GDS- 11 POWER FLOW OF DOUBLE LOOPED PLANETARY GEAR SYSTEM

Transcription

1 MPT00- Fkoka The JSME international onferene of Motion and Power Transmission No.5-7,00, Fkkoka,Japan GS- POWER FLOW OF OUBLE LOOPE PLANETARY GEAR SYSTEM *Tsnei YAA YAA Engineering Conslting Offie -7-8 Komaba, Toride, Ibaraki, Japan NNT-Y@asahi-net.or.p Keyword : Power Transmission, Planetary Gear, Power Flow, Transmission Ratio, CVT Abstrat The doble looped planetary gear system (LPS is omposed with two sets of the single looped planetary gear system (SLPS that inldes a planetary gear mehanism and a ontinosly ariable transmission (CVT. epending on opied position of CVT inside LPS, LPS is diided to two types: exlsie CVT and inlsie CVT type. LPS is possible to ontrol otpt speed sensitiely by CVT. and sable for a transmission of hybrid ehiles. Bease LPS has two loop irits from the topologial point of iew, arios types of power flow appear in the irit. This paper deals with lassifiation of the power flow type of LPS. At first, the athor introdes the harateristi diagram regarding to anglar eloity of planetary gear mehanism, that explains lassifiation of power flow of SLPS and speed ariation range inded by CVT operation. Seondly onsidering diiding ondition of power flow in a planetary gear mehanism, he intends to apply the diagram to LPS and presents an extended diagram that shows ombination of power flow of SLPS. Moreoer, following explanation abot the extended diagram, he presents a table showing whole type of power flow of LPS. Finally a pratial example of LPS and its power flow are explained.. P refae system forms two loops topologial irit. Therefore the LPS seems to be onstrted with two sets of SLPS and makes many kinds of onstrtion type by ombination of shaft onnetion. Eery onstrtion type has its own type of power flow restrited by its kinematis ondition. For the sake of abndant ariation of this system design of LPS is ery omplex. Therefore there were no design methods of LPS in well prospet. This paper presents a new method for designing LPS by extending the diagram deeloped for designing SLPS. K Type Positie iretion of Vetors and M K-H Type Fig. Generalized Planetary Mehanism K-H-V Type The system that is onstrted with a planetary gear mehanism and a CVT has been sed onentionally for atomotie transmission. In this paper sh system is named as a single looped planetary gear system (SLPS. SLPS has arios types of onstrtion depending on how to onnet a CVT with three kinds of element of planetary gear mehanism: sn gear, planetary gear and internal gear. Bease of arios ombination of its onnetion, it was ery diffilt to design an optimal SLPS. Therefore, designing SLPS, a designer had been onstrained to rely pon his own experiene. For the prpose to sole the omplex problem, the athor already introded a harateristi diagram regarding to anglar eloities of planetary gear mehanism and presented a design method to be able to oerlook whole systems of SLPS. By the way thogh the power flow type of SLPS is aried aording to onstrtion of system, sine the presented diagram shows kinematis ondition of SLPS, power flow style an be indiated by loation of ation point of the system in the diagram []. The doble looped planetary gear system (LPS is onstrted with a CVT and two sets of planetary gear mehanisms. One of shaft of eah planetary gear mehanism in the system is onneted with CVT and the 78. Planetary gear mehanism and its harateristis Planetary gear mehanism has basially three kinds of shaft onneted with eery element: sn gear, arrier and internal gear. Aording to Rssian lassifiation of planetary gear mehanism, H indiates arrier and K sn gear or internal gear the enter of whih oinides with the enter of mehanism. Therefore K-H type is the most general mehanism shown as Figre that has, as an element, sn gear, internal gear and arrier. This paper takes p K-H type, bt the reslts of the paper an be extended to other types: K and K-H-V. Here etor parameters of the mehanism are denoted as follows: anglar eloity, torqe M and power P. In this paper transmission ratio is defined as a ratio between two anglar eloities and is indiated by as a symbol for the prpose of distintion from standardized transmission ratio i whih defines the ratio as na/nd where na is rotational speed of drien gear and nd is that of driing gear. Therefore the ratio i is explained by absolte ale, bt the transmission ratio has a sign and does not depend on role whih gear is driing. As a matter of orse the is a fntion of the nmber of gear teeth. Moreoer the relatie transmission ratio b a is

2 MPT00- Fkoka The JSME international onferene of Motion and Power Transmission No.5-7,00, Fkkoka,Japan denoted by a ratio of relatie anglar eloity to the eloity a of element a, and its definition is as follows: a b ba b a = a a = b ab = (Willis s Formla A blak box introded in the paper explains the general planetary mehanism that has three terminals onneted with elements of planetary mehanism. Here eah terminal is independent on whih element of planetary gear mehanism is onneted with the shaft of blak box. By the aboe definition ( Willis's formla aording to relatie transmission we an introde following basi formlas that defines general relation among anglar eloities in planetary gear mehanism In the aboe eqations the sffix nmber of eery parameter orresponds to the nmber of terminal of blak box that indiates shaft end able to onnet with a shaft of other deies loated in the ot side of the planetary mehanism. These relations an be represented by a line J in Cartesian o-ordinate [], the ertial and horizontal axis of that are gien as ratios of anglar eloities / and / shown in Fig.. Now this oordinate is named as the harateristi diagram. In this figre J line passes always throgh a point (, and its tangent is gien by. Sine tangent is gien by onstrtion of planetary mehanism, eery J line represented in the ba ( harateristi diagram orresponds to their own planetary one. Therefore radiated line grop of J passing throgh a point (, represents whole planetary mehanism denoted by haing three elementary shafts. On the other way the denoted by Eq.( explains power diiding relation between two terminals and []. Moreoer the an be allated from / that is X axis and from that proides J line. Let s name the as power diiding fator. P = P = Here the sign of represents the diretion of power flow, bease pls sign of indiates that both diretions of power flow P and P of two terminals are the same eah other, and also mins sign explains riers diretion eah other. Table shows the relation erss power flow behaior. In the eqation (, defines J line and / is gien by horizontal axis of the oordinate. Therefore the power diiding fator orresponds to eery point on J line as shown in Fig.. From the aboe relation ( Fig. Relation and J line ( Fig. Charateristi Coordinate Table Power flow type and power diiding fator 79

3 MPT00- Fkoka The JSME international onferene of Motion and Power Transmission No.5-7,00, Fkkoka,Japan between and J line, we an say that eery point along J line indiates power diiding relation and operational behaior of planetary mehanism. Therefore whole area in the harateristis oordinate lassifies power flow diretion and distribtion of power between two terminals and as shown in Fig.. In the ase where two shafts of a planetary mehanism are onneted with other mehanism R and a losed looped planetary mehanism (CLPM is onstrted as shown in Fig.5, the relationship between / and / of an otside mehanism R is represented by a line T passing throgh the origin of the harateristi diagram. Therefore two lines J and T interset at a point tp. This rossing point tp is the ation point at whih power flow behaior is indiated in Fig.. If the otside mehanism is CVT (Continos Variable Transmission, the inlination of T line that is gien by transmission ratio aries ontinosly and then the rossing point moes along J line. Therefore power distribtion among elementary shafts and power flow diretion of eery shaft aries in aordane with the position of ation point on J line.. Behaior of LPS. J line of LPS Preios setion shows that J line represents power flow behaior of CLPM that is onstrted by one planetary mehanism and one CVT. Sh system is alled as the single looped planetary gear system (SLPS. Here or sbet is the system LPS that has two sets of planetary mehanism and one CVT. This system is lassified with two types as shown in systematial figre (Fig.6. Howeer sine the type (b (exlsie CVT type in this figre an be treated as the same as the preios stdied system (CLPM, this paper will stdy on the type (a that is inlsie CVT type. In the sbet system eery planetary mehanism and has own relationship among anglar eloities as follows: + ( + ( Moreoer two terminals and are onneted with R (CVT haing transmission ratio r, and there is following relationship between eloities of these two terminals ( = r ( â á á á ã â â á á á ã á á á á â ã ã â ã Fig.5 CLPM and relation between T and J line Using X-Y oordinate the axis of whih is denoted as X = Y =, two J lines explained by the eqation ( are drawn as Fig.7 []. In this figre Ja line passes throgh two points (, 0 and (,, and the other line Jb passes throgh two points (, 0 and (, /r. Bease the transmission ratio r aries ontinosly, inlination of Jb line hanges and Jb is represented by grop of radiation line the enter of whih is loated at the point (, 0. Therefore interseting point of two J lines moes on Ja line shown as a broad line R (b R Eqialent system Fig.6 System of LPS 80

4 MPT00- Fkoka The JSME international onferene of Motion and Power Transmission No.5-7,00, Fkkoka,Japan J b Fig 7 Two J lines of LPS (,r max (,r min ab in Fig.7. This broad line represents operational area of the system LPS.. Power diiding fator of LPS Eah planetary mehanism or has own power diiding fator, where =PP for and is represented as = P5P.. Bease is gien by a fntion of (= X, we an obtain the following formla: P X 5 = =, = = (5 P X P X where X is the ale of X axis at the ross point tp of two J lines and is obtained from Eq.( as follow: X, (, r, (, = (6 ( r(,. In the system both terminals and are onneted with eah other throgh CVT and if there is no loss in the system, following relation mst be satisfied P, P + P. (7 Then, onsidering = r, we an obtain following that is power distribtion relation at the terminal, P (,, X = = = (8 P X r( > 0 < 0 5,, Table Power Flow iiding > > > 0 S T X S T 8 In the aboe eqation (8, the amont of represents whether P is bigger than P5 or not and the sign of indiates whether power flow diretion of P is the same as that of P5 or not. Therefore in the ase terminal is otpt, power flow diretion among three terminals, and are lassified to two ases: S and T as shown as Table aording to. The index S explains the ase where is larger than zero and this means both powers of and stream into terminal. Moreoer S- is the ase where amont of power of terminal is bigger than that of.. Classifiation of power flow in LPS For the ase < 0, the harateristis diagram shown as X =, Y = nder the ondition = r lassify many kinds of power flow type as Fig. 8. For the different ases onerning to that are > >0 and >, there are different type diagrams of power flow behaior orresponding to these ases. The figre 8 represents the ombination of power flow style of eery planetary mehanism shown as Table. Here orrespondene of terminal nmber in Table with the planetary mehanism is as follows: =, = and = Moreoer in the figre 8 Greian letter indiates the same lassifiation symbol of power flow type shown as Table, and the first letter explains power flow area of represented by Ja, and the seond letter means that of. From the figre 8, we an see LPS has nine ombinations of power flow style, and and preisely sixteen ases if we diide to two ases and. Thogh ombination of power flow type shown in Fig.8 an make arios models of total power flow of LPS, obtained all models are not always realized bease of mehanial reqirement for operation. The reqirement is sh a ondition as that the one of two terminals of CVT shold be inpt and the other otpt. To satisfy this ondition the terminals and of both planetary

5 MPT00- Fkoka The JSME international onferene of Motion and Power Transmission No.5-7,00, Fkkoka,Japan Table Combination of Power Flow in LPS Combination S S Combination T mehanisms shold be onneted with eah other throgh CVT. Table shows obtained reslts of power flow model LPS in the ase that the terminal is otpt. In the other ase that the terminal is inpt, whole diretion of power flow shown in Table hange to reerse diretion. From this table we an see that power irlation exists generally in LPS withot a ombination and.. Pratial model and its power flow Considering the ondition of two J lines whih satisfies the relation shown in Fig.7, we an obtain a system shown as Fig.9 as a pratial example. This model has two planetary gear mehanisms and a belt type CVT. model onstrtion of both planetary gear mehanisms is the same and the gear ratio between sn gear and internal gear is. Moreoer the transmission ratio r is positie, bease CVT is belt type. From allating X nder these ondition by Eq.(6, speed ariation harateristis of LPS regarding to the transmission ratio r of CVT is obtained as shown as Fig.0. This figre shows that for positie r, X exists in the region larger than,. Then the power flow type of this region orresponds to and. Fig. 0 Relation of X s r CVT Fig.9 Pratial Example of LPS For type power flow, the model of Fig.9 has power irlation in a loop and power flows passing throgh and oin at the terminal as otpt power. In this type region transmission ratio r is smaller than ritial ale r. Here the ritial ale r is explained as follow: Moreoer ptting Fig.7 pon Fig.8, we an see that Ja line passes throgh,, and area from right down to left p. Now, let s sppose the 8 r (, = (9 (,

6 MPT00- Fkoka The JSME international onferene of Motion and Power Transmission No.5-7,00, Fkkoka,Japan Moreoer in this ase, absolte ale of is larger than and power flow diiding type takes S- ase shown in Table. Then the amont of power at terminal is bigger than. When the transmission ratio r inrease oer a ritial point r, the sign of X hanges that means rotational diretion of otpt beomes reerse and also power flow type hanges to from. Therefore in this region the diretion of irlation power is reerse to the region and power load of beomes to be heaier than that of. Table shows the relation between ariation of r and power flow behaior in the system shown in Fig.9. Table Variation of Power Flow Type with r 0 r r r r Smmary isssions of this paper an be smmarized as follows: a The harateristis diagram for SLPS was extended to lassify power flow styles of LPS. b In LPS there are sixteen styles of power flow. Eery style of power flow of LPS was shown in Table. d Power flow models of LPS withot a ombination of and hae power irlation inside the system. e Considering model of LPS as a pratial example and allating relation between otpt speed and ariation of transmission ratio of CVT, kinematis behaior of the system was explained. Referene Tsnei,Yada, "Closed looped differential mehanisms onstrted with planetary gear and non-step ariator", Pro. rd world ongress for theory of mahines and mehanisms, Kpari Ygoslaia, Sep. -0 (97, V.97-9, Tsnei Yada, "esign of appliation mehanism of gear (7", Siene of Mahine (in Japanese, Vol.50,No.(998,89-9 Tsnei Yada, "esign of appliation mehanism of gear (", Siene of Mahine (in Japanese, Vol.50,No.9(998, Tsnei Yada, "esign of appliation mehanism of gear (6", Siene of Mahine (in Japanese, Vol.5,No.9(000,