~~~....,r-
Suffix 01 - Test Level 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
50
It is the Ratio of Pressure to Deformation
Uniform Compression
FI,
y
Uniform Shear
.....J .....
Non-uniform Compression
Non·uniform Shear
Foundnlion
Fy
Block
c ~!2~ "
z
Soil
und~r
y
A y
~!2. Ay
UnifonTI Compression
Force ~v Applied to the Foundation Block Resting over the Soil
E 1 C ~1.l3~ /, u \l-v· IvA 4 G ro 1 I-v A
---
E
G=
2(1 + v) A
~ If
ro2
Coefficient of Non- Uniform Compression
Coefficient of Uniform Shear
Coefficient of Non- Uniform Shear
C .J.. = 0.5 Cu C 1=1.5
C,
51
•
Foundation Supported directly over Soil
•
Foundation Supported over Piles
Linear Springs F
k =----'-=C xA x x T
Rotational Springs ko=MO=CDxl f) v xx
F
k y =---"'-=C u xA y
F
k
=_Z
Z
z
=C xA T
M¢
k. =-=Cxl 'I'
¢
'I'
zz
52
Soil Mass participation
oo==:;>
No-Soil Mass participation
Embedment Effect
DO==:;>
Results in increased Damping
Soil 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?
53
Vertical pile stiffness (k v ) and Lateral pile stiffness ( k h )
• Foundation: • Pile:
Length 'L', Width 'B' and Depth 'H' 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
"'ff } { Coemcien t as Proposed
{co'm:':, Aft" BM"O} Tablel-14 pp48
033 )
043
4 45
0.52 0.56 0.60 0.68
5 6
041 0.64 0.65
This empirical relationship provides a fairly good estimate of influence coefficient of a single pile
54
Case Studies Field Perform·ance
55
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 Ji
0
d·,..e:--+_.::l,
.1 .. : "- '\. .J r , ""
/
11
o
--I
20
!
I
40
"Bearln!!
"
I _·+-+-t--t-"1
60
80
100
Vibration In microns
Amplitude along Bearing Height 200 MW TG Foundation
56
• 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
I3ctlow
o o~_~
, i
Compressor
o
_ Base Plate
o
i
I
o
o o
D ,~-----
I
PLAN
----
o
LC
-===='==:;::==~_ 0
Vibration pick up Location
~\r-::-!~~-~~~~~1!
SECTION
Motor Compre~sor Unit on a Block Foundation
57
Vibration measurement records at various pick-up locations
Longitudinal
Transverse
Vertical
40
Foundation Base frame Channel
40
20
Base Plate Motor Tank
Compressor
NRV Piping
25 60/420
~ I I 500
1500
150
125
150
90
300
~
I I 2600 I 11000
100
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 X N /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.
58
• A reciprocating compressor on a frame foundation was to be located inside a plant 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.
59
,----------- -
Machine
/
I
..
1 [J . ~t· i,(_
"
'1[:':::_: '
,. ..
Detail· A
.
Isolation Pad f Cork 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
60
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 10 4 kN/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.
61
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.
26.0 OJ
o '"
-- -
I {9-- -
2 45 67 -e----®3 - - - - - - - ®® - - -- - -- -- - ® - ® - . Bearing #
--------'
A 210 MW T G Foundation (Typical) - Top Deck Plan Showing Column and Bearing Locations
62
Bearing Vibrations
~
75
ji'
50
§
s
Horilonlal
75
50
.g
? 25
n
25
0E
< 0 j..LILL.lL..UIl...LJLL.lL..UIlJ 2
3
Vertical
Axial
Bcaring Numbers
Bearing Nwnbers
JOO
4
5
0
6
Bearing Numbers
~
2
III Unit 2 Bearing Level Amplitudes Turbo Generator Units! & 2
Top Deck Vibrations
i~ ~,-
I(,
\6
"
16
I I I \
rI I
j
I
"---
.:.100 (I zon Cols A
I)
B
" , ,
169
2<
-I
I)
r:
\
I I
I
200 -200
49
\
I
I
12 \0
I \
I
L
"
L
I
\
I
·200 () 201l -2-00
F
\ \ \ \ \ \ I
,
I)
:100 -200 0200 -200 I) ZOO -200 I) '201l II K L
A~,i.r!J,Amp-lil\I!l~..lm,i~[,\lfl~.l
Amplitude Variation in Columns Along Height Axial Amplitudes
64
• 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 customer nor by machine manufacturer.
65
Col A 1,!llil
Unll I
-
1
To be
noted that scales are d,lfferent Ihthese
, ,;dlagrams Fr~'1l1en~y
-
in rPM
--'1 1
I i
, '0
1(0
,
I .i
1JLi'" ,
10
10
,
10
Frequency in C1'M
F!'(\I\I",1
