Proceedings of Shanghai 2017 Global Power and Propulsion Forum

30th October – 1st November, 2017 http://www.gpps.global

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GPPS-2017-0199

CASE STUDY ON THE SUBSYNCHRONOUS VIBRATION BY EXTERNAL FORCES IN INTEGRALLY GEARED CENTRIFUGAL

COMPRESSOR

Seunghoon Shin Hanwha Power Systems sh23.shin@hanwha.com

Republic of KOREA

Kyungdae Kang Hanwha Techwin

kyungd.kang@hanwha.com Republic of KOREA

Taewook Lee

Hanwha Power Systems kifuyu.lee@hanwha.com

Republic of KOREA

Chansun Lim Hanwha Power Systems

chansun.lim@hanwha.com Republic of KOREA

ABSTRACT This paper presents two field cases of forced sub-

synchronous vibration (SSV) in the integrally geared centrifugal compressor (IGCC). The SSV cases happened by external forces such as aerodynamic force from impellers and transmitted bull-gear force through thrust collar. Test and FEM analysis are used to resolve the SSV problem. Using the results, the most effective factor for attenuating the SSV is found. And based on experience of author’s company (HPS), the anti-SSV plots are plotted. Through the SSV plots, this study verifies the relation between the bearing stiffness and the SSV by external forces. Furthermore, it can be used as a bearing design guide to avoid the SSV by external forces.

INTRODUCTION The SSV problem is one of the most difficult things to

resolve in the turbo machinery industry. Due to its difficulty, many SSV studies have been researched for a long time. They could be divided into two groups by excitation sources. The first one involves the self-excitation, or instability such as oil whip and whirl. The other is categorized by SSV from external forces.

Until now, many studies of SSV from self-excitation have published. Whalen et al. [1] studied the SSV by instability and Yang et al. [2] studied the SSV by pad flutter. Even though the researches of SSV originated from the external forces are not enough compared to those from self-excitation, the rising trend of power and flow rate of IGCC requires more extension of the former area of research. Thus, this paper focuses on the SSV problem caused by external forces in the IGCC and suggests its solution

AERODYNAMIC FORCED VIBRATION The first case involves the SSV of pinion shafts in high

pressure gas compressor at site. Figure 1 shows the high pressure gas compressor and the specification of the compressor is described in Table 1. This compressor is integrally geared type and has one pinion and two impellers attached on each end.

Figure 1 High pressure gas compressor

Table 1: Specification of compressor

List Spec.

Environment Gas LNG

Inlet pressure 22 bar(G)

System performance Flow rate 65,000 kg/hr

Outlet pressure 50 bar(G) Shaft power 2900 kW

Figure 2 shows spectrum plot data of the this compressor

when it was initially operated at site. The SSV appeared in frequency domain. Test overall vibration exceeded the

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allowable vibration limit due to its vibration. It was predicted to show by excessive aerodynamic force of impellers while the discharge pressure of compressor increased. The aero-induced disturbances such as impeller stall, diffuser stall, rotating stall and surge can cause SSV in the centrifugal compressor. (D. Fred Marshall et al. [3])

Figure 2 Spectrum plot of pinion in a high pressure

compressor

The rotor-dynamics analysis result and bearing design of this pinion are reviewed to find the cause of its vibration. Table 2 shows the rotor-dynamics analysis result of pinion and Table 3 shows the bearing design of this compressor. Rotor-dynamic analysis results are satisfied with design criteria of API617

Table 2 Rotor-dynamics analysis result of the pinion shaft

List Result Criteria Lateral vibration

at rated speed 6.3um < 16.6um

Transient vibration at critical speed

20um < 94um

SM 21% > 13.9% Log-dec. 0.44 > 0.1

Table 3: Design parameters of the bearing List Spec.

Bearing type Tilting pad journal bearing Journal diameter 65mm

Pad length 55mm Pad No. 5 EA

Pivot type Rocker back Oil grade ISO VG 32

The studies of design parameters for attenuating the SSV

were conducted. a. Bearing instability

Tilting pad bearings are applied to this pinion shaft. All design parameters are confirmed in design criteria.

b. Seal design The seal clearance is confirmed it was designed

appropriately.

c. Swirl excitation The possibility is high. So swirl brake is installed,

but the sub-synchronous vibration trend was not changed.

d. Structural resonance The modal testing was performed to check the actual

resonance of support structure (support frame, oil tank, gear box). The support structure’s margin is enough to avoid the effect of resonance.

e. Bearing clearance Some test was performed to check the bearing

characteristic’s effects. Table 4 shows the three cases by variable design parameters and Table 5 shows rotor-dynamics analysis results at each case. Original case is initial bearing design caused SSV. Case 1 test was performed for more stable in the view of rotor-dynamics. Log-dec. parameter means stability of rotor from aerodynamic forces of impellers. Log-dec. of case 1 is higher than it of original test. But the SSV not disappeared. Case 2 test is performed for bearing stiffness increase. The bearing stiffness of case 2 is higher than it of original, but damping of case 2 is lower than it of original. As a case 2 test result, the SSV disappeared by only bearing stiffness increase.

Table 4 Bearing characteristic by variable test cases

Case Stg Kxx (N/m)

Kyy (N/m)

Dxx (Ns/m)

Dyy (Ns/m)

Original #1 2.37 E+08

3.40 E+08

9.09 E+04

1.18 E+05

#2 2.82 E+08

3.62 E+08

1.01 E+05

1.21 E+05

Case 1 #1 2.19 E+08

3.10 E+08

7.04 E+04

9.28 E+04

#2 2.49 E+08

3.29 E+08

7.78 E+04

9.68 E+04

Case 2 #1 2.78 E+08

3.69 E+08

8.65 E+04

1.08 E+05

#2 3.10 E+08

3.87 E+08

9.38 E+04

1.11 E+05

Table 5 Rotor-dynamics analysis results by variable test cases

Case SM(%) AF Predicted vibration(um)

Log-dec.

Original 21 6.3 6 0.3/0.29 Case 1 24 10.7 6 0.4/0.29 Case 2 21 6.6 7.5 0.24/0.23 Through these test results, the most dominant parameter

affecting SSV is the bearing stiffness of pinion. This SSV was attenuated by bearing stiffness’s increase.

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Figure 3 rotor-bearing system

Figure 3 shows this rotor is expressed as simple rotor-

bearing system If the forcing function is given by F(t) = F0 cos ωt, the

equation of motion becomes

푚푥 + 푐푥 + 푘푥 = 퐹 푐표푠휔푡 (1) The particular solution of Eq. (1) is also expected to be

harmonic, Eq. (2) is assumed form,

xp(t) = X cos ωt (2) By substituting Eq (2) into Eq. (1), Eq. (3) is obtained. Damping is negligible by bearing clearance test results. (c = 0)

m (-ω2 X cos ω t) + k (X cos ω t) = F0 cos ω t (3)

(k - mω2) X cos ω t= F0 cos ω t (4) Using Eq. (4), vibration amplitude is expressed in Eq. (5)

X =

(5)

Where, F0 = forces including aerodynamic force and centrifugal

force m = mass of impeller ω = operation speed k = bearing stiffness X = vibration amplitude According to Eq. (5), the vibration attenuating by bearing

stiffness’s increase is demonstrated.

Figure 4 Sub-synchronous vibration plot by aerodynamic

forces Based on experiences of HPS, a SSV plot by aerodynamic

force was plotted in Figure 4. It includes the relationship between the bearing stiffness and the SSV resulted from the aerodynamic force of impellers. And it can be useful for the bearing design if high pressure turbo machinery.

Empty symbols in plot are the forced SSV issued compressors at site. The stable area in plot means the possibility is low and unstable area means possibility is high in the view of SSV.

Cross coupled term (Qa) means aerodynamic force level of impellers in API 684 and it is summation value of aerodynamic cross coupled term from the each stage impeller in pinion.

If the designed aero cross coupled term is located the right side of SSV plot I apply line (cross coupled term 6E5*N/m), bearing design can be considered to meet with the minimum recommend bearing stiffness using this plot. But if the designed aero cross coupled term is located left side of SSV plot I apply line, this plot may not be considered.

BULL-GEAR FORCED VIBRATION

The second case of another SSV in the large compressor occurred in pinion shafts. Thrust collars often chosen to support the axial forces of pinion in IGCC instead of the thrust bearing. Because the thrust collar design has advantage over the thrust bearing design in terms of power consumption. But the forced vibration from a bull shaft can be transferred to pinion shaft through thrust collar. The axial force on the bull-gear can drive the sub-synchronous lateral vibration in pinion, it was showed in pinion as the bull-gear synchronous vibration frequency and its harmonic components. (Andrew Crandall et al. [4])

Figure 5 shows a large size compressor, which had a bull-gear forced SSV problem. Table 6 shows the specification of this compressor.

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Figure 5 Large size compressor

Table 6: Specification of compressor

List Spec.

Environment Gas air

Inlet pressure 1.013 bar(G)

System performance Flow rate 100,000 Nm3/hr

Outlet pressure 16 bar(G) Shaft power 15 MW

When the large compressor is operated, SSV appeared in

pinion. Figure 6 shows spectrum plot data of pinion in frequency domain. Bull-gear’s synchronous component and harmonics components appeared in pinion. The overall vibration exceeded the allowable vibration limit due to these vibration components.

Figure 6 Spectrum plot of pinion in the large compressor

To solve the vibration problem of this case, the same

solution as the first case was applied and it was successful. For this case, the analysis using FEM was adopted to verify the relationship the bearing stiffness and the SSV resulted from transmitted forces from a bull shaft. Figure 7 shows the FEM analysis model of bull-gear and pinion. Figure 8 shows spectrum plot of pinion at low bearing stiffness in analysis, and Figure 9 shows spectrum plot at high bearing stiffness in analysis. The vibration attenuating by bearing stiffness increase is found through these analysis results.

Figure 7 FEM model of bull gear and pinion

Figure 8 Spectrum plot of pinion at low bearing stiffness of

pinion in analysis

Figure 9 Spectrum plot of pinion at high bearing stiffness of

pinion in analysis

Figure 10 shows a SSV plot based on experiences of HPS, which is used as bearing design guide of pinion bearings to decrease the excessive transmitted vibration from a bull shaft to pinion shafts.

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Figure 10 Sub-synchronous vibration plot by bull-gear

Empty symbols in plot are the forced SSV issued

compressors. The stable area in plot means the possibility of SSV is low and unstable area means the possibility of SSV is high.

Bull-gear shaft assembly mass term can be estimated as bull-gear force level and it is summation value of bull-gear, shaft and coupling mass. Because the bull-gear force and bull-gear shaft assembly mass have direct relationship in a large compressor.

If the bull-gear shaft mass is located in right side of SSV plot II apply line (bull-gear shaft mass 1500kg), bearing design can be considered to meet with the minimum recommend bearing stiffness by using this plot. Otherwise, it means bull-gear force does not cause the SSV in pinion.

CONCLUSION This paper suggested the solution of forced SSV for

integrally geared centrifugal compressor. The bearing stiffness is found it is the most effective factor for removing the SSV by external forces such as aerodynamic and bull-gear. And SSV plots based on experience of HPS were plotted. They verify the relationship bearing stiffness and SSV by external forces, experimentally. These also can be used as bearing design guide to avoid the SSV by external forces. When a IGCC design for low SSV is required, satisfying with required minimum bearing stiffness is recommended and it have to be considered excessively bearing temperature increase.

NOMENCLATURE SM = Separation margin from resonances or critical

speeds Log-dec. = Logarithmic decrement AF = Amplication factor HPS = Hanwha Power Systems

IGCC = Integrally geared centrifugal compressor RCA = Root cause analysis API = American petroleum institute SSV = Sub-synchronous vibration

REFERENCES [1] John K. Whalen and Malcolm E. Leader, “Solving stability problem while commissioning a 100MW turbine generator set”, Proceeding of the Thirty-second Turbo machinery Symposium, 2003 [2] Seong Heon Yang, Chaesil Kim and Yong-bok Lee, “ Experimental Study on the characteristics of pad fluttering in a tilting pad journal bearing”, Tribology International, July 2006 Issue 7, pp 686-694 [3] D. Fred Marshall and James M. Sorokes, “A review of aerodynamically induced forces acting on centrifugal compressors, and resulting vibration characteristics of rotors”, Proceeding of the Twenty-ninth Turbo machinery Symposium, 2000, pp 263-280 [4] Andrew Crandall and Dara Childs, “Bull gear runout as a source of subsynchronous, lateral, vibration in integrally geared compressor pinions”, GPPF-2017-85, Proceedings of the 1st Global Power and Propulsion Forum, 2017 [5] J. Jeffrey Moore, Massimo Camatti, Anthony J.Smalley, Giuseppe Vannini and Luc L.Vermin, “ Investigation of a Rotordynamic Instability in a High Pressure Centrifugal Compressor Due to a Damper Seal Clearance Divergence”, 7th IFToMM-Conference on Rotor Dynamics, Vienna, Austia, 25-28 September 2006 [6] J. Jeffrey Moore and Mark J. Kuzdzal, “Rotordynamic Stability Measurement during Full-Load Full-Pressure Testing of a 6000 PSI Reinjection Centrifugal Compressor”, Proceeding of the Thirty-first Turbo machinery Symposium, 2002 [7] Singiresu S. Rao, “Mechanical Vibrations”, Pearson Prentiss Hall. Four edition, 220–249 [8] API 617, 7th Edition, (2002), “Axial and Centrifugal Compressor and Expander-Compressor for Petroleum, Chemical and Gas Industry Services” [9] API 684, 2nd Edition, (2005), “API Standard Paragraph Rotordynamic Tutorial: Lateral Critical Speeds, Unbalance Response, Stability, Train Torsional, and Rotor Balancing”