Power Flows and Torque Analyses of an Independently Controllable Transmission with a Parallel Type

Transcription

1 roceedgs of the World Cogress o Egeerg 0 Vol III, July 6-8, 0, Lodo, U.K. ower Flows ad orque alyses of a Idepedetly Cotrollable rasmsso wth a arallel ype Gua-Shyog Hwag*, Chug-Ch L, Der-M say, Jao-Hwa Kuag, ad zue-lh Cher bstract depedetly cotrollable trasmsso (IC) wth a rallel type s a ovel, ftely, ad cotuously varable trasmsso mechasm. he rallel type IC ca produce a requred agular velocty, whch s depedetly cotrolled by a cotroller ad ot affected by the agular velocty of the put power shaft. hs study derves the equatos of power flows ad s troduced the rallel type IC. prototype of the rallel type IC s mplemeted for demostrato, ad correctess of the derved equatos s vestgated by the expermet of statc for the prototype. Idex erms depedetly cotrollable trasmsso (IC) wth rallel type, plaetary gear tra, trasmsso-coectg member, free-trasmsso ed I. IRODUCIO the automato egeerg, may applcatos have Iwdely employed ftely ad cotuously varable trasmsso (IV, CV), because CVs are cable of provdg ay rato betwee ad put speeds. By CVs cotuous rages of trasmsso ratos ad depedet trasmsso of selected s, the optmal codtos of power trasmssos ca be acheved. herefore, to desg a effcet CV s frequetly a mportat ad terestg topc for may researches. Varous researches have focused o the desg of CV. For example, Gott classfed cotuously varable trasmssos to be four dfferet categores: tracto, belt, ratchetg, ad hydraulc systems []. Muco et al., preseted the system of cotuously varable power splt Mauscrpt receved March 8, 0; revsed prl 7, 0. hs work was supported by the atoal Scece Coucl of awa uder the grat (SC E-0-00). Gua-Shyog Hwag s wth the Dertmet of Computer Scece ad Iformato Egeerg, ahua Uversty, Cha-y Couty 648, awa (*Correspodg author, phoe: ; fax: ; e-mal: gshwag@mal.hu.edu.tw). Chug-Ch L s wth the Dertmet of Mechacal & Electro-Mechacal Egeerg, atoal Su Yat-Se Uversty, Kaohsug 8044, awa (e-mal: m @studet.sysu.edu.tw). Der-M say s wth the Dertmet of Mechacal & Electro-Mechacal Egeerg, atoal Su Yat-Se Uversty, Kaohsug 8044, awa (e-mal: derm@mal.sysu.edu.tw). Jao-Hwa Kuag s wth the Dertmet of Mechacal & Electro-Mechacal Egeerg, atoal Su Yat-Se Uversty, Kaohsug 8044, awa (e-mal: kuag@faculty.sysu.edu.tw). zue-lh Cher s wth the Dertmet of Electrcal Egeerg, atoal Su Yat-Se Uversty, Kaohsug 8044, awa (e-mal: tlche@ee.sysu.edu.tw). ISB: ISS: (rt); ISS: (Ole) trasmsso (CVS), whch cossts of a varable pulley set couplg a plaetary gear tra []. arrsh proposed CV mechasms comprsg frst ad secod plaetary gear sets [3]. Betez et al., descrbed a IV cludg oe-way clutches ad two plaetary gear tras [4]. Hsu ad Huag preseted a systematc methodology to effectvely smplfy the desg of automatc trasmssos wth rallel-coected plaetary gear tras [5]. Bottgloe ad Matrota proposed a MG-IV, whch s composed of the couplg of a CV, a plaetary gear tra ad two ordary trasmssos wth a costat trasmsso rato [6]. Lahr ad Hog preseted the cam-based IV of ratchetg drve type [7]. ovel mechasm wth a depedetly cotrollable power trasmsso, referred to as a depedetly cotrollable trasmsso (IC) wth a rallel type, had bee proposed the prevous studes [8-9]. d the kematc characterstcs of the rallel type IC also had bee demostrated. he rallel type IC s a ftely ad cotuously varable trasmsso mechasm, ad ca produce a requred agular velocty, whch s depedetly cotrolled by a cotroller ad ot affected by the agular velocty of the put power shaft. he rallel type IC, for example, could be utlzed the automatc trasmsso systems ad the varable speed wd turbes. hs study derves the equatos of power flows ad s troduced the rallel type IC. prototype of the rallel type IC s mplemeted for demostrato ad the correctess of the derved equatos s vestgated by the expermet of statc for the prototype. II. RLLEL YE IC rallel type IC s a trasmsso mechasm possessg four rotatoal shafts used to coect to the put power source, the power ed, the cotroller, ad the free-trasmsso ed, respectvely. s depcted Fg., a rallel type IC s composed of two plaetary gear tras, respectvely dcated by ad B, ad two trasmsso-coectg members, respectvely dcated by D ad E. Each plaetary gear tra has three rotatoal shafts dcated by O, D, E ad CR, BD, BE, respectvely. I plaetary gear tra, shaft O coects to the power ed ad shafts D, E coect to trasmsso-coectg members D ad E, respectvely. I plaetary gear tra B, shaft CR coects to the cotroller ad shafts BD, BE also coect to the trasmsso-coectg members D ad E, respectvely. I trasmsso-coectg member D, shaft

2 roceedgs of the World Cogress o Egeerg 0 Vol III, July 6-8, 0, Lodo, U.K. SD could coect to the source of put power, whereas trasmsso-coectg member E could coect to the free-trasmsso ed by shaft SE.. Basc Requremets of Kematcs o acheve the fucto ad performace of the rallel type IC, the former study had establshed the basc requremets of kematcs as follows [8]: () BD D () CR O BE E (3) where deotes the agular velocty of the rotatoal shaft dcated by ts subscrpt, α ad β are the costat multples. he kematc rameters α ad β ca be used to determe the speed ratos betwee the rotatoal shafts, ad the the cofgurato of the IC mechasm. B. ostve-rato laetary Gear ra postve-rato plaetary gear tra, used ths study ad show Fg., cludes a frst su gear ps mouted o the rotatoal shaft pss, a secod su gear ps mouted o the rotatoal shaft, at least oe compoud plaet gear set cludg gears pp, pp, as well as meshg wth the frst ad secod su gears, ad a plaet gear carrer. postve-rato plaetary gear tra meas that the shafts of the frst ad secod su gears, whe the carrer s fxed, have the same drecto of rotato. herefore, ts basc speed-rato, whch s defed as the rato of the relatve veloctes of the two su gears shafts respectvely wth respect to the carrer, s cosequetly postve ad caot be equal to [0]. he basc speed-rato of a postve-rato plaetary gear tra, deoted by 0, ca be also mathematcally expressed as 0 pss pp ps (4) ps pp where s the teeth umber of the gear dcated by ts subscrpt. Output ower Iput ower O SD D D BD B E BE E SE CR Free-rasmsso Cotroller C. rragemet of the arallel ype IC practcal arragemet of the rallel type IC s schematcally show Fg. 3. I the postve-rato plaetary gear tras ad B, the shafts of the frst su gears pss ad, smlar to the shafts O ad CR show Fg., are coected to the power ed ad the cotroller, respectvely. he fucto of the rotatoal shafts,, ad B are also smlar to those of the shafts D, E, BD ad BE, respectvely. herefore, by referrg to Eqs. () ad (3), the followg equatos ca be also obtaed (5) cmg3d pss B or cmg3e cmg E (6) I the trasmsso-coectg members D ad E, the rotatoal shafts cmsd ad, smlar to the shafts SD ad SE show Fg., are coected to the put power source ad the free-trasmsso ed, respectvely. ccordg to Eq. (4), the basc speed-ratos of the plaetary gear tras ad B, deoted by 0 ad 0 B, ca be rewrtte as follows: 0 pss pp ps (7) B ps psb pp ppb psb (8) ppb D. Desg Formulas of arallel ype ICs ccordg to the former study [8], the desg formulas of the rallel type IC had bee derved as follows: 0 0, ( ) f, ad f III. OWER FLOWS D ORQUE LYSES I ths study, a put shaft s defed as troducg a postve power to the IC ad cosequetly the ad the speed have the same sese of rotato ad carry the same sg. Coversely, a shaft troduces a egatve power whle the ad the speed carry opposte sgs. he power troduced by the shaft of the IC ca be (9) Fg.. Coceptual structure of the IC wth a rallel type pss pss pp pp ps ps Output ower Iput ower Cotroller D cmgd pss cmsd cmgd cmg3d pp ps ppb psb B pp ps pp B B ps B E cmge cmge cmg3e Free-rasmsso Fg.. ostve-rato plaetary gear tra Fg. 3. rragemet of IC wth a rallel type ISB: ISS: (rt); ISS: (Ole)

3 roceedgs of the World Cogress o Egeerg 0 Vol III, July 6-8, 0, Lodo, U.K. mathematcally expressed as (0) where ad deote the power ad troduced by the shaft dcated by ts subscrpt, respectvely.. ower Flows ad orque alyses of a laetary Gear ra Whle eglectg frcto losses, the sum of power troduced by a plaetary gear tra show Fg. wll be zero accordg to the coservato of eergy,.e. 0 () pss I a statoary operatg codto, a plaetary gear tra wll also yeld the equlbrum codto that the sum of all exteral s actg o the shafts s equal to zero,.e. [0-] 0 () pss By referrg to Eqs. (4), (0)-(), the followg results ca be also obtaed (3) 0 pss ( 0 ) pss (4) B. ower Flows ad orque alyses of a arallel ype IC Whe cosderg the rallel type IC show Fg. 3, the power troduced by the cotroller shaft ca be mathematcally expressed as cotroller cotrollercotroller pss B (5) pss where pss, accordg to Eq. () ad the smlar fucto betwee the shafts pss, ad the shaft O, CR, respectvely. he put power s trasmtted to the plaetary gear tras ad B by the shafts ad, therefore t ca be expressed as put putput cmsdcmsd (6) Referrg to Eqs. (9) ad (4) yelds ( ) ( 0 ) pss pss ( ) ( ) pss B pss B (7) (8) By substtutg the results of Eqs. (5), (7), ad (8) to Eq. (6), the put power ca be rewrtte as ( ) ( ) ( ) put pss (9) he troduced by the shaft pss ca be derved by rearragg Eq. (9),.e. ( ) (0) put pss pss B ( ) By substtutg ad referrg to the results show Eqs. (5) ad (0), the power troduced by the shaft pss ca be obtaed as pss pss ( ) pss () put cotroller ( ) From Fg. 3, the power troduced by the free-trasmsso ed s freetrasmsso freetrasmsso freetrasmsso B B Referrg to Eqs. (7), (9), ad (3) also yelds 0 pss 0 0 ( ) ( ) pss ( ) 0 pss pss B pss B ps () (3) (4) (5) By substtutg the results show Eqs. (6), (0), ad (3)-(5), the power troduced by the free-trasmsso ed ca be rewrtte as pss ( ) freetrasmsso ( ) put (6) he show Eq. (0) ca be further rewrtte as where pss cmgd 0 cmsd. cmgd put cotroller (7) From Eqs. () ad (6), the troduced by the free-trasmsso shaft ca be also rewrtte as where freetrasmsso 0 0 cmge cmg E. cmgd cmge cmg E put IV. DEMOSRIO OF IC ROOYE (8) o vestgate ad demostrate the correctess of the aalyses show the prevous secto, ths study proposes a prototype of the rallel type IC ad mplemets a test-bed of the prototype for expermet.. Dmesoal arameters of IC rototype Fgure 4 schematcally shows the desg of the prototype of the rallel type IC. I the IC prototype, the costat multples show Eqs. () ad () are chose to be ad. 5. ccordg to Eqs. (7) ad (8), the basc ISB: ISS: (rt); ISS: (Ole)

4 roceedgs of the World Cogress o Egeerg 0 Vol III, July 6-8, 0, Lodo, U.K. speed-ratos of the plaetary gear tras ad B wll be 0 3 ad 0. 5, respectvely. By referrg to Eqs. (5)-(8), the teeth umbers of the gears used the IC prototype are chose as lsted able. By substtutg the teeth umber, the basc speed-rato ad the costat multple, Eqs. (7) ad (8) ca be obtaed as follows:.4. 5 (9) put cotroller free trasmsso put (30) 3 B. Expermetal Results of IC rototype ad Dscusso Fgure 5 llustrates the cofgurato of expermetal test-bed of the IC prototype, ad Fg. 6 shows the test-bed the expermet of statc. able shows the obtaed expermetal data, ad Fg. 7 s a plot about the calculatg values ad the least square approxmato of (.5cotroller ) / put ad free trasmsso / put. he BLE. ORQUE VLUES (m) put cotrollert free trasmsso B BLE. EEH UMBERS OF GERS USED I IC ROOYE Gear cmgd cmgd cmg3d cmge cmge cmg3e ps eeth umber Gear ps pp pp psb psb ppb ppb =. 5 put cotroller, B= free trasmsso put eeth umber theoretcal values of (.5cotroller ) / put ad free trasmsso / put are.4 ad /3 accordg to Eqs. (9) ad (30). he results of the least square approxmato, calculated by Mcrosoft Excel, about the expermetal values are.38 ad By comrg the approxmate equalty betwee the theoretcal ad expermetal values of (.5cotroller ) / put ad free trasmsso / put, the match of these values ca be cocluded. herefore, the correctess of the derved equatos has bee verfed. Fg. 4. rototype of the rallel type IC IC strumetato amplfer trasducer KYOW WGI-400 KYOW -5KMCB strumetato amplfer trasducer KYOW WGI-400 KYOW -5KMCB sgal V. COCLUSIOS I ths study, the power flows ad aalyses of the rallel type IC are vestgated ad ther aalytcal equatos are derved. prototype of the rallel type IC s mplemeted for demostrato ad the correctess of the derved equatos has bee vestgated ad verfed. Because the rallel type IC ca produce a requred agular velocty, whch s depedetly mapulated by a cotroller ad ot affected by the put agular velocty, t could be appled to varable speed wd turbes ad automatc trasmsso systems. he further researches about the performace ad applcato of the rallel type IC are also proceedg. Fg. 5. Cofgurato of test-bed ISB: ISS: (rt); ISS: (Ole)

5 roceedgs of the World Cogress o Egeerg 0 Vol III, July 6-8, 0, Lodo, U.K Fg. 6. test-bed of IC prototype expermet values for free trasmsso put expermet values for. 5cotroller put least square approxmato freetrasmsso of put least square approxmato of.5cotroller.38 put REFERECES []. G. Gott, Chagg gears: he developmet of the automotve trasmssos, 99, SE, Warredale,. [] V. H. Muco, Z. Lu, J. E. Smth, M. Kmckewcz ad B. Cowa, Desg of cotuously varable power splt trasmsso systems for automotve applcatos, roc. IMechE, art D: J. utomoble Egeerg, 00, Vol. 5(4), [3] B. E. arrsh, Cotuously varable trasmsso, US atet B, 00. [4] F. G. Betez, J. M. Madrgal ad J. M. del Castllo, Iftely varable trasmsso of ratchetg drve type based o oe-way clutches, SME J. Mech. Des., 004, Vol. 6(7), [5] C. H. Hsu ad R. H. Huag, Desg of rallel-coected Epcyclc-type automatc trasmssos wth two fudametal geared ettes, roc. IMechE, art D: J. utomoble Egeerg, 008, Vol. (3), [6] F. Bottgloe ad G. Matrota, MG-IV: ftely varable trasmsso wth optmal power flows, SME J. Mech. Des., 008, Vol. 30(), 603. [7] D. Lahr ad D. Hog, Operato ad kematc aalyss of a cam-based ftely varable trasmsso, SME J. Mech. Des., 009, Vol. 3(8), [8] G. S. Hwag, D. M. say, J. H. Kuag ad. L. Cher, Kematcal aalyss of a ovel trasmsso mechasm wth steady-speed for varable speed wd turbes, 00, roceedgs of SME urbo Expo 00: ower for Lad, Sea ad r, Jue 4-8, Glasgow, UK. [9] G. S. Hwag ad D. M. say, Idepedetly cotrollable trasmsso mechasm, awa atet I3973, 00 ( Chese). [0] H. W. Muller, Epcyclc drve tras, aalyss, sythess, ad applcatos, 98, (Waye State Uversty ress, Detrot). [] E. eestr ad F. Freudeste, systematc approach to power-flow ad statc-force aalyss epcyclc spur-gear tras, SME J. Mech. Des., 993, Vol. 5(3), Fg. 7. lot of expermetal values CKOWLEDGME he facal support of the atoal Scece Coucl of awa uder the grat (SC E-0-00) s gratefully ackowledged. ISB: ISS: (rt); ISS: (Ole)