Fatigue failure analysis of last stage blade in a low pressure steam turbine

\ PERGAMON

Engineering Failure Analysis 5 "0887# 82Ð099

Fatigue failure analysis of last stage blade in a low pressure steam turbine Hyo!Jin Kim R + D Center\ Korea Heavy Industries + Construction Co[\ Ltd\ 444 Guy`ok!Don`\ Chan`won\ 530!681\ Korea Received 09 September 0887^ accepted 00 September 0887

Abstract Failures occur from time to time in power plants\ as they do in other engineering structures[ Most investigations of blade failures end with a metallurgical analysis[ But to correct a blading problem requires more than positive identi_cation of the mechanisms involved[ In this paper\ a mechanical analysis is performed with the metallurgical analysis for competent analysis of blade failure[ The mechanical analysis capable of predicting stress and dynamic characteristics of turbine blades is presented to increase steam turbine availability by decreasing blade failures[ The analysis is illustrated by the case study[ Þ 0888 Elsevier Science Ltd[ All rights reserved[ Keywords] Dynamic stress analysis^ High cycle fatigue^ Finite element analysis^ Blade failures^ Blade vibration

0[ Introduction 0[0[ Background A failure condition may initiate due to a number of phenomena\ each having the ability to introduce a situation that can force a unit from service ð0Ł[ The most common failure mechanisms which occur within a mature unit are normally those associated with either sympathetic or forced vibrations\ those caused by transient operating conditions\ and those which occur as the result of the transported and accumulated corrosive ions in the working ~uid[ Failures occur from time to time in power plants\ as they do in other engineering structures[ However\ they are not always examined closely to identify the causes[ Similarly\ when the failures are observed from time to time\ repairs are often made without any careful analysis being undertaken[ Most blade failure investigations end with a metallurgical report ð1Ł[ A metallurgical examination of the blade estab! lishes whether the failure was due to substandard material\ or if the presence of ~aws\ machine marks\ or corrosion pits created local stress raisers not accounted for in the allowable stress limits of the blade design[ A fracture surface of the blade can suggest that fatigue is a more probable S0249Ð5296:88:, ! see front matter Þ 0888 Elsevier Science Ltd[ All rights reserved PII] S 0 2 4 9 Ð 5 2 9 6 " 8 7 # 9 9 9 2 3 Ð X

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H[!J[ Kim:En`ineerin` Fracture Analysis 5 "0887# 82Ð099

failure mechanism[ But to correct a blading problem requires more than positive identi_cation of the mechanisms involved[ In this paper\ a mechanical analysis is performed with the metallurgical analysis for competent analysis of blade failure[ The mechanical analysis capable of predicting stress and dynamic charac! teristics of turbine blades is presented to increase steam turbine availability by decreasing blade failures[ The _nite element technique is used to predict natural frequencies\ steady and dynamic stresses of turbine blades[ The analysis is illustrated by the case study[ The case discussed is blade failure in the last stage of a low pressure steam turbine[ The analysis identi_es a successful turbine blade repair for safe operation[ The importance of a competent analysis of a failure is emphasized in assuring future safe operation[ 0[1[ Observation of the failure Two blades were found to have fractured in the last stage of a low pressure steam turbine[ The last stages of large condensing turbines operate in the wet steam region[ Water droplets formed cause abrasion on the leading edge of the blade[ The leading edge of the blade is protected by the attachment of a Stellite shield ð2Ł[ The crack initiated at the point of the shield[ A failure analysis was performed to avoid further similar failures of the blades[ 1[ Metallurgical analysis Two failure blades were provided for examination[ The chemical compositions of the blades were examined\ as shown in Table 0[ It was con_rmed that the design material was used in the blades[ Figure 0"a# and "b# show a view of the fracture surfaces\ and the tell!tale beach marks indicative of fatigue are obvious[ The beach marks reveal evidence of high cycle fatigue by blade vibration and dynamic stress as likely contributors to the failure[ This indicates that there must have been a vibration condition su.cient to propagate cracking from initial defects formed at the leading edges of the blades[ Observation in the SEM con_rmed that the initial defects at the leading edges were not formed by a corrosion pit[ The presence of machine marks for attachment of the shield is assumed at the point of crack initiation[ 2[ Mechanical analysis It is identi_ed from the metallurgical analysis that there must have been a vibration condition su.cient to propagate cracking from initial defects formed at the leading edges of the blades[

Table 0 Chemical composition C

Si

Mn

P

S

Ni

Cr

Mo

V

Cu

9[07

9[15

9[36

9[93

9[91

9[28

02[1

9[63

9[91

9[98

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H[!J[ Kim:En`ineerin` Fracture Analysis 5 "0887# 82Ð099

Fig[ 0[ Fracture surfaces of blade[ Table 1 Engineering constants Temperature ">C# Data

099

199

299

399

499

Density "kgf:m2# Thermal conductivity "092×kgf!m:s!m!>C# Young|s modulus "0900×Pa# Speci_c heat "kgf!m:kgf!>C# Coe.cient of thermal expansion "a×095#

5[26 0[88 60[29 4[41

5[52 0[89 43[11 4[59

9[17 5[77 0[70 47[95 4[66

6[02 0[62 50[94 5[92

6[27 0[51 3[16 5[25

Therefore\ a mechanical analysis capable of predicting stress and dynamic characteristics of turbine blades is needed to increase steam turbine availability by decreasing blade failures[ Finite element analysis needs to be performed because of the complex geometry and boundary conditions such as blade[ Engineering constants of the blade for the analysis are presented in Table 1[ 2[0[ Finite element modeling Geometry data for the blade is necessary for _nite element modeling[ The geometry data was obtained from a multi axis coordinate measuring machine\ which traces the pro_le and root at various locations[ Figure 1 shows a representative _nite element model for a single blade segment[ The eight!node solid element is utilized for the _nite element modeling[ Each node has six degrees of freedom[ 2[1[ Steady stress analysis The bladed disk structure experiences large centrifugal forces at the operating speed[ The steam bending forces are normally very small "less than 09)# and do not contribute much to the steady

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Fig[ 1[ Finite element model for a single segment bladed disk[

stresses[ However\ the steam bending forces determine the dynamic stress level at any per!rev excitation frequencies[ The governing equation for the _nite element model of the bladed disk subjected to centrifugal force is given by ðKeŁ"Ue#  ðFeŁ

"0#

where ðKeŁ is the sti}ness matrix\ ðFeŁ is the centrifugal force vector and "Ue# is the resulting displacement vector of the bladed disk _nite element model[ Typically\ this equation is solved only for one single repetitive segment "one blade or blade group# of a tuned bladed disk\ since all repetitive segments would experience identical stress distributions[ 2[2[ Modal analysis The equation of motion ð3Ł of the complete bladed disk for free vibration "neglecting Coriolis: damping matrices# can be represented by ðMŁ"U Ý #¦ðKŁ"U#  "9#

"1#

where ðMŁ is the mass matrix\ ðKŁ is the sti}ness matrix and "U# is the displacement vector of the bladed disk[

H[!J[ Kim:En`ineerin` Fracture Analysis 5 "0887# 82Ð099

86

2[3[ Dynamic stress analysis Dynamic stresses experienced by a bladed disk structure are caused by the harmonic forcing patterns as seen by the stage[ It is the motion of the rotating blades through a non!uniform\ spatially _xed ~ow _eld that generates these harmonic forces on the rotating blades[ The frequencies of these forcing spectra are a function of the rotor speed\ and in the case of a resonant or near resonant operation under these harmonic forces\ the rotating stage can su}er a signi_cant reduction in the design life[ This is due to the material damage resulting from high cycle fatigue[ Some of the factors that can possibly cause non!uniform ~ow around the circumference include nozzle wakes\ leakage ~ows\ geometry variation of nozzles\ and steam extractions at stage inlet[ The solution of the harmonic response of a structure which has imposed harmonic excitation "per!rev# can be obtained by the solution of the governing equation of motion ðMŁ"U Ý #¦ðCŁ"U þ #¦ðKŁ"U#  "F"t##

"2#

where ðMŁ\ ðCŁ and ðKŁ are the mass\ the damping and sti}ness matrices[ "U Ý #\ "U þ # and "U# are the acceleration\ the velocity and the displacement matrices[ 3[ Results and discussion A review of the stresses shows maximum calculated values of steady stresses occurred in the root hooks[ The steady stress at the crack initiation site on the vane\ as shown in Fig[ 2\ is calculated

Fig[ 2[ Steady stress distribution[

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Fig[ 3[ Campbell diagram of blade[

to be substantially less than that in the root\ reinforcing the premise that failure is related to the dynamic response of the blade[ Natural frequencies and corresponding mode shapes were calculated\ with no forcing applied[ Natural frequencies and mode shapes were obtained by extracting eigenvalues and eigenvectors from the system equations[ To assist the user to interpret frequency results\ a Campbell diagram\ as shown in Fig[ 3\ is plotted to illustrate the relationship of mode frequencies to rotor speed ð4Ł[ The diagram shows the blade natural frequencies increasing as rotor speed increases from 9 to 2599 rpm as a consequence of the stress sti}ening[ Dynamic stresses for each of the _rst seven modes of the blade were calculated[ It is indicated that dynamic stress will be high if the third torsional mode is excited[ The Campbell diagram plot reveals the third torsional mode to be very close to the eighth per!rev[ The mode shape of the third torsional mode is shown in Fig[ 4[ The torsional modes have maximum stress occurring at the vane edge as shown in Fig[ 5\ consistent with the point of crack initiation found in metallurgical examination[ As the result of the mechanical analysis\ initial defects such as machine marks for the attachment of the shield\ or corrosion:erosion pits need to be prevented at the point of dynamic stress concentration for decreasing blade failure[ Otherwise dynamic characterization at the location of the initial defect must be changed to prevent blade failure[ As illustrated by the case study\ the analysis is able to provide critical details on the structural behavior of the blade[ Therefore\ the analysis is used to guide\ and support the plant manager|s decision to avoid a costly\ unplanned outage[

H[!J[ Kim:En`ineerin` Fracture Analysis 5 "0887# 82Ð099

Fig[ 4[ Third torsional model[

Fig[ 5[ Dynamic stress distribution[

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References ð0Ł Hambling P[ Modern power station practice[ Oxford] Pergamon Press\ 0880[ ð1Ł Furtado HC\ Collins JA\ Le May I[ Risk Economy and Safety\ Failure Minimisation and Analysis 0887^64[ ð2Ł Sanders WP[ The procurement of replacement steam turbine blading[ Norwark] Turbomachinery International Publications\ 0886[ ð3Ł Omprakash V\ Lam T\ Gruwell D\ McCloskey TH[ PWR\ 0883^15]048[ ð4Ł Roemer MJ\ Hesler SH\ Rieger NF[ Sound and Vibration 0883^ May[