ping jiang - modal analysis for steam turbine-generator machine table-top foundation

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Modal Analysis for Steam Turbine/Generator Machine Table-Top Foundation

Ping Jiang, P.E., MSCE

WorleyParsons Group Inc., 2675 Morgantown Road, Reading, Pennsylvania, 19607; PH (610)855-2734; FAX (610)455-2727; email: [email protected] ABSTRACT This paper presents an alternative technique to the modal analysis of machine foundations. The frequency dependent soil impedance (stiffness & damping), soil-foundation-machine system modeling techniques and the system natural frequencies and mode shapes are addressed in the paper. Through comparative study of the methodologies for identifying the foundation rigid body motion modes and local member motion modes, this study proposes the use of the Dynamic Magnification Factors (DMF) to determine the acceptability of natural frequencies and mode shapes. This paper introduces an alternative technique for analyzing the excitation potential of the natural modes of vibration and presents a practical methodology by using a Dynamic Magnification Factor (DMF) curve to analyze the dynamic behavior of the foundation members within the full range of machine operating speeds. All analysis studies, techniques, criteria and methodologies presented and described in the paper are using an actual engineering project as an example. 1 INTRODUCTION

Steam Turbine/Generator (STG) machines in fossil or gas turbine power plants usually are set on table-top type foundations (Figure 1). The modal

analysis of the foundation is the most critical and fundamental study of the dynamic properties of these foundation structures under vibrational excitation.

Figure 1: STG Foundation 3D View

26842010 Structures Congress 2010 ASCE

Structures Congress 2010

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The traditional method of the modal analysis (Reference 1) is to identify which foundation natural frequenices (or modes) could potentially occur within the resonance exclusion zone (typically 15% of the machine normal operating speed) or machine critical frequencies exclusion zone (typically 5% of the critical speeds). Another method is to assess the excitation potential modes within the exclusion zone (Reference 2). In many cases, the results of both analyses are inadequate. The natural frequencies determined are often too tightly spaced and will often have a mode falling within the exclusion zones. However, after further forced vibration response analysis, results will most likely show the predicted foundation vibration responses are within the limits of the allowable design criteria (either vendor provided dynamic analysis criteria or ISO standards) (Reference 3). This paper presents an alternative modified technique for analyzing the excitation potential of the natural modes of vibration of the foundation based on a practical methodology using a Dynamic Magnification Factor (DMF) curve to analyze the dynamic behavior of the foundation members over the full range of machine operating speeds. 2 FINITE ELEMENT MODEL In order to accurately simulate the foundation mass/stiffness distribution, a finite element computer model is utilized to perform the foundation dynamic analysis. A sample of the finite element analysis (FEA) model

used for this study is illustrated in Figure 2. The accuracy of the modal analysis (natural frequencies and mode shapes studies) depends upon using the proper modeling techniques for the soil-foundation-machine system. For critical machine foundations, such as the Steam Turbine Generator (STG) foundation used in this example, or a foundation with dimensionless frequency ao > 1, the frequency dependent impedance of soil (the supporting media) needs to be considered in the analysis. For above ao is defined as

where R = equivalent foundation radius m = circular frequency of the

machine normal operating speed

Vs = shear wave velocity of the soil

In this example, a soil supported STG foundation is used. The soil impedance is calculated from DYNA5 (Reference 4). The soil impedance stiffness and damping constants at 60 Hz (the machine normal operating speed) is shown in the Figure 3. The soil dynamic stiffness obtained from DYNA5 is the global stiffness of the supporting soil which should be distributed to the bottom of the foundation base mat. The distribution is based on the influence area of the base nodes of the finite elements at the bottom of the FE model. The reinforced concrete table-top foundation is modeled using solid finite elements in STAAD Pro (Reference 5). The STG machine

masses are modeled in the STAAD FEA model as point loads.



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Figure 2 STG Foundation STAAD Pro Solid Finite Element Model Design Data: Machine running speed = 3600 rpm (normal operation) Base Mat: 29.87m (L) x 16m (W) x 2.438m (T)

Columns: 1.524m X 3m X 9.9m (H) Table Top: 2.388m thick (Turbine Area), 3m thick (Generator Area)

Foundation Total Self Weight = 59220kN The Weight of Machine = 11440kN

Figure 3 The Soil Impedance

Base Mat

Table-top Bearing Points



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3 ACCEPTANCE CRITERIA

The following foundation acceptance criteria was provided by the vendor.

a. The natural frequencies of the foundation must be determined for all speeds up to 4140 rpm (69Hz)

b. All natural frequencies of the soil-foundation-machine system should be low enough to get a low-tuned foundation. The modal frequencies of the foundation, including the longitudinal and transverse beams, must fall outside of an operating-speed-specific range extending from -10% to +15%, between 3240 rpm (54Hz) and 4140 rpm (69Hz) for 3600 rpm operation.

Particular attention must be paid to mode shapes with maximum amplitudes in Z and Y - direction at the interface points for the bearings and casings.

c. The natural frequencies of the foundation should not be closer than 5% of the horizontal (X-direction) and vertical (Y-direction) damped critical natural frequencies of the turbine-generator components (Table 1).

Table 1 THE DAMPED CRITICAL NATURAL FREQUENCIES (RPM) OF THE TURBINE AND GENERATOR ASSEMBLY



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4 ANALYSIS RESULTS

STAAD Pro (Version V8i) is utilized to perform the modal analysis. Figure 4 shows the natural frequencies for the soil-foundation-machine system. In Figure 5, 6 & 7, three fundamental mode shapes (they are rigid body motion modes) are shown .

Figure 4 The Foundation Natural Frequecies

For Mode 1, the natural frequency fz1 = 2.973Hz. It is one of the fundamental modes with a significant mass participation in transverse direction (Z direction). It is one of the significant rocking modes about the X axis.

Figure 5 The Mode Shape for Mode 1 For Mode 2, the frequency fx2 = 3.914Hz. It is one of the fundamental modes with a significant rocking mode about the Z-axis.

Figure 6 The Mode Shape for Mode 2 For Mode 4, the natural frequency fy1 = 6.911Hz. It is one of the fundamental modes with a significant mass participation in the Y-axis.



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Figure 7 The Mode Shape for Mode 4

Further investigation shows the first 10 modes (Figure 8) are all below the operating-speed-specific exclusion range (54Hz ~ 69Hz). These modes are most likely the rigid body motion modes of the overall foundation.

Figure 8 The first 10 modes with their frequencies

This satisfies the Acceptance Criteria b which requires the natural frequencies of the system to be low enough to get a low-tuned foundation. Usually, the lower modes mostly represent rigid body motions of the foundation (whole foundation vibration). The higher modes mostly represent local vibration motions of the foundation local members. Therefore local vibration has to be investigated to satisfy the acceptance criteria.

To confirm if the natural frequencies of the local structural members vibration modes meet the Acceptance Criteria c, in additional to using visual identification (Figure 9), an alternate method to assess the system natural frequency, the DMF concept, is proposed.

Figure 9 The Mode Shape 53, fxyz = 60.544Hz

5 HARMONIC FORCE STEADY STATE ANALYSIS & DYNAMIC MAGNIFICATION FACTOR (DMF)

A steady state analysis is performed by applying a unit harmonic force on the local member in the foundation model. Figure 10 depicts an isometric view of this foundation for a local beam at the turbine end beam on the table top of the foundation.

Figure 10 A unit harmonic force acts on the FEA model



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Dynamic Magnification Factor Y direction

00.20.40.60.8

11.21.41.61.8

1 6 10

14.4

20.3

25.1

31.4

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39.6

41.6

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47.9

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53.9

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59.5

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68.3

70.3 73

frequency

DM

F

From the Steady State Analysis result, the curve of dynamic response displacement in the frequency domain is shown in Figure 11 below.

Figure 11 The displacement response in frequency domain for the local member

Figure 12 DMF in frequency domain in vertical direction

In the curve (Figure 11), the frequencies corresponding to the peak displacements are the natural frequencies for the local member. For example the last peak close to the right end of the curve, occurs at a frequency of 60.544Hz (corresponding with mode 53).

We can also apply a unit static force at the same location on the beam to have a static displacement at this spot. Then the Dynamic Magnification Factor (Reference 6 & 7) is

DMF = dynamic / static In common practice, if DMF < 2.5, resonance response rarely occur. From the curve of DMF vs. natural frequencies shown in Figure 12 below, the maximum DMF in the Y-direction (vertical direction) is 1.70 at 3.8Hz. The DMF is less than 0.5 for the natural frequencies within operating-speed-specific exclusion range (54Hz~69Hz),



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This means that the amplitude of dynamic vibration response displacement is less than the static displacement at that local point. Therefore the resonance effect is negligible.

Theoretically, DMF can also be defined as (Reference 6)

= / n Where, = Damping ratio = Excitation frequency n = Natural frequency

When the resonance exclusion zone is 15% of operating-speed, it means

= / n 0.85 or 1.15.

Then

DMF = 1/ [(1-0.85^2)^2 + (2*0.08*0.85)^2]^0.5

= 3.23 (assume = 0.08)

Or

DMF = 1/ [(1-1.15^2)^2 + (2*0.08*1.15)^2]^0.5

= 2.69 (assume = 0.08)

This shows that DMF method can be used to reliably qualify a foundation that has a frequency in the exclusion zone. So it can be concluded: If the Dynamic Magnification Factor (DMF) at a natural frequency on the local member is less than 2.5, this local

member vibrating mode can be ignored from the natural frequency criteria assessment.

6 REFERENCES

1. ACI 351.3R-04 (2004), Foundation for Dynamic Equipment.

2. DIN 4024 part 1, Machine Foundations, April 1998

3. ISO 10816 (1995), Machine Vibration Evaluation of Machine Vibration by Measurements on Non-rotating Parts.

4. DYNA5, Geotechnical Research Centre, The University of Western Ontario.

5. STAAD Pro v8i, Bentley System, Inc.

6. Joseph W. Tedesco, William G. McDougal & C. Allen Ross (1999), Structural Dynamics: Theory And Applications, Addison-Wesley.

7. ASCE Publication (1987), Design of Large Steam Turbine-Generator Foundations



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ping jiang - modal analysis for steam turbine-generator machine table-top foundation

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