ON THE DETERMINATION OF BEARING SUPPORT PEDESTAL STIFFNESS USING SHAKER TESTING R. Subbiah Siemens Energy, Inc., 4400 Alafaya trail, Orlando FL 32817 USA Abstract An approach that enables rotor dynamists to determine the bearing support steel structural conditions and the associated stiffness values through shaker testing is presented. This paper highlights the postulation there is no single pedestal stiffness value that can be applied in rotor dynamic models to compute cylindrical (first) and conical (second) modes of a rotor. First rotor bending mode can be reverse engineered from operation data; however, assessment of support stiffness for the second mode is often difficult to obtain accurately because it usually occurs above the operating speed of the machine and is not measured or remains beyond over speed test limits. A way to obtain the second rotor mode stiffness accurately is by shaker testing. More than twelve shaker tests carried out by the author indicates that the cylindrical (static) and conical (dynamic) support stiffness values were distinctly different for turbine-generator rotor systems. Shaker test results also showed a consistent ratio (usually 2 to 1) existed between them. Shaker test data enables engineers to further assess the pedestal structural conditions by comparison of dynamic stiffness and/or the second rotor critical frequencies between turbines on the same rotor train. In summary, a validated evaluation approach is presented in this paper to obtain support stiffness values and the comparative structural condition of pedestals. Introduction Predicting critical speeds is very important in any rotating machinery design. Particularly so when hold speed requirements (in turbo-machinery) dictate avoiding critical speeds in a specified speed range. This is only possible with models that accurately represent the rotor, oil-film bearing dynamic characteristics and the support structural stiffness as well. There were numerous publications [1-4] that discussed the need for accurate representation of these parameters in rotor dynamic models. In this paper, the author discusses determining the nominal bearing support pedestal stiffness values via shaker tests. The discussions in this paper are to lay out processes to achieve the following: a) Determination of static and dynamic bearing support stiffness through shaker testing b) Evaluation of the relative stiffness of the two similar designs in a unit or in an another unit c) Criteria for stiffening the support structure d) Acceptance criteria/guideline for the bearing support and rotor conical frequency in reference to operating frequency e) Determination of optimal test configuration Shaker tests confirmed that there is no single support stiffness value that can be applied in rotor dynamic models to compute all rotor critical frequencies because the support stiffness value is mode-shape dependant. Investigations of various rotor support systems led to two different support stiffness values (static and dynamic) corresponding to first and second rotor modes respectively. Although support stiffness for the first bending mode can be reverse engineered from operation data, second mode stiffness can not be obtained that way, because, the second mode normally occurs above the operating speed or was not measured. A way to obtain the dynamic stiffness accurately is by shaker testing. Shaker test results showed a constant ratio existed between the two stiffness values; however, they were distinctly different. It should be noted that the frequencies measured by shaker tests represent the rigid support conditions of rotor. As such, the reported rotor critical frequencies were normally higher or similar to those obtained in operation when oil-film dynamic characteristics were accounted for. Two different turbine structures were tested and the details are discussed in this paper. Shaker Testing Process: Figure 1 shows the electrical shaker, accelerometer locations on the rotor and the bearing supports and other parts of the turbine structure. Variable frequencies drive (VFD), which is connected to a power source that enables varying the shaker speed. Rotational force due to the unbalance weights housed on either end of the shaker motor excites the rotor and the bearing support structure attached to it. Shaker speed is varied from 0 RPM up to 125% of operating speed. Rotational unbalance force of the shaker excites both vertical and horizontal modes of rotor and the structure attached. When the frequency (rotational speed of shaker) of the shaker matched with one of a natural frequency of the bearing support or the rotor or the other coupled structure, peak response of the corresponding mode can be observed in the frequency spectrum of the signal analyzer. At each bearing, the frequency sweep can be repeated to confirm consistency and repeatability of the measured data. Figure 2 shows the shaker installed on two different LP bearing structures.
End-wall X,Y,Z End-wall X,Y,Z Strongback TDC X,Y Strongback TDC X,Y,Z Shaker Y Rotor Y, Z Strongback Hor. X,Y,Z Y Y X Y Z s= Axial, Y-axis= Vertical & Z- axis= Horizontal Figure 1: Test Setup Showing Shaker and Accelerometer locations Adapter Plate Adapter Plate Figure 2: Shakers Mounted on Two Different Bearing Structures Through Adapter Plates A maximum unbalance weight setting of (weight x eccentricity) 25-30 in-lb was used in shaker testing. Typical shaker force vs speed curve is shown in Figure 3. Piezoelectric accelerometers were magnetically attached to the rotor and the bearing strong backs. The accelerometer signals were calibrated prior to testing. The responses to shaker excitation forces were measured using these accelerometers attached to the rotor and the bearing pedestal supports (vertical and horizontal directions). The acceleration output signals were electronically double-integrated to obtain displacements in mils (thousands of an inch) peak-to-peak.
12000 11000 10000 9000 @ 2200 RPM the force is ~8,000 lbf 8000 Force (lbs p-p) 7000 6000 5000 4000 3000 2000 1000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 Speed (RPM) Figure 3: Shaker Unbalance Force Vs Shaker Speed in RPM Example 1: LP Turbine System with Vintage Shrunk-on disc Design Shaker tests were performed for a train with two identical LP rotors; one of them is shown in Figure 4. Pertinent geometrical details are provided in Table-1. Generator End Turbine End Figure 4: LP Double Flow Turbine Assembly View Shaker tests were performed on four LP bearings of the Unit. Bode plots were obtained for the pedestal structure and the rotor through the shaker speed range of 0 RPM to 2400 RPM and are shown in Figure 5. The first LP rotor critical frequency corresponding to first bending mode in the vertical direction was identified at 1200 CPM (Cycles Per Minute) in the spectrum with the SE (Shaker end of the rotor) and NSE (Non-shaker end of the rotor) peak responses crossed the phase angle at 90 degrees. Similarly, the second rotor vertical critical frequency corresponding to second bending mode was identified at 2080 CPM when the peak responses of the SE and NSE were 180 degrees apart in phase (NSE phase at 240 and SE phase at 60 with a difference of 180). The bearing support mode was also identified at 1678 CPM. This mode is similar to second mode of rotor with the bearing support cones moving in vertical plane and at 180 degrees out-of-phase to each other.
Table-1: LP Rotor Geometrical Data shown in Figure 4 Location (From Turbine End) Diameter, in Length, in Coupling Flange 48 13.5 Overhang from Gland 24 22 Gland to Gland 37 220 Overhang from Gland 24 37 Coupling Flange 48 13.5 Rotor Material: Steel Total Weight ~ 200,000 lbs Cylindrical Bearings 24 x24 1 st Rotor Frequency=1200 2 nd Rotor Frequency CPM = 2085 CPM Bearing Support Frequency= 1678 CPM Figure 5: Frequency Spectrum by Shaker test on a LP turbine How to assess the acceptability of the measured frequencies Siemens guideline is to have no measured rotor frequencies within +/- 3 Hz of the operating frequency (in this case, it is 30 Hz) and no bearing pedestal frequencies within +/- 2 Hz of the operating frequency. However, if frequencies are identified within the above frequency avoidance zone, they are acceptable, if units have been operating within ISO 7919-2 (shaft Vibration) and 10816-2 (pedestal vibration) vibration levels and/or within vendor s operating experience. Static and Dynamic Bearing Pedestal Stiffness Definition Before going over the next section on the bearing support stiffness evaluation, it would help readers to understand the terminologies used to refer static and dynamic stiffness. Hard spring support stiffness that shapes up the first rotor bending mode (often known as, Cylindrical or Translational mode) is referred as, Static Stiffness [5]. Similarly, the second rotor bending mode (known as Conical Mode ) has been associated with soft spring support stiffness. It is referred here as, Dynamic Stiffness. In general, static bearing support stiffness value is always tested higher than the dynamic support stiffness and in many cases, dynamic stiffness is about half of static stiffness. See Figure 6.
Hard Spring Effect Soft Spring Effect Figure 6: Hard and Soft Spring Effects that shapes Static and Dynamic Stiffness Bearing Support Stiffness Evaluation For each of the bearing support pedestals, the static stiffness values (k) were obtained from the applied force (F) and the corresponding vibration response (x) as shown in the equation below: 8 2 k = ( ). 386,000 ( me) f x 2 ( ) where k = stiffness in million lbf/in me f x = mass unbalance = rotational frequency = measured vibration response, mils p-p Ideally, the static stiffness is computed at zero frequency. However, during on-site measurements, noise levels dominate at the low frequency spectrum and hamper identification of useful signals. Minimum shaker speed range that usually provides better response amplitudes just above the background noise was selected. Measured pedestal stiffness vs rotor frequency plot for the LP turbine pedestal (shown in Figure 4) is shown in Figure 7. Static Stiffness for 1 st rotor mode ~1.23 E06 N/mm Dynamic Stiffness for 2 nd rotor mode ~0.6 E06 N/mm Figure 7: Static (7 E06 Lbf/in) and Dynamic (3.5 E06 Lbf/in) Stiffness Plots
Measurement errors: Background noise levels introduce errors in measured response amplitudes Differences between the actual and the calculated unbalance force magnitudes Errors introduced by double integration of the acceleration signals to determine displacement amplitudes Error in phase lag between estimated force and the measured responses Error introduced by unknown structural interactions (For example, end wall mode could induce excessive bearing support response and suppress real frequencies or bring in spurious frequencies) Rotor Dynamic Models for Rigid Supports The measured bearing support stiffness values from shaker tests (described in the previous section) were utilized in rotor dynamic models to compute rotor critical frequencies in rigid support condition (without oil film support). It is a good practice to apply the average value of the measured stiffness of pedestals in rotor dynamic models in the beginning of calculations and make fine adjustments to pedestal stiffness to match with the measured rotor frequencies through shaker testing. Rotor Dynamic Models with Oil-film and Bearing Support Characteristics The bearing support structural stiffness values derived from the rotor dynamic models, used to match shaker tested rotor frequencies, were applied to the full rotor dynamic models (with oil film) and the rotor critical speeds were recalculated. Table-2 provides the results comparing shaker tests, operation data and calculations. Measured first rotor bending critical frequencies by shaker and operation tests are very similar. The second rotor bending critical speed was not observed in operation because no data was available above the rated speed of 1800 RPM. The calculated first and second rotor critical speeds were lower than those obtained by shaker tests. They also have qualitative agreement with the calculated rotor modes as shown in Figure 8. Similar mode shapes were calculated for the rotor configuration in operation with oil film bearing and pedestal stiffness properties. Based on shaker test results, a well separated pedestal and the rotor modes/frequencies from operation speed was observed. Therefore, it was concluded that the bearing support structures were adequately stronger for the configuration discussed in Example 1. Based on the conclusions, there was no need to stiffen the bearing support structures. Figure 8: Calculated Rotor First Bending mode in Rigid Supports: f= 1196.3 CPM (tested ~ 1200 CPM) and second Bending mode: f= 2084.5 CPM (tested ~ 2080 CPM) Table-2: Rotor Bending Critical Frequencies Shaker Test, CPM Operation Data, RPM Calculations, RPM Bearing # 1 st Mode 2 nd Mode 1 st Mode 2 nd Mode* 1 st Mode 2 nd Mode LP1-TE 1200 2013 ~1200 >1800 1170 2000 LP1-GE 1200 2005 ~1200 >1800 1170 2000 LP2-TE 1200 2048 ~1200 >1800 1170 2000 LP2-GE 1200 2085 ~1200 >1800 1170 2000 Turbine operation speed is 1800 RPM- No critical speed data available above 1800 RPM Example 2: Another Vintage Design of LP Turbine System The primary reason for discussing this example 2 is to demonstrate how shaker tests can help determining relative structural (health) conditions of bearing support pedestals.
Identification of Relative Strengths of Similar Pedestal Structures by Shaker Testing Shaker Tests help identifying relative strength or relative stiffness of bearing support pedestals of similar designs. Out of ten shaker tests conducted on LP pedestals, the author observed only one turbine train exhibited dissimilar stiffness between bearing support pedestals(of identical design) and is shown in Figure 9. LP1 turbine/rotor comprises of bearings 1 and 2 and LP2 turbine/rotor comprises of bearings 3 and 4. Turbine2 Turbine1 BRG4 BRG3 BRG2 BRG1 Figure 9: Rotor Frequencies of the LP Turbine Assembly The dissimilarity of pedestal condition was observed in the measured pedestal stiffness values and with the second rotor vertical critical frequencies of LP1 and LP2 turbines as well. Table 3 shows the rotor geometry of one LP rotor. The other LP rotor/turbine is identical. Table 3: : LP Turbine Geometrical Data shown in Figure 9 Location (From Turbine End) Diameter, in Length, in Coupling Flange 42 6.5 Overhang from Coupling 25 68.5 Disc to Disc Average 43 173 Overhang from Coupling 25 113 Coupling Flange 44 6 Rotor Material: Steel Total Weight ~ 250,000 lbs Cylindrical Bearings 25 x25 Several test conditions were applied for this rotor train. These test conditions are described below: a) Rotors at rest (0 RPM) when turbine rotors were uncoupled from the generator. b) Rotors at rest (0 RPM) and all rotors in the unit were coupled with oil lift pressure applied c) All Rotors Coupled + turning at turning gear (TG) speed of 3 RPM and supported with static oil lift Pressure, d) All Rotors Coupled + Rotors at TG speed+ oil lift support + condenser vacuum of 26 inches of Hg, e) Unit over in operation & over speed condition. Shaker test results for this rotor train are summarized in Table-4. Configuration in (a) lists measured rotor frequencies of two LP turbine rotors that were not coupled with the generator and exciter rotors. When tested with this configuration, the first rotor frequencies were the same for LP1 and LP2 rotors; however, the LP2 rotor second modal frequencies were measured about 280 CPM lower than those of the LP1 rotor (around 1764 CPM). The corresponding dynamic pedestal stiffness was about 6 times lower (about 1.0 E06 Lbf/in) than the static stiffness (about 6.5 E06 Lbf/in). Since pedestal mode and second rotor vertical frequency was lower and came below the operating speed, another test was recommended with all rotors coupled to understand the system better. When all rotors in the train were coupled, the frequencies were measured as shown under (b). As can be seen from Table-4, the second frequency of LP2 rotor has increased by about 120 CPM. Similarly, the measured pedestal stiffness for the second mode increased almost twice. Variety of support conditions was tested to see how they influence the measured rotor critical frequencies. As can be seen with test configurations (b), (c) and (d), the measured frequency variations are minimal. All the tests performed helped to conclude that shaker testing with rotors coupled and at rest (0 RPM) configuration is optimal.
Table 4: Lateral Rotor Critical Frequencies of the LP Rotors (in CPM) Shown in Figure 9 Brg. # 0 RPM 0 RPM TG + oil lift TG+ oil lift + Start Up & L P rotors Al l Rotors (c) Vacuum (d) Ov er Speed (e) uncoupled from Generator (a) Coupled+ oil lift (b) 1 1 mode 1250 1 st mode 1250 1st mode 1250 1st mode 1250 1st mode 1230 2 nd mode 2081 2 nd mode 2120 2nd mode 2115 2nd mode 2084 2nd >1970 2 1 st mode 1250 1 st mode 1250 1st mode 1250 1st mode 1250 1st mode 1230 2 nd mode 2038 2 nd mode 2110 2 nd mode 2102 2nd mode 2080 2nd >1970 3 1 st mode 1250 1st mode 1250 1st mode 1250 1st mode 1250 1st mode 1230 2 nd mode 1764 2nd mode 1884 2nd mode 1862 2nd mode 1850 2nd mode 1870 4 1 st mode 1250 1st mode 1250 1st mode 1250 1st mode 1250 1st mode 1230 2 nd mode 1764 2nd mode 1882 2nd mode 1866 2nd mode 1850 2nd mode 1900 From Table-4, it can be observed that the measured rotor critical frequencies are very similar for shaker test conditions b) through d) with those reported in e) for operating condition. It should be noted that the first bending rotor frequencies were very similar on all of the shaker test conditions. This is because rotor exerts compressive load on both ends of the pedestal support springs during the formation of first bending mode; consequently, structural weakness or abnormalities are not magnified in compressed spring mode whereas, the second bending mode (otherwise called conical mode) magnifies structural weakness (if exist) in bearing pedestals or spring supports. These variations can be measured accurately through shaker testing. It can also be concluded that the-already weaker bearing support structural condition can provide incorrect pedestal stiffness values during shaker tests, if rotors were uncoupled. The pedestal mode at 1882 CPM was further tested by holding the shaker speed constant at 1882 CPM on bearing 4 (SE end). With this test condition, responses at various parts of the LP turbine such as support cone, end wall, horizontal joint areas were acquired on both SE (bearing 3) and NSE (bearing 4) ends by moving accelerometers. This test is called, Static Deflection Shape (SDS) test. The SDS test structure was modeled by connecting co-ordinates of all points where responses were measured. Responses were superimposed in the SDS model and the mode shape corresponding to 1882 CPM was obtained. The SDS mode shape of this mode is shown in Figure 10. The bearing cones at the SE and NSE are moving vertically out-of phase to each other. Figure 10: Bearing Cones in Reverse Vertical Mode for LP2 pedestals To further understand the tested pedestal mode behavior, a Finite element model of one LP turbine structure shown in Figure 11 was generated to study the structural behavior at the frequencies and mode measured at 31.4 Hz (1882 Cycles per Minute) by shaker test. Figure 11 shows the mode shape which is called, Reverse
Vertical of the two bearing support cones that are moving in vertical direction out-of-phase. The corresponding calculated frequency was 31.8 Hz (1908 CPM). Figure 11: Bearing Support Cone Reverse Vertical Mode: Tested at 31.4 Hz Calculated at 31.8 Hz Based on analyses, additional stiffening of the pedestal cone supports was implemented to further remove the frequency away from 30 Hz. Discussions Shaker test results for two turbines/rotors and four Low Pressure bearings (Figure 4) were discussed in Example-1. Two rotor modes (first and second) and a support structure mode were measured as shown in Figure 5. The rotor and the support frequencies were found well separated from the operating frequency of 30 Hz. Further, the static and dynamic pedestal stiffness of all four bearing support structures were similar indicating that pedestal structures remained strong as it was originally designed. Although shaker tests helped identifying structural conditions and the stiffness values most accurately, it could be seen more of an intrusive test and could impact outage schedules. In customer perspective, this test may cost them money and time by extending the outages. Instead, a Passive Test was proposed to perform first which is less intrusive and has minimal impact on maintenance schedules. Instrumentation used in passive tests is very similar to those used in shaker testing. Passive testing can be done during regular maintenance outages. However, over speed data collection is recommended to determine if second rotor critical speeds are close to operating speed. Passive tests provide structure frequencies and rotor 1x and 2x spectrums that are helpful to identify both first and second rotor modes. Pedestal stiffness can not be derived directly as was possible with shaker tests. If passive test results become inconclusive, shaker tests can be recommended. The last two letters in the Passive Test response tags shown on the left are response measurements in three directions: SA- Axial SV- Vertical SH- Horizontal Figure 11: Passive Test Instrumentation In example -2, shaker test results showed distinct difference of health conditions between two identically designed pedestals. Both frequency and stiffness information led to identifying the weaker bearing support structure in the unit. This example motivates the need for good service record maintenance of machinery. As a preventive measure, service records of rotor critical speeds and bearing pedestal frequencies over the service life of machines would help the root cause investigation. Any changes of frequencies would provide clues about the possible damages and the time frame that occurred. Due to various operating conditions in service, it is likely that support structure may get softer or weaker. One way to confirm the real structural condition is through shaker testing.
Conclusions and Recommendations Shaker tests can be used to provide the comparative strength or weakness of bearing support structures of similar designs for in-service turbo-machines Various boundary conditions used in shaker tests are reported. It was found that all rotors coupled and at rest (0 RPM) condition provided the most acceptable test condition to obtain rotor frequencies and the support stiffness values as well Shaker tests provide an opportunity to measure bearing pedestal stiffness values accurately Static bearing support stiffness can be determined from shaker tests and the dynamic stiffness can be established using 50% of the static stiffness. SDS test can be utilized to obtain detail modal behavior of the pedestal structure SDS test results can also help developing better boundary conditions for Finite Element Model (FEM) of turbine casings to understand modal behavior. Calibrated FE models of the support structure would help for potential corrective action plans such as additional stiffening or detuning of frequencies Passive Test at operating condition provides the easiest approach to obtain rotor and structure frequencies instead of shaker tests. Shaker test can be resorted to when passive test data becomes inconclusive Acknowledgements The author wants to thank Siemens management for their constant support of this work References: 1. Subbiah, R, Bhat, R.B., and Sankar, T.S., Response of Rotors Subjected to Random Support Excitations Journal of Vibration, Acoustics, Stress and Reliability in Design, 1985. 2. Rouch, K.E. McMains, T.H., and Stephenson, R.W., Modeling of Rotor-Foundation Systems Using Frequency-Response Functions in a Finite Element Approach ASME Journal,1989, pp. 157 3. Gasch, R. Vibration of Large Turbo-Rotors in Fluid-Film Bearings on an Elastic Foundation, Published in Journal of Sound and Vibration, 1976, Vol. 47, No. 1, pp. 53-73 4. Feng, N.S., and Hahn, E.J., Numerical Evaluation of an Identification Technique for Flexibly Supported Rigid Turbo-machinery Foundations Sixth IFToMM International Conference on Rotor Dynamics, Sydney, 2002, pp. 854-861. 5. Vance, J., Rotor dynamics of Turbo machinery, John Wiley & Sons, 1988