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Design parameters for continuously , Universidad Polite Polite form Since 1996, when the first agricultural tractor with CVT transmission was shown, the presence of this type of transmissions has been Since the emergence of the power-shift transmissions in CVT transmissions (with continuous variation) were the outside, relative to management and driving strategies, but dierent on the inside. Later, Deutz introduced the Agrotron TTV and New Holland introduced the TM series with a continuous TVT transmission. Most recently, Mas- sey Ferguson has developed Dyna-TV transmission and McCormick has developed VTX. Their structures are * Corresponding author. Tel.: +34 913 365 854; mobile: +34 618 807 499; fax: +34 913 365 845. E-mail addresses: pilar.linaresupm.es (P. Linares), valeriano.mendez upm.es (V. Mendez), h.catalanupm.es (H. Catalan). 1 Tel.:+34 913 365 854; mobile: +34 618 807 499; fax: +34 913 365 845. 2 Tel.:+34 917 308 355; mobile: +34 616 981 407. 3 Tel.:+34 914 293 822; mobile: +34 605 445 597. Available online at Journal of Terramechanics xxx Journal ARTICLE IN PRESS agricultural tractors, the requirement to combine the engine and transmission to increase productivity in the tractors performance, has led to stepped transmissions with a greater number of gears. The introduction of com- puting in tractors allows the possibility of managing both factors automatically and simultaneously. However, with a high number of gear shifts it is necessary to place a high number of clutches or hydraulic brakes to govern the trans- mission. Under these circumstances, the appearance of CVT technology in agricultural tractors, paved the way installed in agricultural tractors beginning in 1996. Fendts VARIO was surprising because of its originality; it was not related to its equivalent in an automobile. It split the power in two ways and joined it again later on. It was innovative but much easier to use than to understand. Then, Steyr- Cases S-MATIC arrived at a series production, which was also a power split, but very dierent. On the other hand, in Germany, Claas has a vehicle, Xerion, with a sim- ilar transmission: HM-I, which later led to HM-II 2. Cla- as meanwhile replaced it with ZFECCOM CVT. Then, John Deere was incorporated into the CVT family with two transmissions AUTOPOWR which were the same on increasing. All companies oer them in their products range. Nevertheless, there is little technical documentation that explains the basics of its operation. This report shows all types of CVT transmissions: non-power-split type and power-split ones, as well as the three types used in agricultural tractors, hydro-mechanical power-split transmissions (3 active shafts, input coupled planetary; 3 active shafts, output coupled planetary and 4 active shafts). The report also describes the design parameters of a type of CVT transmission, which use a power-split system with 3 active shafts as well as the fundamental relations among them. Crown Copyright C211 2010 Published by Elsevier Ltd. on behalf of ISTVS. All rights reserved. Keywords: CVT; Transmission; Hydro-mechanical power-split transmission; Hydrostatic CVT; Tractor transmission 1. Introduction to an integral management and to the development of driv- ing strategies, which improve productivity and comfort. transmissions using planetaries P. Linares a,b,1 ,V.Mendez a Research Group “Tractors and Tillage” b Dpto. Ingeniera Rural, E.T.S. Ingenieros Agronomos, Universidad c Dpto. Matematica Aplicada, E.T.S. Ingenieros Agronomos, Universidad Received 6 February 2009; received in revised Abstract 0022-4898/$36.00 Crown Copyright C211 2010 Published by Elsevier Ltd. on behalf doi:10.1016/j.jterra.2010.04.004 Please cite this article in press as: Linares P et al., Design parameters for continuously transmissions using planetaries with 3 active shafts, J Terramechanics (2010), variable power-split with 3 active shafts a,c, * ,2 , H. Catalan a,c,3 Politecnica de Madrid, Spain cnica de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain cnica de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain 14 April 2010; accepted 19 April 2010 (2010) xxxxxx of Terramechanics of ISTVS. All rights reserved. variable power-split doi:10.1016/j.jterra.2010.04.004 ARTICLE IN PRESS Nomenclature 2 P. Linares et al./Journal of Terramechan presented in the German Yearbook Agricultural Engineer- ing 15. These kinds of transmissions have been well received by farmers because of their clear advantages, such as comfort, C ring gear (or clutches in Fig. 12) C a clutch a C d clutch d CVT continuously variable power-split trans- mission CVU continuously variable unit divider planetary CVT power-split transmission with the PGT in the input node e CVT unit input shaft em mechanical input shaft to the PGT F forward f shaft connected to the variable path (called floating shaft) g eciency HMT hydro-mechanical transmission i 1 internal transmission in CVT unit; trans- mission ratio between PGT and CVU i 2 internal transmission in CVT unit; trans- mission ratio between PGT and coupling i m internal transmission in CVT unit; trans- mission ratio between CVU and coupling i t overall transmission ratio engine-wheels I t transmission ratio in the CVT Unit k f torque ratio of the floating shaft (M f /M em in divider planetary; M f /M om in summing planetary) k m torque ratio of the mechanical path (M om /M em in divider planetary; M em / M om in summing planetary) k teeth ratio in the PGT (Z C /Z P ) M em torque in mechanical input shaft to the PGT M f torque in shaft connected to the variable branch, called floating shaft Mixed transmission transmissions with a shiftable combina- tion of dierent modes of work M om torque in mechanical output shaft to the PGT MR mechanical regenerative power flow n rotation speed N power n 1 rotation rate in shaft 1 of the variator (connected to the coupling) n 2 rotation rate in shaft 2 of the variator (connected to the floating shaft) Please cite this article in press as: Linares P et al., Design parameters for continuously transmissions using planetaries with 3 active shafts, J Terramechanics (2010), ics xxx (2010) xxxxxx ease of handling, and response to the most diverse require- ments. However, there is not a systematic theory of opera- tion to study them, which is a disadvantage in presenting the transmission characteristics. n C1 rotation speed in ring gear number 1 (in a commercial CVT transmission) n e rotation speed in CVT input shaft N e input power in CVT unit n em rotation speed in mechanical input shaft in PGT n f rotation rate of the floating shaft (shaft connected to the variable path) n m rotation speed in shaft between planetary gear train N m power in mechanical shaft n o rotation speed in CVT output shaft n om rotation speed in output shaft in PGT n out rotation speed in output shaft in Fig 12 (after even clutches box) NR non-regenerative power flow N v Power in variable shaft o CVT unit output shaft om mechanical output shaft from the PGT om rotation speed of the mechanical output shaft(s) from the PGT P sun gear PGT planetary gear train PS planet carrier R reverse gears R f transmission ratio of the floating shaft R t transmission ratio in the mechanical path of the planetary system R tb transmission ratio in the lockup point R v transmission ratio in the CVU Shaft to shaft non-splitted CVT transmission Summing planetary CVT power-split transmission with the PGT in the output node TTM transmission teaching model (CVT power-split transmission with the PGT in the output node) Variator continuously variable unit VR variable regenerative power flow VU continuously variable unit X mt power distribution in mechanical path X vt power distribution in variable path Z number of teeth Z c number of teeth of the ring gear Z p number of teeth of the sun gear variable power-split doi:10.1016/j.jterra.2010.04.004 2. Types of CVT transmissions The main feature of CVT transmissions is a stepless speed change. A continuous variable unit that allows infi- nite gear ratios, must be incorporated. There are dierent types of CVT transmission systems which can be classified according to several criteria: C15 Power flow. C15 Type of variator. C15 The nature of its components. The first criterion of classification is power flow (Fig. 1). In the non-split type, there is only a single path for the power to flow through. These CVTs are addressed as “Shaft to Shaft” 7. On the contrary, in the split type, the power is split in two paths and then rejoined. In addi- P. Linares et al./Journal of Terramechan ARTICLE IN PRESS tion, there are the mixed-flow CVTs, which have two power flow paths (brakes and clutches) which allow it to operate in dierent modes, such as split or non-split, or in several other patterns (Fig. 1). Two types of variators exist, mechanical and hydraulic. Within the mechanic type, there are belt, chain and roller- based variators (toroidal transmission). These are used in the CVT transmission found in cars, motorcycles and trac- tor prototypes. As for hydraulic variators, there are another two types: Hydrostatic Transmission, and torque converters. According to the third criterion of classification, the nat- ure of the components included in the CVT transmission, there are several dierent categories. The components can be all-mechanical, all-hydraulic, or a combination of mechanical and hydraulic elements (HM). Within the all- mechanical type, both split and non-split exist. The split type, hydrostatic and hydrodynamic transmissions, how- ever, is not present in all-hydraulic transmissions. Mixed mechanical-hydraulic transmissions can be split or in series configurations. Fig. 1. Types of CVT transmissions with respect to the power flow. CVU: continuously variable unit (variator). Please cite this article in press as: Linares P et al., Design parameters for continuously transmissions using planetaries with 3 active shafts, J Terramechanics (2010), 3. Power-split CVT transmissions Power-split transmissions divide the power into two paths, one with fixed transmission ratio (the mechanical path) and another which includes the variator (the variable path). Both rejoin in the output shaft. The CVT eect is provided by the path with the variator. There are three dierent types of commercial transmis- sions (Fig. 2): C15 3 active shafts: s Input coupled planetary or summing planetary. s Output coupled planetary or divider planetary. C15 4 active shafts: bridge type planetary. The definition of “active shaft” refers to those connected to the planetary gear train (PGT), the true mechanical heart of the CVT system. When there are 3 active shafts, the PGT has one mechanical input shaft (em), one or sev- eral output shafts (om) and a single floating shaft con- nected to the variator (f). On the other hand, in the 4 active shafts type, also known as “bridge type” 18, the two variator shafts are connected with the PGT. In the transmissions with 3 active planetary shafts there are two nodes, one at the input of the CVT unit, and the other one at the output. Two basic configurations are known 7; the dierence between them depends on the position of the PGT. In the input coupled planetary (sum- ming planetary), the PGT is the output node and the input node is the coupling. In the output coupled planetary (divi- der planetary), the input node is the PGT and the output node is the coupling. For each layout there are 3 patterns of operation according to the flow of power through the CVT, see Fig. 3 9. If the power flowing through one of the paths is greater than the input, the power is said to be regenera- tive. In contrast, when the power flow through each of the two paths is lower than the input, the power is said to be non-regenerative. In the regenerative power scheme, since there are two paths, situations can arise: C15 The power through the fixed path is greater than the input power (mechanical regenerative). C15 The power through the variable path is greater than the input power (variable regenerative). Kress 7 of John Deeres Technical Center, laid out the fundamentals which explain how this type of transmission operates, but there was no series production for tractors for many years. Recently, CVT transmissions and power split have started to be used in the automobile industry, for implementation in hybrid vehicle transmissions 19 as well as in agricultural tractors. Renius 13, Renius and Resch 14, Renius et al. 15 have explained and commented on existing tractor CVT transmissions. Hsieh and Yan 5, ics xxx (2010) xxxxxx 3 Sheu et al. 17,Lu9, Shellenberger 18, Mangialardi and Mantriota 10,11, Mantriota 12 and Gomez 4 have variable power-split doi:10.1016/j.jterra.2010.04.004 ARTICLE IN PRESS 4 P. Linares et al./Journal of Terramechan studied power flow and performance under dierent oper- ating conditions. Studies made in transmissions provided Fig. 2. Types of commercial hydro-mechanical power-splitting CVT transmission rotation in CVT input shaft, n o : rotation in CVT output shaft, n em : rotation in rotation rate in shaft 1 of the variator (connected to the coupling). Fig. 3. Possible power flow in dierent operation modes. Up: divider planetary; down: summing planetary. (a) The power flow produces split function. (b and c) The power flow leads to power recirculation. PGT: planetary gear train; VU: variator. Lu 9. Please cite this article in press as: Linares P et al., Design parameters for continuously transmissions using planetaries with 3 active shafts, J Terramechanics (2010), ics xxx (2010) xxxxxx with belt mechanical variators prove that those with sum- ming planetaries render a better mechanical performance. In order to compare variators which are hydrostatic trans- missions, they must be equal and only the position of the PGT can be changed. This is not true in commercial trans- missions, because those with divider planetary transmis- sions have a hydrostatic element which is much more sophisticated (variable displacements unit, type bent-axis hydraulics units and very large displacements and oset angles). On the other hand, although the PGT is more sophisticated and they have several maneuvering elements, in summing planetary transmissions there is a simpler var- iator, with conventional hydraulic units. As a result, com- paring performances between the two types is not easy. s. HMT: hydro-mechanical transmission. PGT: Planetary gear train, n e : mechanical input shaft in PGT, n om : rotation in output shaft in PGT, n 1 : variable power-split doi:10.1016/j.jterra.2010.04.004 of the input shaft remains constant, at that shaft the sin- ARTICLE IN PRESS 4. Elements of a power-split CVT with 3 active planetary shafts The basic elements of a CVT transmission are (Fig. 2): C15 CVT unit input shaft (e). Rotation rate: n e C15 CVT unit output shaft (o). Rotation rate: n o C15 Coupling or junction: 2-shaft node: s One connected to the variable path. s One connected to the mechanical path. C15 Planetary gear train (PGT): Node with, at least, 3 active shafts: s Mechanical input shaft to the PGT (em). Rotation rate: n em . s Mechanical output shaft(s) from the PGT (om). Rotation rate: n om . s Shaft connected to the variable path, called floating shaft (f). Rotation rate: n f . C15 Variator (CVU: continuously variable unit): with 2 shafts: s Shaft 2: Connected to the floating shaft (rotation rate n 2 ). s Shaft 1: Connected to the coupling (rotation rate n 1 ). C15 Internal mechanical transmissions: s Connection between PGT and variator (i 2 ). s Connection between variator and coupling (i 1 ). s In the mechanical path (i m ). 5. Parameters for power-split CVTs with 3-shaft planetaries In order to understand the operation of CVT transmis- sions, it is useful to define a series of parameters by which they are characterized. The famous paper of Kress 7 con- tains (besides other systems) the complete model of power- split systems with 3-shaft standard planetaries. The authors developed their parameter study on this basis, however they did so with structures which contain an additional ratio of gear wheel(s) between the planetary and the second junction point. This enlargement of the basic structures by i m can better accommodate commercial power-split sys- tems with internal transmissions between planetary and junction point. Definitions of internal transmission ratios are given by Fig. 2 based on the methodology of Kress 7: C15 Transmission ratio in the mechanical path of the PGT: R t . C15 Transmission ratio in the floating element of the PGT: R f . C15 Transmission ratio in the CVT unit: I t . The ratios between the speeds of the PGT shafts are expressed by the basic speed equations as shown in Fig. 2, by means of parameters k m and k f 8, which repre- sent the share of torque for the two paths assuming no P. Linares et al./Journal of Terramechan power losses. The lockup is the point at which a power-split CVT transmission becomes purely mechanical, the floating Please cite this article in press as: Linares P et al., Design parameters for continuously transmissions using planetaries with 3 active shafts, J Terramechanics (2010), gle point is the unit. In Fig. 4, the distance between the dierent vertical lines is an arbitrary distance, considering the unitary distance between the input and the floating shafts. Vertical lines rep- resenting R t and R f are placed at a specific distance from the floating shaft. This distance is determined by the lockup transmission ratio corresponding to the PGT when this shaft is active. Once the organization of the PGT and the variation of the transmission ratio on the floating shaft are known, the point of the input shaft is joined to the ends of the line defined by the transmission ratio on the floating shaft. The shaft being stationary and the transmission ratio as the lockup ratio, R tb . When calculating a CVT transmission, the first step is to analyze the PGT in order to achieve the lockup transmission ratio and the values for parameters k m and k f . Once the ratios for the lockup point transmission and the floating element are known, we can calculate the trans- mission ratio for the PGT using the following formula, which is valid for all types of transmissions (divider and summing planetaries): R t R tb R f 1 C0 R tb 6. Power distribution in a power-split CVT transmission Once the lockup transmission ratio is known, we can determine the distribution of power and its status at any given time (Tables 1 and 2). The diagram showing the power distribution curves allows us to determine the status of the transmission: Non-regenerative (NR); mechanical regenerative (MR) and hydraulic or variable regenerative (VR). In both types of transmission when the transmission ratio is negative, the power is regenerative through the hydraulic path (VR). However, the behavior is dierent in the case of positive transmission ratio. In divider planetaries, power is non- regenerative up to the lockup transmission ratio, and from that point on it is mechanical regenerative. In summing planetaries, power is mechanical regenerative up to the lockup transmission ratio, and from that point on it is non-regenerative. The operative status of the transmission can also be shown by means of the diagram in Fig. 4, based on the studies made by Fredriksen 2. In this model, there are as many vertical axes as shafts contained in the PGT, that is, input shaft, floating shaft and as many output shafts as it may have. Fig. 4 shows only one output shaft. The speed for each shaft is shown, taking the speed relative to the input shaft. Thus, on the floating shaft we have indicated the transmission ratio R f and on the output shafts, we have indicated the transmission ratio for the PGT when the shaft is active. If we assume that the speed ics xxx (2010) xxxxxx 5 lines thus obtained correspond to the maximum and mini- mum shaft speeds. The intersection of the two lines with variable power-split d