PARTICULAR RELIABILITY CHARACTERISTICS OF TWO ELEMENT PARALLEL TECHNICAL (MECHATRONIC) SYSTEMS

Transcription

1 Maagm Sysms Produco Egrg No 3 7 pp 3 8 PARICULAR RELIABILIY CHARACERISICS O WO ELEMEN PARALLEL ECHNICAL MECHARONIC SYSEMS Zbgw MAUSZAK Marm Uvrsy o Szczc Absrac: h papr characrzs h basc dsrbuos o alur o lms ha cosu h chcal mcharocal sysms: oal Wbull ormal log ormal dsrbuo. h dscrpo o wo lm paralll chcal sysms wh rlably characrscs has b mad. Spcc cass ar sudd whr up m o h chcal sysm lms hav oal Wbull ormal log ormal dsrbuos ad whr h sysm cosss o wo pars wh paralll rlably srucur ad o dr yps o dsrbuos o lms up ms. h ordr o lms h aalyss dos o mar. h rlva characrscs o rlably or a sysm wh wo paralll lms ar prsd: up m dsrbuo uco o h sysm sysm rlably up m probably dsy o h sysm h sysm alur sy. Ky words: chcal mcharocal sysm dsrbuos o lms alur dsrbuos o alurs o wo lm paralll chcal sysms INRODUCION h combao o mchacal lcrcal lcroc pumac lms o o oprag chcal sysm has b calld rc yars a mcharoc dvc sysm. Each o hs lms has a spcc characr o durably damag suscpbly ad rlably. Rlably o dvcs ad mcharoc dvc compos s dscrbd by mahmacal modls dsrbuos o radom varabls ad parcularly h characrscs o rlably whch drcly ac h rlably characrscs o mcharoc dvcs o whch hy ar cludd. h mos commoly usd mahmacal modls o sudyg h rlably o chcal dvcs ar dsrbuos o radom varabls: oal Wbull ormal logarhmo ormal ormal rucad a zro gamma bomal Broull Posso hyprgomrc gomrc ad procsss: Posso ormal Markov ad sm Markov. Dsrbuos ar probablsc modls ad procsss ar sochasc modls [ 3 4 5]. I complx rsposbl chcal ad mcharoc sysms a combao o mchacal lcrcal lcroc pumac oprag compos o a cohr chcal sysm rsrvg compos ar o usd. h smpls rsrvg cosss a paralll cluso o h sam compo o h sysm whch rplacs h damagd compo a h m o h prmary alur. I mor complx chcal sysms h ucos o h dcv par may b ak by a dr sysm compo wh dr oprag characrscs ad hus wh dr rlably characrscs. Each o h compos may hav a dr durably damag ad rlably characr whch s dscrbd by h mahmacal modls sascal dsrbu os ad parcularly h characrscs o rlably whch drcly ac h rlably characrscs o a chcal sysm hy cosu. h mos commoly usd mahmacal modls o sudyg h rlably o chcal dvcs ar dsrbuos o radom varabls: oal Wbull ormal logarhmo ormal ormal rucad a zro gamma bomal Broull Posso hyprgomrc gomrc ad procsss: Posso ormal Markov ad sm Markov. Dsrbuos ar probablsc modls ad procsss ar sochasc modls [ 3 4 5]. I urhr aalyss h smpls ad h mos commo modls ar assumd: oal Wbull ormal or logarymo ormal. May yars o ld ss ad daabass avalabl o alur o compos ad chcal qupm dca ha spcc dsrbuos or hr rlably characrscs ca b arbud o spcc compos ad dvcs as wll as o h ypcal yps o damag [ ] abl.

2 4 Maagm Sysms Produco Egrg 37/ Z. MAUSZAK Szczgól charakrysyk zwodoścow dwulmowych rówolgłych sysmów chczych Compo dvc abl. ucos o alur sy o slcd compos ad dvcs as wll as ypcal yps o damag Dsrbuo o ucos o alur sy yp o damag small rubbr pars such as sals daphragms Wbull caasrophc oal compos ad qupm damagd by xral acors oal agg Wbull gamma lcroc lms oal vry slow war oal dvcs wh a doma umbr o movg pars Wbull rapd war corrosv war Dsrbuo o ucos o alur sy ormal logarhmo ormal gamma Up m o h h lm s a radom varabl wh a dsrbuo dd by h ollowg characrscs: rlably o h compo... R P probably dsy o h compo up m d... d alur sy o h compo d l R... d R 3 h cd up m o h compo I h x par h aalyss o our dsrbuos s gv as a xampl ad h slcd characrscs o rlably composos o lms o mcharoc dvcs ar prsd. I h gv xampls h prsao s lmd o composos o dsrbuos or wo lms. CHARACERISICS O HE ANALYZED RELIABILIY DISRI BUIONS I h work blow [] parcular cass o dsrbuo composos ar aalysd. Expoal dsrbuo Expoal dsrbuo s usul or sg h rlably o such dvcs whch ar h rsul o mpac o shock loads so calld dscr smul. Expoal dsrbuo ca b usd o s h rlably o qupm ad compos : chags o h chcal codo ad h rsulg damag s rrvrsbl h lvl o rssac war rssac s cosa whch mas o damag causd by agg drvd rom cumulav xoro damag s h rsul o xral or ral radom shock racos dscr smul. Up m characrscs =... o a compo ar as ollows: rlably o h compo probably dsy o h compo up m R d... E 4 R 5 6 alur sy o h compo h cd up m o h compo Wbull dsrbuo Wbull dsrbuo dscrbs h m o ormal opra o o such dvcs whch damag s dpd ay damag causs loss o qupm up m ach u cosss o a sucly larg umbr o homogous compos. h lm has a Wbull dsrbuo wh h paramrs α β = wh s characrscs ak h orm: rlably o h compo probably dsy o h compo up m alur sy o h compo h cd up m o h compo cos. 7. E 8 A spcal cas o Wbull dsrbuo s a Raylgh dsrbuo whch h paramr α =. Normal dsrbuo h ormal dsrbuo s a modl o rlably o ay chcal objc whch hr ar damags rsulg rom h agg procss cludg war. hs s o b usd a dscrbd radom varabl dpds o a umbr o phoma ad causs o o whch ca b cosdrd doma. h compo τ up m has a ormal dsrbuo wh h probably dsy has h orm R 9 E.

3 Maagm Sysms Produco Egrg 37/ 5 Z. MAUSZAK Szczgól charakrysyk zwodoścow dwulmowych rówolgłych sysmów chczych ad s dsrbuo uco whr s h cd up m o a compo ad σ s s varac. h ormal dsrbuo s dd or all R whl h radom varabl τ bg h up m o h lm aks oly ogav valus. O ca pu up wh such a adquacy o h modl whr h probabls P{τ <} ar glgbly small o largr ha masurm rrors. I ordr o wr smplr ad mor cov up m characrscs o h lm wh ormal dsrbuo h characrscs o h ormal dsrbuo N probably dsy has b usd: ad h dsrbuo uco O ca h wr h characrscs o h sysm compos h orm: probably dsy o h compo up m rlably o h compo alur sy o h compo I cas o cao accp h assumpo ha h probabls P{τ <} ar glgbly small o should us h rucad ormal dsrbuo a whch m h aul r oprao o h compo aks oly ogav valus τ I hs cas h rlably characrscs o lms has h orm: probably dsy o h compo upm rlably o h compo alur sy o h compo Logarhmo ormal dsrbuo Logarhmo ormal dsrbuo rlably hory o h bass o h mprcal rsarch characrzs mal compos sa agu l h srgh o mals subjcd o prologd oprao srss as wll as lcroc compos up m. h compo τ up m has logarhmo ormal dsrbuo wh h radom varabl Y=lτ s ormally dsrbud whh paramrs N σ. Usg h probably dsy ad dsrbuo uco o h ormal dsrbuo N compo rlably characrscs o logahmoormal dsrbuo ca b wr as: probably dsy o h compo up m rlably o h compo alur sy o h compo h cd up m o h compo CHARACERISICS O HE DISRIBUIONS O WO ELEMEN PARALLEL ECHNICAL SYSEMS Hr h aalyss o lm sysm wh a paralll rlably srucur s prsd. h sam dsgaos whch hav b dd h prvous sco wll b usd. Sc h lms ar dpd ad h sysm 3 dx x 4 R 5 R. dx x 6 R 7 R 8 9 R. l l 3 l l R 4 l l 5 E 6

4 6 Maagm Sysms Produco Egrg 37/ Z. MAUSZAK Szczgól charakrysyk zwodoścow dwulmowych rówolgłych sysmów chczych s workg lawlssly ul h damag o all h compos: h up m dsrbuo s E d 36 P... P 7 h sysm rlably R probably dsy o h sysm up m alur sy o h sysm has h orm h cd up m o h sysm wh paralll rlably srucur s h quao 3 shows ha s rarly possbl o calcula h cd up m o h sysm h lc orm. Ev or smpl dsrbuos h cd up m o h sysm s qu complcad. I a parcular cas all compos o h sysm hav h sam up m dsrbu os. hs happs usually wh svral compos prorm o ad h sam uco. o prorm o compo s suc hror h rmag lms ar ho rsrvg ad ha cas o = or =.. h or a sysm wh a paralll srucur cossg o dcal compos rlably characrscs hav h orm: h dsrbuo uco o h sysm up m h sysm rlably R probably dsy o h sysm up m alur sy o h sysm h cd up m o h sysm 8 j j j j j 9 3 E j d 3 3 R h ollowg rlably characrscs o sysms wh a paralll wo lm srucur ad dr yps o compos up m dsrbuos hav b drmd. h ordr o compos s arbrary dos o mar or h dpdc. h rs compo has h up m o h oal dsrbuo wh h paramr λ ad h scod o h Wbull dsrbuo wh h paramrs αβ. Rlably characrscs o h sysm ak h orm: h dsrbuo uco o h sysm up m h sysm rlably R probably dsy o h sysm up m alur sy o h sysm h rs compo has h up m o h oal dsrbuo wh h paramr λ ad h scod o h Wbull dsrbuo wh h paramrs σ. Rlably characrscs o h sysm ak h orm: h dsrbuo uco o h sysm up m h sysm rlably probably dsy o h sysm up m alur sy o h sysm R h rs compo has h up m o h oal dsrbuo wh h paramr λ ad h scod o h logarhmo ormal dsrbuo wh h paramrs σ. Rlably characrscs o h sysm ak h orm: h dsrbuo uco o h sysm up m l 44 45

5 Maagm Sysms Produco Egrg 37/ 7 Z. MAUSZAK Szczgól charakrysyk zwodoścow dwulmowych rówolgłych sysmów chczych h sysm rlably R probably dsy o h sysm up m alur sy o h sysm h rs compo has h up m o h Wbull dsrbuo wh h paramr αβ ad h scod o h ormal dsrbuo wh h paramrs σ. Rlably characrscs o h sysm ak h orm: h dsrbuo uco o h sysm up m h sysm rlably probably dsy o h sysm up m alur sy o h sysm h rs compo has h up m o h Wbull dsrbuo wh h paramr αβ ad h scod o h logarhmo ormal dsrbuo wh h paramrs σ. Rlably characrscs o h sysm ak h orm: h dsrbuo uco o h sysm up m h sysm rlably probably dsy o h sysm up m alur sy o h sysm l 46 h rs compo has h up m o h ormal dsrbuo wh h paramr σ ad h scod o h logarhmo ormal dsrbuo wh h paramrs σ. Rlably characrscs o h sysm ak h orm: l l 47 R l l l R l l l l 55 l l l 56 h dsrbuo uco o h sysm up m h sysm rlably R probably dsy o h sysm up m alur sy o h sysm l 57 l 58 l l 59 CONCLUDING REMARKS I chcal sysms parcularly mcharoc sysms rsrvg h sysm compos s popular. I h prsd maral spcc xampls o compos rsrvg ar show wh h compos ar o rsrvd by h objcs o h sam yp wh h sam characrs cs o rlably bu wh h ucoal rsrvg by a dr compo wh a dr rlably characrs cs s usd. I cas o rsrvg by h sam compos wh h sam alur dsrbuos h aalyss o rlably characrscs s rlavly smpl ad dd by h dpdcs I ohr cass s complx. REERENCES [] Prażwska M. d.: Nzawodość urządzń lkroczych. WKŁ. Warszawa 987. [] Rausad M. Høylad A.: Sysm Rlably hory: Modls Sascal Mhods ad Applcaos. Scod do. Irscc. Nw Jrsy: Wly 4. [3] Salh J. H. Maras K.: Rlably: How much s worh? Byod s smao or prdco h prs valu o rlably. Rlably Egrg ad Sysm Say. Vol. 9 6 pp [4] Soskow B.S.: Nzawodość lmów urządzń auomayk. WN. Warszawa 973. [5] Ważyńska ok K. Jaźwńsk J.: Nzawodość sysmów chczych. PWN. Warszawa 99. [6] Mauszak Z.: Charakrysyk zawodoścow wlolmowych srukur mszaych odawalych. Collco o rsarch paprs o h Balc Assocao o Mchacal Egrg Exprs No 4 Mchacal Egrg o h Balc Rgo. Kalgrad Sa chcal Uvrsy. Kalgrad 4 pp [7] Mauszak Z.: Charakrysyk zawodoścow klkulmowych sysmów chczych o srukurz szrgowj rówolgłj o różych rozkładach czasów zdaośc. Collco o rsarch paprs o h Balc Assocao o Mchacal Egrg Exprs No 4 Mchacal Egrg o h Balc Rgo. Kalgrad Sa chcal Uvrsy. Kalgrad 4 pp l l l 6

6 8 Maagm Sysms Produco Egrg 37/ Z. MAUSZAK Szczgól charakrysyk zwodoścow dwulmowych rówolgłych sysmów chczych [8] Mauszak Z.: Slcd say modls o lms ad sysms h g room. Iraoal Scc Joural Problms O Appld Mchacs. Gorga Comm o Iraoal drao or h Machs ad Mchacs. bls 4 No 4 4 pp [9] Nowakowsk.: Bazy wdzy w badaach zawodośc maszy. Marały Korcj Naukowj "Mody dośwadczal w budow ksploaacj maszy roboczych chologczych oraz środków rasporu". Wydawcwo Polchk Wrocławskj. Wrocław Szklarska Poręba 993 s [] Mauszak Z.: Szczgól charakrysyk zawodoścow szrgowych sysmów mcharoczych. Suda Marały Polskgo Sowarzysza Zarządzaa Wdzą. Nr 45 s dr hab. ż. Zbgw Mauszak pro AM Marm Uvrsy o Szczc aculy o Mchacal Egrg Isu o Shp Powr Pla Oprao ul. Wały Chrobrgo 7 5 Szczc POLAND mal: z.mauszak@am.szczc.pl Arykuł w polskj wrsj językowj dosępy a sro rowj czasopsma. h arcl Polsh laguag vrso avalabl o h wbs o h joural