Modeling and Analysis ofElevated Skid Mounted High Speed Compressor Structure
GT STRUDL User’s Group Presentation
Atlanta, GA June 24-26,2009
Jonathan Guan, P.E.
Houston, Texas
[email protected] 832-351-6847
Modeling and Analysis ofElevated Skid Mounted High Speed Compressor Structure
Topic Outline
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 HPSpeed: 7,242 to 11,522 rpmEquipment Weight
Compressor: 30.8 KipsSteam turbine: 54.0 KipsSkid: 31.3 KipsPiping: 6.0 Kips
Total Machine + Skid WT = 122 Kips
Design Overview
Study Soil Report
Start Preliminary Design
GenerateDynamic Impedance
DeriveExcitation Force
Create Geometry Model
Perform Dynamic Analysis
Check CriteriaFine Tune
Foundation Geometry
Request for MoreGeotech./Vendor Info
No
Yes
Detail DesignFoundation
Study Design Data
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
Steam Turbine-Compressor Skid.
FrameWorks Model:
Steam Condenser
Preliminary Design
Using FrameWorks 3D model to obtain the foundation center of gravity:
Preliminary Design
Equipments + Foundation Concrete Foundation Only
Dynamic Properties
In Veletsos Model, the Dynamic Impedance Expressed as:
)()( 000 aciaakKI dds
Dynamic Equilibrium Equation:
)(tFXKXCXM
Mode Vertical Horizontal Rocking Torsion
Static Spring Constants
Dynamic Impedance
14 vv
vRG
K
2
8 hhh
RGK
138 3
rrr
RGK3
16 3tt
tRGK
vvv ciakK 0 hhh ciakK 0 rrr ciakK 0 ttt ciakK 0
Dynamic Properties
The classic single lumped mass machine-foundation-soil system with circular foundation on elastic half-space summarized by Richart, Woods, Hall (1970):
A Frequency Independent Model, Applied for 0 < a0 <1.0
a0: Dimensionless frequency.
Motion Spring Constant Reference
Vertical Timoshenko & Goodier (1951)
Horizontal Bycroft (1956)
Rocking Borowicka (1943)
Torsion Reissner & Sagoci (1944)
14 RGK y
87
)1(32
RGK x
138 3RGKrz
3
316 RGK ry
Dynamic Properties
sVRa
0
Dimensionless frequency, a0
Where:
ω: machine speed – equipment;
R: foundation radius – foundation;
Vs: shear wave speed – soil.
Dynamic Properties
Dynamic Stiffness:
)( 0akkK ds
Dynamic Damping:
00 )( aackC ds
Dynamic Ratio:
cr
dscr C
aackCC 00/
Critical Damping:
MKCcr 2 (translational) IKCcr 2 (rotational)
Dynamic Properties
b1 to b4 in expression above are dimensionless functions of μ. Given by Veletsos for different type of soils.
Veletsos’ Model – Dynamic Stiffness and Damping Coefficients:
Dynamic Properties
Veletsos Model, kx & cx to Frequency Relation in Horizontal Mode:
cx is independent of a0 ,
or the frequency.
kx in sandy soil is kind of sensitive to a0 , or the frequency.
Dynamic Properties
Veletsos Model, kθ & cθ to Frequency Relation in Rocking Mode:
cθ is independent of a0 ,
or the frequency.
kθ in clay soil is very sensitive to a0 , or the frequency.
Dynamic Properties
Veletsos Model, kz & cz to Frequency Relation In Vertical Mode:
cz is independent of a0 ,
or the frequency.
kz in clay soil is very sensitive to a0 , or the frequency.
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:
gVG s /2
1/2
2/2
2
sp
sp
VVVV
For soils that are not close to saturation, μ can be obtained:
Empirical Correlations for Vs (Imai 1977):337.091NVs
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:
)(tFKYYCYM
)()( tSinSaMtF f
)(2
tSinSe
gW
f
)(2
tSinSe
gW
f
)(2 tSinA
CBAf 2
The amplitude of a harmonic forcing function of the Harmonic Loading Condition in GTSTRUDL:
(B = C = 0)2Af
Where:
Sf = 2.0, service factor for centrifugal compressor.
GTSTRUDL Harmonic Load Command:
Dynamic Properties
ISO 1940 G2.5 for Turbo-Compressor
API 617 for Centrifugal Compressor
e = 0.1/ω = 0.1/(2πx200) = 8.0x10-5(in)
e = 0.25/f0
= 0.25/(12,000 rpm) =2.0x10-5(in)
For Compressor Foundation Design
For New Equipment Testing(For Equipment Vendor)
)/(1.0 sine )/(25.00 minfe
Industrial Standard:
Dynamic Properties
Calculating Amplitude of Harmonic Force:
Equipment Rotor Weight
Compressor 2922 lbm
Steam-Turbine 1175 lbm
UNIT LBS FEET SEC CYCLEHARMONIC 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 0.03 4 FORCE Y A 0.00060 PHASE 0.0$1 2 FORCE X A 0.00024 PHASE 0.03 4 FORCE X A 0.00060 PHASE 0.0END OF HARMONIC LOAD$
f
r Seg
WA
35
102.10.212
100.80.32
2922
45
108.40.212
100.80.32
1175
Geometry Modeling
Tabletop with Skid Finite Element Modeling:
Plate elements continuity violation
How to Set the Elevation?
Model with Plates and Beams
The dilemma of modeling to accurate mass elevation or column length?
Tabletop mass c.g. elevation
Compressor skid
Geometry Modeling
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
Maxwell Model For Vibration of Viscoelastic Foundation
Physically Similar to Shock Absorber
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.
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 A = 28.5 in2
Equation shall satisfy:Es·Isx = Ee·Iex (1)
(Stiffness in y-y is not critical)
ksi
IIEE
ex
sxse 500,9
12/18121910000,29
3
Note:
E of Filled Epoxy Grout can be ignored. It’s only 1/3 of Regular concrete.
xx
y
y
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 ofElevated Skid Mounted High Speed Compressor Structure
QUESTIONS?
Jonathan Guan, P.E.
Jacobs EngineeringHouston, Texas
[email protected] 832-351-6847