447. Assessment of damage risk function of structural components under vibrations

Transcription

1 447. Assessmen f damage risk funcin f srucural cmnens under virains J. Dulevičius, A. Žiliukas Kaunas Universiy f Technlgy, Kesuci s. 27, LT-4432 Kaunas, Lihuania jnas.dulevicius@ku.l, ananas.ziliukas@ku.l (Received 25 January 2007; acceed 0 March 2007) Asrac. In he analysis f reliailiy f cnsrucin elemen in he case f aging under virains, evaluain f risk funcin is f grea imrance. In racice, he alied cnsan risk funcin inensiy is arximae. The inensiy funcin mus e evaluaed imely. Hwever, his effr requires numerus exerimenal daa. This aricle cnsiders a simlified arach fr sluin f he afremenined rlem. Prvided cmarisn f exerimenal and ained hereical resuls cnfirm he validiy f he resened arach. Keywrds: reliailiy, risk funcin mdels, risk funcin inensiy.. Inrducin Virains may induce aging mechanisms in ielines, ums, mrs r any her srucures, which have sme virain envirnmen. Funcins f cnsrucin elemen failure are usually deermined y means f exerimenal research. Therefre hereical analyses in he evaluain f risk funcins simlify his effr. Many sudies have een deved evaluain f jecs reliailiy [-4]. Hwever, research f risk f failure f cnsrucin cmnen due aging under virains is scarce [5,6]. Evaluain f his effr is descried susequenly failed cmnens, due aging under virains, are relaced wih new cmnens. Risk funcin due aging r failure frequency is n increasing rgress. Therefre, he jecive is analyze risk funcin a any ime inerval. 2. Basic Assumins is cnsidered siive when 0 in a shr ime inerval (erid) (, + ). When 0 failure analyses ecme indeenden, hen failure cun in. An assumin is made ha Risk funcins inensiy ( ) ime inerval 0 and are descried as cincidenal variale ( ) cmnen relacemen afer each failure is raidly iniiaed and relacemen ime is f n imrance. Funcin is Pissn s rcess inensiy funcin, and is increasing risk funcin. If is n inerrued during ime inerval, hen is assciaed wih an increasing direcive f. funcin ( ) F deendan frm firs failure ime and n frequency funcin ( ) Therefre [5]: 20

2 ( ) = f( ) [ F( ) ] () Resuling in: ( ) = ex[ ( ) ] F (2) When F ( ) and fllwing lim ( ) = In his case, an indescriale effec is encunered. If ( ) is siive, hen i is cnsidered ha he firs failure ime has an exnenial direcive. Therefre, simlified effr is aained. Hwever, ( ) may increase in ime. Resuling in: ( ) h ( β) =, (3) where,β. If all cmnens have he same funcins h, hey have he same β value. If i is ssile siive, and h ( ) deermines ( ) assume ha all cmnens have he same value. This is frequenly used in racice, since deerminain f β value is fairly cmlicaed. T cnsider β value e siive as is incrrec. 3. Risk Funcin Mdels The fllwing are risk funcin mdels: linear, exnenial and Weiull [6]. Linear mdel: ( ) ( β) = + (4) Exnenial mdel: ( ) ex( β) = (5) Weiull mdel due numerus addiinal arameer requiremens, is seldm used. Weiull mdel has a mre arriae usage when daa is availale in aundance. Exressins (4) and (5) sugges he need have saring risk funcin inensiy and failure inensiy ( ) variale frm arameer β. Hwever, deerminain f β requires significan amun f exerimenal daa. f are cnsidered indeenden [6]: I is knwn ha failure inensiy ( ) and funcin ( ) ( ) f ( ) = (6) f( x) dx The analyses evaluain (6) f his equain des n rvide accurae resuls [7]. The es funcin as resened in mdel in Fig.. resuls wuld e acquired y arximaing red ( ) 202

3 ( ) max a Fig.. Simlified failure inensively mdel T In he inerval 0 < < a funcin may e descried as in he arameers f Weiull when = 2 = 2. In his manner mde is resened y hree arameers: rimary m and ( ) failure inensiy, exliain erid, afer his effr eginning f failure inensiy cmmencemen characerized inensiy. Assuming inensiy mdel ssile resenain: ( ), =, +, when = a; (7) when = ; when > here failure inensiy, when =. Assuming exnenial mdel: ( ), when = a; =, when = ; ex, when > (8) 4. Presenain f mdel acceance arval The rlem is in deermining he lcain f he equimen and he assciaed virain secrum. Fr accelermeers, virain is an inu he insrumen. The ranges f frequency and he amliude f such virains can e sizeale. Nrmal lan virain f his kind is 203

4 cnsideraly differen frm virain due a seismic evens, which is n an aging rlem u a design even rlem. Analyzing amic elecrical cnsrucin cmnens uniy energeic nrms NUREG/CR 5378 [8] in sur resenain f risk funcin inensiy arameer β f variale ime effr. This effr is resened in ale [8]. Tale. Risk funcin inensiy arameer β in ime, h 2 * * * * 0 4 * 0 5,2 * 0 5 β, /h Linear Exnenial mdel mdel,2 * 0-5,4 * 0-5,9 * 0-5,8 * 0-5 2,6 * 0-5 2,5 * 0-5 3, * 0-5 3,0 * 0-5 3,4 * 0-5 3,4 * 0-5 3,6 * 0-6 3,5 * 0-5 Average 2,6 * 0-5 2,6 * 0-5 Therefre averageβ effr is he same in h mdels as β = 2, 6* 0 Basing n his analyses f risk funcin inensiy may e resened, hen /h [8]. Calculain resuls are resened in ale 2. /h. = 2, 0* 0 Tale 2. Parameer ( ) changes in ime, h 2 * * * * 0 4 * 0 5,2 * 0 5 Linear mdel 3,04 * 0-5 4,08 * 0-5 5,2 * 0-5 6,6 * 0-5 7,2 * 0-5 8,24 * 0-5 ( ), /h Exnenial mdel 3,36 * 0-5 5,6 * 0-5 9,4 * 0-5 5,8 * ,4 * ,3 * 0-5 Furher, afer he acceance f mdel ased n (7) and (8), analyses f risk funcin inensiy are resened. Calculain resuls are lised in ale Linear mdel: = 3, 04* 0 /h; 4 = 4*0 h; = 4, 08* /h. 0 Exnenial mdel: = 5, 6* 0 /h; = 3, 36* 0 /h. NUREG/CR 5378 arameer's resened resuls are cmared wih calculains ffered in mdel cnsidered as lised in ale 3.

5 Tale 3. Cmarisn f numerical and exerimenal resuls, h 2 * * * * 0 4 * 0 5,2 * 0 5, /h Linear mdel Exnenial mdel ex calc errr, ex calc errr, % % 3,04 * 0-5 3,04 * 0-5 3,36 * 0-5 3,36 * 0-5 4,08 * 0-5 4,08 * 0-5 5,6 * 0-5 5,6 * 0-5 5,2 * 0-5 5,4 * ,5 9,4 * 0-5 9,2 * , 6,6 * 0-5 6,08 * 0-5 -,3 5,8 * 0-5 5,2 * ,8 7,2 * 0-5 6,53 * ,3 26,4 * ,8 * ,0 8,24 * 0-5 7,8 * ,3 44,3 * ,8 * ,0 5. Resuls. Presen sudy rses a simlified arach fr deerminain f failure risk inensiy. The arach is alicale in he analysis f reliailiy f cnsrucin cmnens ha underg aging due virains. 2. When analyzing reliailiy, i is sufficien ssess exerimenal daa in he eginning f cmnen erain and susequenly failure risk inensiy values are e analyzed y he rsed mdel. 3. The alicailiy f he mdel in engineering rlem slving is cnfirmed y cmarisn f exerimenal and hereical values. References [] Aldus, D. Prailiy Arximains f he Pissn Cluming Heurisic. Sringer Verlag, New Yrk, 989, 285. [2] Bhaacharya, R., Waymire, E. Schasic Prcesses wih Alicains. Wiley, New Yrk, 990, 395. [3] Chung, K. L., Williams, R. J. Inrducin Schasic Inegrain. 2 nd ed, Birkhauser, Bsn, 990, 230. [4] Bhaacharya, R., Waymire, E. A Basic Curse in Prailiy. Sringer, New Yrk, 2000, 22. [5] Žiliukas, A. Technical diagnsic and railiy f aircraf. Technlgija. Kaunas, 998, 223. (in Lihuanian). [6] Žiliukas, A. Mechanics f safey imran srucures. Technlgija. Kaunas, 200, 88. (in Lihuanian). [7] Barzilvih, E., Mezenceva, V., Savenkv, M. Reliailiy f aircraf sysem. Mscw. Transr, 982, 82. (in Russian). [8] Andren J. Wlfrd, Crwin L. Awd, and W. Sc Resener, Aging Risk Assessmen Mehdlgy: Demnsrain Sudy n a PWR Auxiliary Feed waer Sysem, NUREG/CR 5378, EGG 2567, DRAFT