Seismic Analysis of an Axial Blower using ANSYS

Transcription

1 Seismic Aalysis of a Axial Blowe usig ANSYS Hyug-Bi Im LG Electoics, Ic., Coe echology Goup Seoul, Koea Sewa Kim LG Electoics, Ic., Coe echology Goup Seoul, Koea Jitai Chug Hayag Uivesity, Mechaical Egieeig Seoul, Koea Abstact A seismic aalysis is oe of cucial desig pocedues of a axial blowe used i uclea powe plats. he blowe should withstad ad opeate ude emegecy situatios such as eathquake. Fo the seismic aalysis, we pefomed modal aalysis ad the evaluated Requied Respose Spectum (RRS) fom the give Floo Respose Spectum (FRS). Pio studies have bee doe simila to this method [1][]. A fiite elemet model of the blowe is established by usig commecial FEM softwae, ANSYS. Afte the fiite elemet modelig, atual fequecies, mode shapes ad the paticipatio factos ae obtaied fom the modal aalysis. he RRS is acquied by umeical appoach o the basis of the piciple of mode supepositio. We wee able to veify the stuctual safety of the axial blowe ad cofimed the validity of the peset seismic aalysis esults. Itoductio Equipmet used at uclea powe plats equies obust ad eliable desigs because i case of disaste, such as eathquake, small damage ca tu ito a upedictable esult. Blowe used at uclea powe plats is impotat because of such easo. Cuetly, Wyle ad Ellis & Watts of the Uited States pefom most of the seismic aalysis ad desig i Koea. Authos coducted expeimets i ode to impove seismic techology i Koea. Seismic techology ca be oughly categoized ito aalysis ad expeimet. he ideal way is testig the fial poduct but this has to make the actual pototype, which is expesive ad time cosumig task. Like may othe egieeig pocesses, fiite elemet method was used, istead. I ode to coduct seismic aalysis, it is ecessay to pefom modal aalysis ad calculate RRS fom the FRS. I this pape, desied data fom the modal aalysis will be obtaied fom ANSYS usig axial blowe model. hose data will be used i umeical aalysis fo calculatig RRS, which is essetial data fo desigig axial blowe. heefoe, it was possible to detemie whethe the axial blowe is safe though RRS. Deivatio of Equatio of Motio Befoe gettig ito seismic aalysis, it is ecessay to model mathematical eathquake. Fom this model, the motio of equatio of axial blowe will be deived. Eathquake applies foces to all 6 Degees of Feedom(DOF), howeve otatioal compoets ae egligible. I most cases, two dimesioal taslatio foces accout fo most of the eathquake eegy. I most of eathquake poof desig, it is assumed that vetical foces ae egligible because of the gavity, howeve, i this pape, all 3 taslatioal foces ae cosideed. he followig equatio goves the motio i 1 DOF system [4][5]. F = m v& (1) ( v& z& ) + k( v ) = 0 m v& + c z ()

2 whee v(t) is the absolute displacemet of mass m, z(t) is the absolute displacemet of the suface ad w(t) = v(t) z(t), which deotes displacemet of mass m elative to the suface. I most cases aalysis is doe by suface acceleatio istead of suface displacemet because a seismomete measues the suface acceleatio [4]. Displacemet of the suface ca be obtaied fom itegatig the acceleatio data twice. Cotaily, it is possible to measue the displacemet of the suface ad calculate the acceleatio data by diffeetiatig the measued data twice but this method will cay cosideable eo. Equatio (3) shows the suface acceleatio. Figue 1, A sigle DOF system Figue. A multi DOF system v & = w&& + z&&, v& z& = w&, v z = w (3) Equatio (4) is deived fom equatio (3) ad equatio (). m w& + cw& + kw = mz& (4) Equatio (4) shows that if we assume z(t) is egligible, seismic desig will be possible by excitig dyamic load, m z&. Now it is possible to expad the 1 DOF system ito multi DOF system, which has followig equatio of motio [4]. whee [ m ]{ w& [ c ]{ w& + [ k]{ w = [ m]{ z& + (5) { w { v { z = (6)

3 Fiite Elemet Aalysis Figue 3. Fiite elemet model usig ANSYS I ode to coduct FEA o the axial blowe, each pat should be modeled popely pio to aalysis. he stuctual base ad fa casig of the fa was modeled usig Shell63 elemet i ANSYS 5.5. Youg s modulus is Pa ad desity is kg/m 3. Elemet Lumped Mass1 was used fo the impelle ad valve. Moto was modeled with Beam4 elemet with suface aea of m ad momet of ietia 3 4 of I z = m, I x = m 4. Figue 3. is the modeled axial blowe with total elemets of 760. As most of eathquake wave have fequecies less tha 33 Hz, if the esoace fequecy of the axial blowe is less tha 33 Hz, oveloaded stess fom esoace may happe. I this case, stess value calculated by Squae Roots of Sums of Squae (SRSS) method should be compaed to allowed stess value i ode to assue the safety of the stuctue. N 1 σ = σ = σ + σ + L + σ (7) = 1 he load coditios iclude, dead weight of the equipmet, iteal pessue o fa housig, Opeatig Basis Eathquake (OBE) ad Safety Shutdow Eathquake (SSE). I this pape, dead weight of the equipmet, iteal pessue o fa housig ad SSE ae cosideed. he axial fa is mouted with acho bolt o the floo bouday coditios of FEA wee modeled accodigly. able 1. though able 3. show atual fequecy aalysis esults. able 1. Paticipatio facto ad effective mass i the X-diectio Mode Fequecy Paticipatio facto Ratio Effective mass Mass factio E E-16.68E E E E E

4 able. Paticipatio facto ad effective mass i the Y-diectio Mode Fequecy Paticipatio facto Ratio Effective mass Mass factio E E E E E E E able 3. Paticipatio facto ad effective mass i the Z-diectio Mode Fequecy Paticipatio facto Ratio Effective mass Mass factio E E E E We discove that the fist mode is less tha 33Hz; theefoe it is ecessay to coduct seismic aalysis. Also we see the paticipatio factos ae diffeet o each diectio because of the stuctual chaacteistic. Figue 4. shows the fist mode shape. Geeally, the eathquake waves ae give as adom fuctio i time domai. I ode to obtai stuctual espose, Respose Spectum Aalysis (RSA) method is widely used because combiig fequecy spectum of eathquake wave ad modal fequecy yields RRS. If the fist mode fequecy exists ude 33Hz, esoace is likely to occu. heefoe it is ecessay to calculate the atual fequecy fom modal aalysis ad fid acceleatio value fo each mode fom espose spectum. he it is possible to obtai combied stess fom eathquake waves o all 3 diectios by uig RSA by esults fom ANSYS ad the usig SRSS method fom equatio (7). Figue 5. though Figue 7. shows stess distibutio egadig dead weight, iteal pessue ad SSE load, espectively. able 4. Summay of stess value esults Compoets Combied stess(psi) Allowable stess(psi) Pipe stess ,600 Maximum stess of fa 0, ,600 Dwye gauge stess ,600 Valve stess ,600 able 4. summaizes stess values fom othe tha eathquake waves. he highest stess value should be less tha the allowable stess.

5 Figue 4. Fudametal mode shapes of the axial blowe Figue 5. Stess distibutio subject to dead weight Figue 6. Stess distibutio subject to pessue Figue 7. Stess distibutio subject to SSE load Requied Respose Spectum I ode to solve coupled odiay diffeetial equatio, such as equatio (5), othogoality of omalized mass factio fom the modal aalysis is utilized [4][5]. Supepositio method is used to expess { w as show i equatio (8). { w = [ ]{ η = { φ η () t φ (8) = 1 whee [ φ ] is modal matix, { φ is modal vecto ad ( t ) η is modal coodiate. Equatio (9) is witte i tems of modal coodiates ad was obtaied fom combiig equatio (8) ad equatio (5).

6 [ m ][ ]{ & η + [ c][ φ]{ & η + [ k][ φ]{ η = [ m]{ z& Multiplyig [ φ ] to equatio (9) yields equatio (10). φ (9) [][ φ m][]{ φ & η [ φ] [ c][ φ]{ & η + [ φ] [ k][ φ]{ η = [ φ] [ m]{ && z whee [ φ ] is omalized modal matix ad [ ] equatio (10) becomes equatio (11) [4]. th equatio of equatio (11) is as follows; + (10) c is othogoal dampig matix. By usig othogoality, \ { & η [ ζ ω ]{ & η + [ ω ]{ η = [ φ] [ m]{ z& + \ \ \ (11) & η + ζ ω & η + ω η = µ z& (1) whee ζ is modal dampig atio ad µ is paticipatio facto, which is eeded fo seismic aalysis. µ is obtaied fom ANSYS mode aalysis ad equatio (13), sigle DOF equatio will be used to obtai ζ [][4]. v& + ζω v& + ω v f ( t) (13) = whee m is mass, c is dampig costat, k is spig stiffess, c m = ζω, k m = ω, f ( t) = F ( t) m ad ω is atual fequecy of the system. Whe expadig this system to multi degees of feedom, ζ becomes ζ = c m ω. c was set to 0.03 ad m is the effective mass, obtaied fom ANSYS modal aalysis. I equatio (1), z& & deotes FRS. If we assume modal displacemet η ad floo displacemet z i t as η = H e ω, z = Ze, the equatio (1) becomes equatio (14). ( ω ω + iω ζ ω ) H e = µ ω Ze fom the equatio (14), we fid fequecy espose fuctio, (14) H. H µ ω Z = (15) ω ω + iωζ ω () t η could be foud by isetig {w as follows. H ito η ( t ) = H e ad agai usig η ( t ) with equatio (8) gives = { w { φ η ( t ) = { φ H e = { W e = 1 = 1 (16) Absolute displacemet, {v is calculated fom equatio (17). { v { w + { z = (17) ote that the assumptios wee { v = { V e, { w = { W e ad { z { Z e =. heefoe it is possible to fid ot oly absolute positio but also the acceleatios fo each compoet fom the ext equatio. { V = ω { W ω { Z ω (18)

7 whee { V { W {, Z, ae absolute displacemet, elative displacemet ad magitude espectively. Also acceleatio is descibed as ω { V = { V&, ω { W = { W&, ω { Z = { Z&, acceleatio of the absolute displacemet is show i equatio (19). { V & { W&& + { Z& = (19) I ode to fid acceleatio of th ode, we take the absolute value of equatio (19) V & = W&& + Z& (0) whee V & is the acceleatio of absolute displacemet o th ode, W & + Z& is the sum of acceleatio of elative displacemet ad magitude o th ode. Equatio (0) is the RRS equatio. Figue 8. exhibits RRS of the uppe pat of the blowe, which is coected to the data acquisitio system. Figue 9. is the RRS of the lowe pat of the blowe, which is coected to the floo mout. Figue 8. ad Figue 9. shows RRS up to 100 Hz. I eality, eathquake waves have fequecy as high as 33 Hz Fequecies above 33 Hz ae ae ad they ca be eglected. As show i gaphs, RRS less tha 33 Hz does ot exceed 10G. As it was uable to fid ay chage i atual fequecy ad stuctual defect i this pape, the axial blowe ca be cocluded safe agaist the eathquake. Figue 8. Requied espose spectum at ode 1306 i (a) the x-diectio (b) the y-diectio (c) the z-diectio

8 Figue 9. Requied espose spectum at ode 440 i (a) the x-diectio (b) the y-diectio (c) the z-diectio Coclusio I this pape, the axial blowe was modeled ad udegoe mode aalysis i ANSYS. Data fom mode aalysis, such as modal paticipatio facto ad effective mass wee used to detemie fequecy espose fuctio ad the modal coodiate fuctio. he supepositio method is applied to yielded modal coodiate fuctio i ode to fid RRS. By obtaiig RRS, it was possible to detemie the safety of the axial blowe used i the uclea powe plat. I this pape, RRS of the axial blowe exhibits stable coditio ad did t exceed 10G ude most eathquakes. Howeve, whe Y-diectio fequecy is above 50 Hz, RRS value exceeds 10G. It is kow that fequecy of the eathquake waves seldom go above 33 Hz, but the stuctual safe should be thought. As the axial blowe is weak i Y-diectio fequecy, it is desiable to eifoce the moutig bolt to the suface i ode to esue safety. Refeeces 1) J. Lee, J. Kim, P, Jug, J, Jug, Seismic aalysis of axial blowe fo uclea powe plat use, Joual of Koea Society fo Noise ad Vibatio Egieeig, Vol. 9, pp , ) J. Lee, J. Kim, P. Jug, Seismic aalysis of ai puifie o Ulji uclea powe plat, Joual of Koea Society of Mechaical Egiees, Vol. B, pp , ) D.J. Ewis, Modal estig: heoy ad Pactice, Buel & Kjae Koea Ltd. 4) Leoad Meiovitch, Aalytical Methods i Vibatios, Macmilla Publishig Co., 1970, New Yok, New Yok 5) Leoad Meiovitch, Meiovitch Methods of Aalytical Dyamics, McGaw-Hill Book Compay, 1970, New Yok, New Yok 6) William. homso, Maie Dillo Dahleh, heoy of Vibatio with Applicatio, 5th Ed., Petice Hall, 1993, Eglewood Cliffs, New Jesey

9 7) Sigiesu S. Rao, Mechaical Vibatios, 3d Ed., Petice Hall, 1995, Eglewood Cliffs, New Jesey 8) Daiel J. Ima, Egieeig Vibatios, d Ed., Petice Hall, 001, Eglewood Cliffs, New Jesey 9) ANSYS Ic, Asys Dyamics: Uses Guide fo Revisio 5.1, ANSYS, Pesylvaia