NONLINEAR DYNAMIC ANALYSIS OF A MORPHING PULLEY BELT DRIVE TRANSMISSION SYSTEM

Transcription

1 NONLINEAR DYNAMIC ANALYSIS OF A MORPHING PULLEY BELT DRIVE TRANSMISSION SYSTEM By Reza Fashd A hess submed n confomy wh he equemens fo he degee of Doco of Phlosophy Gaduae Depamen of Mechancal and Indusal Engneeng Unvesy of Toono Copygh 4 by Reza Fashd

2 Nonlnea Dynamc Analyss of a Mophng Pulley Bel Dve Tansmsson Sysem Reza Fashd Doco of Phlosophy Depamen of Mechancal and Indusal Engneeng Unvesy of Toono 4 ABSTRACT Ths docoal eseach pesens nonlnea dynamc analyses of a mophng pulley bel dve ansmsson sysem. In a mophng pulley ansmsson sysem, dffeen dve aos ae acheved by dsceely vayng he pulley damee. The bel dve sysem consss of a ensonng mechansm, as well as a dve and dven pulley. A new appoach s poposed fo he ensonng mechansm o fulfll he pefomance equemens and ensue smooh shfs. Howeve, he dven pulley ypcally possesses hgh neal loads leadng o excessve bel vbaons and falue due o fague. In addon, dung a dve ao shfng and he esulng change n he pulley damee, he bel expeences sudden load vaaons causng excessve vbaons. To emedy hese excessve vbaons, a one-way cluch n combnaon wh a oque lme s nsalled beween he dven pulley and he load. Ths foms a nonlnea vbaon educon sysem ha paal dsengagemens beween he pulley and he accessoy. Dynamc analyss s essenal fo desgnng a bel dve sysem. Howeve, lmed publshed wok has been found povdng a complee dynamc analyss of a mophng pulley sysem. Ths docoal eseach povdes a dynamc model of he mophng pulley ansmsson sysem usng vaous ools and analyss appoaches, namely he mehod of mulple scales, numecal echnques and expemens. Lagange s enegy mehod s used o oban he equaons of moon. A peodc soluon unde hamonc, esonan, and nonesonan excaons ae acheved hough he mehod of mulple scales. The effecs of dffeen desgn paamees on he sysem pefomance ae suded fo vaous hamonc excaons. The obusness of he poposed nonlnea vbaon educon appoach s pesened hough s mplemenaon n a bel dve sysem. II

3 ACNOWLEDGEMENTS I am healy gaeful o my supevso, Pofesso Jean Zu, whose encouagemen, gudance and suppo fom he nal o he fnal sages enabled me o develop an undesandng of he eseach. I am vey gaeful o my colleague Al Sab fo hs help and asssance houghou hs poec. My paens deseve specal menon fo he nsepaable suppo and payes. Wods fal me o expess my appecaon o my wfe, Mayam, whose dedcaon, love and pessen confdence n me, has aken he load off my shoulde. Lasly, I offe my egads and blessngs o all of my colleagues n Vbaons Dynamcs and Mechaoncs Laboaoy (VDML) a he Unvesy of Toono who suppoed me dung my docoal eseach. Reza Fashd Apl 4 III

4 Table of Conens: Chape INTRODUCTION.... A New Tansmsson Technology Auomove Indusy Wnd Enegy Havesng Mophng Pully Tansmsson Mophng Pulley Toohed Bel Tensone Vbaon Reducon Sysem One-Way Cluch Toque Lme Advanages of he new ansmsson Challenges of he desgn... 4 Chape Leaue Revew Dynamcs of Bel Dve Sysems Dynamcs of Axally Movng bel Effecs of a Tensone... IV

5 .4 Nonlnea Cluch Desgn and Analyss of a Nonlnea Cluch Applcaons of a one-way cluch Cluch Mehods of Nonlnea Dynamc Analyss Obecves Conbuons Chape 3 Desgn of a Tensonng Mechansm Inoducon Desgn dynamc analyss equaons of moon Expemen Resuls and Dscussons Summay and Conclusons... 6 Chape 4 Nonlnea Vbaon Reducon Sysem Inoducon Modelng One-Way Cluch V

6 4.. Toque Lme Combned Nonlnea cluch Equaons of Moon Nonlnea Dynamc Analyss Non-Resonan Excaon Resonan Excaon Resuls and Dscussons Summay and Conclusons Chape 5 Dynamc Analyss Dung a Shf Inoducon Modelng Equaons of Moon Dynamc Analyss Resuls and Dscusson Response o Hamonc Excaon Inpu Pulsaon Response o Tansen Load Dve Rao Shfng Summay and Concluson... Chape 6 Summay and Fuue Wok... 5 VI

7 6. Summay Desgn of a Tensonng Mechansm Nonlnea Vbaon Reducon Sysem Dynamc Analyss of Mophng Pulley Sysem Dung a Shf Summay of Conbuons Fuue Woks... Refeences..3 VII

8 Ls of Fgues Fgue.. Mophng Pulley and Pulley Segmens Couesy of Vcccog... 8 Fgue.. The ansmsson Opeang wh Vaous Dve Raos... 8 Fgue.3. Convenonal Tensone... Fgue.4. Spng Type One-Way Cluch... Fgue.5. Fcon Plae Toque Lme... 3 Fgue 3.. Schemac of he Modelng of he Sucue Fgue 3.. Sac Equlbum Analyss of he Sysem... 4 Fgue 3.3. Tensone Conveo Mechansm... 4 Fgue 3.4. Tensone Mechansm Acon n 3 Dffeen Condons of Gea Rao Fgue 3.5. Foce Equlbum Analyss of he Tensone Mechansm Fgue 3.6. The Gude Ral Pofle Fgue 3.7. Fee Body Dagam of Dynamc Loads n he Sysem Fgue 3.8. Schemacs of he Expemenal Modal Analyss Tes Seup Fgue 3.9. Fequency Response Funcon of he Roaon of he Mophng Pulley Fgue 3.. Dynamc Tenson of he Bel n Span fo =8,, and mm VIII

9 Fgue 3.. Dynamc Tenson of he Bel n Span fo =8,, and mm Fgue 3.. Dynamc Tenson of he Bel n Span 3 fo =8,, and mm- Inpu un oque on he dvng pulley... 6 Fgue 4.. Bel Dve Sysem wh a Nonlnea Cluch Fgue 4.. Tansmed Toque hough Vbaon Reducon Sysem Fgue 4.3. Foue Coeffcens vs. Vbaon Amplude fo a Sysem wh a one-way Cluch... 9 Fgue 4.4. Foue Coeffcens vs. Vbaon Amplude fo a Sysem wh a Combned Nonlnea Cluch... 9 Fgue 4.5. Fequency Response Funcon of p Exposed o N.m Inpu Hamonc Toque on he Inpu Sysem wh only he one-way cluch... 9 Fgue 4.6. Fequency Response Funcon of p Exposed o N.m Inpu Hamonc Toque on he Inpu Sysem wh he combned one-way cluch and he oque lme 93 Fgue 4.7. Fequency Response Funcon of p Exposed o N.m Inpu Hamonc Toque on he Inpu Compason of All Cases Fgue 4.8. Tme Doman Compason of p fo he Thee Cases of wh One-Way Cluch, wh he Combned Nonlnea Cluch, and Lnea Sysem Fgue 5.. Schemacs of Bel Dve Tansmsson Sysem IX

10 Fgue 5.. Schemacs of Mophng Pulley n an Up-Shf... Fgue 5.3. Schemacs of Mophng Pulley n a Down-Shf... Fgue 5.4. Roaonal Speed of Mophng Pulley Dung a Shf... 6 Fgue 5.5. Theoecal Fequency Response Funcon of p Exposed o Un Hamonc Inpu Toque on he Dve Pulley... 7 Fgue 5.6. Tme Doman Compason of p Exposed o Un Hamonc Inpu Toque on he Dve Pulley, Resonance Excaon... 8 Fgue 5.7. Tme Doman Compason of p Exposed o Tansen Load Due o an Upshf on he Dven Pulley... 9 Fgue 5.8. Domnan Naual Fequences of he Sysem a Dffeen Load Condons Fgue 5.9. Peak Values of Oupu Dynamc Toque n Dffeen Roaonal Speeds... Fgue 5.. Peak Values of Oupu Dynamc Toque n Dffeen Load s Roaonal Inea... X

11 Ls of Tables Table 3-. Lnea Dsplacemen n he Tensone Pulley n x-decon Accodng o he Dve Pulley Radus... 4 Table 3-. Cuve Geomecal Paamees Table 3-3. Naual Fequences of he Sysem Table 4-. Geomecal Chaacescs of Roang Elemens... 7 XI

12 Nomenclaue A a b C c c C d C d E F f f F p F G Aea of he bel coss secon The angula confguaon of he h bel span Lnea paamee elaed o he gudng al Angula confguaon of he bel spans Lnea paamee elaed o he gudng al Dampng Max Cluch dampng Dagonal dampng max Dampng of he h bel span Dvng pulley denfyng ndex The facon of esponse peod when he cluch s dsengaged Young s modulus Focng veco Specfcally defned sep funcon The h phase angle The h Foue coeffcen Foce appled o he pn Inal foce of he ensonng mechansm Nonlnea veco XII

13 g H J k k c d k l l am l M M m N p Elemens of he nonlnea veco The h phase angle The h egen value Tansfomed nonlnea veco Idle denfyng ndex Roaonal nea of he h pulley Sffness max Foue paamee Cluch sfness Dagonal sffness max Sffness of he h bel span Lmng paamee Egen value Lengh of he ensone am Lengh of he h bel span Mass max Focng funcon measuemen nose Mass max elemens The h dampng paamee Physcal dsplacemen measuemen nose Dven pulley denfyng ndex XIII

14 q Q Q T T, U V c n, X y Modal vaable veco Dven oque Inpu oque The angula dsplacemen of he h pulley Densy Radus of he h pulley Tme Tensone am denfyng ndex The h me scale Tenson n he h span Inal enson of he h bel span Max of egen vecos The ccal speed Excaon fequency Fequency The h naual fequency Physcal vaable veco The angula confguaon of he ensone Physcal dsplacemen The h modal dampng paamee XIV

15 CHAPTER INTRODUCTION Dynamc behavou of a mophng pulley ansmsson sysem s suded houghou hs eseach. The mophng pulley ansmsson s a bel dve sysem ha offes seveal mpovemens and conbuons fo dffeen nduses such as auomove and wnd enegy havesng. A mophng pulley can change s damee whle engaged o a bel. The mophng pulley s compsed of seveal sub-pulleys wh dffeen damees ha can ake each ohes place by swappng small segmens of one pulley fo segmens of anohe. When all he segmens ae swapped, he anson fom one pulley sze o anohe s compleed. Changng he damee of he mophng pulley povdes dffeen dve aos o he ansmsson sysem.

16 Bel dve sysems possess complcaed dynamc behavou due o he complance of he bel. In addon, gven he complexy of he neacon beween he mophng pulley and he bel dung a dve ao shfng, he mophng pulley ansmsson possesses complex dynamc behavou leadng o sgnfcan desgn challenges. A small excaon fom he oang sysem such as a pulley eccency o flucuang npu oque can nduce excessve vbaons o he bel dve sysem. The effecs of he smulaed vbaons become moe sgnfcan when he opeang oay speed s close o he esonance fequency. Achevng bel dynamc sably s also a challenge n hgh speed opeaons. A bel dve sysem eques a cean ange of peenson fo mananng dynamc sably. Snce he geomey of he bel dve sysem vaes dung a dve ao shfng, specal consdeaons ae equed fo he desgn of he ensonng mechansm o avod excessve dynamc enson due o dve ao shfng. Dung a dve ao shfng, he bel expeences sudden enson changes esulng n sgnfcan ansen loads. Theefoe, a vbaon educon sysem s essenal o mnmze he ansen dynamc loads. A nonlnea vbaon educon mechansm s poposed o mgae excessve dynamc loads. The vbaon educon sysem consss of a oque lme and a one-way cluch. Boh he ensonng mechansm and he vbaon educon sysem nduce complcaed and ofen nonlnea dynamc behavou o he sysem. Ths docoal eseach s devoed o he sudes he dynamc behavou of he ansmsson sysem hough analycal and expemenal mehods.

17 . A NEW TRANSMISSION TECHNOLOGY Tansmssons ae essenal elemens n oay powe sysems n dffeen nduses. Bel dve sysems n pacula ae ofen used n heavy machney, auomove, wnd ubne, and many ohe nduses. Due o he gowng demand n enegy savng equemens fo auomove ndusy, he mophng pulley ansmsson s a pefec canddae o eplace exsng ansmssons. Wnd enegy havesng ndusy can also benef fom dffeen desgn advanages ha hs ansmsson sysem offes... AUTOMOTIVE INDUSTRY The auomove ndusy seeks o ake advanage of a lo of new echnologes o fulfll enegy consevaon and emsson educon equemens. Inceasng he enegy effcency of vehcles by edesgnng vehcle s componens has been he mao focus of eseach and developmen acves n he auomove ndusy. Fo a vehcle, he fuel consumpon and gas emssons depend on many componens pmaly he powean []. The engne and he ansmsson sysem ae he wo man componens of a vehcle s powean. Tansmssons ae ccal elemens n vehcle pefomance and fuel consumpon []. Fo he same benef n fuel consumpon, s moe cos effecve o nves n developmen of he ansmsson sysem o ncease he enegy effcency of he powean, compaed o developng he engne [3]. I s advanageous, o developmen and manufacung cos savngs, o seek a moe effcen ansmsson. Cuen ansmsson echnologes can benef fom mpovemens n effcency, pefomance, o 3

18 boh. Cuenly, hee ae vaous ypes of ansmssons used n auomove ndusy o fulfll dffeen desgn and pefomance equemens. Convenonal manual ansmssons ae 95 pecen effcen, whch s he hghes oveall effcency fo a mechancal ansmsson n he auomove ndusy [4]. An auomaed manual ansmsson poenally has he same effcency as a convenonal manual ansmsson. In manual ansmssons, he engne s dsconneced fom he es of he powean dung a shf. Thee s an neupon n oque ansmsson dung a dve ao shfng [5]. The loss of powe ansmsson dung a shf esuls n lack of dvng comfo, whch s he man dsadvanage of manual ansmssons [6]. Thee ae seveal ypes of auomac ansmssons fo auomove ndusy. The convenonal auomac ansmssons ae desgned wh abou 85 pecen effcency. The effcency s lowe compaed o he manual ansmssons manly due o losses fo he hydaulc pump and wase of enegy n he oque convee [4]. The bel dve connuously vaable ansmsson s anohe ype of auomac ansmsson ha s esmaed o have an effcency of 85 pecen. The man benef of he bel dve connuously vaable ansmssons s ha allows he engne o opeae n he mos effcen oaonal speed [4]. Thee s no uncomfoable dscee dve ao shfs fo hs desgn. Howeve, he lowe effcency compaed o he convenonal auomac ansmsson s manly due o paasc losses dung nomal opeaon [7]. Dffeen ansmsson echnologes wh he benefs and ssues ae no able o fulfll all pefomance equemens, comfo, and elavely low cos fo mass poducon 4

19 fo he auomove ndusy. Thee s a song demand fo a fully auomac ansmsson ha can povde a wde ange of desgn equemens fo he auomove ndusy, whle mpovng effcency. The mophng pulley bel dve ansmsson sysem s desgned o povde hghe effcency and dvng comfo as well as o fulfll a wde ange of pefomance equemens fo he auomove ndusy... WIND ENERGY HARVESTING Wnd enegy s a enewable souce ha s eadly avalable. Alhough wnd enegy s eadly avalable, s nensy s unpedcable and changes fequenly. A ansmsson sysem s needed o keep he eleconc geneao nsde wnd ubnes spnnng a a specfc pm as o opeae a s hghes effcency. Gven he unpedcable naue of he npu and he equemen fo a seady pm on he geneao sde, a need fo a vaable effcen ansmsson ases. Vaable speed wnd ubnes ae exensvely developed n ode o mpove enegy poducon effcency. The mpovemens ofen depend on how well he oo speed maches he wnd speed. In he case of a close mach beween he ubne oo speed and he wnd speed, maxmum powe can be geneaed. Tubnes wh a vaable speed ansmsson can opeae a a educed speed n nose sensve envonmens as well as hgh speeds n wnd fams. Manufacung coss ae lowe fo ubnes wh hghe oo speed due o lowe oque on he shaf [8]. Cuenly, hee ae hee pncpally dffeen ansmsson echnologes used n wnd ubnes. In a consan speed wnd ubne, a fxed speed ansmsson conneced o 5

20 an eleccal powe geneao lms he powe geneaon o a specfc oo speed. Ths lmaon n oay speed educes enegy poducon effcency, and he ansmssons ae epoed o suffe fom sho falue lves [8]. Vaable speed powe eleconcs ae ofen used fo ubnes wh fxed speed ansmssons ha ae conneced o a vaable speed geneao. The fequency of AC cuen s adused o a fxed value, fo example 6 Hz, by means of powe eleconcs. The powe eleconcs offe he advanages of a vaable oo speed, whle he man dsadvanage s hgh cos [9]. Usng vaable speed ansmssons ae no so common fo he wnd ubne ndusy due o lack of an avalable auomac ansmssons poven o addess elably and effcency ssues []. The convenonal and auomaed manual ansmsson sysems ae no suable fo wnd ubnes due o he dsengagemen beween he oo and he geneao dung a dve ao shfng. In addon, because of he low effcency of he bel dve connuously vaable ansmsson, only by a one pecen ncease n he enegy poducon could be acheved n exemely hgh wnds []. Wnd ubne ndusy wll gealy benef fom a ansmsson echnology ha allows fo an effcen dve ao shfng whou necessy of dsengagemen beween he oo and he geneao dung a shf. The mophng pulley ansmsson s desgned o offe an effcen auomac vaable ansmsson echnology wh no essenal powe dsengagemen fo dve ao shfng. 6

21 . MORPHING PULLY TRANSMISSION The mophng pulle ansmsson echnology, noduced by Wong n 5 [], s a new bel dve vaable ansmsson sysem ha offes seveal benefs compaed o he convenonal ansmsson sysems. The man componens of he ansmsson ae he mophng pulleys, ensonng mechansm and vbaon educon sysem. Heeby he man componens of he ansmsson ae noduced... MORPHING PULLEY The man componens fo dve ao shfng n ansmsson ae he mophng pulleys ha can change he damees whle engaged wh an axally movng bel ha s unde enson. Each mophng pulley s compsed of wo, o moe, sub-pulleys of dffeen damees. The sub-pulleys ae dvded no a cean numbe of pulley segmens. To change dve aos fom one o anohe, pulley segmens ae apdly nseed laeally no poson n whch a new sub-pulley wll engage wh he bel. Hgh speed acuaos ae used fo shfng he pulley segmens. When all he segmens ae swapped, he anson fom one sub-pulley sze o anohe s compleed. Fgue. llusaes he mophng pulleys and segmens fo a pooype of mophng pulley. The pulley segmens only move whle hey ae no engaged wh he bel and ae no ansmng any load. When he ansmsson s no pefomng a shf, opeaes lke a nomal oohed pulley and bel sysem, whch s an effcen and elable fom of mechancal enegy ansmsson. Fgue. shows he schemacs of he mophng pulley ansmsson opeang wh dffeen dve aos. 7

22 Fgue.. Mophng Pulley and Pulley Segmens Couesy of Vcccog Dve Load Dve Toque < Load Toque Dve Speed > Load Speed Dve Toque = Load Toque Dve Speed = Load Speed Dve Toque > Load Toque Dve Speed < Load Speed Fgue.. The ansmsson Opeang wh Vaous Dve Raos The dve ao shfng n a mophng pulley ansmsson does no eque dsengagemen of he dve fom he load. Ths advanage dffeenaes hs desgn fom a wde ange of manual and auomac ansmsson sysems. In fac, he only cuenly used ansmsson sysem ha does no eque dsengagemen dung a dve ao shfng s he connuously vaable bel dve desgn. In addon, unlke a convenonal connuously vaable bel dve ansmsson sysem, he mophng pulley ansmsson does no possess any paasc losses dung nomal opeaon. Fuhemoe, he dve ao shfng pocess n he mophng pulley ansmsson demands mnmal enegy due o he pulley segmens movemen along wh he pulleys axes whle hey ae no engaged 8

23 wh a bel. Hence, he mophng pulley ansmsson offes a wde ange of benefs fo dffeen applcaons... TOOTHED BELT A oohed bel s used fo he mophng pulley ansmsson o avod enegy loss caused by bel slppage and dy fcon and paasc losses. The oohed bel consss of a enfocemen fbe backng and eeh ha ae moulded ono s nne suface. The pulley and ooh pofle exhb pem machng dung nomal opeaon and povde a smooh anson dung shfng. When coecly ensoned, hee should be no slppage beween he pulleys and he bel. The oohed pulleys ae ofen used o ansfe moon fo ndexng o mng puposes...3 TENSIONER The mophng pulley ansmsson undegoes unquely lage dynamc flucuaons fo whch a ensonng mechansm s necessay o ensue dynamc sably and sysem flexbly. Fgue.3 shows a bel dve sysem wh a convenonal ensonng mechansm. A ensone s equed fo a bel dve sysem o povde ensle pe-load n he bel fo ensung dynamc sably. A convenonal ensonng mechansm ypcally consss of an dle pulley ha s conneced hough a flexble on o he bel dve sucue. The flexbly of he on s o be adused o une he dynamc popees of he bel dve sysem o desable values. 9

24 Peensoned Bel Peensoned Bel Tensone Spng - Peensoned Fgue.3. Convenonal Tensone The ensonng mechansm s a ccal pa of he bel dve sysem due o he specfc opeaonal equemens. Dung a dve ao shfng, he bel dve ansmsson undegoes a change n he confguaon of he bel and pulleys. Usng a convenonal ensonng mechansm esuls n a huge vaaon of peenson. In addon, he dynamc popees of he sysem, such as naual fequences, need o be uned by selecon of appopae ensone sffness. Theefoe, an unconvenonal ensone desgn s equed o fulfll dffeen opeaonal equemens...4 VIBRATION REDUCTION SYSTEM The mophng pulley ansmsson s desgned fo dffeen applcaons such as auomove and wnd ubne. I s expeced ha he man cause of falue n he bel dve sucue s due o fague. Mgang hgh dynamc loads mpoves he fague lfe of he bel dve s componens.

25 Fo wnd powe geneaon applcaons, powe flucuaons due o dynamc loads can cause undesable nose n he oupu powe. In he vehcle s powean, he engne pulsaon s a consan souce of hamonc excaon. In addon, he dve ao shfng can cause sgnfcan dynamc loads due he sudden shfs. The ypcal lage neal loads mpose hgh dynamc loads n he ansmsson sysem. In ode o mnmze he effecs of undesable dynamc loads, a passve nonlnea vbaon educon sysem s desgned. The man componens of he vbaon educon sysem ae a one-way cluch and a oque lme ha ae nsalled n sees, fomng a nonlnea cluch. The nonlnea cluch connecs he ansmsson o he load, whch ypcally has a lage nea. The oneway cluch allows elave moon s only one decon and dsengages he cluch n he evese decon. The oque lme allows ansfeed oque hough he cluch o a cean sauaon lm, called he lmng oque. Fo oques hghe han ha lm, he oque lme sas sldng and consequenly he ansfeed oque sauaes a he lmng oque...4. One-Way Cluch One-way cluches ae effecve devces o mgae vbaon poblems and has been poven o be useful on ohe applcaons. These mechancal elemens ae mouned n he load pah beween a pulley and a dven shaf. Dffeen ypes of one-way cluches pefom essenally he same funcon, namely ha of decouplng pulley oaons n he non-dven decon caused by pulley vbaons. In essence, he pulley and dven shaf ae allowed o oae elave o each ohe when he cluch dsengages.

26 Unlke a one-way cluch, n a egula locked cluches, he dynamc foces ae decly ansmed back along wh he bel causng sysem oaonal dynamc loads o go hough he couplng. Usually, he amoun of foce needed o dsengage he one-way cluch s adusable o su he applcaon. Thee ae dffeen ypes of of one-way cluches among whch he spag ype s poposed due o he obusness of he desgn. Schemacs of a spag ype one-way cluch mechansm ae shown n Fgue.4. Fgue.4. Spng Type One-Way Cluch The spng cluch consss of hee pas: an npu hub, an oupu hub, and a spng. The nsde damee of he spng s slghly smalle han he ousde damee of he wo hubs. When he pas ae assembled and one hub s oaed n he decon ha he spng s wound, he spng waps down ghly on boh hubs causng he cluch o dve. The geae he foce he ghe he spng gps he hubs. When he oaon s evesed, he spng loosens s gp and slps. In he fee decon hee s slgh dag caused by he spng beng slghly smalle han he dums. Ths fcon can be used o ceae a non adusable oque lme as well. Fgue.4 shows he schemacs of he

27 spng ype one-way cluch. A spng ype one-way cluch s seleced fo he bel dve ansmsson due o low cos, small sze and adusably of hs ype of one way cluches...4. Toque Lme A oque lme s an auomac devce ha poecs oay equpmen fom damage by mechancal oveload. A oque lme may lm he oque by slppng (as n a fcon plae cluch), o uncouple he load enely (as n a shea pn). In a fcon plae oque lme hee ae wo oay plaes ha connec he wo oay shafs ogehe. The plaes ae pessed owad each ohe by an axal foce and ansfe he oay load hough he fcon foce. If he ansfe oque exceeds a cean lm, called he lmng oque, and ovecome he fcon beween wo plaes, he wo plaes sa o slp. Consequenly, he couplng sas sauang he ansfeed load a he lmng oque. The lmng oque can be adused usng he axal pessng foce. Fgue.5 shows he schemacs of a fcon plae oque lme ha s poposed fo he mophng pulley bel dve sysem. Fcon plaes Tansfeed oque Axal foce Fgue.5. Fcon Plae Toque Lme 3

28 .3 ADVANTAGES OF THE NEW TRANSMISSION The novel bel dve ansmsson offes wde anges of he advanages ove exsng ansmsson sysems fo dffeen nduses such as auomove and wnd enegy havesng. The oveall ansmsson sysem effcency s mpoved due o low enegy equemens fo dve ao shfng and no enegy equemen fo nomal opeaons. The new ansmsson elably povdes he hgh effcency of a oohed bel dve mechansm and he connuy of a mophng pulley. Is obus desgn s well-sued o hgh oque applcaons and ulzes duable, elable oohed pulleys o ansm powe. A wde ange of dve aos, by usng wo mophng pulleys, and closely spaced aos povde compaable pefomance o a connuously vaable ansmsson sysem n ems of effcency and load handlng Usng oohed pulleys o ansm powe, he dve ao shfng occus whle he ansmsson s ansmng load, whou elyng on fcon o flud couplng. Unlke a fxed dve ao ansmsson, such as manual ype, he mophng pulley ansmsson does no eque a dsconnecon n he powean dung dve ao shfng. The capably of pefomng a shf unde load, s wde gea ange, and shfng whou a dsconnecng cluch ensues maxmum effcency and vesaly n opeaon fo he poposed desgn..4 CHALLENGES OF THE DESIGN As a new echnology, hee ae challenges assocaed wh desgn of he new mophng pulley ansmsson sysem. The componens of he ansmsson ofen eque 4

29 dealed desgn analyss and opmzaon o fulfll dffeen equemens dependng on he applcaon. In pacula, a gea deal of equemens s decly elaed o dynamc behavou of he bel dve sysem. Ths eseach s focused on he dynamc analyss of he mophng pulley ansmsson sysem wh specal aenon o ccal componens and maes such as ensonng mechansm, vbaon educon sysem, and dynamc behavou of he sysem unde hamonc and ansen load. I s necessay o manan a pope ange of peenson n a bel sysem o ensue dynamc sably of he bel. Convenonally desgned ensones do no fulfll all he desgn equemens of he bel dve ansmsson, as he vaaon of he confguaon of he bel dve sysem dung a dve ao shfng mposes sgnfcan devaon n he amoun of peenson. Theefoe, a obus ensonng mechansm s equed n ode o povde an appopae ange of peenson n dffeen dve aos. In mos applcaons s deseable o mnmze he flucuaon of he oupu oque fom he ansmsson. In auomove ndusy, he oupu oque may cause excessve nose and hashness n he vehcle neo space. Smlaly n he wnd ubne ndusy, a powe geneao eques a smooh oaonal npu powe wh mnmal flucuaons. In addon, fague based falues ae mao causes of sucual falue fo a ansmsson sysem and ae decly elaed o dynamc. A flucuang oque fom a ansmsson could poenally cause sgnfcan poblems n powe geneaon. To mnmze he undesable vbaons, a vbaon educon sysem s equed fo he ansmsson sysem. 5

30 Dynamc analyss of he ansmsson sysem ha ncludes he necessay dynamc elemens such as he ensonng mechansm and he vbaon educon sysem s equed n ode o povde he essenal npu nfomaon fo he desgn pocess. Howeve, bel dve sysems ofen possess complex dynamc behavou due o he flexbly of he bel. Couplng beween he bel longudnal and he pulleys oaonal vbaons as well as he vbaons of he ensonng mechansm nduces complexy n he dynamc behavou of he bel dve sysems. In addon o he complex dynamc behavou of a convenonal bel dve sysem; he mophng pulley sysem, n pacula, undegoes complcaed geomecal changes ha nfluence he bel and pulley coupled vbaons dung a dve ao shfng. Theefoe, due o he complexy of he ansmsson desgn pocess, s essenal o develop an nclusve dynamc model ha coves he man dynamc elemens of he ansmsson. Snce pemaue fague falues ae ofen due o excessvely hgh amplude dynamc loads, an n-deph dynamc analyss s necessay fo he pupose of desgnng he sysem agans pe-maue fague based falues. The dynamc loads appled o he dffeen componens of he sysem, such as dynamc bel enson o dynamc hub-load, ae equed o be deemned and conolled n a cean ange o ensue ha he sucual desgn cea s me. 6

31 CHAPTER LITERATURE REVIEW The poposed mophng pulley ansmsson sysem possesses complex dynamc behavou. Dung a dve ao shfng, a sudden enson vaaon occus n he ansmsson sysem as a esul of changes n he confguaon of he bel dve sysem. Due o he complexy of he ansmsson sysem and he dve ao shfng pocess, s a challenge o pedc he dynamc esponse of he sysem o he ansen load caused by he dve ao shfng. In addon, n ode o mnmze he effecs of dynamc load, a passve vbaon educon sysem wll be used. The passve vbaon educon sysem ncludes a one-way cluch and a oque lme ha ae nsalled n sees wh he oupu 7

32 pulley and he load. The passve sysem possesses nonlnea dynamc behavou due o dsconnuy n he cluch oque. Dynamc analyss of he ansmsson sysem s an essenal pa of he desgn pocess. Paculaly, o desgn he sucual elemen of he ansmsson agans fague, s necessay o oban he dynamc loads ha ae appled o he ansmsson sysem, such as he dynamc bel enson and dynamc hub-load. In addon, an axally movng bel possesses complex dynamc behavou leadng o sgnfcan desgn challenges. A small excaon fom he oang sysem such as pulley eccency o flucuang npu oque can cause vbaons wh hgh ampludes n he bel dve sysem. The vbaons become moe sgnfcan when he opeang oang speed s close o he esonance fequency. Achevng bel dynamc sably s also a challenge n opeaons wh hgh oay speed [3]. In addon o he complex dynamc behavou of a ypcal bel dve sysem, he mophng pulley bel dve sysem holds s own pacula desgn challenges. Desgnng a ensonng mechansm ha ensues mananng an appopae ange of peenson n all dve aos eques a gea deal of dynamc analyss. The poposed vbaon educon sysem s also nvolved wh nonlnea dynamc behavou of dffeen elemens ha ae nvolved wh he sysem. To addess hese challenges, hs eseach s devoed o he dynamc analyss of such a mophng pulley bel dve sysem.. DYNAMICS OF BELT DRIVE SYSTEMS Thee ae wo mao modes of vbaons occung n bel dve sysems, namely he longudnal and he ansvese bel vbaons. In he longudnal bel vbaon, he 8

33 oaonal neas oscllae abou he pn axes, and cause longudnal bel defomaon. Dung such vbaons, he bel spans behave smla o lnea spngs. In ansvese vbaons, he bel spans osclae vecally elave o he bel axal decon, smla o a au spng. Boh ypes of vbaons may be exced by flucuang oque fom he dve o dven pulleys, pulley eccences, unusual pulley adus and bel popees, o moon of he pulley suppos [4]. Vaous appoaches aken o sudy he dynamc analyss of bel dve sysems ae dscussed n hs secon.. DYNAMICS OF AXIALLY MOVING BELT A movng bel s ofen modeled as a sng ha s unde enson wh axal velocy. Sudyng he longudnal and ansvese vbaons of a movng sng as a model of a bel has saed snce ealy 95s. In 95, Sack suded he behavou of sandng waves n a bel unde enson [5]. The effecs of bendng n he bel wee negleced consdeng small eos fo mos bel dve sysems. Theefoe, he bel was modelled as a movng sng n he absence of he bendng gdy. Also, he wave moon was assumed o be supeposed wh he bel longudnal moon. The model of he sysem wh he bel dd no nclude any couplng beween he ansvese and longudnal vbaons of he bel. In 978, Ulsoy e al. examned nonlnea ansvese bel vbaon esponse n a sysem composed of a ensonng mechansm and seveal bel spans [6]. The effecs of oque vaaons on he dynamc ensons n dffeen bel spans wee suded n hs wok. I was shown ha he dynamc ensons cause paamecal excaon leadng o laeal vbaons n bel spans. Smlaly, Chanon suded he 9

34 seady-sae esponse of an axally movng sp subeced o a consan laeal foce fxed n space [7]. Ths model was used o sudy he me doman laeal vbaons of a bel unde enson. In 99, Wcke pesened he classcal vbaon analyss of axally movng connua unde enson ha ncluded couplng beween he laeal and longudnal vbaons [3]. Ths model was exensvely used by ohes o model bel dve sysems n dffeen hamonc and non-hamonc, assumng couplng beween ansvese and longudnal vbaons of he bel when a ensone s nvolved. In 996, Moon and Wcke connued wh hs modellng appoach o nvesgae he nonlnea vbaons of bel dve sysems by assumng he bel s exced by pulleys eccency [8]. Accodng o Moon and Wcke, eccency can lead o dynamc nsably n hgh axal velocy of he bel. A smla appoach fo sudyng he vbaon of an axally movng sng s suded by Chaung, when he sng had geomec nonlneay and anslang acceleaon [9]. Oz modeled he bel as a Eule-Benoull beam unde hgh enson whle he bendng sffness was no negleced n he equaons of moon []. Smla appoach connued by Pellcano n 6 []. Pellcano pefomed a deep analyss of he numecal and expemenal esuls egadng he complex dynamcs of axally movng sysems such as sub-hamonc esponses, amplude modulaons, and chaos n he pesence of bendng gdy. In 6, Ha nvesgaed he bfucaon and chaos of a movng vscoelasc sng undegong hee-dmensonal vbaons []. Thee s a geomecal nonlneay n hs modelng caused by hee-dmensonal couplng beween

35 he laeal and longudnal vbaons. ovuov used fne elemen mehod o solve he equaons of moon of a movng bel unde enson [3]. These mehods fo dynamc analyss of he bel as a complex dynamc sysem has been used n he desgn and analyss of bel dve sysems..3 EFFECTS OF A TENSIONER Alhough he movng bel dynamc behavou s well suded, he sysems ha nclude bel and ohe desgn complexes, such as mophng pulley sysems, sll eque a gea deal of n-deph dynamc analyss eseach. Dynamc analyss of bel dve sysems s manly focused on he coupled vbaons beween he ensone and he bel. Cassdy e al. developed he dea of ensone devce n bel and pulley sysem and pefomed a dynamc analyss on a bel dve sysem [4]. The oaonal vbaons of pulleys n bel dve sysems ae geneally domnan compaed o he laeal vbaons of he bels. Howeve, due o he geomey o he naue of couplng beween he longudnal and ansvese vbaons of he bel and he vbaons of he ensonng mechansm, he appoaches aken fo dynamc analyss of bel dve sysems ae ofen nvolved wh nonlnea phenomena. Sudyng of he nonlnea oaonal vbaons due o ensonng mechansm n a bel dve sysem saed eale by dffeen eseaches such as Abae [5]. Abae pesened a model whee he Runge-ua mehod was used fo solvng he nonlnea equaons of moon n a apd acceleaon-deceleaon poblem n he pesence of a ensonng mechansm wh fcon dampng. Effecs of bel axal velocy s suded by

36 Beckman [6] whle was shown ha a seched bel ceaes a nonlnea behavou leadng o couplng of he bel and ensone vbaons. Hwang suded he oaonal vbaons of bel dve sysems and pedced he onse of he bel slp [7]. Zhang and Zu suded he nonlnea fee vbaon of vscoelasc dffeenal consuve law [8]. They pedced he nonlnea naual fequences and fequency esponse amplude of he sysem usng peubaon mehod. The same auhos suded foced vbaon of he vscoelac movng bels exced by he eccency of pulleys [9]. They also pefomed he modal analyss of a bel dve sysem. A mehod of obanng he physcal chaacescs of he ansvese vbaon powe flow hough movng ubbe bels was poposed by won [3]. Pake used a hybd dscee-connuous model whee he moons conss of oaons of he pulleys, oaon of he ensone am, and ansvese vbaons of he connuum bel spans adacen o he ensone o nvesgae he dynamc behavou of a bel dve sysem [3]. Lavos e al. also developed a numecal model and smulaon sofwae o smulae he mng dve ansmsson ncludng a ensone [3]. Tonol e. al, consdeed he effecs of shea defomaons n dynamc modelng of bel dve Sysems [33]..4 NONLINEAR CLUTCH A dve ao shfng n he newly developed mophng pulley ansmsson sysem causes hgh amplude dynamc loads. In addon, he hgh nea load ha s expeced o be ypcal fo hs applcaon s anohe eason fo he hgh amplude dynamc loads. The poposed nonlnea cluch s conss of a one way cluch and oque

37 lme ha ae nsalled n sees o connec he load o he ansmsson sysem. The pupose of he nonlnea cluch s o educe he magnude of dynamc loads n he bel dve sysems. Dynamc analyss of bel dve sysems wh pecewse nonlnea elemens, smla o he poposed nonlnea cluch, s challengng due o he complexy of he mul degee of feedom modelng. The hamonc balance mehod was ofen used o oban he peodc esponses of nonlnea sysems, paculaly hose possessng pecewse nonlneay. In hamonc balance mehod, Foue sees ae used o expand he vaables and focng funcons. Ths wll lead o map he dynamc sysem fom he me doman no he fequency doman [34] [37]. Howeve, he hamonc balance mehod fals o povde he closed fom soluons of he dynamc sysem wh pecewse nonlneay. The closed fom soluons of he dynamc sysem ae ofen benefcal fo desgn assessmen puposes. Theefoe, classcal peubaon mehods ae ulzed o fnd he appoxmaed soluons o nonlnea equaons of moon when a closed fom soluons s needed [38] [4]. In hs wok, he mehod of mulple scale s used fo obanng a closed fom dynamc esponse of a pooyped bel dve sysem wh a pecewse nonlnea cluch. Though he dynamc sysems wh pecewse nonlnea elemens ae ofen used n ndusy, vey lle wok has been found n hs aea consdeng mulple paamees such as pecewse nonlnea dampng. Fo nsance, n a vey smla wok pesened by Zhu and Pake [38], he nonlnea dynamc analyss neglecs he effecs of he nonlnea cluch dampng foce. In addon, he dynamc sudes of a bel dve sysem wh a 3

38 nonlnea cluch ncludng a oque lme have no been found n leaue. In hs eseach, he effecs of sysem and cluch dampng and ohe desgn paamees on he dynamc behavou of a bel dve sysem ncludng a pecewse nonlnea cluch hough he classcal peubaon mehod of mulple scales s nvesgaed..4. DESIGN AND ANALYSIS OF A NONLINEAR CLUTCH One-way cluch sysems have been used commonly n ndusy fo oque conol applcaons. In 978, sh e al., developed hee dffeen mechansms of one-way cluch n ode o conol vbaon n a helcope powean [4]. They developed a spng, spag and amp olle one-way cluch and analyzed he pefomance of dffeen desgns. Compason of dffeen aspecs of a ansmsson sysem, n ems of wegh, duably, wegh and cos s epoed fo desgn puposes. In 993, Fz pesened a hgh capacy feewheel fo oque conveo applcaons [4]. In hs desgn, a mechancal dode s used n he ansmsson of an Indy Ca fo vbaon conol puposes. Ths mechancal dode one-way cluch ulzes adcally oened sus whch povde a gd, posve lockup n he dvng decon whle allowng fee, non-conac ove-unnng n he feewheelng decon. The effcency of he sysem ncludng he passve vbaon sysem has been evaluaed hough a numbe of expemens. In 994, Fz e al., analyzed he effec of oveunnng speed on powe dsspaon n mechancal dode ype one-way cluch. Evaluaon of he mechancal dode one-way cluch n ems of oque capacy and dynamc behavou s pesened n hs wok [43]. 4

39 Ths wok pesens an evaluaon of he mechancal dodes oveunnng chaacescs. Mechancal dodes of vaous szes and wh vaed nenal gap have been oveun a dffeen speeds. Speeds, oveunnng oques and lubcan empeaues ae ecoded and oveunnng powe dsspaon chaacescs of mechancal dodes ae pesened n abula and gaphc foms. In 995, Fz connued he pefomance evaluaon of a mechancal dode oneway cluch sysem by lookng a he lock-up mes n he sysem [44]. The effec of lubcan vscosy was suded on he dynamc pefomance of he mechancal dode ype one-way cluch. Ruh developed a powdeed meal pocke fo he mechancal dode one-way cluch [45]. Ruh dscusses he basc desgn concep, desgn sess lms, powdeed meal maeal selecon and pocessng fo hese one-way cluch plaes. A olle amp one-way cluch s analyzed by eme n 995 [46]. Rolle floa s defned as a condon whee he olle loses conac wh he olle way. Ths condon decly nfluences he dynamc pefomance of he olle cluch and s analyzed n hs wok. The olle amp mechansm s modeled as a fou lnkage mechansm and knec analyss s used o evaluae he pefomance of he one-way cluch sysem n dffeen condons. The analycal esuls ae compaed wh expemenal daa o ndcae he poenal hazads of excessve aceway un ou. Snce he pefomance of one-way cluch s dependen on s mang aces, falue of he cluch ace s assumed o be he falue of he whole cluch sysem. eme 5

40 nvesgaed hs ssue by vefyng he olle amp one-way cluch ace sess equaons usng fne elemen analyss [47]. The hook sess calculaed hough fne elemen model s compaed o he analycal fomulaon and sasfacoy esuls wee used o vefy he sess equaons. The obecve of hs wok was o vefy he esuls of hese sess equaons. Fz pesened he ulmae sengh of mechancal dode ype one-way cluches n a pape publshed n 996 [48]. A mehod of pedcng mechancal dode ulmae sengh s pesened n hs wok. The sengh of mechancal dode s dependen upon he su snce lockup foces ae suppoed by he su. By calculang he column bucklng sengh of he sus, a pedcve measue fo deemnng cluch load cayng capacy s oulned. Expemenal daa on oveload falue due o su bucklng s pesened and compaed o he calculaed falue oque fo a ypcal mechancal dode one-way cluch. The expemenal daa ncludes no only he maxmum oque a falue, bu also povdes aces showng he elasc and plasc esponse egons of he su n compesson. Resuls of hs sudy ndcae ha mechancal dode ulmae sengh s exemely hgh fo he devce's wegh and volume and ha he ulmae sengh can be pedced wh suffcen accuacy o allow elable desgns. In 997, Chesney and eme, [49], esablshed a genealzed analycal model fo sess equaons n a olle amp one-way cluch. Opmal desgn of a olle amp one-way cluch fo a sae dve s pesened by Xue and Pyle [5]. The sae dve cluch s a one way olle cluch and a key componen n a sae moo ha s used o cank nenal 6

41 combuson engnes. The sae dve cluch ansms oque fom an eleccal moo o a ng gea mouned on a cankng shaf n an engne hus canks he engne. The cluch also pevens he whole sae fom damage caused by dve slppage and bael cackng, whch ae wo mao falue modes fo he sae dve. In addon, nsuffcen oque capacy esuls n dve slppage whle excessve hgh hoop sess on he cluch bael ng causes bael cack. To elmnae he dve slppage falue, he cluch should be desgned wh hgh oque capacy. Hgh oque capacy, howeve, s a cause of hgh hoop sess on he bael ha may esul n he cacked bael falue. Hghe oque capacy and lowe hoop sess ae wo compleely oppose desgn decons. Theefoe, an opmal desgn appoach was pesened n hs wok o maxmze oque capacy of he cluch and mnmzng hoop sess on he bael. An opmzaon model was deved based on he mechansm of he cluch and a sensvy analyss s used o selec he mos effecve paamees fo he opmzaon n hs mulple vaables opmzaon. A consan su angle was noduced o educe changng su angle dung he cluch woks. A case sudy showed ha he opmal desgn appoach mpoved cluch desgn [5]. Dvelne vbaon s usually assocaed wh fcon cluch dynamcs. Howeve, he olle one-way cluch can also be a souce of vbaon. An n-deph dynamc analyss of a olle one-way cluch was conduced by Alds and eme n 998,, by fndng he naual fequences of one-way cluch sysems. Analycal modelng and expemens wee pefomed n ode o nvesgae effecs of dffeen desgn paamees on he 7

42 dynamc behavou of a one-way cluch [5]. In hs wok, he feewheel-mode esonan esponse of a olle one-way cluch sysem was pedced. The sudy begns by makng some fundamenal smplfyng assumpons, whch leads o an equvalen one-way cluch sysem spng ae. The olle one-way cluch sysem was hen modeled as a smple massspng-mass sysem, fom whch he applcaon of appopae bounday condons yeld he desed fundamenal esonan fequences. Ths analyss mehod was appled o a numbe of olle one-way cluch sysems, and he esuls wee compaed o numecal smulaon and expemenal esuls..4. APPLICATIONS OF A ONE-WAY CLUTCH CLUTCH One way cluch sysems can manan consan enson whle wndng o unwndng we, pape, flm, head, ec. hey can also be used fo deconal oque conol applcaons, fo example n one-way scew dves. Oveload Poecon s anohe applcaon of one-way cluches. They can also be used n posonng and many ohe mechansms fo moon conol puposes. Howeve, one-way cluches ae ofen used fo vbaon educon puposes n oay sysems. The nonlneay of dynamc oque ansfeed by a one-way cluch s he benefcal fo educng dynamc loads. Though he applcaon of one-way cluch sysems fo dffeen oay sysems s exensve, leaue on dynamc analyss s lmed. An expemenal analyss of spag ype one way cluches fo an a ubne sae n e engnes was pesened by Venay e al. [5]. Ths wok denfed sldng dung engagemen of he cluch and he effecs of 8

43 he sldng on one-way cluch dynamc popees. ng and Monahan, nvesgaed he funconal deals of a wap-spng ype of one-way cluch [53]. A powean sysem ncludng a one-way cluch was analyzed n ode o opmze he shf conol saegy n an auomac ansmsson by Han and Y [54]. A smla desgn was pesened by Goez e al. [8]. A gea shf conol saegy based on he dynamc esponse of a powean sysem ncludng a one-way cluch s analyzed, emphaszng he effec of one-way cluch n mnmzng he enegy loss. In 4, Benez e al. pesened an nfnely vaable ansmsson, based on he use of one-way acon cluches, belongng o he famly of acheng dves was descbed [55]. The mechancal foundaons and numecal smulaons wee pefomed o nvesgae he behavou of he gea-box n geneal mechancal ndusy and s pospecve use n auomobles and self-popelled vehcles. The sysem ncludes one-way cluches, fee wheels o oveunnng cluches, and wo epcyclc gea sysems. The knemacs opeang pncples behnd hs sysem was descbed followed by a numecal smulaon of he dynamc analyss. A pooype was consuced and esed o assess s mechancal effcency fo dffeen educon aos and he smulaons wee suppoed by expemenal daa. Nonlnea behavou analyss of a paed spu gea sysem wh a one way cluch was used by Glleong o vefy whehe a one-way cluch s effecve fo educng osonal vbaon [56]. A gea sysem wh a one-way cluch showed nonlnea behavou, such as sofenng nonlneay and ump phenomena. The oscllang 9

44 componen of he dynamc ansmsson eo was educed ove he ene fequency ange compaed o a sysem whou a one-way cluch. An mpoan use of one way cluch sysems s n bel dve oay sysems. Due o flexbly of he bel, a bel dve sysem s vey esponsve o dynamc loads. Paculaly, n fon end accessoy dve (FEAD) sysems, he effecs of dynamc loads on sysem vbaons ae sgnfcan. Usually FEAD s a bel dve sysem ha ansfes pescbed moon fom a cankshaf o dffeen accessoes such as he alenao, powe seeng, a condonng and wae pump hough he enson and moon of a flexble bel. Flucuaons of he engne s oay speed due o fou soke engne mechansm behave as a consan souce of dynamc load o he FEAD sysem. One-way cluch s a common nonlnea vbaon educon elemen n FEAD sysems o avod excessve dynamc loads. The dynamc load of FEAD can be conolled usng oque dsengagemen of a one-way cluch sysem. FEAD sysems undego complcaed dynamc loads paculaly n acceleang and deceleang peod. Oveunnng alenao decouple s a passve vbaon educon sysem fo FEAD ha ncludes a one way cluch and mnmzes he dynamc loads. An oveunnng alenao pulley was developed and analyzed n a epo pesened by Solfank and elm [57]. The pesened cluch s a speed-dependen dampng elemen paallel wh a spng. Fne elemen sudes of bel ceep on he pulley was pefomed by Solfank and elm [57]. Ths wok descbed he dynamc behavou of a 3

45 bel dve sysem by lookng a he dy fcon beween he pulleys and he bel. The model assumed popoonal oque o pulley load speed fo a one-way cluch. In 999, ng and Monahan developed a one-way pulley fo auomove FEAD sysem n ode o mnmze he dynamc esponse of he FEAD sysem [58]. An oveunnng pulley wh negal wap spng one-way cluch was used o add a ugged and elable elemen o he FEAD sysem n ode o elmnae nose poblems assocaed wh excessve dynamc enson. A smla echnology was developed and pesened by Xu and Anchak n 4 [59]. In hs wok an oveunnng alenao decouple (OAD) s noduced o eplace he sold alenao pulley n ode o decouple he alenao oo nea fom he FEAD. The OAD s a passve vbaon absobe sysem ha ncludes a one-way cluch n sees wh a uned mass absobe mechansm. Usng he uned mass absobe, he esonance fequency of he sysem s shfed n ode o avod he load flucuaon fequency comng fom he cankshaf. The one-way cluch also avods engagemen of he alenao wh he FEAD dung engne deceleaons. Ths dsengagemen s advanageous dye o he nonlnea dynamc effec of he one-way cluch on he dynamc esponse of he FEAD as a dynamc sysem. Usng OAD, excessve nose, vbaon and hashness poblem assocaed wh he FEAD sysem can be avoded. In addon, s known ha FEAD dynamc behavou affecs he effcency. Accodng o Hawley e al., mpovng he FEAD dynamc pefomance s benefcal fo avodng CO poducon [6]. Also, usng OAD, s amed o mnmze dynamc enson n FEAD sysem n ode o avod bel and 3

46 pulleys pe-maue falues. Thompson and Bechko nvesgaed dffeen vbaon conol soluons fo engnes wh cylnde deacvaon by suggesng he use of a oneway cluch and a flexble on [6]. Use of a conolled alenao decouple fo nose and vbaon educon n FEAD s also suggesed by Fz [6]..4.3 METHODS OF NONLINEAR DYNAMIC ANALYSIS Alhough he lnea and nonlnea dynamc analyss of bel dve sysems s suded exensvely, s challengng o sudy he dynamc behavou of sysem ha ncludes a movng bel n combnaon wh nonlnea dynamc elemen. Fo example n he mophng pulley ansmsson sysem, he poposed passve vbaon educon sysem ha ncludes a one-way cluch and a oque lme nduces pecewse nonlneay o he sysem. In addon, he dve ao shfng pocess causes dynamc nonlneay ncludng he couplng beween he bel and pulleys vbaons and he ensonng mechansm and he changng adus of he mophng pulleys. Theefoe, he dynamc model of he ansmsson conans hghly nonlnea elemens and s complex o solve analycally. Though applcaons of he passve vbaon educon sysems such as oneway cluches, oque lmes and dy fcon vbaon dampe ae exensve, leaue on he dynamcs analyss s lmed. The ecen mehods of nonlnea dynamc analyss fo bel dve sysems ae suveyed n hs secon. The nonlneay ha exss n he mos n he dynamc elemens of he ansmsson sysem s ofen due o he cleaance ype nonlnea ems assocaed wh he one-way cluch and he oque lme. Hamonc balance mehod s a sem-analycal 3

47 appoach ha s ofen used o oban peodc esponses of nonlnea sysems, paculaly hose possessng cleaance ype nonlneay. By assumng a peodc moon fo he vaables of dynamc model, Foue sees wll be used o expand he vaables. Ths wll lead o map he dynamc sysem fom he me doman no he fequency doman. Usng he sandad echnque of hamonc balance, he dynamc analyss of a mechancal sysem wh combned paamec excaon and cleaance ype nonlneay s pesened by Blankenshp and ahaman [34]. Anohe use of hamonc balance mehod s pesened by Leamy and Pekns, whle hey obaned he nonlnea peodc esponse of engne accessoy dves wh dy fcon ensones [35]. An expemenal dynamc analyss of sysem wh a cleaance nonlneay ncludng a spag-ype one-way cluches fo an a ubne sae n e engnes s pesened by Venay e al. [5]. Ths wok denfed sldng dung engagemen of he cluch. ng and Monahan nvesgaed he funconal deals of a wap-spng ype of one-way cluch [53]. An oveunnng alenao pulley ha s vey smla o poposed one-way cluch was analyzed n a epo pesened by Solfank and elm [57]. The cluch was a speed dependen a speed-dependen dampng elemen paallel wh a spng. Fne elemen sudes of bel ceep on he pulley s pefomed by Solfank and elm [57]. Ths wok descbed he dynamc behavou of a bel dve sysem by lookng a he dy fcon beween he pulleys and he bel. The model assumed popoonal oque o pulley load speed fo a one-way cluch. Dy fcon s anohe ype of nonlneay ha possesses smla behavou o he cleaance ype nonlneay. Sudyng he dy fcon dampng n bel dve sysems ae 33

48 suded by analyzng he Coulomb dampng a he ensone pvo. Bake e al. modeled a Coulomb-damped ensone am and solved he equaons of moon by employng Runge-ua numecal negaon [63]. A complex modal analyss pocedue fo a bel dve sysem s pesened by ave e al. [64] consdeng equvalen vscous dampng n ode o model he ensone am wh dy fcon dampng. Leamy and Pekns, [35] used smla model o [7] and added a fcon dampe a he ensone am pvo. A fouh/ffh ode Runge-ua mehod was employed o solve he nonlnea equaons of moon. In hs wok, he nonlnea dynamc effecs of he fcon wee descbed and he mpac of a ensone wh fcon was examned. Alhough he dynamc behavou of sysems wh movng bel s well suded; dynamc analyss of a mophng pulley ansmsson sysem has no been found n he leaue. A gea deal of n-deph dynamc analyss s equed fo desgnng he ensonng mechansm and he vbaon educon sysem. I s also necessay o develop a dynamc model of he ansmsson sysem ha povdes he necessay npu fo he sucual desgn of he sysem. Hence, hs docoal eseach s focused on he sudes of he nonlnea dynamc behavou of he mophng pulley ansmsson sysem..5 OBJECTIVES Ths docoal eseach s focused on he analycal sudes of he dynamc behavou of he mophng pulley bel dve ansmsson sysem. The scope of wok ncludes desgnng a ensonng mechansm fo mananng an appopae ange of peenson n dffeen dve aos. In addon, desgn and analyss of a passve vbaon 34