Theoretical and experimental study of a power split continuously variable transmission system Part 2

Transcription

1 851 Theoretical and experimental study of a power split continuously variable transmission system Part 2 G Mantriota Dipartimento di Ingegneria e Fisica dell Ambiente, Università della Basilicata, C.da Macchia Romana, Potenza, Italy Abstract: In this work, theoretical and experimental results related to the power ow and eyciency of a power split continuously variable transmission ( PS- ) system are reported. By means of two separate phases of operation, an original solution is studied that allows an increase in the transmission eyciency through the generation of a ow without recirculation of power. The experimental results related to the second phase of operation of the PS- are reported. Such results are compared with those found through a theoretical model of the transmission. The advantages in terms of eyciency in comparison with a traditional system are shown. A possible operational scheme for the PS- is nally reported through which it is possible to increase the ratio range by means of a cyclical repetition of the operational phases. Keywords: continuous variable transmission, power split, in nitely variable transmission, power transmission, eyciency, test rig NOTATION ô, ô PS- transmission ratio in the PS1 PS2 rst and in the second phases A, B shafts ô PS1 maximum value of the PS- C clutch max transmission ratio in the rst continuously variable phase transmission ö angular velocity FR xed ratio mechanism ö synchronism angular velocity S FR* xed ratio mechanism situated upstream of the PS- P power 1 INTRODUCTION PG planetary gear PS- power split system Over the past years, automotive engineering has shown RR ratio range considerable interest in continuously variable trans- T torque mission (). In numerous works, studies have been aimed at the development of the system performè eyciency ance. Ample scienti c development has, for instance, è, è eyciency of the PS- in the 1 2 occurred within the toroidal systems [1 5] which rst and in the second phases are now showing appreciable improvements compared ô transmission ratio with their initial performance. Recent studies [ 6 7] on ô, ô min minimum and maximum value of s with a metallic belt for operation under non-static max the transmission ratio conditions are also aimed at improving the eyciency of ô PS, ô min PS minimum and maximum value of the by optimizing axial thrusts. max the PS- transmission ratio In recent studies [4, 5, 8 10], prototypes of the V-belt, or the toroidal, have been proposed to The MS was received on 7 July 2000 and was accepted after revision increase the ratio range of systems, but at a disadfor publication on 5 March vantage to the eyciency. In previous studies [11, 12] the

2 852 G MANTRIOTA present author studied the power ows and eyciency in (closed C, open C ). With the PS- system proposed in reference [ 13] it is possible to obtain an identical B A in nitely variable transmission (IVT), or rather continuously variable transmission with an endless ratio range. ratio range to that of the without power It showed, in particular, how it is not possible for an recirculation. IVT to have a power ow without recirculation. A parallel PS- is obtained (Fig. 1), joining it in An original power split (PS- ) system able a rst phase to shaft A (clutch C closed, clutch C A B to guarantee a ow without recirculation of power was open). In this rst phase (subscript 1) a maximum value proposed in previous work [13] with the aim of improving the eyciency of the. The PS-, through two the maximum transmission ratio, max ô of the PS- transmission ratio, ô PS1, smaller than, is separate phases of operation, allows only a fraction of imposed, while ô =ô max PS1 min. The theoretical and the input power to circulate in the internal, with experimental results related to min the power ows and evident advantages in terms of eyciency. In subsequent eyciency of the PS- in the rst operational phase work [14], experimental results related to the perform- were described in Part 1 [ 14]. ance of the PS- in its rst phase of operation was Following the notation in Fig. 1, the transmission reported. ratios of the single elements are In the present work, the performance of the original PS- is appraised in the second phase of operation. Using a special test rig, the input and output powers, as well as the power crossing the internal, are measured using a prototype of the PS-. The experimental results are compared with those obtained by means of a ô = ö 2 ö 3, ô FR = ö 5 ö 3 ô PG = ö 6 Õ ö 5 ö 4 Õ ö 5, ö 1 =ö 2 =ö 4 theoretical model, and the advantages are shown in terms of eyciency compared with the internal. In the rst phase, the global transmission ratio (clutch Finally, the possibility of increasing the ratio range of C closed, clutch C open) is expressed by A B the PS- through the cyclical repetition of the two operational phases is shown. ô = ö 6 =ô +ô (ô Õ ô ) (2) PS1 ö FR PG FR 1 The values of the planetary gear transmission ratio, ô PG, 2 POWER SPLIT SYSTEM WITH TWO and the xed ratio mechanism transmission ratio, ô FR, PHASES may be determined by [13] (1) An original functional solution for the PS- system ô = ô Õ ô PS PG 1 max PS1 ô min (3) able to guarantee a power ow without recirculation for Õ ô max min every value of the ratio gear has been proposed in referô = ô Õ ô ô ence [13]. The system (Fig. 1) comprises a PS- in PS FR 1 max PG max (4) 1Õ ô which it is possible, with the aid of two clutches, C and PG A C, to join to shaft A (closed C, open C ) or shaft B In particular, having imposed ô =ô = B A B min PS min Fig. 1 Schematic of a PS- system with two phases

3 THEORETICAL AND EXPERIMENTAL STUDY OF A PS- SYSTEM. PART possible to notice how the output power is always greater than the power crossing the. Assume that the eyciency of the PS- system has a unit value. In the second phase, it is easy to demon- strate that the ratio of the output power, P, and the PS power circulating in the, P, can be expressed by ô PS1, the ô will be equal to ô min FR independently of the value of ô min PS1. Suppose that shaft max B (Fig. 1) has an angular speed equal to ô ö. The xed ratio mechanism situated max 1 above the split-path system, FR*, will then have a transmission ratio equal to ô. In this way, synchronism between shaft 4 and shaft max B of the is generated. Without interruption of the power transmission, in the second phase (Fig. 2), by closing clutch C and subsequently opening clutch C, the PS- is joined to A B shaft B and assumes a series con guration. With the transmission components remaining unchanged (, ô, ô ), the global transmission ratio in this second FR PG phase (subscript 2) becomes ô PS2 =ô max C ô PG +(1Õ Replacing (3) and (4), the following is obtained: ô PS2 = P P PS2 =1Õ RR ô Õ ô PS1 max (RR max (9) Õ 1)ô PS2 where RR denotes the ratio range, i.e. RR = ô max ô min (10) In Fig. 3 the ratio P /P PS2 as a function of ô is found for ô PS1 max =1.25. ô PG ) A ô FR ô BD (5) The power that crosses the ranges from 50 per ô PS1 max (ô Õ ô min ) +ô min (ô max Õ ô ) (ô max Õ ô min )ô ô max (6) From equation (6) it can be seen that, when ô =ô max, the global gear ratio is ô PS2 =ô PS2 min =ô PS1 max (7) While the ô from the maximum value returns to its lowest value, the ô continues to increase until the value ô PS is reached. In fact, for ô =ô max, from equation (6) for any value of ô min PS1 it follows that max ô PS2 max =ô max (8) Then, in the second phase, the global gear ratio changes from ô PS1 to ô max. The advantage of max such a functional solution is obviously in terms of deliverable power and eyciency. It is cent (ô =0.5) to 20 per cent (ô =2) of the total power. This result certainly determines a bene t in terms of eyciency because the is the component with the smallest eyciency. 3 TEST RIG In this work, the experimental tests were conducted in order to appraise the performance of the PS- system during the second operational phase ( Fig. 4). In Fig. 5 the scheme of the test rig, analogous to that used in reference [ 14], is shown. To simulate the second phase of operation of the PS-, the motor was connected to shaft 4 (Figs 1 and 5), producing the con guration in series of the PS-. The test rig simulates the PS- in the second phase of operation without the xed ratio mechanism situated above the split-path system (Figs 2 and 5). The experimental tests were conducted with the same Fig. 2 Second phase: series PS- system

4 854 G MANTRIOTA Fig. 3 P /P PS as a function of ô with no losses (ô PS1 max =1.25) Fig. 4 Test rig components (, planetary gear, xed ratio mechan- Two torque-tachometers (Figs 4 and 5) measure the ism) used for the tests of the rst phase of operation input ( TT1) and the output ( TT3) values of the PS- [14], as foreseen by the PS- proposed in reference system, and a third (TT2) measures the power in shaft 4 [13]. The PS- system was realized with a rubber of the transmission. Each torque-tachometer was V-belt (Gerbes RF 210b). Having chosen connected to the transmission shafts by using exible ô couplings (J ). PS1 =1.25, the test rig has a commercial planetary gear max with ô =0.5 (Andantex SR20), in which the gear The test rig drive was obtained by means of an a.c. PG carrier receives the motion by a timing belt. The motor with three magnetic poles driven through an constant-ratio transmission ( FR) was obtained by inverter. Using a pneumatic disc brake, the output means of a timing belt pulley (ô =0.5). The torque torque was obtained. A regulation valve was used to FR and the angular speed were measured by means of regulate the driving pressure of the brake through which torque-tachometers (model TT/9000, 50 N m, Tekkal ). it was possible to vary the resistant torque of the

5 THEORETICAL AND EXPERIMENTAL STUDY OF A PS- SYSTEM. PART Fig. 5 Diagram of the test rig

6 856 G MANTRIOTA PS- system. The data coming from the torque- have the xed ratio mechanism situated above the tachometers were sent by an ampli er and PC for data PS-, having a gear ratio equal to ô = FR* acquisition and storage. ô =2. Therefore [equation (6)], ô =ö /ö max PS2 6 1 reported in Fig. 5 has the expression 4 POWER FLOW AND EFFICIENCY OF THE ô = ô PS PS2 1 (ô Õ ô max )+ô min (ô Õ ô min ) max PS- SYSTEM (ô Õ ô max )ô min (11) Õ Õ The experimental test results on the eyciency used In order to nd the relationship of the global gear ratio in the test rig were reported in Part 1 [14]. Tests of the in the second operational phase of the PS-, the power ows and eyciency of the PS- were perthe theoretical and experimental value is due to the pres- ô must be multiplied by 2. The perfect match between PS2 formed for diverent values of the electric motor driving frequency. In this work, only the experimental results ence in equation (5) of the planetary gear ratio train and concerning a motor driving frequency of 50 Hz the xed ratio that remain rigorously constant during (1000 r/min) are reported. In order correctly to simulate the diverent conditions of operation. the original transmission PS- proposed in reference The torque of the gear carrier, T, was calculated 5 [13], the synchronism speed of 1000 r/min is double that through the equation of equilibrium with respect to used for estimating the eyciency of the rst operational rotation ( Fig. 5) for the planetary gear train: phase (500 r/min) [14]. Actually, the presence of a xed ratio transmission above the PS- with a gear ratio T =T 5 6 T 4 (12) equal to ô =ô The eyciency of the planetary gear train can be deter- FR* is expected in the drive. Therefore, in the max present case, having chosen mined by ô =2 in the calculation of the PS- compoè = 6 6 PG T ö + T ö = T ö T ö max nents [ 14], the speed of shaft B in the second operational 6 6 T ö + (T T )ö phase has to be double that of shaft A of the rst phase (13) (Fig. 1). Tests were performed at diverent values of the in which T and T are the torques measured by torquetachometers TT2 and TT3 (Fig. 5), while the angular 4 6 gear ratio, equal to 0.4, 0.8, 1.2, 1.6, 2 and 2.3. The torque and angular speed measurements of the three speed of the gear carrier, ö, can be determined by ô 5 PG shafts allowed evaluation of the power ows, the planetary [equation (1)]. gear train eyciency and the global eyciency of the In Fig. 7 the angular speeds of shafts 4 and 5 com- PS-. pared with the angular speeds of shaft 6 are reported The behaviour of the global gear ratio related to that (ö =ö /ö, ö =ö /ö ), while in Fig. 8 the 4/ /6 5 6 of the is reported in Fig. 6. The test rig does not eyciency of the planetary gear train related to the Fig. 6 PS- transmission ratio as a function of ô

7 THEORETICAL AND EXPERIMENTAL STUDY OF A PS- SYSTEM. PART Fig. 7 Non-dimensional angular velocities of the planetary gear train as a function of ô Fig. 8 EYciency of the planetary gear train as a function of ô (T 6 =40 N m) variation in ô for T =40 N m is reported. For ô = imental results, correctly highlighting the eyciency PS 6 PS 0.62 (ô =2.3), because of the elevated relative speed variation related to the gear ratio. between the gearing axis (Fig. 7) the eyciency is low, The PS- is designed to have a ow without recirculation of power. In Fig. 9 the ratio between the around With the growth in ô, the relative angular speeds of the gearing shafts decrease and therefore input power [P =T ö =(T Õ T )ö ] and the the eyciency of the planetary gear train increases, reaching a maximum value equal to around when ô = ques T and T are measured by using torque- 1 4 PS- input power (P =T ö ) is shown. The tor- PS (ô =1.15). The theoretical behaviour obtained by tachometers TT1 and TT2 (Fig. 5). PS the PennestrÌ` model [15] agrees very well with the exper- For ô =0.4, the ratio P /P is maximum and is PS2

8 858 G MANTRIOTA Fig. 9 P /P PS as a function of the transmission ratio ô approximately 0.6. With growth in ô, the fraction of power that crosses the actually decreases to around 0.15 for ô =2.3. The theoretical curve was drawn by means of the equilibrium equation of power: P P PS = è PG Õ C ô PG +(1Õ ô PG ) ô FR ô D C ô PG ô +(1Õ ô )Õ è ô PG FR PGD è FR è +è Õ PG C ô PG +(1Õ ô PG ) ô FR ô D (14) Equation (14) contains the eyciency of the PS- components (PG,, FR). The eyciency of the xed ratio mechanism, obtained with a timing belt, is considered constant and equal to è =0.98. The eyciency FR of the planetary gear train, è, is calculated by means PG of the PennestrÌ` model [15], while è is calculated using the interpolator curve equations of the eyciency experimental results [14]. The experimental results agree with those found by using equation (14) and diverge slightly from the curve obtained by hypothesizing null losses [equation (9)]. The PS- eyciency as a function of the resistant torque, T, is reported in Fig. 10 for ô =2.3. The 6 eyciency quickly reaches values larger than 0.8, with the maximum value equal to for T =42 N m. The 6 expression of the eyciency can be easily determined: ô ô Õ è p PS ô PG 4 = FR (15) p è Õ ô 5 PG PS è = Õ p è 6 = PGA p 4 +1 B p 5 2 p p (16) 4 è è p FR 5 It can be seen (Fig. 10) that there is good agreement between experimental results and theoretical results obtained through equation (16), with an exception made for values of torque around 40 N m. Corresponding to each test, in Fig. 10 the value of the internal eyciency is also shown. It is important to note (Fig. 2) that the ratio between the resistant torque of the, T, and the PS-, T, has the expression (ignoring 3 6 the losses): K T 3 T 6 K = ô FR (1 Õ ô ) =0.25 (17) PG Therefore, the resistant torque of the is one-quarter of that of the PS-. This justi es the low eyciency of the, which does not reach 0.7. The ratio 0.25 between the torques also implies the possibility of the PS- reaching an output torque 4 times higher than the maximum torque of the. The gap between the eyciency of the PS- and that of the reaches values of 0.36 for low torque values, while it is around 0.25 for each torque larger than 40 N m ( Fig. 10). The notable diverence can be attributed to the low value of the fraction of power that crosses the compared with the total fraction (Fig. 9). Nevertheless, for ô =2.3 the lowest value of the planetary gear train eyciency occurs, around 0.95 (Fig. 8), which produces a global eyciency of the PS- of no larger than

9 THEORETICAL AND EXPERIMENTAL STUDY OF A PS- SYSTEM. PART Fig. 10 EYciency of the and PS- system as a function of the output torque (ô =2.3) In Figs 11 to 15, the results obtained for the other partially compensated for by the increase in eyciency of values of ô are shown. The gap between the eyciency the planetary gear train (Fig. 8). of the PS- and that of the decreases with increase in ô, which is actually elevated to ô =0.8, 5 PS- SYSTEM WITH A HIGH RATIO which has an average diverence of 0.2. For ô =0.4 RANGE the gap decreases to an average of approximately Such results are essentially due to the increase in the fraction of power that crosses the (Fig. 9), only The PS- described above makes it possible to reach a ratio range of the transmission equal to that of the Fig. 11 EYciency of the and PS- system as a function of the output torque (ô =2.0)

10 860 G MANTRIOTA Fig. 12 EYciency of the and PS- system as a function of the output torque (ô =1.6) Fig. 13 EYciency of the and PS- system as a function of the output torque (ô =1.2) internal. The maximum gear ratio (Fig. 1) is obtained at the end of the second operational phase with the PS- that is driven by shaft B and the with the minimum gear ratio. With such conditions, shaft A rotates with an angular speed equal to RR ö. 1 The ratio range could be increased by cyclically repeating the operational phases of the PS-, by means of, for instance, the scheme in Fig. 16. The xed ratio mechanism situated above the PS- is made up of a gear- ing. The rst phase in which the PS- is driven by shaft A is obtained through the meshing of wheels g 1 and g and with clutch C closed. Wheels g and g have 2 A 1 2 a unitary gear ratio. In this phase, ô varies from ô to ô min, while ô varies between ô max PS and ô min PS1. At max the end of the rst phase (ô =ô ), wheels g and g are also meshed together and have max a gear ratio 1 3 equal to ô. A synchronism between shafts B and max

11 THEORETICAL AND EXPERIMENTAL STUDY OF A PS- SYSTEM. PART Fig. 14 EYciency of the and PS- system as a function of the output torque (ô =0.8) Fig. 15 EYciency of the and PS- system as a function of the output torque (ô =0.4) b is then generated, and it is therefore possible to close to RR, the mesh of g and g puts shafts A and a in 4 5 clutch C. Guaranteeing thereby the continuity of synchronism ( Fig. 16), and it is therefore possible to B motion, it is possible to move on to the second phase close clutch C. It is now possible to repeat the rst A after opening clutch C and placing g and g out of operational phase after opening clutch C and placing A 1 2 B mesh. In this phase, ô varies from ô to g and g out of mesh. In this phase, ô varies from ô max ô 1 3 and ô min, while ô varies between ô, while ô varies between ô min PS PS1 and ô max. max max PS At the end of the second phase (ô =ô max ), and RR ô min PS1. shaft a rotates at a speed equal to ö (ô /ô At the end of max this phase, shaft b rotates with a speed 1 max )= RR ö. If wheels g and g have a gear ratio min equal of ö RR ô Therefore, if wheels g and g have max 4 6

12 862 G MANTRIOTA Fig. 16 PS- system with a high ratio range a gear ratio equal to RR ô, shaft B is synchron- the gear ratio behaviour of the PS- related to ô max ized with b (Fig. 16). By closing clutch C and sub- for the case in which ô B PS1 =1.25 is reported. The four sequently opening clutch C, the second phase is phases that characterize max the operation of the PS- A repeated. The ô varies from ô to ô max, while bring the value of ô from 0.5 to 8, thereby allowing a ô min PS varies between RR ô PS PS1 and RR ô max. ratio range equal to RR =RR2 =16. max PS Guaranteeing the continuity of motion, through the The ratio range of the transmission could subrepetition of the two operational phases previously sequently be increased by repeating the two phases with described, it is therefore possible to obtain a total ratio other pairs of gear wheels and alternatively driving the range equal to PS- from shafts A and B. In conclusion, by cyclically repeating n times the two operational phases, it is RR PS = RR ô max ô min =RR2 (18) possible to obtain a ratio range of the PS- equal to Hypothesizing ô min =0.5 and ô max =2, in Fig. 17 RRn. The PS- with a large ratio range preserves for Fig. 17 PS- system with a high ratio range: PS- transmission ratio plotted against ô (ô PS1 max =1.25)

13 THEORETICAL AND EXPERIMENTAL STUDY OF A PS- SYSTEM. PART Fig. 18 PS- system with a high ratio range: P /P PS as a function of ô with no losses (ô PS1 max =1.25) each phase the advantages in terms of power and ows are determined for the second phase of operation eyciency previously examined. In particular, the ow of the PS-. The experimental results are compared obtained is always without power recirculation. For with those obtained through a mathematical model, example, without losses, in the phases in which the driving showing good agreement. In each measure, the internal occurs through shaft B, the ratio P /P continues and the PS- operated with the same percentage PS2 to have expression (9). Figure 18 reports the behaviour of torque in comparison with the maximum. There- of the ratio P /P related to the global gear ratio fore, the eyciency of the PS- has been compared PS using the scheme of operation in Fig. 16. In this case, with that of the internal. during the phases in which the PS- is driven by The greatest advantage of the PS- proposed in shaft A, the power that crosses the again ranges this work is related to the absence of recirculation power from 50 to 80 per cent of the total power [14]. In the crossing the and comprising between 15 and 60 per phases in which the driving occurs through shaft B, the cent of the total power. Such a result in uences the power ranges from 20 to 50 per cent of the total. global eyciency of the PS- which is notably superior The bene ts in terms of eyciency are entirely analogous to the. Obviously, because the is the compoto those previously examined. The original solution pro- nent with the least eyciency, the gap between the two posed in this research work could, for instance, be interesting eyciencies is as large as the fraction of power that for heavy vehicles mainly because of the elevated crosses the is small. Finally, a driving scheme of ratio range, the reduced torque on the internal and the PS- has been proposed that makes it possible the enhanced eyciency. to increase the ratio range through cyclical repetitions 6 CONCLUSIONS of the phases of operation. These results are encouraging and could be used for further development of this technology for use in urban transport or heavy vehicles. In this research work, experimental results relating to the power ows and eyciency of an original PS- system are reported. The PS- makes it possible to obtain a power ow without recirculation and a ratio REFERENCES range equal to that of the internal. It works through two separate phases of operation, each of which 1 Continuously variable transmissions for passenger cars. is used for a speci c interval of the gear ratio. SAE special publication SAE/PT-87/30, By means of a special test rig, the eyciency and power 2 Paul, M. s driving the future of transmission

14 864 G MANTRIOTA technology. In International Congress on Continuously variable power split transmission. In International Variable Transmission ( 99), 1999, pp Congress on Continuously Variable Transmission ( 99), 3 Machida, H., Miyata, S., Imanishi, T. and Tanaka, H. High 1999, pp performance traction drive on the compact car for 10 Yamada K. Parametric modeling and analysis of IVT. In the 21st century. In Proceedings of 1998 Fisita World International Congress on Continuously Variable Congress, 1998, F98T147. Transmission ( 99), 1999, pp Hohn, B. R. and Pinnekamp, B. The Autark Hybrid: a 11 Mangialardi, L. and Mantriota, G. Comments on: universal power train concept for passenger cars. In Maximum mechanical eyciency in nitely variable trans- International Gearing Conference, 1994, pp missions. Mechanism and Mach. Theory, 1998, 33(4), 5 Machida, H. Traction drive up to date. In Mangialardi, L. and Mantriota, G. Power ows and International Congress on Continuously Variable eyciency in in nitely variable transmissions. Mechanism Transmission ( 99), 1999, pp and Mach. Theory, 1999, 34, Carbone, G., Mangialardi, L. and Mantriota, G. Theoretical 13 Mantriota, G. Power split continuously variable transmodel of metal V-belt drives during ratio changing speed. mission systems with high eyciency. Proc. Instn Mech. Trans. ASME, J. Mech. Des., 2001, 123, Engrs, Part D, Journal of Automobile Engineering, 2001, 7 Carbone, G., Mangialardi, L. and Mantriota, G. Comments 215(D3), on axial thrust and torque of metal V-belt drives in transient 14 Mantriota, G. Theoretical and experimental study of power conditions. Trans. ASME, J. Mech. Des. (submitted). split continuously variable transmission systems. Part 1. 8 Vahabzadeh, H., Macey, J. P. and Dittrich, O. A split- Proc. Instn Mech. Engrs, Part D, Journal of Automobile torque, geared-neutral in nitely variable transmission Engineering, 2001, 215(D7), mechanism. In Proceedings of 23rd Fisita International 15 PennestrÌ`, E. and Freudenstein, F. The mechanical eyciency Congress, 1990, Vol. 1, pp of epicyclic gear trains. Trans. ASME, J. Mech. Des., 1993, 9 Kmicikiewicz, M., Cowan, B. and Arques, P. Continuously 115,