KINEMATICS OF TWO SIMPLE PLANETARY GEARS

ARPN Journl of Engineering nd Applied Sciences 2006-2017 Asin Reserc Pulising Network (ARPN). All rigts reserved. www.rpnjournls.com KINEMATICS OF TWO SIMPLE PLANETARY GEARS V. I. Nekrsov 1, O. O. Gorskov 1, R. A. Zignsin 1, N. S. Zkrov 1 nd G. N. Spitko 2 1 Tyumen Industril University, Tyumen, st. Volodrskogo Russi 2 Kurgn Stte University, st. Gogoly,Kurgn, Russi E-Mil: ettm@k.ru ABSTRACT Multi-speed plnetry ger trnsmissions (PGTs) ve limited ppliction. Two nd tree-speed plnetry ger trnsmissions were used in GGT (ydromecnicl trnsmission); in recent yers te numer of gers in GGT s een growing. Wit te increse of te numer of ger, te complexity of te PGT is growing significntly. Te PGT wit two degrees of freedom for 8 gers requires 24 gerweels nd for 16 gers it requires 48 gerweels. Tis rticle descries te structurl metods of reliztion of te kinemtic cpcities of two simple tree-link plnetry gers connected in series. Keywords: simple plnetry ger, sun ger, crrier, stellites, epicyclicl weel, kinemtics, structure. 1. INTRODUCTION Te modern LTVs (Lnd Trnsport Veicles) including rod trins require te ppliction of te multispeed trnsmissions tt provide te optiml opertion mode of te engine in te wide rnge of opertion conditions. 16-speed trnsmissions of te modern rod trins ve rnge (reduction rtio of lower nd upper gers) D 17, intervl (reduction rtio of te neigouring gers) q 1.21. Te trditionl metods of design led to te increse of te dimensions nd weigt of te trnsmission units. More often, te plnetry gers re used in suc trnsmissions. Te plnetry gers re instlled on te output of te MGB (multi-speed ger ox) in te weel reduction gers or finl reduction gers, in PGBs (plnetry ger oxes) consisting of severl rows of plnetry gers. Plnetry gers nd teir vrint - rmonic drives tt re crcterized y te smll dimensions nd weigt stisfy more completely te requirement to te decrese of te specific mount of metl of te mcines mong ll types of mecnicl gers. Tis is connected to te multitreding effect nd te ppliction of te internl tooting [1]. 2. KINEMATIC CAPACITIES OF TWO SIMPLE PLANETARY GEARS WITHOUT INTERFACE REDUCER Te increse of te use efficiency of gerweels cn e reced due to te more complete use of te kinemtic cpcities of plnetry gers. A simple PG consisting of te tree links: sun ger (), n epicyclic weel () nd crrier () wit stellites is crcterized y te internl prmeter K = Z /Z = 1.5-5, wic is equl to te numer of teet Z of te epicyclic weel nd Z of te sun ger. It cn provide 7 gers in te ger modes, 5 forwrd gers: 1) U = K +1; 2) U = (K+1)/K; 3) direct ger U = 1.0; 4) U = K/(K+1); 5) U = 1/(K+1); two reverse gers: 1R) U = -K; 2R) U = - 1/K. A sign "-" points out te cnge of direction rottion of te link in te output of te plnetry ger. Te upper index points out te stopped link, te lower indices point out te links of input nd output of te torsion torque. For exmple, te first slow ger U is relized t te stopped epicyclic weel (), wen te torsion torque is delivered to te sun ger () nd wen te torque is removed from te crrier (). Te PG cn lso provide 3 gers in te integrtion modes wen te torsion torque is delivered to te two links wit te different rottionl rte nd it is removed from te tird one. Te kinemtic cpcities of te trnsmission unit increse significntly t te series connection of two plnetry gers. At lest 5 5 = 25 vrints of te forwrd gers cn e cieved nd lso te dditionl gers wen te reverse gers re ctivted in series. Figure-1 sows te kinemtic sceme of te trnsmission unit type 10R4 (10 forwrd gers nd 4 reverse gers), consisting of two simple plnetry gers connected in series nd its ry digrm wit te tles of te clutces positions. Te upper positions of te ger clutces correspond to te ger: 1R) U = -K; te lower positions: 1) U = K +1. Te kinemtic cpcities of te units re convenient to represent in form of te ry digrms. Te orizontl scles re te vlue of te reduction rtio in te logritmic form. On te low orizontl te upper scle is uniform in te logritmic scle; te lower scle is vlue of te reduction rtio in te pysicl terms. Te rys emerge from te point 0. Te rys directed to te rigt point out te decelerting gers, te fltter te ry, te igger te reduction rtio. Te verticl ry crcterizes te ger wit U = 1.0. Te rys directed to te left point out te ccelerting gers, te fltter te ry, te smller te reduction rtio. 3486

ARPN Journl of Engineering nd Applied Sciences 2006-2017 Asin Reserc Pulising Network (ARPN). All rigts reserved. www.rpnjournls.com Figure-1. Kinemtic sceme of te trnsmission unit type 10R4, consisting of te simple plnetry gers connected in series nd its ry digrm. Te work of te unit is clerly seen. For exmple, t te first ger (see te tle ove) te torsion torque from te input sft is trnsmitted y te clutc A in te left (L) position to te ring ger, te centrl sft nd te sun ger () of te first PG wit K 1 = 1.62. Te clutces B nd F re in te rigt (R) neutrl position. Te clutc C lso in te rigt position stops te epicyclic weel () regrding te csing. Te clutc D in te middle (M) position delivers te incresed torsion torque from te crrier () to te ring ger of te input sft of te second PG wit K 2 = 3.3. Te clutc E in te left (L) position delivers te force to te centrl sft nd te sun ger () of te second PG. Te clutc is in te rigt (R) neutrl position. Te clutc G lso in te rigt position stops te epicyclicl weel () regrding te csing. Te clutc H in te middle (M) position delivers te torsion torque from te crrier () to te ring ger of te output sft. On te ry digrm, two rys correspond to tis ger U from te point 0 to te rigt nd up to te point 1 on te upper orizontl. Te reduction rtio of te first ger will e U 1 = (K 1 +1)(K 2 +1) = (1.62+1)(3.3+1) = 11.27; lq U 1 = 1.05. For te 10 t ger U 10 = 1/U 1 = 1/11.27 = 0.089; lq U 10 = -1.05. Te rnge of te unit is very ig D = U 1/U 10 = 11.27/0.089 = 126.6. A simple series connection of two plnetry gers does not provide te necessry effect. As Figure-1 sows, every PG cn relize only tree forwrd gers (two gers t te stopped epicyclic weel (), one is direct ger) nd one reverse ger t te stopped crrier (). As result, 10 reverse gers were otined (1 10 ove te upper orizontl, 3 3 = 9 + 1 ger wen connecting te reverse gers - 2 nd ger) nd 4 reverse gers (1R-4R under te lower orizontl). Te gers re not optimlly locted, symmetriclly to te point 0; tis point sould e closer to te ger 10. Te intervls etween te gers re too ig nd tis mkes te ger cnge more difficult. Te direct connection of two plnetry gers excludes te gers wit te stopped sun ger (), te interfce reducer etween te plnetry gers is necessry. Te prolems of coordintion of two plnetry gers rise. It is necessry to select te internl prmeters K of te plnetry gers in te wy tt te igger numer of gers cn e relized t teir rtionl distriution in te rnge D. In Figure-2, te two ry digrms re sown: ) K 1 = 1.62 nd ) K 1 = 2.0; tey crcterize te work of two plnetry gers connected in series. 3487

ARPN Journl of Engineering nd Applied Sciences 2006-2017 Asin Reserc Pulising Network (ARPN). All rigts reserved. www.rpnjournls.com Figure-2. Distriution of vlues of reduction rtio in te rnge wile connecting two plnetry gers wit different internl prmeters: ) K 1 = 1.62; ) K 1 = 2.0. Te five rys etween te lower orizontls reflect te work of te first plnetry ger. For exmple, in Figure-2, t K 1 = 1.62 te equl segments were otined 0.21 in logritmicl scle. From te points: -0.42; -0.21; 0.0; 0.21 nd 0.42 te verticl lines emerge. Te vlues of te reduction rtios for PG wit different internl prmeters re sown on te upper orizontls (topdown) from K 2 = 1.5 to K 2 = 5.0 t te vrious conditions of PG tt re connected y te ds lines. Te conditions of PG re sown: down to te rigt 1) U = K + 1; to te left 5) U = 1/(K+1); top to te rigt 2) U = (K+1)/K; to te left 4) U = K/(K+1); direct gers re mrked y te verticl lines coming out from te ends of rys ) K 1 = 1.62 ) K 1 = 2.0. Te segments etween te points on every line point out te intervls etween te neigouring gers. In Figure-2, it is clerly seen tt te distriution of intervls ccording to te rnges is not uniform; some points coincide lmost completely, te intervl 1.62 is too ig nd mkes te ger cnge difficult. It is preferle to ve te distriution wit smll equl intervls; tis will provide te comfort of ger cnging. Te nlysis of Figure dt 2 sows tt te distriution from te upper prt of te figure cn e used s sis. For exmple, te ry digrm in Figure-1 corresponds to te row in Figure 2, t K 2 = 3.3. 3. KINEMATIC CAPACITIES OF TWO SIMPLE PLANETARY GEARS CONNECTED BY INTERFACE REDUCER Figure-3 sows kinemtic digrm of te unit type 21R10 nd ry digrm wit te tle of position of ger clutces on te different gers for two plnetry gers configured linerly - one y one. Te first PG s K 1 = 1.62; te second PG s K 2 = 2.0; te interfce reducer is locted etween tem. Te upper positions of ger clutces correspond to te ger 1) U = K +1; te lower positions - 1R) U = -K. In te ry digrm, te input of te torsion torque into te unit is mrked y te point 0 on te tird orizontl from te ottom. It sows te vlues of te reduction rtios in te logritmic nd nturl form. Te dditionl ger 1 d, sown in te lower orizontl, is formed y te two consequent reverse gers. 21 out of 25 ger vrints cn e relized, teir distriution in te rnge is sown on te upper orizontl nd corresponds to te second upper orizontl in Figure-2,. 3488

ARPN Journl of Engineering nd Applied Sciences 2006-2017 Asin Reserc Pulising Network (ARPN). All rigts reserved. www.rpnjournls.com Te instlltion of te interfce reducer etween te plnetry gers llowed to stop te sun ger weels of te plnetry ger y te clutces D nd E, to relize te gers 2) U = (K+1)/K nd 4) U = K/(K+1), nd lso to optimize te position of te row of te reduction rtios due to te displcement to te lower gers. Wen incresing te reduction rtio of te interfce reducer te point 0 corresponding to te input sft is sifted to te left incresing te reduction rtio of te 1 st ger. Figure-3. Kinemtic digrm of te trnsmission unit type 21R10, consisting of two simpleplnetry gers wit te interfce reducer nd its ry digrm. On te first ger, te torsion torque from te input sft is delivered y te clutc A in te left (L) position to te ring ger, te centrl sft nd te sun ger () of te first plnetry ger wit K 1 = 1.62. Te clutces B nd G in te rigt (R) condition stop te epicyclic weels () regrding te csing. Te clutc C lso locted in te rigt (R) position delivers te incresed torsion torque from te crrier () to te ring ger of te driving gerweel of te interfce reducer. Te clutces D nd F re in te neutrl (N) position. Te clutc E in te rigt position delivers te torque incresed y te interfce reducer to te centrl sft nd te sun ger weel () of te second PG wit K 2 = 2.0. Te clutc H in te middle (M) position delivers te incresed torsion torque from te crrier () to te ring ger of te output sft. On te ry digrm, tree rys from te point 0 to te rigt nd up correspond to tis ger: U of te first PG, ten te ry of te interfce reducer, ten U of te second PG to te point 1 on te verticl orizontl. Te reduction rtio of te 1 st ger will e U 1 = (K 1 +1) U c.p. (K 2 +1) = (1.62+1) 2.6 (2.0+1) = 20.44; lq U 1 = 1.31. For te 21 st ger, it is U 21 = 1/(K 1 +1) U c.p. 1/(K 2 +1) = (1/2.62) 2.6 (1/3) = 0.33; lq U 21 = -0.48. Te rnge of te unit is ig D = U 1/U 21 = 20.44/0.33 = 61.9. 3489

ARPN Journl of Engineering nd Applied Sciences 2006-2017 Asin Reserc Pulising Network (ARPN). All rigts reserved. www.rpnjournls.com Te distriution of gers in te rnge is close to te optiml. Te 1 st ger wit U 1 = 20.44 provides te "creeping" motion mode, for exmple, wen mnoeuvering on te nrrow site during te lodingunloding works. 4. KINEMATIC CAPACITIES OF TWO SIMPLE PLANETARY GEARS WHEN INSTALLING ADDITIONAL GEAR BOX Te equl smll intervls etween te gers cn e provided wen instlling te dditionl ger ox in front of te plnetry ger. In Figure-4, te kinemtic digrm of te sft-plnetry MTGB (multistep trnsfer ger ox) type 16R4 (16 forwrd gers nd 4 reverse gers) nd its ry digrm. Two pirs of gerweels mrked y 1, 2, nd te clutc A tt is locted etween tem on te min sft re used in te mode of te front splitter. Te first PG (left) wit te internl prmeter K 1 = 1.62 is used on 4 forwrd motion modes nd one reverse ger. Te second PG wit K 2 = 5.5 is used s te rer dditionl reducer - uxiliry ger ox. It relizes two vrints of gers: first - direct ger - clutc F in te second (rigt) position, second - slow - clutc F in te first (left) position. On te first ger of MTGB te torsion torque during te left position of te clutc A is delivered from te min sft to te 1 pir of gerweels, lter long te clutc D in te rigt position to te drive xis of te sun ger () of te first PG. At te sme time, te clutc C is locted in te left (neutrl) position, nd te clutc D in te second (middle) position stops te epicyclic weel () regrding te csing. Te torque is removed y te clutc E in te second position from te crrier () to te drive xis of te sun gerweel of te second PG. Te clutc F in te left position of te epicyclic weel () of tis PG is lso stopped regrding te csing of te unit, incresed torsion torque from its crrier is delivered to te crrier () of te rigt PG in te mode of te nonequlizing differentil. On te ry digrm, tree rys elong to tis ger: from te point 0 on te left nd up te ry 1 to te rigt nd down, ten te ry U 1, = K 1 +1, nd te ry U 2, =K 2 + 1 to te point 1 on te lower orizontl wit U 1 = 29/1. D = U 1/U 16 = 29.51/0.785 = 37.6. Figure-4. Kinemtic digrm of MTGB type 16R4 wit two plnetry gers in te ger modes nd te rigt PG in te nonequlizing differentil mode. 3490

ARPN Journl of Engineering nd Applied Sciences 2006-2017 Asin Reserc Pulising Network (ARPN). All rigts reserved. www.rpnjournls.com 5. TECHNICAL AND ECONOMICALASSESSMENT OF MORE COMPLETE USE OF KINEMATIC CAPACITIES OF TWO SIMPLEPLANETARY GEARS Te plnetry ger oxes in comprison wit te sft-drive ger oxes possess severl dvntges: little iger coefficient of efficiency, te ig ger compctness, te decrese of te teet module wile cnging from te simple ger oxes to te plnetry ger oxes; it provides te increse of te lifetime, noiselessness of opertion, te iger reduction rtio for te sme dimeters of te gerweels cn e otined. Te increse of te numer of gers mkes te plnetry ger oxes more complicted. Plnetry ger oxes wit two degrees of freedom for 8 gers require 24 gerweels, nd for 16 gers tey require 48 gerweels. Te numer of degrees of freedom is one ger more tn te numer of te control elements ctivted on one ger. Te numer of gerweels decreses significntly t tree degrees of freedom of te PG - 12 nd 16 gerweels correspondingly [2]. Even t tree freedom degrees of te plnetry ger ox te efficiency of use of te gerweels is not ig, te intensity coefficient of te use of te gerweels equl to te rtio of te numer of forwrd gers to te numer of used gerweels for it Ki = 8/12 = 0.67 nd Ki = 16/16 = 1.0 is not ig. Te iger Ki, te smller te dimensions nd te specific mount of metl of te unit re [3]. Te considered digrm of te MTGB in Figure- 4 simplifies te trnsmission of te veicle, reduces its dimensions nd weigt. For exmple, 16-stepped rtio ger trnsmission of te veicle KrAZ-260 consists of two mssive units (ger ox 340 kg nd trnsfer ger ox 360 kg), 20 gerweels nd differentil on 9 sfts nd one xis controlled y seven clutces; distriution of ger is not optiml in te rnge equl to 14.08; te intervls re cnging from 1.08 to 1.29. Ki = 16/20 =0.8 is lso not ig. At te digrm type 16R4, sown in Figure-4, t teir optiml distriution in te incresed rnge te sme 16 gers re provided y six gerweels of te externl tooting, tree plnetry gers nd seven clutces [3]. Trnsmission unit type 21R10, sown in Figure 3, s ig indictor of efficiency of te use of gerweels. Tking into ccount tt every PG consists of five gerweels, we will get Ki = 21/(2 5 + 2) = 1.75. REFERENCES [1] Kudryvtsev V.N. nd Kirdysov Y.N. (Eds.). 1977. Plnetrnye peredci. Sprvocnik [Plnetry Trnsmission. Guide]. Leningrd: Msinostroenie. p. 536. [2] Nosov N.A. 1972. Rscet i konstruirovnie gusenicnyk msin [Clcultion nd Design of Trck-Lying Veicles]. Leningrd: Msinostroenie. p. 560. [3] Nekrsov V.I. 2001. Mnogostupencty trnsmissiy. Konstruktsiy, konstruirovnie i rscet: Ucenoe posoie [Multi-Stepped Trnsmission. Structure, Design nd Clcultion: Tecing Guide]. Kurgn: Pulising House of Kurgn Stte University. p. 155. 8. SUMMARY Te more complete use of kinemtic cpcities of two simple plnetry gers connected in series decreses significntly te dimensions nd te specific mount of metl of te trnsmission units, te effect intensifies due to te instlltion of interfce reducer nd dditionl ger ox in front of te PG etween te plnetry gers. 9. CONCLUSIONS Te offered metod of design llows creting te competitive compct trnsmission units of low specific mount of metl. 3491