1. GT STRUDL User’s Group Presentation Atlanta, GA June 24-26,2009
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

2. Topic Outline Design Overview Preliminary Design Dynamic Properties
Modeling and Analysis of Elevated Skid Mounted High Speed Compressor Structure
Topic Outline
Design Overview
Preliminary Design
Dynamic Properties
Geometry Modeling
Dynamic Analysis
Beyond Moore’s Law

3. 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: Kips
Piping: Kips
Total Machine + Skid WT = 122 Kips
Dynamic analysis is required for 500 HP or greater or machinery with total weight more than 5000 lbs per JACOBS standard. Since it shows that this is a steam-turbine compressor, a elevated structure or a table top type supporting structure shall be designed.

4. Design Overview Study Design Data Study Soil Report Start
Preliminary Design
Request for More
Geotech./Vendor Info
Generate
Dynamic Impedance
Derive
Excitation Force
Create
Geometry Model
If you concluded after the preliminary study that the foundation need to be supported on piles, more geotechnical investigation will be requested. Geotechnical engineer also need your input on foundation weight and dimension to finalize the dynamic properties.
If the dynamic properties are included within the geotechnical report, you need to provide them with the foundation and equipment information, dimensions and weight.
Calculate the exitation force from the unbalanced mass criteria.
Perform
Dynamic Analysis
Check Criteria No
Fine Tune
Foundation Geometry
Yes
Detail Design
Foundation

5. 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)
People are more sensitive than the machine. So if the design result can meet the standard not disturb people. That should be not a problem to satisfy the machine criteria. The chart also show the limit of structures. But it is beyond the limit of the machine. If the vibration can be taken by machine. It should not be a problem for the structure.

6. Preliminary Design Purpose: Based on:
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.

7. Preliminary Design FrameWorks Model: Steam Condenser
Steam Turbine-Compressor Skid.
Steam Condenser

8. Preliminary Design
Using FrameWorks 3D model to obtain the foundation center of gravity:

9. Preliminary Design
Concrete Foundation Only
Equipments + Foundation

10. Static Spring Constants
Dynamic Properties
Dynamic Equilibrium Equation:
In Veletsos Model, the Dynamic Impedance Expressed as:
Mode
Vertical
Horizontal
Rocking
Torsion
Static Spring Constants
Dynamic Impedance

11. 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
Spring Constant
Reference
Vertical
Timoshenko & Goodier (1951)
Horizontal
Bycroft (1956)
Rocking
Borowicka (1943)
Torsion
Reissner & Sagoci (1944)
A Frequency Independent Model, Applied for 0 < a0 <1.0
a0: Dimensionless frequency.

12. Dynamic Properties Dimensionless frequency, a0 Where:
ω: machine speed – equipment;
R: foundation radius – foundation;
Vs: shear wave speed – soil.

13. Dynamic Properties Dynamic Stiffness: Dynamic Damping: Dynamic Ratio:
Critical Damping:
(translational)
(rotational)

14. 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.

15. 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.

16. 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.

17. 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.

18. Dynamic Properties
Dynamic Stiffness and Damping Coefficients:

19. Dynamic Properties
At The Speed: f = 7242 Hz:

20. Dynamic Properties At The Speed: f = 11522 Hz: Changes less than 0.2%
The damping ratio increase with the exciting fore frequency. From Veletsos’ equation for dynamic stiffness and damping coefficients on slides 14 indicates that a0 great than 10, and the soil is granular soil, the changes can negligible.

21. Dynamic Properties Equivalent Foundation Radius:
(The Original Veletsos’ Studies Was on Circular, Massless Disk)

22. Dynamic Properties
Evaluation of Static Stiffness of Circular Footing on Inhomogeneous Half-space (Werkle and Waas):
In a real world, the homogeneous half-space rarely exits. Because the stiffness of soil increase downward as the overburden and thus the confining pressure increase. The lack of homogeneity is in practical case often circumvented by intuitively choosing an equivalent, representative value of the soil shear modulus.

23. Seismic Downhole Survey
A seismic downhole survey can be used to determine the dynamic shear module. This is the economic alternative to crosshole testing. Since there will be only one borehole is placed.

24. Seismic Downhole Survey
P-Wave:
S-Wave:
Whereas shear waves can propagate only through the mineral skeleton of a soil, fluids offer no shear resistance. P waves can propagate through both the mineral skeleton and the pore water.

25. Seismic Downhole Survey

26. Seismic Downhole Survey
To Determine Soil Moduli from in-situ testing data:
For soils that are not close to saturation, μ can be obtained:
Empirical Correlations for Vs (Imai 1977):
The dynamic shear module, G has been derived from the the survy data. Standard Penetration Count, N, at nearby boring sites, can be used to get the approximate shear speed. They are correlated. Imai of Japan reported the correlation, and Prakash and Puri (1981, 1984) successfully applied the above relationship in predicting dynamic soil properties at different depths.
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.

27. Seismic Downhole Survey
The dynamic shear module, G has been derived from the the survy data. Standard Penetration Count, N, at nearby boring sites, can be used to get the approximate shear speed. They are correlated.

28. Dynamic Properties

29. Dynamic Properties Dynamic Unbalance Forces:
The Dynamic Equilibrium Equation:
GTSTRUDL Harmonic Load Command:
On the left is the GTSTRUDL harmonic load command.
Where:
Sf = 2.0, service factor for centrifugal compressor.
The amplitude of a harmonic forcing function of the Harmonic Loading Condition in GTSTRUDL:
(B = C = 0)

30. Centrifugal Compressor
Dynamic Properties
Industrial Standard:
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)
f0 is the max. continuous operating speed. API standard is for new equipment test, it will be quite small compare with ISO When we dealing with the unbalanced force issue, vendor’s mechanical engineer and design firm’s structural engineer are often having different interest when dealing with the rotor unbalanced force, just be careful.

31. Dynamic Properties Calculating Amplitude of Harmonic Force: Compressor
Equipment
Rotor Weight
Compressor
2922 lbm
Steam-Turbine
1175 lbm
UNIT LBS FEET SEC CYCLE
HARMONIC LOADING 2 'FREQUENCY FROM 7,000RPM TO 12,000RPM-IN PHASE'
JOINT LOAD SIN FREQ FROM TO AT 1.0
1 2 FORCE Y A PHASE 0.0
3 4 FORCE Y A PHASE 0.0 $
1 2 FORCE X A PHASE 0.0
3 4 FORCE X A PHASE 0.0
END OF HARMONIC LOAD
Do not use “eXω=0.1” as a constant for variable speed unbalance force. That may result of over conservative. Since eccentricity of machine rotor should not increase as the speed decrease.

32. Model with Plates and Beams
Geometry Modeling
Tabletop with Skid Finite Element Modeling:
Tabletop mass c.g. elevation
Plate elements continuity violation
Compressor skid
How to Set the Elevation?
The dilemma of modeling to accurate mass elevation or column length?
Model with Plates and Beams

33. Maxwell Model For Vibration of Viscoelastic Foundation
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.
STATUS SUPPORT JOINT -
1029 TO 1041 BY TO 1054 BY 2 -
1085 TO 1097 BY TO 1110 BY 2 -
1141 TO 1153 BY TO 1166 BY 2 -
1197 TO 1209 BY TO 1222 BY 2 -
1253 TO 1265 BY TO 1278 BY 2 -
1309 TO 1321 BY TO 1334 BY 2 -
1365 TO 1377 BY TO 1390 BY 2 -
1421 TO 1433 BY TO 1446 BY 2 –
…………………………………….
JOINT RELEASES MOMENT X Y Z
………………………………………
FORCE X Z KFY 720 DAMPING 0.70 $
3102 TO 3112 BY TO 3127 BY 2 -
FORCE X Y KFZ DAMPING 0.4
2020 TO 2568 BY TO 3100 BY 56 -
FORCE Y Z KFX DAMPING 0.40
Physically Similar to Shock Absorber
Maxwell Model For Vibration of Viscoelastic Foundation

34. Geometry Modeling Dynamic Stiffness and Damping Distribution:
Dynamic sprint constants and damping ratio are not distributed onto every note. Since the element dimension is so small, only 1’x1’. It will make the foundation model simple.

35. 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) y x x y
Note:
E of Filled Epoxy Grout can be ignored. It’s only 1/3 of Regular concrete.

36. Geometry Modeling Skid Modeled in Solid Elements:
Converted Steel Frame Elements
Filled Grout Elements
Exhaust Opening

37. 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.

38. 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.

39. 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.

40. Beyond Moore’s Law Multiple Core Processors Beyond Moore’s Law:
Commonly cited as “Processor speeds double every 18 months”, Moore’s Law actually states that the doubling effect is relative to the number of transistors that can be put into a chip. But by 2003, that doubling effect started to wane, and by 2004, it came to very visible halt. As single core processors rapidly reach the physical limits. The amount of performance gained by the use of a multi-core processor is strongly dependent on the software algorithms and implementation.

41. 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

42. 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.

43. Time to Solve Eigenproblem
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
11 Min. 8 Sec.
26 Min. 8 Sec. √
2 Min. 13 sec.
6 Min. 14 Sec.
43.8 Sec.
4 Min. 25 Sec.
Time to solve Eigenproblem including solving the eigenpriblem and time to transform eigenvectors to joints. Tome to transfer eigenvectors to joints improved from 395 sec. to less than 1 second, 0.45 sec. It the implement speed was not considered, it would more than take 26 min. If both commands are used, it will take only 4 min. and 25 sec. It is practically acceptable. Large Problem Size command handling the virtual memory issue. GTSELANCZOS command improves eigenvalue analysis in dealing with computer RAM, virtual memory and hard drive.

44. Jonathan.guan@jacobs.com 832-351-6847
Modeling and Analysis of Elevated Skid Mounted High Speed Compressor Structure
QUESTIONS?
Jonathan Guan, P.E.
Jacobs Engineering
Houston, Texas