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International Journal of Pressure Vessels and Piping 81 (2004) 825–835 www.elsevier.com/locate/ijpvp

Risk-based inspection and maintenance systems for steam turbines Kazunari Fujiyamaa,*, Satoshi Nagaia, Yasunari Akikunib, Toshihiro Fujiwarab, Kenichiro Furuyab, Shigeru Matsumotob, Kentaro Takagib, Taro Kawabatac a

Power and Industrial Systems R&D Center, Industrial and Power Systems and Services Company, Toshiba Corporation, Yokohama, Japan Thermal and Hydro Power Division, Industrial and Power Systems and Services Company, Toshiba Corporation, Tokyo/Yokohama, Japan c Keihin Product Operations, Industrial and Power Systems and Services Company, Toshiba Corporation, Yokohama, Japan

b

Abstract The risk-based maintenance (RBM) system has been developed for steam turbine plants coupled with the quick inspection systems. The RBM system utilizes the field failure and inspection database accumulated over 30 years. The failure modes are determined for each component of steam turbines and the failure scenarios are described as event trees. The probability of failure is expressed in the form of unreliability functions of operation hours or start-up cycles through the cumulative hazard function method. The posterior unreliability is derived from the field data analysis according to the inspection information. Quick inspection can be conducted using air-cooled borescope and heat resistant ultrasonic sensors even if the turbine is not cooled down sufficiently. Another inspection information comes from degradation and damage measurement. The probabilistic life assessment using structural analysis and statistical material properties, the latter is estimated from hardness measurement, replica observation and embrittlement measurement. The risk function is calculated as the sum product of unreliability functions and expected monetary loss as the consequence of failure along event trees. The optimum maintenance plan is determined among simulated scenarios described through component breakdown trees, life cycle event trees and risk functions. Those methods are effective for total condition assessment and economical maintenance for operating plants. q 2004 Elsevier Ltd. All rights reserved. Keywords: Risk-based maintenance; Steam turbine; Database; Inspection; Event tree; Unreliability; Life cycle; Failure; Damage

1. Introduction In Japan, the cost-effective maintenance of power plants is required under the trend of more competitive power generation market. Recently, risk-based maintenance (RBM) has been introduced to fossil power plants for the solution of utility’s requirements [1]. The object of introducing RBM is to provide the rational basis of decision making for life cycle maintenance planning. There are three categories in the risk assessment, that is, qualitative, semi-quantitative and quantitative approach. The semiquantitative approach is widely used for various plants, being well known as the risk ranking matrix approach. The quantitative approach has the advantage to solve the optimization problem numerically, which enables to apply various mathematical tools.

* Corresponding author. E-mail address: [email protected] (K. Fujiyama). 0308-0161/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2004.07.005

The RBM system has been developed to perform the probabilistic risk analysis coupled with inspection systems. The RBM system comprises life cycle event trees, unreliability function analysis for field failure database and risk-cost analysis for various maintenance scenarios. Unreliability represents the failure probability here as the function of operation hours and number of starts. The basis of unreliability analysis is the statistical database of field failure and damage related to the operation history. For global application of the quantitative RBM method, various ways are considered to compensate for the lack of statistically meaningful number of data. The RBM system can be customized to specific users by modifying the unified master curve for unreliability analysis. For customizing the system, the inspection information of specific unit is useful for obtaining posterior unreliability functions by modification of prior unreliability functions. To reduce outage time, the air-cooled borescope and the heat resistant ultrasonic sensors are provided for turbine inspection before the turbine is not cooled down sufficiently.

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Life assessment information is also useful for obtaining probability of creep and fatigue cracking life by stochastic simulation analysis. With several examples, it is demonstrated here how the quantitative RBM system helps the decision making on life cycle plant maintenance planning and economical management.

monetary loss due to the accidents along the scenario of life cycle event trees. (7) Maintenance planning. Maintenance scenarios are planned as the life cycle sequence of failure events and related preventive actions. The risks and preventive costs are calculated over the total life cycle for selecting the optimum maintenance scenario.

2. Basic flow of the risk-based inspection and maintenance procedure

3. Damage and failure modes of steam turbines

Fig. 1 shows the basic flow of the risk-based inspection and maintenance procedure. Each step has the role as follows: (1) Component breakdown trees. A steam turbine unit can be divided into many components. The level of component breakdown might be decided according to the level of maintenance action. (2) Life cycle event trees. Though the event tree is usually expressed as the sequence of success/fault nodes, it is used here for describing the chain action of one component failure leading to another component failure because steam turbine components are closely assembled each other and rotating in high speed. (3) Master field database. The failure, inspection and repair history database is established for various types units over 30 years. The database is formed as a relational database of unit, components, location, event and operation history. (4) Unreliability analysis. The failure probability is defined here as the unreliability. The cumulative hazard function method is used for deriving the unreliability functions of operation hours or start-up cycles. (5) Inspection and life assessment. The unit specific unreliability functions are obtained as the posterior unreliability functions after detected event from inspection. For degradation and damage accumulation phenomena, probabilistic life assessment is used for simulating future unreliability. (6) Risk assessment. The risk is defined here as the sum product of the unreliability functions and the expected

Fig. 1. Basic flow of risk-based inspection and maintenance procedure.

Fig. 2 shows a component breakdown tree of a steam turbine unit. Those components show various types of degradation, damage and failure phenomena according to temperature, stress, environment and materials. Fig. 3 shows degradation, damage and failure modes of steam turbine major components [2,6]. For high- and intermediate-pressure (HIP) portions, the typical events are creep induced deformation, thermomechanical fatigue cracking and steam flow induced erosion. For low pressure (LP) portion, the typical events are environmental assisted fatigue cracking and steam flow induced erosion. The features of events are described as follows for major components. (1) HIP rotor. High centrifugal stress and high temperature cause creep deformation such as rotor bowing. The rotor bowing causes vibration and rubbing with bearings and casings. Creep damage accumulation causes creep void

Fig. 2. Component breakdown tree.

K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835

(4)

(5)

(6)

Fig. 3. Degradation, damage and failure modes of steam turbine major components.

formation and cracking at highly stressed portions such as bore and wheel hooks. Thermomechanical fatigue damage accumulation causes cracking at the wheel corner portion. (2) LP rotor. High centrifugal stress, high vibratory stress and corrosion environment causes corrosion fatigue at the wheel section. (3) HIP moving blade. High centrifugal stress and high temperature causes creep deformation such as lifting.

(7)

(8)

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The lifting causes rubbing with casings or nozzles and finally cracking. Creep damage accumulation causes creep void formation and cracking at the highly stressed portion such as dovetail hooks. Oxide scale brought by steam flow causes erosion. Vibratory stress causes high cycle fatigue cracking and fretting fatigue at the contact portion. LP moving blade. High centrifugal stress, high vibratory stress and corrosion environment causes corrosion fatigue cracking. Droplet brought by steam flow causes erosion. HIP nozzle. Oxide scale brought by steam flow cause erosion. Pressure difference at each stage and high temperature cause downstream deflection of nozzle diaphragm. HIP casing. High pressure stress and high temperature cause creep deformation. The creep deformation causes assembling mismatch and steam leak due to stress relaxation at the flange and the tightening bolt. Creep and thermomechanical fatigue damage accumulation causes cracking at the nozzle fit radius and other stress/ strain concentration portions. Valve. Creep and thermomechanical damage is the same as casings. Oxide scale brought by steam flow causes erosion at the shield plates. Oxidation at the shaft and valve body contact portion causes valve shaft sticking. Pipe. Creep damage accumulation causes creep void formation and cracking preferably at the weld portion. Water induction causes thermomechanical or thermal shock cracking.

Fig. 4 shows the event trees coupled with component breakdown trees based on the above information. This is the basis of the following analysis.

Fig. 4. An example of event trees for steam turbine unit.

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Fig. 5. Cumulative hazard functions for turbine rotor bowing fitted individually.

4. Unreliability analysis 4.1. Master field database The master field failure database has the data rows of plant name, component name, occurrence date, operation hours, start-up cycles, event contents, event cause and repair actions. Every event is related to operation hours and startup cycles until the events occur. For the events detected at the scheduled inspection, the estimated hours and cycles are adopted using reference operation history tables. 4.2. Field data analysis method: Cumulative hazard function method [3] The unreliability function is derived through cumulative hazard function method for the field failure database. The event data are stacked in the order of time or cycles for the same mode of failure and the same type of turbines. Estimated cumulative hazard function is expressed as follows ^ kÞ ¼ Hðt

k X i¼1

1 n þ 1 Ki

Fig. 7. Unified cumulative function for rotor bowing.

where, tk is event occurrence time at the k-th event, n is total number of samples including non-failure data. Regression of cumulative hazard function H(t) is conducted using the two-parameter Weibull plot expressed in the following equations. HðtÞ Z ðt=hÞm ln HðtÞ Z m ln t K m ln h

(2) (2 0 )

where h, m are regression constants. Unreliability function F(t) is calculated as follows FðtÞ Z 1 K RðtÞ Z 1 K expfKHðtÞg

(3)

where R(t) is reliability function. Eqs. (1)–(3) are also applied for cycle N dependent events using N instead of t. To overcome the lack of sufficient numbers of data, two approaches are adopted. One is the unified unreliability function approach and the other is the empirical unreliability function approach. Those two approaches are described below. 4.3. Unified unreliability function approach: example of rotor bowing

(1)

Fig. 6. Unreliability functions for turbine rotor bowing fitted individually.

If the dominant parameter of an event is known, unified master curve can be obtained by normalization. Here, rotor

Fig. 8. Unified unreliability function for rotor bowing.

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Fig. 11. Machine output class dependence for cycles at 50% unreliability for nozzle erosion events.

Fig. 9. Hours based cumulative hazard functions.

bowing phenomena is taken as an example though this event is prevented now due to the improvement of manufacturing and design. Figs. 5 and 6 show the cumulative hazard functions and unreliability functions against operation hours for two types (A-type and B-type) rotors. The type-B rotor regression is conducted with only two events. Here, the hazard function fitting against time (operation hours) is better than that against number of starts as reported elsewhere [5]. The time dependence comes from that the rotor bowing is one of the creep deformation phenomena. It depends on stress, temperature and material conditions. As the rotor bowing is one of the creep phenomena, the time is normalized by creep rupture time, that is, t/tr. Figs. 7 and 8 show the good unique correlation of cumulative hazard functions and t/tr for the two types of turbines, expressed by the following equation. HðtÞ Z

mc0 t =hc0 tr ðs; T; lÞ

(4)

where hc0, and mc0 are regression constants, s is stress, T is temperature and l is material strength parameter such as hardness or tensile strength, etc.

Fig. 10. Cycle based cumulative hazard functions.

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Eq. (4) indicates that the unreliability function of the specific unit can be estimated only by knowing design conditions or service conditions and material properties. 4.4. Empirical approach: example of nozzle erosion In the case of nozzle erosion, It is difficult to find the explicit parameters dominating erosion process. Figs. 9 and 10 show total regression results of cumulative hazard functions against operation hours and number of starts, respectively, expressed by the following equations. HðtÞ Z ðt=ht0 Þmt0

(5)

HðNÞ Z ðN=hN0 ÞmN0

(6)

where ht0, hN0 and mt0, mN0 are regression constants Eqs. (5) and (6) fit the whole data well enough but still indicate discrepancy between the turbine output types at some extent. Here, we introduce a modifying approach using hours or cycles at 50% unreliability based on the unified unreliability function. We show the modification results for cycle dependent unreliability functions or cumulative hazard functions.

Fig. 12. Empirical cumulative hazard functions of erosion for various nozzles.

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Modified cumulative function is obtained by using the modifying coefficient N50/N50,0, where N50,0 is number of starts at 50% unreliability for the unified curve of Eq. (6). mN0 N (8) HðNÞ Z N 50 =hN0 N50;0 Figs. 12 and 13 show the estimation results if the modifying coefficient approach. The estimation curves fits actual data reasonably even for the insufficient data.

5. Inspection system and unreliability function Fig. 13. Empirical unreliability functions of erosion for various nozzles.

Fig. 11 shows the relationship between number of starts at 50% unreliability N50 and output class index I that is proportional to output capacity. N 50 shows almost monotonic decreasing relationship with I, expressed as follows N50 Z aI b

(7)

where a and b are regression constants.

5.1. Quick visual and ultrasonic inspection system The visual and ultrasonic inspection gives useful information for adjusting the prior unreliability functions. To reduce the outage time for inspection, quick inspection systems have been developed. Fig. 14 shows an air-cooled borescope inspection system for nozzle erosion/failure detection. Magnet wheels attached to the inspection head move along the nozzle front, and remote observation by CCD camera is easily done

Fig. 14. Air-cooled borescope visual inspection system.

Fig. 15. Heat resistant UT system (left: application to components; right: the detail of carriage).

K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835

Fig. 16. Prior and posterior unreliability functions for moving blade erosion.

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at temperature below 300 8C after machine shutdown. This may require about a couple of days. Fig. 15 shows a heat-resistant UT system for casing or valve defect detection. The moving head contains a couple of heat resistant UT sensors with the supply system of high temperature coupling medium to attach the system to a hot wall of about 300 8C. This system is used for detecting casing or valve inner defect and bolt cracking. Fig. 16 shows the posterior unreliability functions of moving blade erosion calculated by the prior unreliability function of nozzle erosion and the prior unreliability of moving blade erosion. Cycles to erosion event of nozzle is subtracted from cycles to erosion event of moving blade.

Fig. 17. Life assessment system coupled with non-destructive measurement system.

Fig. 18. Life assessment procedures based on analysis and non-destructive measurement.

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The cycle difference values and cumulative hazard function values are coupled and fitted again by Eq. (2). The obtained posterior unreliability function shows higher unreliability for small cycles indicating immediate occurrence of moving blade erosion after nozzle erosion.

5.2. Degradation/damage measurement and life assessment system [4,5] Fig. 17 shows a degradation/damage measurement and life diagnosis system schematically. Degradation and damage are measured by the hardness measurement system, replica observation technique and embrittlement measurement system. Life assessment system is programmed to calculate creep and fatigue life calculation using evaluation master curves and machine information. Fig. 18 shows the deterministic life assessment procedures [7]. Creep and fatigue damage is calculated by cumulative damage rule using the life assessment master curves. The feature of the procedure is that life assessment master curves are derived from material condition data measured by the hardness measurement system and the embrittlement measurement system. Creep and fatigue life evaluation curves are derived from hardness values measured for post-serviced components. Crack growth rate and fracture toughness are derived from FATT value converted from electrochemical polarization parameters using experimental master curves. Probabilistic life assessment requires statistical material properties [5,8]. Fig. 19 shows material creep rupture data including unused, laboratory aged and service used plotted

Fig. 19. Unified plot and regression of creep rupture for unused, aged and serviced materials.

Fig. 20. Cumulative probability of creep rupture life ratio derived from the unified master curve.

using stress/hardness ratio and Larson–Miller parameter. Fig. 20 shows the unified statistical distribution of experimental/estimated creep life ratio based on the whole creep rupture data and the master regression curve. It can be used as the simulated unreliability function of creep life of actual component. When narrower distribution is required, the data for statistical analysis should be selected carefully according to the specification of manufacturer.

Fig. 21. An example for the optimization of maintenance interval for rotor bowing.

K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835

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Fig. 22. PC based RBM system window view of risk assessment of rotor bowing.

6. Risk assessment and maintenance planning [5,6] Risk is defined here as the sum product of unreliability functions and expected monetary loss for every event in the event trees. The risk functions are specified by plant information and inspection information. Monetary loss is calculated for all expected items related to unscheduled outage and recovery action. Two ways of optimizing maintenance planning are presented below, that is, the optimization of maintenance intervals and the optimization of life cycle maintenance scenarios. 6.1. Maintenance interval optimization: example of rotor bowing Fig. 21 shows an example of the optimization of maintenance intervals for rotor bowing. The event tree is restricted to include typical three events for simplification. Those three events: (a) rotor bowing; (b) narrow axial clearance; (c) vibration, have different risk functions. The total risk function is determined by the sum of the three risk functions. The maintenance cost index is defined as the total cost of preventive maintenance action averaged per year for the subscribed events. The total risk is increasing function of operation hours and the cost index is proportional to

Fig. 23. Event trees, unreliability functions and risk functions for nozzle erosion.

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Fig. 24. The optimization of life cycle maintenance scenario for nozzle erosion.

the reciprocal of maintenance hours-based interval. The total cost curve is obtained by the sum of risk and maintenance cost showing a concave curve. If the income by operation is proportional to operation hours, the shaded area is recommended to decide the optimum maintenance intervals. The rotor bowing events are decreasing currently due to the improvement of manufacturing process, design and operation. Fig. 22 shows an example of the personal computer based RBM system window view of risk assessment of rotor bowing.

cost but runs high risk. The scenario 2 comprises predetermined replace period with the scheduled preventive repair actions during the service period. As the repair cost is relatively low in this case, the sum of risk and cumulative preventive costs remains low level. The scenario 3 comprises early replacement of erosion resistant upgraded nozzle and long term use of the upgraded one. It arises higher cost in the early period but relatively lower increase in the total cost for long period. The comparison of total cost gives the optimum maintenance scenario for the same period.

6.2. Maintenance scenario optimization: example of nozzle erosion Fig. 23 shows the event tree, the unreliability functions and risk functions of nozzle erosion event. Nozzle erosion event [A] shows relatively high unreliability but low cost for recovery action. The risk function is relatively low. For other events [B], [C], [D], lower unreliability and high recovery cost result in the same level risk as event [A]. The total risk is increasing function of operation period. Here, operation period is taken as operation hours but number of starts also applicable. Fig. 24 shows scenario case study for nozzle erosion events and maintenance action. The scenario 1 comprises predetermined replace period without preventive repair action during the service period. It requires no maintenance

Fig. 25. Application concept for risk-based engineering.

K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835

7. Concluding remarks The quantitative RBM method for steam turbines was presented. Statistical formulation of failure probability as the function of time or cycles were very effective way to estimate the risk for various modes of failure and the chain of successive failure. The RBM system has various features as follows (1) Describe plant maintenance scenario by component breakdown trees and life cycle event trees. (2) Assign default unreliability function to every event by statistical analysis of master filed failure database. (3) Customize the unreliability functions can be modified reflecting the inspection information and probabilistic life assessment. (4) Optimize maintenance intervals using risk functions, cost functions and income functions. (5) Optimize maintenance scenario using life cycle event trees and total cost analysis. Those features are useful for wider application, not restricted to the steam turbine plant. The application

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of risk-based engineering is shown in Fig. 25. The quantitative method provides feedback and optimization of design, manufacturing and operation parameters. Those approaches will lead more economical and reliable plant design, manufacturing and management of plants.

References [1] Sakai S. J Jpn Inst Metals 2002;66(12):1170–6 [in Japanese]. [2] Fujiyama K, Fujiwara T. Proceedings of ICF10, \DATA\CONTENT\0868\PAPER.PDF (CD-ROM). Amsterdam: Elsevier; 2001. [3] Nelson W. Applied life data analysis. New York: Wiley; 1982. [4] Fujiyama K, Saito K, Harada S, Ahiko N, Itoh Y. Proceedings of CREEP7. Tsukuba: Japan Society of Mechanical Engineers; 2001 p. 69–74. [5] Fujiyama K, Fujiwara T, Kodama H, Saito K, Kichise H, Okazaki M. J Soc Mater Sci Jpn 2003;52(1):28–33 [in Japanese]. [6] Fujiyama K, Saito K, Fujiwara T, Kodama H, Kichise H, Okazaki M, Takagi K. J Jpn Inst Metals 2002;66(12):1199–205 [in Japanese]. [7] Kimura K, Fujiyama K, Muramatsu M. Curr Jpn Mater Res 1988;3: 247–70. [8] Fujiyama K, Takaki K, Nakatani Y, Yoshioka Y, Itoh Y. Mater Sci Res Int 2002;8(3):134–9.

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Risk-based inspection and maintenance systems for steam turbines Kazunari Fujiyamaa,*, Satoshi Nagaia, Yasunari Akikunib, Toshihiro Fujiwarab, Kenichiro Furuyab, Shigeru Matsumotob, Kentaro Takagib, Taro Kawabatac a

Power and Industrial Systems R&D Center, Industrial and Power Systems and Services Company, Toshiba Corporation, Yokohama, Japan Thermal and Hydro Power Division, Industrial and Power Systems and Services Company, Toshiba Corporation, Tokyo/Yokohama, Japan c Keihin Product Operations, Industrial and Power Systems and Services Company, Toshiba Corporation, Yokohama, Japan

b

Abstract The risk-based maintenance (RBM) system has been developed for steam turbine plants coupled with the quick inspection systems. The RBM system utilizes the field failure and inspection database accumulated over 30 years. The failure modes are determined for each component of steam turbines and the failure scenarios are described as event trees. The probability of failure is expressed in the form of unreliability functions of operation hours or start-up cycles through the cumulative hazard function method. The posterior unreliability is derived from the field data analysis according to the inspection information. Quick inspection can be conducted using air-cooled borescope and heat resistant ultrasonic sensors even if the turbine is not cooled down sufficiently. Another inspection information comes from degradation and damage measurement. The probabilistic life assessment using structural analysis and statistical material properties, the latter is estimated from hardness measurement, replica observation and embrittlement measurement. The risk function is calculated as the sum product of unreliability functions and expected monetary loss as the consequence of failure along event trees. The optimum maintenance plan is determined among simulated scenarios described through component breakdown trees, life cycle event trees and risk functions. Those methods are effective for total condition assessment and economical maintenance for operating plants. q 2004 Elsevier Ltd. All rights reserved. Keywords: Risk-based maintenance; Steam turbine; Database; Inspection; Event tree; Unreliability; Life cycle; Failure; Damage

1. Introduction In Japan, the cost-effective maintenance of power plants is required under the trend of more competitive power generation market. Recently, risk-based maintenance (RBM) has been introduced to fossil power plants for the solution of utility’s requirements [1]. The object of introducing RBM is to provide the rational basis of decision making for life cycle maintenance planning. There are three categories in the risk assessment, that is, qualitative, semi-quantitative and quantitative approach. The semiquantitative approach is widely used for various plants, being well known as the risk ranking matrix approach. The quantitative approach has the advantage to solve the optimization problem numerically, which enables to apply various mathematical tools.

* Corresponding author. E-mail address: [email protected] (K. Fujiyama). 0308-0161/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2004.07.005

The RBM system has been developed to perform the probabilistic risk analysis coupled with inspection systems. The RBM system comprises life cycle event trees, unreliability function analysis for field failure database and risk-cost analysis for various maintenance scenarios. Unreliability represents the failure probability here as the function of operation hours and number of starts. The basis of unreliability analysis is the statistical database of field failure and damage related to the operation history. For global application of the quantitative RBM method, various ways are considered to compensate for the lack of statistically meaningful number of data. The RBM system can be customized to specific users by modifying the unified master curve for unreliability analysis. For customizing the system, the inspection information of specific unit is useful for obtaining posterior unreliability functions by modification of prior unreliability functions. To reduce outage time, the air-cooled borescope and the heat resistant ultrasonic sensors are provided for turbine inspection before the turbine is not cooled down sufficiently.

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K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835

Life assessment information is also useful for obtaining probability of creep and fatigue cracking life by stochastic simulation analysis. With several examples, it is demonstrated here how the quantitative RBM system helps the decision making on life cycle plant maintenance planning and economical management.

monetary loss due to the accidents along the scenario of life cycle event trees. (7) Maintenance planning. Maintenance scenarios are planned as the life cycle sequence of failure events and related preventive actions. The risks and preventive costs are calculated over the total life cycle for selecting the optimum maintenance scenario.

2. Basic flow of the risk-based inspection and maintenance procedure

3. Damage and failure modes of steam turbines

Fig. 1 shows the basic flow of the risk-based inspection and maintenance procedure. Each step has the role as follows: (1) Component breakdown trees. A steam turbine unit can be divided into many components. The level of component breakdown might be decided according to the level of maintenance action. (2) Life cycle event trees. Though the event tree is usually expressed as the sequence of success/fault nodes, it is used here for describing the chain action of one component failure leading to another component failure because steam turbine components are closely assembled each other and rotating in high speed. (3) Master field database. The failure, inspection and repair history database is established for various types units over 30 years. The database is formed as a relational database of unit, components, location, event and operation history. (4) Unreliability analysis. The failure probability is defined here as the unreliability. The cumulative hazard function method is used for deriving the unreliability functions of operation hours or start-up cycles. (5) Inspection and life assessment. The unit specific unreliability functions are obtained as the posterior unreliability functions after detected event from inspection. For degradation and damage accumulation phenomena, probabilistic life assessment is used for simulating future unreliability. (6) Risk assessment. The risk is defined here as the sum product of the unreliability functions and the expected

Fig. 1. Basic flow of risk-based inspection and maintenance procedure.

Fig. 2 shows a component breakdown tree of a steam turbine unit. Those components show various types of degradation, damage and failure phenomena according to temperature, stress, environment and materials. Fig. 3 shows degradation, damage and failure modes of steam turbine major components [2,6]. For high- and intermediate-pressure (HIP) portions, the typical events are creep induced deformation, thermomechanical fatigue cracking and steam flow induced erosion. For low pressure (LP) portion, the typical events are environmental assisted fatigue cracking and steam flow induced erosion. The features of events are described as follows for major components. (1) HIP rotor. High centrifugal stress and high temperature cause creep deformation such as rotor bowing. The rotor bowing causes vibration and rubbing with bearings and casings. Creep damage accumulation causes creep void

Fig. 2. Component breakdown tree.

K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835

(4)

(5)

(6)

Fig. 3. Degradation, damage and failure modes of steam turbine major components.

formation and cracking at highly stressed portions such as bore and wheel hooks. Thermomechanical fatigue damage accumulation causes cracking at the wheel corner portion. (2) LP rotor. High centrifugal stress, high vibratory stress and corrosion environment causes corrosion fatigue at the wheel section. (3) HIP moving blade. High centrifugal stress and high temperature causes creep deformation such as lifting.

(7)

(8)

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The lifting causes rubbing with casings or nozzles and finally cracking. Creep damage accumulation causes creep void formation and cracking at the highly stressed portion such as dovetail hooks. Oxide scale brought by steam flow causes erosion. Vibratory stress causes high cycle fatigue cracking and fretting fatigue at the contact portion. LP moving blade. High centrifugal stress, high vibratory stress and corrosion environment causes corrosion fatigue cracking. Droplet brought by steam flow causes erosion. HIP nozzle. Oxide scale brought by steam flow cause erosion. Pressure difference at each stage and high temperature cause downstream deflection of nozzle diaphragm. HIP casing. High pressure stress and high temperature cause creep deformation. The creep deformation causes assembling mismatch and steam leak due to stress relaxation at the flange and the tightening bolt. Creep and thermomechanical fatigue damage accumulation causes cracking at the nozzle fit radius and other stress/ strain concentration portions. Valve. Creep and thermomechanical damage is the same as casings. Oxide scale brought by steam flow causes erosion at the shield plates. Oxidation at the shaft and valve body contact portion causes valve shaft sticking. Pipe. Creep damage accumulation causes creep void formation and cracking preferably at the weld portion. Water induction causes thermomechanical or thermal shock cracking.

Fig. 4 shows the event trees coupled with component breakdown trees based on the above information. This is the basis of the following analysis.

Fig. 4. An example of event trees for steam turbine unit.

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Fig. 5. Cumulative hazard functions for turbine rotor bowing fitted individually.

4. Unreliability analysis 4.1. Master field database The master field failure database has the data rows of plant name, component name, occurrence date, operation hours, start-up cycles, event contents, event cause and repair actions. Every event is related to operation hours and startup cycles until the events occur. For the events detected at the scheduled inspection, the estimated hours and cycles are adopted using reference operation history tables. 4.2. Field data analysis method: Cumulative hazard function method [3] The unreliability function is derived through cumulative hazard function method for the field failure database. The event data are stacked in the order of time or cycles for the same mode of failure and the same type of turbines. Estimated cumulative hazard function is expressed as follows ^ kÞ ¼ Hðt

k X i¼1

1 n þ 1 Ki

Fig. 7. Unified cumulative function for rotor bowing.

where, tk is event occurrence time at the k-th event, n is total number of samples including non-failure data. Regression of cumulative hazard function H(t) is conducted using the two-parameter Weibull plot expressed in the following equations. HðtÞ Z ðt=hÞm ln HðtÞ Z m ln t K m ln h

(2) (2 0 )

where h, m are regression constants. Unreliability function F(t) is calculated as follows FðtÞ Z 1 K RðtÞ Z 1 K expfKHðtÞg

(3)

where R(t) is reliability function. Eqs. (1)–(3) are also applied for cycle N dependent events using N instead of t. To overcome the lack of sufficient numbers of data, two approaches are adopted. One is the unified unreliability function approach and the other is the empirical unreliability function approach. Those two approaches are described below. 4.3. Unified unreliability function approach: example of rotor bowing

(1)

Fig. 6. Unreliability functions for turbine rotor bowing fitted individually.

If the dominant parameter of an event is known, unified master curve can be obtained by normalization. Here, rotor

Fig. 8. Unified unreliability function for rotor bowing.

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Fig. 11. Machine output class dependence for cycles at 50% unreliability for nozzle erosion events.

Fig. 9. Hours based cumulative hazard functions.

bowing phenomena is taken as an example though this event is prevented now due to the improvement of manufacturing and design. Figs. 5 and 6 show the cumulative hazard functions and unreliability functions against operation hours for two types (A-type and B-type) rotors. The type-B rotor regression is conducted with only two events. Here, the hazard function fitting against time (operation hours) is better than that against number of starts as reported elsewhere [5]. The time dependence comes from that the rotor bowing is one of the creep deformation phenomena. It depends on stress, temperature and material conditions. As the rotor bowing is one of the creep phenomena, the time is normalized by creep rupture time, that is, t/tr. Figs. 7 and 8 show the good unique correlation of cumulative hazard functions and t/tr for the two types of turbines, expressed by the following equation. HðtÞ Z

mc0 t =hc0 tr ðs; T; lÞ

(4)

where hc0, and mc0 are regression constants, s is stress, T is temperature and l is material strength parameter such as hardness or tensile strength, etc.

Fig. 10. Cycle based cumulative hazard functions.

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Eq. (4) indicates that the unreliability function of the specific unit can be estimated only by knowing design conditions or service conditions and material properties. 4.4. Empirical approach: example of nozzle erosion In the case of nozzle erosion, It is difficult to find the explicit parameters dominating erosion process. Figs. 9 and 10 show total regression results of cumulative hazard functions against operation hours and number of starts, respectively, expressed by the following equations. HðtÞ Z ðt=ht0 Þmt0

(5)

HðNÞ Z ðN=hN0 ÞmN0

(6)

where ht0, hN0 and mt0, mN0 are regression constants Eqs. (5) and (6) fit the whole data well enough but still indicate discrepancy between the turbine output types at some extent. Here, we introduce a modifying approach using hours or cycles at 50% unreliability based on the unified unreliability function. We show the modification results for cycle dependent unreliability functions or cumulative hazard functions.

Fig. 12. Empirical cumulative hazard functions of erosion for various nozzles.

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Modified cumulative function is obtained by using the modifying coefficient N50/N50,0, where N50,0 is number of starts at 50% unreliability for the unified curve of Eq. (6). mN0 N (8) HðNÞ Z N 50 =hN0 N50;0 Figs. 12 and 13 show the estimation results if the modifying coefficient approach. The estimation curves fits actual data reasonably even for the insufficient data.

5. Inspection system and unreliability function Fig. 13. Empirical unreliability functions of erosion for various nozzles.

Fig. 11 shows the relationship between number of starts at 50% unreliability N50 and output class index I that is proportional to output capacity. N 50 shows almost monotonic decreasing relationship with I, expressed as follows N50 Z aI b

(7)

where a and b are regression constants.

5.1. Quick visual and ultrasonic inspection system The visual and ultrasonic inspection gives useful information for adjusting the prior unreliability functions. To reduce the outage time for inspection, quick inspection systems have been developed. Fig. 14 shows an air-cooled borescope inspection system for nozzle erosion/failure detection. Magnet wheels attached to the inspection head move along the nozzle front, and remote observation by CCD camera is easily done

Fig. 14. Air-cooled borescope visual inspection system.

Fig. 15. Heat resistant UT system (left: application to components; right: the detail of carriage).

K. Fujiyama et al. / International Journal of Pressure Vessels and Piping 81 (2004) 825–835

Fig. 16. Prior and posterior unreliability functions for moving blade erosion.

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at temperature below 300 8C after machine shutdown. This may require about a couple of days. Fig. 15 shows a heat-resistant UT system for casing or valve defect detection. The moving head contains a couple of heat resistant UT sensors with the supply system of high temperature coupling medium to attach the system to a hot wall of about 300 8C. This system is used for detecting casing or valve inner defect and bolt cracking. Fig. 16 shows the posterior unreliability functions of moving blade erosion calculated by the prior unreliability function of nozzle erosion and the prior unreliability of moving blade erosion. Cycles to erosion event of nozzle is subtracted from cycles to erosion event of moving blade.

Fig. 17. Life assessment system coupled with non-destructive measurement system.

Fig. 18. Life assessment procedures based on analysis and non-destructive measurement.

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The cycle difference values and cumulative hazard function values are coupled and fitted again by Eq. (2). The obtained posterior unreliability function shows higher unreliability for small cycles indicating immediate occurrence of moving blade erosion after nozzle erosion.

5.2. Degradation/damage measurement and life assessment system [4,5] Fig. 17 shows a degradation/damage measurement and life diagnosis system schematically. Degradation and damage are measured by the hardness measurement system, replica observation technique and embrittlement measurement system. Life assessment system is programmed to calculate creep and fatigue life calculation using evaluation master curves and machine information. Fig. 18 shows the deterministic life assessment procedures [7]. Creep and fatigue damage is calculated by cumulative damage rule using the life assessment master curves. The feature of the procedure is that life assessment master curves are derived from material condition data measured by the hardness measurement system and the embrittlement measurement system. Creep and fatigue life evaluation curves are derived from hardness values measured for post-serviced components. Crack growth rate and fracture toughness are derived from FATT value converted from electrochemical polarization parameters using experimental master curves. Probabilistic life assessment requires statistical material properties [5,8]. Fig. 19 shows material creep rupture data including unused, laboratory aged and service used plotted

Fig. 19. Unified plot and regression of creep rupture for unused, aged and serviced materials.

Fig. 20. Cumulative probability of creep rupture life ratio derived from the unified master curve.

using stress/hardness ratio and Larson–Miller parameter. Fig. 20 shows the unified statistical distribution of experimental/estimated creep life ratio based on the whole creep rupture data and the master regression curve. It can be used as the simulated unreliability function of creep life of actual component. When narrower distribution is required, the data for statistical analysis should be selected carefully according to the specification of manufacturer.

Fig. 21. An example for the optimization of maintenance interval for rotor bowing.

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Fig. 22. PC based RBM system window view of risk assessment of rotor bowing.

6. Risk assessment and maintenance planning [5,6] Risk is defined here as the sum product of unreliability functions and expected monetary loss for every event in the event trees. The risk functions are specified by plant information and inspection information. Monetary loss is calculated for all expected items related to unscheduled outage and recovery action. Two ways of optimizing maintenance planning are presented below, that is, the optimization of maintenance intervals and the optimization of life cycle maintenance scenarios. 6.1. Maintenance interval optimization: example of rotor bowing Fig. 21 shows an example of the optimization of maintenance intervals for rotor bowing. The event tree is restricted to include typical three events for simplification. Those three events: (a) rotor bowing; (b) narrow axial clearance; (c) vibration, have different risk functions. The total risk function is determined by the sum of the three risk functions. The maintenance cost index is defined as the total cost of preventive maintenance action averaged per year for the subscribed events. The total risk is increasing function of operation hours and the cost index is proportional to

Fig. 23. Event trees, unreliability functions and risk functions for nozzle erosion.

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Fig. 24. The optimization of life cycle maintenance scenario for nozzle erosion.

the reciprocal of maintenance hours-based interval. The total cost curve is obtained by the sum of risk and maintenance cost showing a concave curve. If the income by operation is proportional to operation hours, the shaded area is recommended to decide the optimum maintenance intervals. The rotor bowing events are decreasing currently due to the improvement of manufacturing process, design and operation. Fig. 22 shows an example of the personal computer based RBM system window view of risk assessment of rotor bowing.

cost but runs high risk. The scenario 2 comprises predetermined replace period with the scheduled preventive repair actions during the service period. As the repair cost is relatively low in this case, the sum of risk and cumulative preventive costs remains low level. The scenario 3 comprises early replacement of erosion resistant upgraded nozzle and long term use of the upgraded one. It arises higher cost in the early period but relatively lower increase in the total cost for long period. The comparison of total cost gives the optimum maintenance scenario for the same period.

6.2. Maintenance scenario optimization: example of nozzle erosion Fig. 23 shows the event tree, the unreliability functions and risk functions of nozzle erosion event. Nozzle erosion event [A] shows relatively high unreliability but low cost for recovery action. The risk function is relatively low. For other events [B], [C], [D], lower unreliability and high recovery cost result in the same level risk as event [A]. The total risk is increasing function of operation period. Here, operation period is taken as operation hours but number of starts also applicable. Fig. 24 shows scenario case study for nozzle erosion events and maintenance action. The scenario 1 comprises predetermined replace period without preventive repair action during the service period. It requires no maintenance

Fig. 25. Application concept for risk-based engineering.

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7. Concluding remarks The quantitative RBM method for steam turbines was presented. Statistical formulation of failure probability as the function of time or cycles were very effective way to estimate the risk for various modes of failure and the chain of successive failure. The RBM system has various features as follows (1) Describe plant maintenance scenario by component breakdown trees and life cycle event trees. (2) Assign default unreliability function to every event by statistical analysis of master filed failure database. (3) Customize the unreliability functions can be modified reflecting the inspection information and probabilistic life assessment. (4) Optimize maintenance intervals using risk functions, cost functions and income functions. (5) Optimize maintenance scenario using life cycle event trees and total cost analysis. Those features are useful for wider application, not restricted to the steam turbine plant. The application

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of risk-based engineering is shown in Fig. 25. The quantitative method provides feedback and optimization of design, manufacturing and operation parameters. Those approaches will lead more economical and reliable plant design, manufacturing and management of plants.

References [1] Sakai S. J Jpn Inst Metals 2002;66(12):1170–6 [in Japanese]. [2] Fujiyama K, Fujiwara T. Proceedings of ICF10, \DATA\CONTENT\0868\PAPER.PDF (CD-ROM). Amsterdam: Elsevier; 2001. [3] Nelson W. Applied life data analysis. New York: Wiley; 1982. [4] Fujiyama K, Saito K, Harada S, Ahiko N, Itoh Y. Proceedings of CREEP7. Tsukuba: Japan Society of Mechanical Engineers; 2001 p. 69–74. [5] Fujiyama K, Fujiwara T, Kodama H, Saito K, Kichise H, Okazaki M. J Soc Mater Sci Jpn 2003;52(1):28–33 [in Japanese]. [6] Fujiyama K, Saito K, Fujiwara T, Kodama H, Kichise H, Okazaki M, Takagi K. J Jpn Inst Metals 2002;66(12):1199–205 [in Japanese]. [7] Kimura K, Fujiyama K, Muramatsu M. Curr Jpn Mater Res 1988;3: 247–70. [8] Fujiyama K, Takaki K, Nakatani Y, Yoshioka Y, Itoh Y. Mater Sci Res Int 2002;8(3):134–9.

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