8/17/2019 T1793-101

1/10

SAFE DIGRM- SIGN D RLIBLTYOL R URBI BLDIG

byurari . Singh

Superisor

John . VargoSenior Engineer

onald M ScifeStress and Vibration Analyt

andames . elo

Analtcal Engineer

Stres and Vibration Group

Steam Turbine, Motor and enerator Division

Dresser-Rand Company

Wllsville, New York

Mur a P  Singh i the Supervisor  of theStress and Vibrtion Gr oup at the SteamThrbine, Motor and Genertor Division

o f Dresser-Rand Company at Wellsville, New  York. He  holds B. S., M.S. ,  and dr r S a b wDesser-Rand Company   for 15 ears.Currl, lad rou robl

 for r ad vbao aal wav a o odr olo,such as nite element  analsis, f r acture

oald Sfr a Srs d Vbrao Er w rRdCoay Wlvll, Nw Yor ary robl ar awd ra of l aals advlo rou our ro H old a S dr haial Er fro lo vrsy ad a mbr of ASE

a ad lad d vbraor S a auord or a ar ara ofbla vbrao, l, a fraur a lud brl aral, u a la

Jo] Varo a Sor r Sr ad Vbo Gou of rrRad Coay' Sa rb, oorad Graor vo Wllvll,Nw Yor H a a S E dr

 fro Plvaa Sa Uvry ada b w rr-Rad Coa for yar T rary roblyof rou o ur aal

rlabl of urb blad ad o udra rar roj bo roduand holoy devlo of urb blad

r Varo a br of A SE ad a auord vral ar or urb blad vbr anal

ABSTRACT

The complex eld of turbine blade vibration has long been inneed of improved tools to help predict the reliability of blading.

 9

o aalss

Jam ll a Aalyil Er r ad Vbao roua Sa Trb, oor ad raor vo of rr-Rad H duad o Uvr of Pb aoow w a S dr aal r Tolo llha b w rr-Rad fo ar la four ar w h Srad Vbrao Grou w r rsobly rod r a ba-

The SAFE interference diaram is resented as such a l. Itpresents much more inforation tha n the widel sedCampbell diagram. In ealuating interferences, the SA dia-gram compars not only the frequencies of exciting haniwith natural frequencies of blades, but also the shape heseharmonics Vth the normal mode shapes of a completely eddisc incuding paketed blading. Exmples are given aseswhere the Campbell diagram predicts a dangerous resancewhil the SFE diagram shows that no resonances eis ih

8/17/2019 T1793-101

2/10

 94 PROCEEDINGS OF THE SEVENTEENTH TURBOMACHINERY SYMPOSM

ae suppoted by expeience. Eampes ae aso poided tosho hen the SAFE diam can pinpoint hat intefeence is ikey to cause the aest bade ibation. Finay, it is shon ho a simpe chane in acketin can be used to chane the bade intefeenc and to aoid daneous opeation.

INODUION

To meet the objectie of desinin eiabe and toube fee

 badin in tubomachiney, the bade natua fequency anaysis is of utmost impotance This is due to the fact tat amost a bade faiues can be attiuted to meta fatiue, hich is caused by aiabe aeodynamic ads actin on the badin. Resutindynamic stesses depend on the natua fequency and the modeshape of the bade, the fequency and shape of the excitin foce,and the eney dissipatin mechanism pesent in the system incuded as dampin.

In the eay days of bade desin, the natua fequencyanaysis as based on the assumption of a sine beam cantie

 eed at the bade oot. Poh and Weave [ 1] shoed that in thecase of a packeted assemby hee a oup of bades ae connected y shoudin, many moe natua fequencies and modesexist hich coud not be pedicted by a sine bade anaysis.This is due to the fact that the oup of bades behae as a system

and ae couped thouh the shoudin. The manitude of equencies and the numbe of modes depends on the numbe of bades in the oup and the stiness of the shoudin. This type of anaysis has expained many bade faiues and heped desines to buid moe eiae bades.

The next impotant step in bade anaysis as due to the eai zation that bades ae mounted on a dis hich can inuence thedynamic behaio of bades. Cacuations incudin the diskshoed that fequencies can be aected and a ne ae numbe of modes exist hich cannot be pedicted by usin a sine packet anaysis. In eaity, a bades and the disk constitute one system hich may o ma not espond to an excitin foce.

Sinh and Schie [2] pesented a nite eement anaysis foa packeted baded disk assemby. They shoed and discussedthe featues of dynamic behaio hich is dient than henthe soudin is 360 deees.

Taditionay, a bade desin is evauated by usin theCampbe Diaam. This pape discusses a method caed theSAFE diaam used by the authos company fo desin eauation of packeted baded disk assembies. It has been used successfuy not ony in expainin faiues and in deeopin eiabe desins, hich otheise oud not have been expained, based on the Campbe diaam.

MODE SHAPE OF A BLADED DISKAND FLUAIG FOR

 A bief desciption of the mode shapes of a baded dis andthe natue of uctuatin foces encounteed in a tubine is po ided to hep undestand the mechanism of esonance and asoto depict aphicay the necessay conditions of esonance.

MODE SHAPE

To dene the dynamics of any mechanica stuctue, theeienaue (natua fequency) and the accompanyin eienecto (mode shape) ae cacuated. In the case of a baded disk, themode shapes hae been descibed as noda diametes and nodacices. Sin and Schie [2] pesented some cacuated modeshapes fo a packete baded disk in tanentia ibation. Thedispacement, fo exampe, of the tip of each bde hen potted ith anua position, shos a sinusoida chaacteistic hich is

desinated as a diameta patten. This is ai fo eithe puetanentia o axia ibation of the bades. A ed disk of 90

 bades is shon in Fiue 1 ibatin in hat aed the sttanentia mode. This hee has 15 packets f ades ith 6 bades in each packet. he impotant featue o e mode shape of Fiue 1 is that not ony ae a six bades in each packet vibatin in phase but a 15 packets ae aso vit in in phase.This is caed the zeo noda diaete mode she ecause theeae no phase chanes in the ibation of a  ades. The 1noda diamete mode shape of the same baded sk is iustated in Fiue 2 . Thee ae to phase chanes in te baded disk hich ae noted by the adia ines fomin the oda diametemode shape. Notice that the six bades ithin ech of te indi

 idua packets ae sti ibatin in phase ith oe anothe in thest tanentia mode shape. The second bade disk shon inFiue 2 has the same mode shpe except the dia ines aeshifted in ocation by 90 deees.

DEFLCTED

UNDELECTEDFigure 1 Zero Nodal Diameter Mode.

Figure 2 One Nodal Diameter Mode.

8/17/2019 T1793-101

3/10

SAF IARAM-A DSIGN AND RLIABILITY TOOL FOR TURBIN BLADIG  95

Each nodal dameter mode sap occurs n a par. The twonodal dameter mode shape of h sae bladed dsk s shown nFgre 3 Agan, the blades whn each packet ars stll vbrat-n n phase wth each othr n te rst tangental mode shape.Ths trend wll contnue untl ch acket s out of phase wthts neghbors. In ths case where e s an odd number of pack-es (15) there wll be a maxmu of 14 phase changes between

 packets or seven nodal dameter.

Figure Two Nodal Diameter Mode.

T he remainder of t he rst tangential fami ly of  mode shapes  for a six b lade packet is shown in Fiure 4. Tese mode sh pesare c omm only called in phaseout of   phase m odes or xed-su pported modes. The signicant characteristic of these m odeshapes is that the number of phase changes within the pac ket

 varies from one to ve. The packet with oe phase chage will form bladed disc nodal diameters eight through 15. The 15 nodal

irst ngenti ngenti ied pported

ngenti ied pported ngenti ied pported

ngenti ied pported ngenti ied pported

AE CANGEFigure  4 Tangential ode Shapes For Six Blade Packet.

dameter mode shape s shown n Fgure 5 . The pack th two phase changes wll form nodal damter mode shapes ough23 hs trend wll contnue untl the packet wth phasechanges forms bladed dsk mode shapes 38 through For a bladed dsk wth 90 blades, the maxmum nube nodaldameters s 45, whch occurs whn a phase change rs be-tween each blade.

Figure   1 Nodal Diaeter ode.

When ths pattern shows a one sne (sne 6) patter, desg-nated as one nodal dameter. If t shows a o sne (s  pat-ter, t s desgnated as two nodal dameter. The mnumber of nodal dameters n bladed dsk assembl half ofthe number of blades for a even number of blades. a dsk

 havng an odd number of blades, the maxmum nodal meters half of the total number of blades nus one. athtcally,the mth mode at one speed can be descrbd as

(6, t) = Y cos (t m6) (1)

  s the natural requency and m s the numb f nodaldameters. The equency of the bladng s depend on thspeed of the turbne, due to the centrgal sten ct.Hence, the natural frequency, , nodal dameter ( nd thturbne speed are requred to descrbe any one mo ue tothe three varables requred, t can only be plotted as a rface. A typcal plot for a packeted bladed dsk s gven n r 6

FLUCTUATING FORCS

Forces mposed on the blade n one complet revol ea-nate om the crcumferetal dstorton n th ow. pres-sure varaton n the ud ow causs the forces to v ccum- ferentally. These foces deped on e elatve poston f ladg wth respect to nozzles and any other nterrutons l struts,etc. In each revoluton, howevr, ades wll expc thesame force pattern makng t a peroc force. Te fo cn be broken nto ts harmonc cntents usng Foure dcoston.

8/17/2019 T1793-101

4/10

 96 PRDNGS OF H SNTNTH TRB HIRY SYPOSI

J

>(ww

 b  q

8/17/2019 T1793-101

5/10

8/17/2019 T1793-101

6/10

 98 PROCEEDINGS OF THE SEVENTEENTH TURBOMACHINERY SYMPOSIUM

12 

- 

-

X

1 

500>ww 5000-

25 ······

........

....................... ....... ........

........

�

-

eo o 9SHAPE· ndal dla

Figure 11 Plot of Interence Points on SAFE Plane.

 o f Figure 11 can be directly   com pared, since they are plotting

identical blade frequencies. 

E UDIE UING HE FE DIGM

Three cases are chosen to demonstrate the use of the SAFEdagram These cases help to show varous advantages n makngrelablty decsons

ase 1 No Design ange ased on te SAFE DiagThs case llustrates that by usng the bladed dsk concept and

the SAFE dagram a costly desgn change was avertedIn the head end stages of steam turbnes, the blade heghts

are elatvely short (less than two nches n heght) and whenther natural frequences are plotted on a tradtonal Campbelldagram a stuaton smlar to that depcted n Fgure 13 fre-quently occurs What s shown n the Campbell dagram s annterference between the rst hamonc of ozzle passng fre-quency 1 NPF) and the three lowest natural frequencymodes of a packeted blade wheel wthn the peratng speedrange These odes are the rst tangental, rst axal and axal-rockng modes Snce nozzle passng frequency s one of the

 prme sources f exctaton n turbnes and the lowest natural blade frequences are the ost easly excted, a large response would be exected Frequently desgn changes ave een maden order to avod these nerferencs The desgn changes madeare ether n the number of nozzle vanes to change the exctngequency or n the blade to chnge te natral frequency Some-tmes, both changes are reured to accomplsh the goal of avod-ng the nterferences These dsgn changes oen result n com- promsng the stage ecency

When the same freuences n the ampbel daram of Fg-ure 13 are plotted n the SFE dagram of Fgure 14, a drentresult occurs The SAFE dagram shows that there s no reso

1

r-

0000

' 0000mmc

' 0000:!

0000

·.

o

.-�--

8 9

P ndl dFigure Plan View of Interference Points.

"C

BKT.HGT. I 99

BKTS N GROUP

NO. OF NOZZLES 7

SPEED RANGE

379

u' +

>uzw:� L

ID 3 5TURBNE SPEED - RPM

TRN(. SRXIAL S

AXIAL U

RXIRL CKING

1ST AXIAL

1ST TFNGNIRL

Figure 13 apbell Diag Sowing Interfeece wit 1 NPF for ase 1

nance, snce only the equences match but not te mode shape(nodal dameters) and, therefore, the response i be small Theshape of the 1 NPF extng frequency wth ozzles occursat the 72 nodal dameter locaton of Fgure  f ts case (150rotatng blades), snce t s reected o the 5 dal dmeter

8/17/2019 T1793-101

7/10

SAFE IRAM-A DESIGN AND RELIABILITY TOOL FOR TURBINE BLADING  99

line Detailed desciption of the otuction of the SAFE dia-am and the validit of eectin sed lines and NPP excita-tion is shon in the liteatue [ 3 ce the numbe of nozze vanes is eneally about haf the ne of otatin blades, theshape of the 1 NPF excitin qncy and the mode shape of the st thee packeted blade eencies will neve match,and a tue esonance will not occ he only occasion when 1 NPF excitation would be esonnt with the lowest ee

 blade fequencies is when the n of nozze vanes and the

numbe of otatin blades ae alo equal Thn both the e-quency and mode shape woud at

STAG NMBR 3 HGHT1299

1300

BD

000

::

=

 

:

11

 

11

1

 

4000

3000

2000

1000

20 30 40 50NODAL l AMTS

Figure 14 SAFE Diagra for Case 1

NO NOLS 78

PACKETS X BLOS/PKT ; BLADES

60

25 6 150

I SINGLf MDE

0 OU L  MDEI

70 80

Staes with Campbell diaams siia to Fiue 13 have oc-cued·o numeous occasions in the authos' expeience How-eve, the failue ate of these shot blade staes has been neli- ible Most of the tubines ae mechanica dive units tat ope-ate ove a lae speed ane, and theefoe, the intefeences between 1 NPF and the lowest blade equencies ae inevit-able at some time in opeation The only explaation fo the ex-cellent eliability of these blades is the SAFE diaam

AE 2- HE AFE DIGM ELP PINPOINAN AEA OF ONEN QUIKLY

This case study is pesented to illustate how use of the SAFEdiaam is used to quickly detemine if a bladed disk intefe-ence exists laded disk natual equencies and mode shapesae calculated By plottin these on a SAFE diaam aon wthoto speed and excitin euency data, a detemination of in-tefeence is made Finally, blade esponse will be calculated atthe inteeence fequency

The tubine disk consists of 18 packets of six blades each Thisdisk is a unifom 10 in thick with a boe diamete of 60 in Ad-ditional infomation is ive below

Numbe of lades 108Blade Heiht 40 inDisk Diamete 190 inNumbe ofNozzles 20Roto Sped 8000 pm

To bein this case study, a taditional Campbell ashown in Fiue 15 is constucted om data om bla acketnatual equency calculations Fo simpicity, only axi odesae consideed hee The Campbel diaam is dawn e focompaison wit the SAFE diaam which is intodu nexThee is an intefeence in the opeati seed ane h 1 XNPF and the axial "U mode The axial "U mode i hac-teized by a "U shaped bendin of the shoud in the l diec-tionNozzle passin fequency is 20 times unnin s Tht is, thee ae 20 nozzles and fo evey evolution a ba fees20 impulses Maximum deection is at the shoud midn anthee ae two node points alon the lenth of the sho

,uz:

CE 2

BKHG 4.

6

5

BK N GROUP 6

NO OF NOZZE 2

� 3 t

2

2 4 6 8

URBNE PEED - RPM

Figure 1 Capbell Diagra for Case 2

1ST AL

Construction of t he SAFE digram begins with cacion o f bladed disk natural equenc ies and m ode sha pes. This  n i- portant dierence; t he source of data for c onstruct io of t hCam pbell iagram is a packet calculati on w ile t he S AFE di-

gram is constructed from data om an entire laded d  clcu-ation. The computer pr ogram TBDYNE [ 4 ] a been dv oeexpressly for  the purp ose  of sol ving bladd isk les.TBDYNE is a nite element pr ogram whic soles rte natu-ral equenc y and m ode shapes ofbladed disks. It is also pabl

 o f perform ing a f  orced res ponse analys is.The SAFE diaam fo this case is shown in Fiu ain,

 fo claity, ony ial modes ae inluded The model us in thiscase consists of thee elements fo the disk fom the bo to th

 oute diamete Theefoe, disk exibility is include n thisanalysis, which is anothe advantae of this type of anal This featue is evident because the equencies of lowe nod ae

8/17/2019 T1793-101

8/10

8/17/2019 T1793-101

9/10

SAF IAAM-A DSIGN AND RLIABILITY TOOL FOR TURBN BLAIG 101

able 2 Response of hre la Pcket Due to 2 D Excitation at 2674 Hz

Blade sequencen packet

12 3

xalstress (ps)

1802

137

Thee numbers represent retly reduced stress levels romthose o the sx blade packet Chann the packeted dsk natural equenc has elmnaed the nteerene and thus ncreasedthe relablty o the whee des

CONCLUSION

Te toos o calculate natura requenes o bladin have become aster more econoca and more accurte n recent years Stll the uplanned and utmey outae o turbomachnery due to blade aures are numerous The study presented heren and the proposed use o the SF aram have helpedto dent possble problem aes and have also heped n lesscosty aster desn canes The concept o the SF daram

s based on e mathn o natural requency and ts catedmode shape wth the extn equency and ts shape s can be used o any rotan symmetrcal system wher he equency o exctaton s a ncton o roatonal speed Sh casesare encountered n axal ompressors as trnes pp and

 ansThe SF daram provdes more normaton n blae

relabty decson process han the tradtonal amll daam The use o the SF daram s proposed n bla elab l

ty evaluaton

EFEENCE

1 Pohl M " Method o Calculatn Vraton uencyand Stress o a Banded Group o Tune Buckets rans oSM 5116 (1956)

2 Snh M and Scher D "Vbratonal Charactstcs oPacketed Bladed Dss SM Paper No 82T137(1982)

 3 Snh M "SF Daram Technoloy Repo ST 16DresserRand Company (1984)

4 TDYN Fnte ement Based Bladed Dsc oramDeveloped b DresserRand Company (1987)

8/17/2019 T1793-101

10/10

102 PROCEEDINGS OF THE SEVENTEENTH TURBO MACHINERY SYMPOSIUM