Modeling and Analysis of
Elevated Skid Mounted High Speed Compressor Structure
GT STRUDL User’s Group
Presentation
Atlanta, GA June 24-26,2009
Jonathan Guan, P.E.
Houston, Texas
Jonathan.guan@jacobs.com
832-351-6847
Modeling and Analysis of
Elevated Skid Mounted High Speed Compressor Structure
Topic Outline
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Design Overview
Preliminary Design
Dynamic Properties
Geometry Modeling
Dynamic Analysis
Beyond Moore’s Law
Design Overview
Project Assignment:
To Design a Recycle Compressor with:
Power:
10,000 HP
Speed:
7,242 to 11,522 rpm
Equipment Weight
Compressor: 30.8 Kips
Steam turbine: 54.0 Kips
Skid:
31.3 Kips
Piping:
6.0 Kips
Total Machine + Skid WT = 122 Kips
Design Overview
Study
Design Data
Study Soil Report
Start
Preliminary Design
Generate
Dynamic Impedance
Derive
Excitation Force
Request for More
Geotech./Vendor Info
Create
Geometry Model
Perform
Dynamic Analysis
No
Check Criteria
Yes
Detail Design
Foundation
Fine Tune
Foundation Geometry
Design Overview
 Design Criteria:
The basic goal in the
design of a machine
foundation is to limit its
motion to amplitudes
that neither endanger
the satisfactory
operation of the
machine nor disturb
people working in the
immediate vicinity.
(Gazetas 1983)
Preliminary Design
Purpose:
• To initialize the
foundation dimension
and arrange columns
• To create the finite
element model for
dynamic analysis
Based on:
• Rule of thumbs
• Vendor data
• Soil Report
• Piping layout
Modeling Tool:
Other Software May Be
Used to Create the
Model.
Preliminary Design
FrameWorks
Model:
Steam TurbineCompressor Skid.
Steam
Condenser
Preliminary Design
Using FrameWorks 3D model to obtain the
foundation center of gravity:
Preliminary Design
Equipments + Foundation
Concrete Foundation Only
Dynamic Properties
Dynamic Equilibrium Equation:
M X C X  K X   F (t )
In Veletsos Model, the Dynamic Impedance Expressed as:
I  K s  kd (a0 )  ia0cd (a0 )
Mode
Vertical
Static Spring
4Gv Rv
K

v
Constants
1 
Dynamic
Impedance
Horizontal
Rocking
8Gh Rh
Kh 
2
8Gr Rr
Kr 
31   
K v k v  ia 0 cv  K h k h  ia 0 ch 
Torsion
3
16Gt Rt
Kt 
3
3
K r k r  ia 0 cr  K t k t  ia 0 ct 
Dynamic Properties
 The classic single lumped mass machine-foundation-soil system
with circular foundation on elastic half-space summarized by
Richart, Woods, Hall (1970):
Motion
Vertical
Horizontal
Rocking
Torsion
Spring Constant
Ky 
4G R
1 
32(1   )GR
7  8
8GR 3
K rz 
31   
16
K ry 
G R3
3
Kx 
Reference
Timoshenko & Goodier (1951)
Bycroft (1956)
Borowicka (1943)
Reissner & Sagoci (1944)
A Frequency Independent Model, Applied for 0 < a0 <1.0
a0: Dimensionless frequency.
Dynamic Properties
Dimensionless frequency, a0
a0 
R
Vs
Where:
ω: machine speed – equipment;
R: foundation radius – foundation;
Vs: shear wave speed – soil.
Dynamic Properties
Dynamic Stiffness:
Dynamic Damping:
C  ks  cd (a0 )  a0
K  k s  k d ( a0 )
Dynamic Ratio:
k s  cd a0   a0
  C / Ccr 
Ccr  
Critical Damping:
Ccr  2 K  M 
(translational)
Ccr  2 K  I 
(rotational)
Dynamic Properties
Veletsos’ Model – Dynamic Stiffness and Damping Coefficients:
b1 to b4 in expression above are dimensionless functions of μ. Given by Veletsos for
different type of soils.
Dynamic Properties
 Veletsos Model, kx & cx
to Frequency Relation
in Horizontal Mode:
 cx is independent of a ,
0
or the frequency.
 kx in sandy soil is kind
of sensitive to a , or the
frequency.
0
Dynamic Properties
 Veletsos Model, kθ & cθ
to Frequency Relation
in Rocking Mode:
 cθ is independent of a ,
0
or the frequency.
 kθ in clay soil is very
sensitive to a , or the
frequency.
0
Dynamic Properties
 Veletsos Model, kz & cz
to Frequency Relation
In Vertical Mode:
 cz is independent of a ,
0
or the frequency.
 kz in clay soil is very
sensitive to a , or the
frequency.
0
Dynamic Properties
Dynamic Stiffness and Damping Coefficients:
Dynamic Properties
At The Speed: f = 7242 Hz:
Dynamic Properties
At The Speed: f = 11522 Hz:
Changes less
than 0.2%
Changes less
than 0.2% .
Dynamic Properties
Equivalent Foundation Radius:
(The Original Veletsos’ Studies Was on Circular, Massless Disk)
Dynamic Properties
Evaluation of Static Stiffness of Circular Footing on Inhomogeneous
Half-space (Werkle and Waas):
Seismic Downhole Survey
Seismic Downhole Survey
P-Wave:
S-Wave:
Seismic Downhole Survey
Seismic Downhole Survey
 To Determine Soil Moduli from in-situ testing data:
G  Vs2  / g
 For soils that are not close to saturation, μ can be obtained:

V /V   2

2  V / V   1
2
p
s
2
p
s
 Empirical Correlations for Vs (Imai 1977):
Vs  91N 0.337
N, standard penetration number, however, the reliability of
such relations is very low, and they should only be used, if
necessary, for preliminary when seismic survey is not done.
Seismic Downhole Survey
Dynamic Properties
Dynamic Properties
Dynamic Unbalance Forces:

The Dynamic Equilibrium Equation:
GTSTRUDL Harmonic Load Command:
MY  CY  KY  F (t )
F (t )  M  a  S f  Sin (t   )
W 
  e   2   S f  Sin (t   )
g
W
 2

   e  S f   Sin (t   )
 g

 A   2  Sin (t   )
Where:
Sf = 2.0, service factor for
centrifugal compressor.
The amplitude of a harmonic forcing function of
the Harmonic Loading Condition in GTSTRUDL:
f  A 2  B   C
(B = C = 0)
f  A  2
Dynamic Properties
 Industrial Standard:
ISO 1940 G2.5
for Turbo-Compressor
API 617 for
Centrifugal Compressor
e    0.1(in / s)
e  f 0  0.25(in / m)
e = 0.1/ω
e = 0.25/f0
= 0.1/(2πx200)
= 8.0x10-5(in)
For Compressor Foundation
Design
= 0.25/(12,000 rpm)
=2.0x10-5(in)
For New Equipment Testing
(For Equipment Vendor)
Dynamic Properties
 Calculating Amplitude of Harmonic Force:
Equipment
Compressor
Steam-Turbine
Rotor Weight
W
A   r  e  S f
 g



2922 lbm
5
 2922   8.0 10 
  2.0  1.2 10 3

  
12
 32.0  

1175 lbm
5
 1175   8.0 10 
  2.0  4.8 10  4

  
12
 32.0  

UNIT LBS FEET SEC CYCLE
HARMONIC LOADING 2 'FREQUENCY FROM 7,000RPM TO 12,000RPM-IN PHASE'
JOINT LOAD SIN FREQ FROM 120.0 TO 200.0 AT 1.0
1 2 FORCE Y A 0.00024 PHASE 0.0
3 4 FORCE Y A 0.00060 PHASE 0.0
$
1 2 FORCE X A 0.00024 PHASE 0.0
3 4 FORCE X A 0.00060 PHASE 0.0
END OF HARMONIC LOAD
$
Geometry Modeling
Tabletop with Skid Finite Element Modeling:
Compressor
skid
Tabletop mass
c.g. elevation
Plate elements
continuity violation
How to Set the
Elevation?
The dilemma of
modeling to accurate
mass elevation or
column length?
Model with Plates and Beams
Geometry Modeling
Why Foundation Modeled as Linear Instead of
Nonlinear Elastic ?
For the small strains (less than about 0.005%)
usually induced in the soil by a properly designed
machine foundation, shear deformations are the
result of particle destortion rather than sliding and
rolling between particles, such deformation is
almost linearly elastic.
Physically Similar
to Shock Absorber
Maxwell Model For Vibration of
Viscoelastic Foundation
STATUS SUPPORT JOINT 1029 TO 1041 BY 2 1042 TO 1054 BY 2 1085 TO 1097 BY 2 1098 TO 1110 BY 2 1141 TO 1153 BY 2 1154 TO 1166 BY 2 1197 TO 1209 BY 2 1210 TO 1222 BY 2 1253 TO 1265 BY 2 1266 TO 1278 BY 2 1309 TO 1321 BY 2 1322 TO 1334 BY 2 1365 TO 1377 BY 2 1378 TO 1390 BY 2 1421 TO 1433 BY 2 1434 TO 1446 BY 2 –
…………………………………….
JOINT RELEASES MOMENT X Y Z
1029 TO 1041 BY 2 1042 TO 1054 BY 2 1085 TO 1097 BY 2 1098 TO 1110 BY 2 1141 TO 1153 BY 2 1154 TO 1166 BY 2 1197 TO 1209 BY 2 1210 TO 1222 BY 2 1253 TO 1265 BY 2 1266 TO 1278 BY 2 1309 TO 1321 BY 2 1322 TO 1334 BY 2 1365 TO 1377 BY 2 1378 TO 1390 BY 2 1421 TO 1433 BY 2 1434 TO 1446 BY 2 –
………………………………………
FORCE X Z KFY 720 DAMPING 0.70
$
JOINT RELEASES MOMENT X Y Z
3102 TO 3112 BY 2 3115 TO 3127 BY 2 FORCE X Y KFZ 12960 DAMPING 0.4
$
JOINT RELEASES MOMENT X Y Z
2020 TO 2568 BY 56 2652 TO 3100 BY 56 FORCE Y Z KFX 10080 DAMPING 0.40
Geometry Modeling
Dynamic Stiffness and Damping Distribution:
Geometry Modeling

Convert Skid Beam, W18X97 to a
Modulus of Elasticity Equivalent Solid
Element:
W18X97 Properties:
Ix = 1910 in4
Iy = 220 in4
y
x
x
A = 28.5 in2
Equation shall satisfy:
Es·Isx = Ee·Iex
(1)
(Stiffness in y-y is not critical)
Ee 
y
Es  I sx 29,000 1910

 9,500ksi
I ex
12183 / 12
Note:
E of Filled Epoxy Grout can be ignored. It’s only 1/3 of Regular concrete.
Geometry Modeling
Skid Modeled in Solid Elements:
Converted Steel
Frame Elements
Filled Grout
Elements
Exhaust
Opening
Dynamic Analysis
Mode Shape:
Mode: 56
Freq: 146.7 c/sec.
As expected, one of the
typical mode shape
shows that the table top
remain rigid while large
deflection observed at
columns and base slab.
The vibrating energy has
been absorbed by the
columns and base slab.
Dynamic Analysis
 Velocity (in vertical Y) vs
Frequency, Out of
Phase Load Case.
 Machine frequency
range: 120 cps to 200
cps.
 Max vertical velocity
found at joint 101,
Vy=0.032 in/sec, within
the “Very Good” range.
Dynamic Analysis
 Acceleration (in X dir.)
vs Frequency, Out of
Phase Load Case.
 The criteria to make
sure machine parts at
attachment point not
overstressed.
 Max Horizontal
Acceleration found at
joint 8128, ax=60.0
in/sec2, < 0.2g.
Beyond Moore’s Law
Multiple Core
Processors
Beyond Moore’s Law
GTSTRUDL Job Monitoring on a
Intel Duo Core CPU at 1.86Ghz
CPU No. 1
Fully Occupied
by GTSTRUDL
CPU No. 2
Not Reached by
GTSTRUDL
Beyond Moore’s Law
Finite Element
Dimension Limit:
It is usually recommended
that the maximum
dimension of an element
should not exceed λ/8 (G.
Gazetas).
λ=V/f
=762ft/s/[120, 192](c/s)
=[4’,6.35’]
λ/8=[0.5’, 0.8’].
Try: Element with
Horizontal Dimension: 1’x1’
Resulting the Tabletop with
• 4373 solid elements;
• 7024 joints;
• 21,000 DOF.
Beyond Moore’s Law
 Dynamic System Solution Implement Comparison:
 Dynamic Model Consist of 4373 solid elements and 7024 joints,
about 21,000 degree of freedoms.
 Max. Velocity and Acceleration Calculated with the Compressor
Speed from 120 – 200 cycle/sec. at 1.0 cycle/sec. step.
GTSTRUDL V29.0 Dynamic Speed Report for the Design Example
Large Problem Size
GTSELANCZOS
Time to Solve
Eigenproblem
Total CPU Time
X
X
11 Min. 8 Sec.
26 Min. 8 Sec.
√
X
2 Min. 13 sec.
6 Min. 14 Sec.
√
√
43.8 Sec.
4 Min. 25 Sec.
Modeling and Analysis of
Elevated Skid Mounted High Speed Compressor Structure
QUESTIONS?
Jonathan Guan, P.E.
Jacobs Engineering
Houston, Texas
Jonathan.guan@jacobs.com
832-351-6847