an integrated approach of risk based maintenance for steam ... · pdf filean integrated...

OMMI, Vol.4, Issue 2, August 2007 www.ommi.co.uk

AN INTEGRATED APPROACH OF RISK BASED MAINTENANCE FOR STEAM TURBINE COMPONENTS.

Kazunari Fujiyama; Takahiro Kubo; Yasunari Akikuni; Toshihiro Fujiwara;

Hirotsugu Kodama; Mitsuyoshi Okazaki; Taro Kawabata. Industrial and Power Systems & Services Company, Toshiba Corporation, Yokohama, Japan

Kazunari FUJIYAMA: Currently, Professor at Meijo University, Department of Mechanical Engineering, Nagoya. Former Toshiba researcher on life assessment of turbines until 2005.

Yasunari AKIKUNI; Thermal & Hydro Power Systems & Services Div. Operation & Maintenance Engineering Dept. of Toshiba Corporation Power System Company

Toshihiro FUJIWARA; Senior manager of Field Engineering, Production & Sourcing Dept. of Toshiba Corporation Power Systems Company

Taro KAWABATA; Chief specialist of Turbine Design and Assembling Dept. of Toshiba Corporation Power Systems Company, specialized in maintenance technology of steam turbines

Hirotsugu KODAMA; Chief Specialist of Operation & Maintenance Engineering Dept. of Toshiba Corporation Power Systems Company, Specialized in steam turbine rehabilitation and maintenance technology.

Takahiro KUBO; Chief Specialist of Corporate Strategic Planning Division of Toshiba Corporation, specialized in the diagnosis technology of turbine materials

Mitsuyoshi OKAZAKI; Quality Expert for Management Innovation of Operation & Maintenance Engineering Dept. of Toshiba Corporation Power Systems Company

http://www.ommi.co.uk

An integrated RBM approach for steam turbine components, K Fujiyama et.al.

AN INTEGRATED APPROACH OF RISK BASED MAINTENANCE FOR STEAM

TURBINE COMPONENTS

Kazunari Fujiyama1, Takahiro Kubo1, Yasunari Akikuni2, Toshihiro Fujiwara2, Hirotsugu Kodama2, Mitsuyoshi Okazaki2 and Taro Kawabata3

1. Power and Industrial Systems R&D Center, Industrial and Power Systems & Services Company, Toshiba Corporation, Yokohama, Japan 2. Thermal and Hydro Power Division, Industrial and Power Systems & Services Company, Toshiba Corporation, Yokohama, Japan 3. Keihin Product Operations, Industrial and Power Systems & Services Company, Toshiba Corporation, Yokohama, Japan Abstract An integrated approach of Risk Based Maintenance was established to make optimum maintenance plans for steam turbine components. The plant specific life-cycle scenario is described through life-cycle event trees of various damage phenomena and maintenance actions for various components. Risks are estimated through probabilistic risk analysis calculating the unreliability as the function of operation hours or start-up cycles and the expected expense for each event. Maintenance plans are determined through the benefit obtained by operational incomes minus risks and maintenance costs. The unreliability is calculated through the cumulative hazard function method using the relational database of actual component failure, damage and repair history. When sufficient field data is not available, the master curve approach is adopted. In this approach, the unified master curves of unreliability functions are expressed by machine parameters such as steam flow, output, temperature, stress and so on. Using the unified master curves, unreliability functions can be easily customized for the subject unit. A personal computer (PC) based RBM system was developed consisting of the field failure database, event trees, statistical analyses, risk analyses and maintenance judgement. Key words: Risk Based Maintenance, Event Tree, Steam Turbine, Life Cycle, Failure, Damage, Database, System 1. Introduction In Japan, long term used fossil power plants are increasing in number and they are serviced in flexible operation such as daily start and stop or peak demand operation. To assure machine reliability, the life assessment technology is used as the tool of preventive maintenance. Recently, the risk based maintenance (RBM) has been introduced to fossil power plants because more cost-effective maintenance is required according to the trend of a competitive power generation market. As steam turbines are used at high temperature, high pressure and high speed and closely assembled with many components, one event could lead to another detrimental event. The event tree is the effective way to describe the scenario of failure events in steam turbines.


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The probabilistic risk assessment can be performed for quantitative risk assessment of steam turbines when coupled with the event tree. In this article, the understanding of the steam turbine degradation, damage and failure events are reviewed and "the life cycle event tree" approach is proposed with the reliability analysis of field failure data. Comprehensive maintenance scenarios are described through the life cycle event tree with the component breakdown trees. The RBM approach 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 inspection information of a specific unit is useful for modifying unreliability functions. To reduce outage time, the air-cooled borescope and the heat resistant ultrasonic sensors are provided for quick inspection. Life assessment information is also useful for obtaining probability of creep and fatigue cracking life by stochastic simulation analysis. A PC-based RBM system is demonstrated here to show how the quantitative RBM system can be performed with master field database. 2. Basic flow of the risk based maintenance procedure Figure 1 shows the basic flow of the risk based maintenance procedure. Each step has a 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 to each other and rotating at high speed. (3) Master field database The failure, inspection and repair history database is established for various types of 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


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monetary losses 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.

Fig. 1: Basic flow of risk-based inspection and maintenance procedure 3. Damage and failure modes of steam turbines Figure 2 shows a component breakdown tree of a steam turbine unit. The components show various types of degradation, damage and failure phenomena according to temperature, stress, environment and materials.

Fig. 2: Component breakdown tree

Steam turbineunit

High and/orintermediate

pressure (HIP)turbine

Low pressure(LP) turbine

Valves &Pipes

Auxiliaryequipment

Rotors

Moving blades

Nozzle box

Nozzles

Inner casings

Outer casings

Tightening bolts

Steam flanges

Rotors

Moving blades

Nozzles

Inner casings

Outer casings

Tightening bolts

Main stop valves

Control valves

Control reheat valves

Stem pipes/welds

Stem flanges

Control equipment

Bearings

Component breakdown treesComponent breakdown trees

Life cycle event treesLife cycle event trees

Unreliability analysisUnreliability analysis

Master field databaseMaster field database

Risk assessmentRisk assessment

Maintenance planningMaintenance planning

InspectionInspection

Life assessmentLife assessment


4

Figure 3 shows degradation, damage and failure modes of steam turbine major components2),6). For high- and intermediate-pressure (HIP) portions, the typical events are creep induced deformation, thermomechanical fatigue cracking and steam flow induced erosion. For the 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 leads to creep void 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 cause creep deformation such as lifting. The lifting causes rubbing with casings or nozzles and finally cracking. Creep damage accumulation leads to 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.

(4) LP moving blade: High centrifugal stress, high vibratory stress and corrosion environment causes corrosion fatigue cracking. Droplets brought by steam flow cause erosion.

(5) HIP nozzle: Oxide scale brought by steam flow causes erosion. Pressure difference at each stage and high temperature cause downstream deflection of nozzle diaphragm.

(6) 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 cause cracking at the nozzle fit radius and other stress/strain concentration portions.

(7) 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.

(8) Pipe: Creep damage accumulation leads to creep void formation and cracking preferably at the weld portion. Water induction causes thermomechanical or thermal shock cracking.


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

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

Event treesParts

Hig

h pr

essu

re tu

rbin

e

Rot

orS

tage

1 b

ucke

tN

ozzl

e bo

x

Nozzles

Buckets

Inne

r cas

ing

Outer casing

Creep-fatigueCreep-fatigue

LiftingLifting

Excess vibratorystress

Excess vibratorystress

Out of ControlOut of Control

RubbingRubbing

Excess scale erosionExcess scale erosion Decay of efficiencyDecay of efficiency

Excess scaleerosion

Excess scaleerosion

Shaft vibrationShaft vibration

WearWear

Unscheduledshutdown

UnscheduledshutdownWearWear

Excess bowingExcess bowing

CrackinitiationCrack

initiationCrackgrowthCrackgrowth FailureFailure

Creep-fatigue damageaccumulation

Downstreamdeflection

Downstreamdeflection RubbingRubbing FailureFailure

FailureFailure

RubbingRubbing

FailureFailure

Steam leakageSteam leakageCrackinitiationCrack

initiationCrackgrowthCrackgrowth FailureFailure

Steam leakageSteam leakageFlange deformationFlange deformation Bolt hole failureBolt hole failure

FailureFailureSteam leakageSteam leakageBody deformationBody deformation Bolt failureBolt failure

FailureFailure

Bea

ring

LP-A turbineLP-A turbine LP-B turbineLP-B turbineIP turbineIP turbineHP turbineHP turbine

Steam pipes・Scale erosion・Deformation・Cracking

Steam pipes・Scale erosion・Deformation・Cracking

Casings, Valves・Deformation・Cracking・Scuffing・Steam leakage・Erosion・Valve shaft sticking /bowing/failure・Bolt/bolt hole failure

Casings, Valves・Deformation・Cracking・Scuffing・Steam leakage・Erosion・Valve shaft sticking /bowing/failure・Bolt/bolt hole failure

Moving Blades・Erosion・Cracking・Lift up・Rubbing, Wear

Moving Blades・Erosion・Cracking・Lift up・Rubbing, Wear

Nozzles・Erosion・Deflection・Rubbing,Scuffing・Cracking

Nozzles・Erosion・Deflection・Rubbing,Scuffing・Cracking

Differentialpressure

Downstreamdeflection

Rotors・Cracking・Bowing・Vibration・Rubbing,Wear

Rotors・Cracking・Bowing・Vibration・Rubbing,Wear

Bearings・Vibration・Rubbing・Wear・Failure

Bearings・Vibration・Rubbing・Wear・Failure

Rubbing,Wear

Moving Blade

Nozzle

Steam flowLiftup

Cracking

Erosion

Steam flow

Cracking

Bowing

Cracking

Bolt/bolt holefailure

Flangedeformation

Cracking


6

Figure 4 shows the event trees coupled with component breakdown trees based on the above information. This is the basis of the following analysis. 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. Examples of database items are shown in Table 1. Every event is related to operation hours and start-up cycles. For the events detected at the scheduled inspection, the estimated hours and cycles are referred to operation history tables.

Table 1: Examples of typical event items in the master field database

Component Portion Event Cause Action Corner radius Crack TMF damage Remove, Weld repair Pipe root Crack Creep-fatigue damage Remove, Weld repair Horizontal joint Steam leak Creep relaxation Machining, Tightening

HIP Outer casing

Female tap thread Crack Creep damage Machining, Nut tightening Nozzle fit radius Crack TMF damage Remove, Weld repair Horizontal joint Steam leak Creep relaxation Machining, Tightening Body Erosion Steam leak Weld repair

HP Inner casing

Female tap thread Crack Creep damage Machining, Nut tightening Vane Erosion Oxide scale induction Weld repair, Surface

treatment Nozzle box Body Wear Vibration Machining, Weld repair Shroud Erosion Oxide scale induction Weld repair HP Bucket

(Moving blade)

Hook Crack Creep-fatigue damage Replace

4.2 Field data analysis: Cumulative hazard function method3) 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. The estimated cumulative hazard function is expressed as follows.

( ) ∑= −+

=k

ik in

tH1 1

1ˆ (1)

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.

H(t)=(t/η)m (2) lnH(t)=mlnt-mlnη (2)'


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where η, m are regression constants. Unreliability function F(t) is calculated as follows. F(t)=1-R(t)=1-exp{-H(t)} (3)

where R(t) is reliability function. Equations (1) to (3) are also applied for cycle N dependent events using N instead of t. Figure 5 to Figure 8 show examples of hours-based and cycle-based regression results of cumulative hazard functions and unreliability functions for several events. In this case, both regression results are acceptable. 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. These two approaches are described in the next section.

Fig. 5: Hours-based regression of cumulative hazard function

Fig. 6: Cycle-based regression of cumulative hazard function

Fig. 7: Hours-based regression of unreliability function

Fig. 8: Cycle-based regression of unreliability function

1

10

100

1000

10,000 100,000 1,000,000Operation hours t

Cum

ulat

ive

haza

rd fu

nctio

n H

, X10

0 HP nozzle erosionHP nozzle erosionHP blade erosionHP blade erosionHP rotor rubbingHP rotor rubbing

0

50

100

0 100,000 200,000Operation hours t

Unr

elia

bilit

y F

, %

HP nozzle erosionHP nozzle erosionHP blade erosionHP blade erosionHP rotor rubbingHP rotor rubbing

1

10

100

1000

10 100 1000Number of starts N

Cum

ulat

ive

haza

rd fu

nctio

n H

, X10

0 HP nozzle erosionHP Nozzle erosionHP blade erosionHP blade erosionHP rotor rubbingHP rotor rubbing

0

50

100


Unr

elia

bilit

y F

, %

HP nozzle erosionHP nozzle erosionHP blade erosionHP blade erosionHP rotor rubbingHP rotor rubbing


8

4.3 Unified unreliability function approach: Example of rotor bowing If the dominant parameter of an event is known, then a unified master curve can be obtained by normalization. Here, the rotor bowing phenomena is taken as an example though this event is prevented now due to the improvement of manufacturing and design. Figures 9 and 10 show the cumulative hazard functions and unreliability functions against operation hours for two types (A-type and B-type) of rotor. 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 elsewhere5). The time dependence arises because 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. Figures 11 and 12 show the good correlation of cumulative hazard functions and t/tr for the two types of turbines, expressed by the following equation.

( ) ( )

0

0,,

cm

cr Tt

ttH

= ηλσ

(4)

where ηc0, and mc0 are regression constants, σ is stress, T is temperature and λ is a material strength parameter such as hardness or tensile strength, etc. Equation (4) indicates that the unreliability function of the specific unit can be estimated only by knowing design conditions or service conditions and material properties.

Fig. 9: Cumulative hazard functions for turbine rotor bowing fitted individually

Fig. 10: Unreliability functions for turbine rotor bowing fitted individually

CrMoV forgings

1

10

100

10000 100000 1000000Operation hours, t /h

Cum

ulat

ive h

azar

d fu

nctio

n, H

,(%)

A-type rotorA-type rotor regressionB-type rotorB-type rotor regression

CrMoV forgings

0

50

100

0 100,000 200,000Operation hours, t /h

Unr

elia

bilit

y, F

,(%

)

A-type rotorA-type rotor regressionB-type rotorB-type rotor regression


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Fig. 11: Unified cumulative function for rotor bowing

Fig. 12: Unified unreliability function for rotor bowing

4.4 Empirical approach: Example of nozzle erosion In the case of nozzle erosion, it is difficult to find the explicit parameters dominating the erosion process. Figures 13 and 14 show total regression results of cumulative hazard functions against operation hours and number of starts respectively, expressed by the following equations.

( ) ( ) 0

0tm

tttH η= (5)

( ) ( ) 0

0Nm

NNNH η= (6) where ηt0, ηN0 and mt0, mN0 are regression constants.

Equations (5) and (6) fit the whole data well enough but still indicate a discrepancy between the turbine output types to 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.

Figure 15 shows the relationship between number of starts at 50% unreliability N50 and output class index I which is proportional to output capacity. N50 shows an almost monotonic decreasing relationship with I, expressed as follows.

βαIN =50 (7)

where α and β are regression constants.

CrMoV forgings

1

10

100

0.1 1Time fraction, t /t r

Cum

ulat

ive

haza

rd fu

nctio

n H

,( %

)

A-type rotorB-type rotorRegression line

CrMoV forgings

0

50

100

0 0.1 0.2 0.3 0.4Time fraction, t /t r

Unr

elia

bilit

y, F

, (%

)

A-type rotorB-type rotorUnified regression curve


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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).

( )0

00,50

50

Nm

NNN

NNH

= η (8)

Figures 16 and 17 show the estimation results of the modifying coefficient approach. The estimation curves fit the actual data reasonably even for insufficient data.

Fig. 13: Hours based cumulative hazard functions

Fig. 14: Cycle based cumulative hazard functions

Fig. 15: Machine output class dependence for cycles at 50% unreliability for nozzle erosion events

1

10

100

1000

10000 100000 1000000Operation hours t , h

Cum

ulat

ive h

azar

d fu

nctio

n H

, X10

0

TYPE-ATYPE-ATYPE-BTYPE-BTYPE-CTYPE-CTYPE-DTYPE-D

1

10

100

1000


Cum

ulat

ive h

azar

d fu

nctio

n H

, X10

0 TYPE-ATYPE-ATYPE-BTYPE-BTYPE-CTYPE-CTYPE-DTYPE-D

N ozzle erosion

100

1000

1 10

M achine index

Cycles at 50% unreliability


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Fig. 16: Empirical cumulative hazard functions of erosion for various nozzles

Fig. 17: Empirical unreliability functions of erosion for various nozzles

5. Inspection and life assessment 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. Figure 18 shows an air-cooled borescope inspection system for nozzle erosion/failure detection. Magnetic wheels attached to the inspection head move along the nozzle front, and remote observation by CCD camera is easily done at temperatures below 300°C after machine shutdown. This may require about a couple of days. Figure 19 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°C. This system is used for detecting casing or valve inner defect and bolt cracking.

Fig. 18: Air-cooled borescope visual inspection system

1

10

100

1000


Cum

ulat

ive h

azar

d fu

nctio

n H

, X10

0


0

50

100


Unr

elia

bilit

y F

, %


CCD camera

magnet rollers


12

Fig. 19: Heat resistant UT system (Left: application to components, Right: detail of carriage) 5.2 Degradation/damage measurement and life assessment 4),5) Figure 20 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. The life assessment system is programmed to perform creep and fatigue life calculations using evaluation master curves and machine information. Figure 21 shows the deterministic life assessment procedure7). The procedure comprises FEM analysis of temperature and stress for the steady and unsteady operations of the specific plant. Creep and fatigue damage is calculated by cumulative damage rules using the life assessment master curves. For condition-based life assessment, the master curves are modified with material condition data measured through the hardness measurement and embrittlement measurement of serviced components. Creep and fatigue life evaluation curves are derived from hardness values for serviced low alloy heat resistant steels and high chromium steels. Crack growth rate and fracture toughness are derived from FATT value converted from electrochemical polarization parameters using experimental master curves.

Fig. 20: Life assessment system coupled with non-destructive measurement system

Details of the carriage

Flexible shaftattachment

Staring rodattachment

Couplingmediumstorage

Magnetroller wheel

High temperatureUT sensors

Digital UT indicatorCoupling mediumsupply pump

Steam turbinevalve body

Flexible shaft driverStaring rod

Life assessmentLife assessment

Enbrirrlementmeasurement

system

Enbrirrlementmeasurement

system

ReplicationReplicationHardness

measurementsystem

Hardnessmeasurement

system

Hou

rs

Cycles Cycles

Hou

rs


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Fig. 21: Life assessment procedures based on analysis and non-destructive measurement Probabilistic life assessment requires statistical material properties5),8). Figure 22 shows material creep rupture data including unused, laboratory aged and service used plotted using stress/hardness ratio and Larson-Miller parameter. Figure 23 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.

Fig. 22: Unified plot and regression of creep rupture for unused, aged and serviced materials

Fig. 23: Cumulative probability of creep rupture life ratio derived from the unified master curve

Operation plan

Operation history

Temperature/stress/strain analysis(FEM)

Parts configurationOperating conditions

Inspection records

Damagecalculation•φc:Time fraction•φf:Cycle fraction

Remnant lifecalculation

Crack initiation

Crack growth

Damage parameterHardness Creep void

Degraded materialproperties

Replication

Hardness ofdamaged ordegradedportions

Embrittlement(Electro-chemical)

Maintenance plan

Creep rupture LCF

Crack growth Toughness

Non-destructiveinspection of

defects

Initial cracksize/shape

Time to rupture

Stre

ss

Cycles

Stra

in

∆K or C*da/d

N o

r da

/dt

Embrittlement

Temperature

KIC

, JIC

Embrittlement

φcφ f

Crackingzone

Operation period

Cra

ck s

ize

Critical size

Limit

Initial size

φc or φf

HV

/HV

o

φc

A-p

aram

eter

Component life

Remnant lifeRemnant life

SofteningSoftening

現状の寿命診断において、非破壊計測の一部変更とFEM解析の省略により診断コストを低減する。ANALYTICAL ASSESSMENT NON-DESTRUCTIVE ASSESSMENT

CrMoV forgings

0.1

1

10

16 18 20 22 24Larson-Miller parameter, P (X1000)

Stre

ss to

hra

dnes

s ra

tio,σ

/HV

, (M

Pa/

HV

)

Unused, Lab. aged, service aged materialsNIMS data sheetRegression curve

CrMoV forgings

0

50

100

0 1 2 3Experimental life/Estimated life

Cum

ulat

ive

prob

abili

ty

F, %


14

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 Figure 24 shows an example of the optimization of maintenance intervals for rotor bowing. The event tree is restricted to include three typical 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 an increasing function of operation hours and the cost index is proportional to 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. 24: An example for the optimization of maintenance interval for rotor bowing

Operation hours

Cos

t ind

ex

Benefitarea

Income from operation

Total expected cost=(A)+(B)

(B)Maintenance cost

(A)Total risk cost=(a)+(b)+(c)

(a)Rotor bowing risk

(b)Rotorvibration risk

(c)Narrow axialclearance risk

Maintenanceopportunity

Bearing wearBearing wear

ShaftvibrationShaft

vibration

Nozzlefailure

Nozzlefailure

Moving blade/wheel failureMoving blade/wheel failure

Bearingfailure

Bearingfailure

RotorBowingRotor

BowingCasingfailure

Casingfailure

Nozzlefailure

Nozzlefailure

Moving blade/wheel failureMoving blade/wheel failure

Casingfailure

Casingfailure

Narrow axialclearance

Narrow axialclearance


15

6.2 Maintenance scenario optimization: Example of nozzle erosion Figure 25 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 of risk as event [A]. The total risk is an increasing function of operation period. Here, operation period is attributed as operation hours but number of starts is also applicable in some cases. Figure 26 shows the 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 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 leads to higher cost in the early period but relatively lower increase in the total cost for long period. If a time point is fixed, the comparison of total cost gives the optimum maintenance scenario clearly.

Fig. 25: Event trees, unreliability functions and risk functions for nozzle erosion

Event trees for nozzle erosion【Event B】Expansion of erosionarea+Out of controlUnreliability Fb:LowLoss B:Medium

【Event A】Excess scaleerosion+Decay of efficiencyUnreliability Fa:MediumLoss A:Small

【Event C】Nozzle vane failureUnreliability Fc:LowLoss C:Large

【Event D】Bucket failureUnreliability Fd:LowLoss D:Large

Risk functionsUnreliability functions

O peration period

Unreliability

FaFbFcFd

O peration period

Risk

Total riskR isk AR isk BRisk CR isk D


16

Fig. 26: The optimization of life cycle maintenance scenario for nozzle erosion 7. PC-based RBM system Figure 27 shows the structure of the database and functions built into the PC-based RBM system. Plant related data and event related data are constructed as a relational database. Risk analysis functions are installed in the system as described in the above sections. Figure 28 shows an example of the personal computer based RBM system window view of risk assessment of rotor bowing.

Risk-cost analysis Life-cycle event tree diagram【Scenario 1】 No repair until parts life(Natural risk)

【Scenario 2】Repeated repair until parts life and replacement topreventive parts

【Scenario 3】Early upgrading to preventive parts without repair





【Event B】Expansion oferosion area+Out of controlUnreliability Fb:LowLoss B:Medium

【Event B】Expansion oferosion area+Out of controlUnreliability Fb:LowLoss B:Medium



【Event A-1】UnreliabilityFa:MediumLoss A:Small


Repair-1Repair-1 Repair-2Repair-2





Replacetopreventiveparts






O peration period

Risk + cost

S cenario 1 Scenario 2

R epair

Reduced risk at retirem ent

O peration period

Risk + cost

S cem ario 1 Scenario 2Scenario 3

Replacem ent topreventive parts

Repair

O peration period

Risk + cost

Scenario 1

P rescribed parts lifeunder high risk

Replacem ent topreventive parts


17

Fig. 27: Database and functions of the PC-based RBM system

Fig. 28: PC based RBM system window view of risk assessment of rotor bowing

Event tree

Rotorshaft

Rotorshaft Rotor

bowingRotor

bowing Labyrinthwear

Labyrinthwear Ef iiciency

decayEf iiciency

decayLabyrinthgap

Labyrinthgap

Shaftvib.

Shaftvib. Rotor

crackingRotor

crackingCrackgrowthCrackgrowth

Rotorburst

Rotorburst

BKTwearBKTwear BKT

crackingBKT

cracking BKTfailureBKT

failure Casingfailure

Casingfailure

Ope

ratio

n ho

urs

Ope

ratio

n ho

urs

Inte

rmed

iate

pre

ssur

e ro

tor

Inte

rmed

iate

pre

ssur

e ro

tor

Inte

rmed

iate

pre

ssur

e- T

ime

base

drIn

term

edia

te p

ress

ure-

Tim

e ba

sedr

TopUnreliabilityCostRisk analysis

Rotor bowing Rotor cracking Rotor bowing Rotor cracking

Rotor bowing Rotor cracking Rotor bowing Rotor cracking

Unreliability functionsF(t)=1-exp{-(t/η)m}

Risk prevention cost Total risk Rotor bowing Shaft vibration Labyrinth clearance Rotor cracking

Risk prevention cost Total risk Rotor bowing Shaft vibration Labyrinth clearance Rotor cracking

Risk prevention cost

TopCondition input$ Risk=∑F(t)×$ Loss

Database

Component Breakdown TableComponent Breakdown Table

Class-1 Component ---- Class-2 component ---- Event Tree ID Class-1 Component ---- Class-2 component ---- Event Tree ID

Plant Operation History TablePlant Operation History Table

Plant Code ---- Year --- Hours --- Starts --- Inspection No. Plant Code ---- Year --- Hours --- Starts --- Inspection No.

Event Data TableEvent Data Table

Event ID --- Plant Code ---Occurrence Date --- Hours ---Starts --- Event Description --- Recovery Action --- Cause Event ID --- Plant Code ---Occurrence Date --- Hours ---Starts --- Event Description --- Recovery Action --- Cause

Unit Design Information TableUnit Design Information Table

Plant Code ---Unit Code --- MW --- Hz --- Fuel --- Type --- MainSteam Pressure --- Main Steam Temperature --- Reheat SteamTemperature --- LSB length --- Materials

Plant Code ---Unit Code --- MW --- Hz --- Fuel --- Type --- MainSteam Pressure --- Main Steam Temperature --- Reheat SteamTemperature --- LSB length --- Materials

Event Tree Information TableEvent Tree Information Table

Event Tree ID --- Event Code --- Event Description ---Consequence of Failure --- Unreliability Coefficient ---Unreliability Exponent --- Number of Statistical Data

Event Tree ID --- Event Code --- Event Description ---Consequence of Failure --- Unreliability Coefficient ---Unreliability Exponent --- Number of Statistical Data

Functions

Calculation of Hazard Functions &Unreliability Functions

Calculation of Hazard Functions &Unreliability Functions

Calculation of Total Risk FunctionsCalculation of Total Risk Functions

Risk -Cost Graph DisplayRisk -Cost Graph Display

Hazard Functions & UnreliabilityFunctions Display

Hazard Functions & UnreliabilityFunctions Display

Select Menu DisplaySelect Menu Display

Component Breakdown Tree &Event Tree Display

Component Breakdown Tree &Event Tree Display

Input Cost DataInput Cost Data


18

8. Concluding remarks

A quantitative RBM method for steam turbines has been presented. Statistical formulation of failure probability as a function of time or cycles was a very effective way to estimate the risk for various modes of failure and the chain of successive failures. The RBM system has various features as follows:

(1) Describe plant maintenance scenario by component breakdown trees and life cycle event trees.

(2) Provide master unreliability functions for events by statistical analysis of field failure database.

(3) Customize the unreliability functions - 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. References 1. S. Sakai, J. Japan Inst. Metals, 66, 12, pp.1170-1176 (2002, in Japanese) 2. K. Fujiyama and T. Fujiwara, Proc. ICF10, ¥DATA¥CONTENT¥0868¥PAPER.PDF

(CD-ROM), Elsevier Science Ltd. (2001) 3. W. Nelson, Applied Life Data Analysis, John Wiley & Sons, Inc. (1982) 4. K. Fujiyama, K. Saito, S. Harada, N. Ahiko and Y. Itoh, Proc. CREEP7, Tsukuba, Japan

Society of Mechanical Engineers, pp.69-74 (2001) 5. K. Fujiyama, T. Fujiwara, H. Kodama, K. Saito, H. Kichise and M. Okazaki, J. Soc. Mat.

Sci. Japan, 52, 1, pp.28-33 (2003, in Japanese) 6. K. Fujiyama, K. Saito, T. Fujiwara, H. Kodama, H. Kichise, M. Okazaki and K. Takagi,

J. Japan Inst. Metals, 66, 12, pp.1199-1205 (2002, in Japanese) 7. K. Kimura, K. Fujiyama and M. Muramatsu, Current Japanese Materials Research, 3,

pp.247-270 (1988) 8. K. Fujiyama, K. Takaki, Y. Nakatani, Y. Yoshioka and Y. Itoh, Materials Science

Research International, 8, 3, pp.134-139 (2002)

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