Damage assessmen in a ein o ced conc e e pedes al based on o a ing
machine y ib a ion analysis
E ik Rosado Tama iz1, Albe o López López1, Da id Po as-Na a o González1
1Ci il Enginee ing Depa men , Ins i u o de In es igaciones Eléc icas (México).
[email p o ec ed], [email p o ec ed] g.mx, da id.[email p o ec ed] g.mx
ABSTRACT
A c i ical ope a ional condi ion o be conside ed in he a igue damage e alua ion in ein o ced
conc e e pedes als o powe plan s gene a ion is he caused by he dynamic e ec s ansmi ed by
he u bo-gene a o in e ms o ib a ions. The s uc u al beha io o he u bo-gene a o unde
dynamics condi ions is a ec ed by i s dimensional cha ac e is ics, he weigh o each componen s and
he pe o mance o each suppo s on e ms o s i ness and damping.
In his s udy, a coupled ini e elemen model FEM o he u bo-gene a o and ein o ced conc e e
pedes al we e de eloped in o de o e alua e he dynamic beha io o he s uc u e and he a igue
damage o di e en eal ope a ional condi ions acco ding o da a ob ained om ield measu emen s.
The FEM de eloped o he pedes al conside s he inclusion o ein o cing s eel s uc u al elemen s
wi hin he conc e e. The me hodology was implemen ed o de e mine he c i ical zones o a igue
ailu e and an es ima e o emaining a igue li e in he pedes al.
Keywo ds: Damage Assessmen , Rein o ced Conc e e, Powe Plan Pedes al, Nume ical Analysis.
1. INTRODUCTION
As pa o i s imp o emen s p ocess he Mexican elec ical sys em hey ca y ou di e en ac ions,
including he mode niza ion o some o he c i ical componen s o he powe plan s gene a ion; wi h
he aim o inc ease i s p oduc ion, as well as o imp o e hei gua an eed ne capaci ies and he ne
uni hea consump ions. In addi ion o his mode niza ion p ocess, i is necessa y o assess he e ec s
o hese changes in he componen s ha no we e modi ied wi h espec o he o iginal design o he
gene a ing uni and in e ac ing di ec ly wi h upg aded componen s.
The s udy case shown in he p esen wo k ocuses on he e alua ion o he dynamic beha io and he
es ima ion o emaining a igue li e in he ein o ced conc e e pedes al o an upg aded s eam u bine
o he uni gene a ion o simple cycle as pa o i s e o i p ocess. The sys em analyzed in his s udy
consis s o a ein o ced conc e e pedes al ha suppo s he u bo-gene a o o he uni gene a ion
h ough eigh adial suppo s and a suppo o axial ype.
The ein o ced conc e e pedes al o he u bo-gene a o is o med by a igid s uc u al sys em o
ein o ced conc e e ames, which has six bays on he eas -wes di ec ion and one bay on he no h-
sou h di ec ion; he dimensions o leng h and wid h o s uc u e a e 51.50m and 16.50m espec i ely,
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Damage assessmen in a ein o ced conc e e pedes al based on o a ing machine y ib a ion analysis
Thi d In e na ional Con e ence on Mechanical Models in S uc u al Enginee ing
Uni e si y o Se ille. 24-26 June 2015.
wi h h ee le els o main loo . Since manu ac u ing and s uc u al d awings [1], he 3D CAD model
was de eloped using comme cial CAD so wa e “SolidWo ks”. In he Figu e 1, shows he global iew
o he geome ical model o he pedes al. The o al mass o he pedes al was e i ied wi h espec
o da a epo ed in design speci ica ions [2].
Figu e 1. Geome ical model o he ein o ced conc e e pedes al.
Fi e componen s comp ise he u bo-gene a o o he gene a ion uni , a o o o a high p essu e (HP),
he i s o o o low-p essu e u bine (LP1), he Jack Sha (JS), he second o o o low-p essu e
u bine (LP2) and he o o o elec ical gene a o . Figu e 2, shows he dis ibu ion and he
geome ical model o hese componen s o he u bo-gene a o .
Figu e 2. Dis ibu ion and geome ical model o he componen s ha comp ise he u bo-gene a o o
he gene a ion uni .
In o de o suppo he u bo-gene a o on he ein o ced conc e e pedes al a e used in o al nine
bea ings, o which six a e o ype cylind ical hyd odynamic loca ed in he high p essu e u bine and in
he wo low p essu e u bines, as well as wo il ing pads bea ings loca ed on he gene a o . These
bea ings ca y he en i e u bo-gene a o o p e en displacemen s in he e ical and ho izon al
di ec ions a he ex emi ies o each u bine and gene a o . Addi ionally, he e is an axial h us
bea ing o p e en displacemen s along he longi udinal axis a he le el o Jack Sha ; which a e
caused mainly by he sum o he loads a he di e en s ages o he u bines. Figu e 3 shows a op
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E ik Rosado Tama iz1, Albe o López López1, Da id Po as-Na a o González1
iew o he loca ion (in ed) o bea ings o u bo-gene a o wi h espec o conc e e pedes al ha
suppo s i .
Figu e 3. A op iew o he loca ion (in ed) o bea ings o u bo-gene a o .
2. FINITE ELEMENT METHOD
Gene ally, he ini e elemen s ess analysis o a p ac ical enginee ing componen consis s o h ee
phases: (a) modeling, (b) analysis, and (c) esul s in e p e a ion.
Phase I: Modeling
In his phase, which is known as he p e-p ocessing phase, an ac ual enginee ing componen is
ep esen ed by an accu a e model o a ini e elemen mesh oge he wi h speci ied loading and
bounda y condi ions. The basic aspec s o modeling wi hin he ini e elemen me hod a e: (a)
elemen selec ion, (b) geome ical modeling, (c) ma e ial modeling, (d) load modeling, and (e)
bounda y condi ion modeling.
Phase II: Analysis
The basic s eps o he analysis phase may be summa ized as ollows:
S ep 1: Selec ion o he ield a iable models.
In he selec ion o he ield a iable models, his s ep is ea ed as a sepa a e p oblem and he ield
unc ions (i.e. displacemen s) inside he elemen a e exp essed in e ms o nodal displacemen s and
shape unc ions.
S ep 2: Fo mula ion o elemen s i ness ma ices.
The displacemen s, s ains and s esses ec o s wi hin each elemen a e de i ed by using he s ain-
displacemen ela ionships and Hooke´s law (cons i u i e equa ions), i ollows ha he s ains a e
cons an wi hin each elemen , i he displacemen s a y linea ly. Then, using a a ia ion (ene gy)
o mula ion, he go e ning equa ion o each elemen is de i ed.
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Damage assessmen in a ein o ced conc e e pedes al based on o a ing machine y ib a ion analysis
Thi d In e na ional Con e ence on Mechanical Models in S uc u al Enginee ing
Uni e si y o Se ille. 24-26 June 2015.
S ep 3: Assembly o he equa ions o he whole domain.
This s ep may depend on he ype o equa ion sol e employed. In his s ep he e alua ion o elemen
s i ness ma ices o all elemen s in he s uc u e and he assembly o hem in o he o e all s i ness
ma ix a e ca ied ou . This is achie ed by adding oge he con ibu ions o he indi idual elemen
s i ness ma ices and nodal elemen ec o s a common nodes.
S ep 4: Applica ion o bounda y condi ions.
This s ep esul s in a educed sys em o linea o no-linea equa ions. The linea i y o he equa ions
depends upon he analysis equi ed.
S ep 5: Solu ion o he educed sys em o equa ions.
In his s ep, ei he di ec o i e a i e p ocedu es may be employed o he solu ion o linea sys ems
o equa ions. The popula di ec me hods a e: he Gauss elimina ion, Choleski ac o iza ion, and
Gauss-Jo dan me hods, whils he common i e a i e sol e s a e he Gauss-Seidel, and Conjuga e
G adien me hods.
Phase III. Resul s In e p e a ion
This is he pos -p ocessing phase, in which he basic in e p e a ion and assessmen o ini e elemen
esul s a e ca ied ou . Analys should be awa e o he accu acy limi a ions o ini e elemen esul s;
he e o e, esul s alida ion o checking ou ha he esul s ob ained a e co ec and eliable is an
essen ial s ep o be conside ed. The ele an esul s may be abula ed o ep esen ed g aphically.
S ess con ou s a e ad an ageous in displaying c i ical s ess-concen a ion zones. Fini e elemen
s ess analysis esul s a e usually checked agains ele an heo ies o ailu e. Figu e 4 shows a gene al
scheme o he ini e elemen analysis.
Figu e 3. Gene al scheme o ini e elemen analysis.
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E ik Rosado Tama iz1, Albe o López López1, Da id Po as-Na a o González1
3. DYNAMIC ANALYSIS OF THE STRUCTURE
The dynamic beha io o he u bo-gene a o and he e ec s ansmi ed o he pedes al in e ms o
ib a ions a e a ec ed by i s dimensional cha ac e is ics, he weigh o each componen s and he
pe o mance o each suppo s on e ms o s i ness and damping. The e o e, i is impo an o
es ablish in he nume ical analysis o he coupled model, le els o e ec i e s i ness ha conside he
e ec s o o o - bea ings - conc e e pedes al in e ac ion.
A coupled nume ical model o he u bo-gene a o and ein o ced conc e e pedes al o a powe plan
gene a ion was de eloped in o de o e alua e he dynamic beha io o he s uc u e. The nume ical
model was de eloped based on he echnique o Fini e Elemen Me hod (FEM) using he comme cial
code ANSYS [3]. In he dynamic e alua ion o he s uc u e we e no modeled geome ically and
nume ically componen s ha do no con ibu e o he s i ness o he pedes al such as casings, mobile
and s a iona y blades, nozzles and s uc u es o he main bea ings. These componen s we e
conside ed as a mass added o he s uc u e.
To simula e he e ec s o he eigh adial bea ings ha suppo he u bo-gene a o , connec ions
coupling o o o - bea ing and bea ing - pedes al sys ems we e pe o med using beam ype elemen s
capable o limi ing he displacemen s and o a ions so ha his elemen only wo k in he equi ed
di ec ion. Fu he mo e, he coe icien s o s i ness o each elemen we e calib a ed wi h espec o
calcula ed alues as epo ed by he manu ac u e on each bea ing and each di ec ion we e
calib a ed.
Nume ical Model
As a s a ing poin o begin wo king on dynamic beha io o he s uc u e i was necessa y o ob ain a
3D CAD model o desc ibe he geome ic cha ac e is ics o he pedes al and u bo-gene a o . In he
Figu es 1 and 2, is shown he de ails o he 3D CAD models o each componen sepa a ely.
Addi ionally, in he Figu e 4 is shown he 3D geome ic coupled model o he u bo-gene a o and he
ein o ced conc e e pedes al.
Figu e 4. 3D geome ic coupled model o he u bo-gene a o and he pedes al.
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Damage assessmen in a ein o ced conc e e pedes al based on o a ing machine y ib a ion analysis
Thi d In e na ional Con e ence on Mechanical Models in S uc u al Enginee ing
Uni e si y o Se ille. 24-26 June 2015.
Fo he nume ical model o he u bo-gene a o ype beam elemen s we e used, se led geome ic
ea u es o each sec ion o he o o s acco ding o hei leng hs, inne and ou e diame e s and he
a ea o he c oss sec ion o each componen , o ep oduce i s geome y as nea ly as possible. I
should be no ed ha he nume ical model was de eloped using ype beam elemen s, since he
con e gence o esul s in e ms o modal shapes and na u al equencies be ween FEM model o he
u bo-gene a o using 3D solid elemen s and o he using beam ype elemen s. In he Figu e 5, is
shown he nume ical model o he u bo-gene a o .
Figu e 5. Nume ical model o he u bo-gene a o , using beam elemen s.
The nume ical model o he pedes al was de eloped using solid 3D elemen s o linea o mula ion
[eigh nodes] o model he simple conc e e combined wi h he link ype elemen s using o model he
longi udinal s eel ein o cemen in he conc e e columns and beams. Addi ionally, he elemen
Re olu e Join is used o ansmi he loads be ween he u bo-gene a o and he pedes al. Simila o
be shown o he u bo-gene a o , in he Figu e 6 is shown he nume ical model o he ein o ced
conc e e pedes al.
Figu e 6. Nume ical model o he ein o ced conc e e pedes al.
The coupled ini e elemen model o he u bo-gene a o and ein o ced conc e e pedes al consis s o
288,731 nodes and 71,240 elemen s in o al.
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E ik Rosado Tama iz1, Albe o López López1, Da id Po as-Na a o González1
Bounda y Condi ions
Bounda y condi ions o he coupled nume ical model we e es ablished o es ic he displacemen s
and ansla ions o he pedes al on i s h ee di ec ions (x, y, and z) a he le el o he ounda ion, as
shown in he Figu e 7.
Figu e 7. Bounda y condi ions o he coupled nume ical model.
Ma e ials P ope ies
The ma e ials used in he manu ac u e o u bine o o s and elec ic gene a o consis o a NiC MoV
alloy s eel, while he pedes al was designed wi h a ma e ial consis ing o a esis an ein o ced
conc e e comp ession ( 'c) equal o 280 kg / cm2 . Table 1, shows he ypes o ma e ials o each o o
and he conc e e pedes al, as well as some o i s main mechanical p ope ies [4, 5].
Table 1. Types o ma e ials o each componen
Componen
Ma e ial
P ope ies
Modulus o
Elas ici y
[Pa]
Densi y
[kg/m3]
Poisson
a io
Yield
s eng h
[MPa]
Tensile
s eng h
[MPa]
High P essu e
Ro o
ST565S Class
2
23 C NiMo
7-4-7
2.03*1011
7,850
0.3
585
690
Low P essu e
Ro o s
ST565S Class
1
23 C NiMo
7-4-7
2.03*1011
7,850
0.3
635
740
Jack Sha
ST573S
-
2.03*1011
7,850
0.3
700
800
Elec ic
Gene a o
-
27 NiC Mo
15-6
2.03*1011
7,850
0.3
600
700
Pedes al
Conc e e 'c = 280 kg/cm2
2.486*1010
2.325
0.17
-
-
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Damage assessmen in a ein o ced conc e e pedes al based on o a ing machine y ib a ion analysis
Thi d In e na ional Con e ence on Mechanical Models in S uc u al Enginee ing
Uni e si y o Se ille. 24-26 June 2015.
Load Cases
Du ing no mal ope a ion o he uni gene a ion and acco ding o hei equency o occu ence, wo
main ypes o load case can be induce damage o he pedes al; hese load case include cons an load
o pe manen ac ions, in addi ion o he epea ed loads a ising om he ope a ion o he u bo-
gene a o and hei co esponding unbalance ib a ions (oscilla ing loads).
Di e en load cases we e de ined based on epo s by he manu ac u e and a e desc ibed below:
Pe manen s Loads
G a i a ional Fo ces a e applied a each suppo knowing weigh o each componen .
To que Fo ces, in he case o he h ee u bines (LP1, LP2 and HP) a e hose o he eac ion o que
esul ing om he s a ic pa s o he o a ion o he u bine o o (opposi e in di ec ion o he o a ion
o he o o ). Fo he case o elec ic gene a o is he esul ing o que o he eac ion o he magne ic
ield o he o o on he s a o windings.
Vacuum Fo ces a e due ha in he condense o low p essu e modules ha e a p essu e less han
a mosphe ic p essu e.
F ic ion Fo ces hese ho izon al o ces co espond o he he mal expansion o High P essu e, Low
P essu e and Gene a o modules.
In he Figu es 8 o 11, shows he di e en ypes o pe manen loads ac ing on he conc e e pedes al.
Figu e 8. Dis ibu ion o g a i a ional o ces on he conc e e pedes al.
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E ik Rosado Tama iz1, Albe o López López1, Da id Po as-Na a o González1
Figu e 9. Dis ibu ion o o que o ces on he conc e e pedes al.
Figu e 10. Dis ibu ion o acuum o ces on he conc e e pedes al.
Figu e 11. Dis ibu ion o ic ion o ces on he conc e e pedes al.
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Damage assessmen in a ein o ced conc e e pedes al based on o a ing machine y ib a ion analysis
Thi d In e na ional Con e ence on Mechanical Models in S uc u al Enginee ing
Uni e si y o Se ille. 24-26 June 2015.
Fa igue Resul s
Based on he esul s om he e alua ion o he dynamic beha io o he ein o ced conc e e pedes al,
conside ing he c i e ion o high cycle a igue S-N cu es, he pe iods o occu ence o each load
condi ion and he ma e ial p ope ies o each column and beam which conside ed he inclusion o
s eel ein o cemen ; damage and li e o he s uc u e o each load condi ion a e de e mined as well
as a cumula i e damage.
In he Figu es 21 o 24, a e shown he global dis ibu ion o li e and damage o each load condi ion as
well as he combina ion o hem. In simila o m o each condi ion and combina ion o loads, he
Figu es 25 o 28 shows he global dis ibu ions o damage o he ein o ced conc e e pedes al.
Figu e 21. Global dis ibu ion o li e in he pedes al unde nominal unbalance load condi ion.
Figu e 22. Global dis ibu ion o li e in he pedes al unde LP s a up-shu down load condi ion.
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E ik Rosado Tama iz1, Albe o López López1, Da id Po as-Na a o González1
Figu e 23. Global dis ibu ion o li e in he pedes al unde GE s a up-shu down load condi ion.
Figu e 24. Global dis ibu ion o li e in he pedes al unde he combina ion o load condi ions.
Figu e 25. Global dis ibu ion o damage in he pedes al unde nominal unbalance load condi ion.
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Damage assessmen in a ein o ced conc e e pedes al based on o a ing machine y ib a ion analysis
Thi d In e na ional Con e ence on Mechanical Models in S uc u al Enginee ing
Uni e si y o Se ille. 24-26 June 2015.
Figu e 26. Global dis ibu ion o damage in he pedes al unde LP s a up-shu down load condi ion.
Figu e 27. Global dis ibu ion o damage in he pedes al unde GE s a up-shu down load condi ion.
Figu e 28. Global dis ibu ion o damage in he pedes al unde he combina ion o load condi ions.
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E ik Rosado Tama iz1, Albe o López López1, Da id Po as-Na a o González1
5. CONCLUSIONS
New conside a ions on he me hodology we e implemen ed o assess he a igue esis ance o
ein o ced conc e e in ela ion o he de ini ion o he S-N Cu es o ein o ced conc e e and i s
ensile s ess. Also, we e de e mine he c i ical zones o a igue ailu e and an es ima e o emaining
a igue li e in he pedes al, which shows ha a e 50 yea s o se ice li e consump ion is 15.84 %.
Then, 315 yea s o se ice a e equi ed o consume 100% o li e in he pedes al. The dynamic beha io
o he u bo-gene a o , as well as he emaining li e in he pedes al can be imp o ed i he s i ness
le els o he bea ings a e modi ied in he high p essu e o o and elec ic gene a o .
I is impo an o conside ha he cumula i e damage will g ow i o he loading cases a e p esen ed
as hey would be, o example, an acciden al unbalance in u bines o he seismic e ec .
ACKNOWLEDGMENTS
The au ho s wish o exp ess hei hanks o he Elec ical Resea ch Ins i u e (IIE) and The Fede al
Elec ici y Commission (CFE) o suppo ing his wo k.
REFERENCES
[1] Gene al Founda ions and S a ic and Dynamic Loads T ansmi ed o he Conc e e Pedes al o he
Tu bine Uni - Re o i P ojec , Fede al Elec ici y Commission (CFE, in Spanish). 2010.
[2] Tu bine, F ames and Equipmen ’s Assembly D awing - Re o i P ojec , Fede al Elec ici y
Commission (CFE, in Spanish). 2010.
[3] ANSYS, Use ’s Manual o S uc u al and dynamics S ess Analysis V14.5.
[4] Tu bine Componen s Ma e ials - Re o i P ojec , Fede al Elec ici y Commission (CFE, in Spanish).
2010.
[5] ASTM A471 / A471M. S anda d Speci ica ion o Vacuum-T ea ed Alloy S eel Fo gings o Tu bine
Ro o Disks and Wheels.
[6] Chai Y.H., Roms ad K.M.(1996), “Cha ac e iza ion o s uc u al damage unde high-in ensi y
seismic loading” , Else ie Science L d, Ele en h Wo ld Con e ence on Ea hquake Engineee ing.
[7] M.A. Mine (1945). Cumula i e damage in a igue, p. A159-A-164. T ansac ions, Ame ican Socie y
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[8] P. Lü, Q. Li and Y Song (2004). Damage cons i u i e o conc e e unde uniaxial al e na e ension-
comp ession a igue loading based on double bounding su aces, p. 3151-3166. Else ie L d.,
In e na ional jou nal o solids and s uc u es, Vol. 41.
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