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Nevertheless, there is little technical documentation that explains the basicsof its operation. This report shows all types of CVT transmissions: non-power-split type and power-split ones, as well as the three typesused in agricultural tractors, hydro-mechanical power-split transmissions (3 active shafts, input coupled planetary; 3 active shafts, outputcoupled planetary and 4 active shafts). The report also describes the design parameters of a type of CVT transmission, which use apower-split system with 3 active shafts as well as the fundamental relations among them.Crown Copyright ? 2010 Published by Elsevier Ltd. on behalf of ISTVS. All rights reserved.Keywords: CVT; Transmission; Hydro-mechanical power-split transmission; Hydrostatic CVT; Tractor transmission1. IntroductionSince the emergence of the power-shift transmissions inagricultural tractors, the requirement to combine theengine and transmission to increase productivity in thetractors performance, has led to stepped transmissionswith a greater number of gears. The introduction of com-puting in tractors allows the possibility of managing bothfactors automatically and simultaneously. However, witha high number of gear shifts it is necessary to place a highnumber of clutches or hydraulic brakes to govern the trans-mission. Under these circumstances, the appearance ofCVT technology in agricultural tractors, paved the wayto an integral management and to the development of driv-ing strategies, which improve productivity and comfort.CVT transmissions (with continuous variation) wereinstalled in agricultural tractors beginning in 1996. FendtsVARIO was surprising because of its originality; it was notrelated to its equivalent in an automobile. It split the powerin two ways and joined it again later on. It was innovativebut much easier to use than to understand. Then, Steyr-Cases S-MATIC arrived at a series production, whichwas also a power split, but very different. On the otherhand, 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 withtwo transmissions AUTOPOWR which were the same onthe outside, relative to management and driving strategies,but different on the inside. Later, Deutz introduced theAgrotron TTV and New Holland introduced the TM serieswith a continuous TVT transmission. Most recently, Mas-sey Ferguson has developed Dyna-TV transmission andMcCormick has developed VTX. Their structures are0022-4898/$36.00 Crown Copyright ? 2010 Published by Elsevier Ltd. on behalf of ISTVS. All rights reserved.doi:10.1016/j.jterra.2010.04.004*Corresponding author. Tel.: +34 913 365 854; mobile: +34 618 807499; fax: +34 913 365 845.E-mail addresses: pilar.linaresupm.es (P. Linares), valeriano.mendezupm.es (V. Me ndez), h.catalanupm.es (H. Catala n).1Tel.:+34 913 365 854; mobile: +34 618 807 499; fax: +34 913 365 845.2Tel.:+34 917 308 355; mobile: +34 616 981 407.3Tel.:+34 914 293 822; mobile: +34 605 445 online at Journal of Terramechanics xxx (2010) xxxxxxJournalofTerramechanicsARTICLE IN PRESSPlease cite this article in press as: Linares P et al., Design parameters for continuously variable power-splittransmissions using planetaries with 3 active shafts, J Terramechanics (2010), doi:10.1016/j.jterra.2010.04.004presented in the German Yearbook Agricultural Engineer-ing 15.These kinds of transmissions have been well received byfarmers because of their clear advantages, such as comfort,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 presentingthe transmission characteristics.NomenclatureCring gear (or clutches in Fig. 12)Caclutch aCdclutch dCVTcontinuously variable power-split trans-missionCVUcontinuously variable unitdividerplanetaryCVT power-split transmission with thePGT in the input nodeeCVT unit input shaftemmechanical input shaft to the PGTFforwardfshaft connected to the variable path(called floating shaft)gefficiencyHMThydro-mechanical transmissioni1internal transmission in CVT unit; trans-mission ratio between PGT and CVUi2internal transmission in CVT unit; trans-mission ratio between PGT and couplingiminternal transmission in CVT unit; trans-mission ratio between CVU and couplingitoverall transmission ratio engine-wheelsIttransmission ratio in the CVT Unitkftorque ratio of the floating shaft (Mf/Memin divider planetary; Mf/Momin summingplanetary)kmtorqueratioofthemechanicalpath(Mom/Memin divider planetary; Mem/Momin summing planetary)kteeth ratio in the PGT (ZC/ZP)Memtorque in mechanical input shaft to thePGTMftorque in shaft connected to the variablebranch, called floating shaftMixedtransmissiontransmissions with a shiftable combina-tion of different modes of workMomtorque in mechanical output shaft to thePGTMRmechanical regenerative power flownrotation speedNpowern1rotation rate in shaft 1 of the variator(connected to the coupling)n2rotation rate in shaft 2 of the variator(connected to the floating shaft)nC1rotation speed in ring gear number 1 (in acommercial CVT transmission)nerotation speed in CVT input shaftNeinput power in CVT unitnemrotation speed in mechanical input shaftin PGTnfrotation rate of the floating shaft (shaftconnected to the variable path)nmrotation speed in shaft between planetarygear trainNmpower in mechanical shaftnorotation speed in CVT output shaftnomrotation speed in output shaft in PGTnoutrotation speed in output shaft in Fig 12(after even clutches box)NRnon-regenerative power flowNvPower in variable shaftoCVT unit output shaftommechanical output shaft from the PGTomrotation speed of the mechanical outputshaft(s) from the PGTPsun gearPGTplanetary gear trainPSplanet carrierRreverse gearsRftransmission ratio of the floating shaftRttransmission ratio in the mechanical pathof the planetary systemRtbtransmission ratio in the lockup pointRvtransmission ratio in the CVUShaftto shaftnon-splitted CVT transmissionSummingplanetaryCVT power-split transmission with thePGT in the output nodeTTMtransmissionteachingmodel(CVTpower-split transmission with the PGTin the output node)Variatorcontinuously variable unitVRvariable regenerative power flowVUcontinuously variable unitXmtpower distribution in mechanical pathXvtpower distribution in variable pathZnumber of teethZcnumber of teeth of the ring gearZpnumber of teeth of the sun gear2P. Linares et al./Journal of Terramechanics xxx (2010) xxxxxxARTICLE IN PRESSPlease cite this article in press as: Linares P et al., Design parameters for continuously variable power-splittransmissions using planetaries with 3 active shafts, J Terramechanics (2010), doi:10.1016/j.jterra.2010.04.0042. Types of CVT transmissionsThe main feature of CVT transmissions is a steplessspeed change. A continuous variable unit that allows infi-nite gear ratios, must be incorporated.There are different types of CVT transmission systemswhich can be classified according to several criteria:? Power flow.? Type of variator.? 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 thepower 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-tion, there are the mixed-flow CVTs, which have two powerflow paths (brakes and clutches) which allow it to operatein different modes, such as split or non-split, or in severalother 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 inthe CVT transmission found in cars, motorcycles and trac-tor prototypes. As for hydraulic variators, there areanother two types: Hydrostatic Transmission, and torqueconverters.According to the third criterion of classification, the nat-ure of the components included in the CVT transmission,there are several different categories. The components canbe all-mechanical, all-hydraulic, or a combination ofmechanical and hydraulic elements (HM). Within the all-mechanical type, both split and non-split exist. The splittype, hydrostatic and hydrodynamic transmissions, how-ever, is not present in all-hydraulic transmissions. Mixedmechanical-hydraulic transmissions can be split or in seriesconfigurations.3. Power-split CVT transmissionsPower-split transmissions divide the power into twopaths, one with fixed transmission ratio (the mechanicalpath) and another which includes the variator (the variablepath). Both rejoin in the output shaft. The CVT effect isprovided by the path with the variator.There are three different types of commercial transmis-sions (Fig. 2):? 3 active shafts:sInput coupled planetary or summing planetary.sOutput coupled planetary or divider planetary.? 4 active shafts: bridge type planetary.The definition of “active shaft” refers to those connectedto the planetary gear train (PGT), the true mechanicalheart 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 4active shafts type, also known as “bridge type” 18, thetwo variator shafts are connected with the PGT.In the transmissions with 3 active planetary shafts thereare two nodes, one at the input of the CVT unit, and theother one at the output. Two basic configurations areknown 7; the difference between them depends on theposition of the PGT. In the input coupled planetary (sum-ming planetary), the PGT is the output node and the inputnode is the coupling. In the output coupled planetary (divi-der planetary), the input node is the PGT and the outputnode is the coupling.For each layout there are 3 patterns of operationaccording to the flow of power through the CVT, seeFig. 3 9. If the power flowing through one of the pathsis greater than the input, the power is said to be regenera-tive. In contrast, when the power flow through each of thetwo paths is lower than the input, the power is said to benon-regenerative. In the regenerative power scheme, sincethere are two paths, situations can arise:? The power through the fixed path is greater than theinput power (mechanical regenerative).? The power through the variable path is greater than theinput power (variable regenerative).Kress 7 of John Deeres Technical Center, laid out thefundamentals which explain how this type of transmissionoperates, but there was no series production for tractors formany years. Recently, CVT transmissions and power splithave started to be used in the automobile industry, forimplementation in hybrid vehicle transmissions 19 as wellas in agricultural tractors. Renius 13, Renius and Resch14, Renius et al. 15 have explained and commented onexisting tractor CVT transmissions. Hsieh and Yan 5,Sheu et al. 17, Lu 9, Shellenberger 18, Mangialardiand Mantriota 10,11, Mantriota 12 and Go mez 4 haveFig. 1. Types of CVT transmissions with respect to the power flow. CVU:continuously variable unit (variator).P. Linares et al./Journal of Terramechanics xxx (2010) xxxxxx3ARTICLE IN PRESSPlease cite this article in press as: Linares P et al., Design parameters for continuously variable power-splittransmissions using planetaries with 3 active shafts, J Terramechanics (2010), doi:10.1016/j.jterra.2010.04.004studied power flow and performance under different oper-ating conditions. Studies made in transmissions providedwith 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 thePGT 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 moresophisticated (variable displacements unit, type bent-axishydraulics units and very large displacements and offsetangles). On the other hand, although the PGT is moresophisticated 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.Fig. 2. Types of commercial hydro-mechanical power-splitting CVT transmissions. HMT: hydro-mechanical transmission. PGT: Planetary gear train, ne:rotation in CVT input shaft, no: rotation in CVT output shaft, nem: rotation in mechanical input shaft in PGT, nom: rotation in output shaft in PGT, n1:rotation rate in shaft 1 of the variator (connected to the coupling).Fig. 3. Possible power flow in different operation modes. Up: dividerplanetary; down: summing planetary. (a) The power flow produces splitfunction. (b and c) The power flow leads to power recirculation. PGT:planetary gear train; VU: variator. Lu 9.4P. Linares et al./Journal of Terramechanics xxx (2010) xxxxxxARTICLE IN PRESSPlease cite this article in press as: Linares P et al., Design parameters for continuously variable power-splittransmissions using planetaries with 3 active shafts, J Terramechanics (2010), doi:10.1016/j.jterra.2010.04.0044. Elements of a power-split CVT with 3 active planetaryshaftsThe basic elements of a CVT transmission are (Fig. 2):? CVT unit input shaft (e). Rotation rate: ne? CVT unit output shaft (o). Rotation rate: no? Coupling or junction: 2-shaft node:sOne connected to the variable path.sOne connected to the mechanical path.? Planetary gear train (PGT): Node with, at least, 3active shafts:sMechanical input shaft to the PGT (em). Rotationrate: nem.sMechanical output shaft(s) from the PGT (om).Rotation rate: nom.sShaft connected to the variable path, called floatingshaft (f). Rotation rate: nf.? Variator (CVU: continuously variable unit): with 2shafts:sShaft 2: Connected to the floating shaft (rotation raten2).sShaft 1: Connected to the coupling (rotation rate n1).? Internal mechanical transmissions:sConnection between PGT and variator (i2).sConnection between variator and coupling (i1).sIn the mechanical path (im).5. Parameters for power-split CVTs with 3-shaft planetariesIn order to understand the operation of CVT transmis-sions, it is useful to define a series of parameters by whichthey 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 authorsdeveloped their parameter study on this basis, howeverthey did so with structures which contain an additionalratio of gear wheel(s) between the planetary and the secondjunction point. This enlargement of the basic structures byimcan better accommodate commercial power-split sys-tems with internal transmissions between planetary andjunction point. Definitions of internal transmission ratiosare given by Fig. 2 based on the methodology of Kress 7:? Transmission ratio in the mechanical path of the PGT:Rt.? Transmission ratio in the floating element of the PGT:Rf.? Transmission ratio in the CVT unit: It.The ratios between the speeds of the PGT shafts areexpressed by the basic speed equations as shown inFig. 2, by means of parameters kmand kf8, which repre-sent the share of torque for the two paths assuming nopower losses. The lockup is the point at which a power-splitCVT transmission becomes purely mechanical, the floatingshaft being stationary and the transmission ratio as thelockup ratio, Rtb. When calculating a CVT transmission,the first step is to analyze the PGT in order to achievethe lockup transmission ratio and the values for parameterskmand kf.Once the ratios for the lockup point transmission andthe 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 andsumming planetaries):Rt Rtb Rf1 ? Rtb6. Power distribution in a power-split CVT transmissionOnce the lockup transmission ratio is known, we candetermine the distribution of power and its status at anygiven time (Tables 1 and 2).The diagram showing the power distribution curvesallows us to determine the status of the transmission:Non-regenerative (NR); mechanical regenerative (MR)and hydraulic or variable regenerative (VR). In both typesof transmission when the transmission ratio is negative, thepower is regenerative through the hydraulic path (VR).However, the behavior is different in the case of positivetransmission ratio. In divider planetaries, power is non-regenerative up to the lockup transmission ratio, and fromthat point on it is mechanical regenerative. In summingplanetaries, power is mechanical regenerative up to thelockup transmission ratio, and from that point on it isnon-regenerative.The operative status of the transmission can also beshown by means of the diagram in Fig. 4, based on thestudies made by Fredriksen 2. In this model, there areas many vertical axes as shafts contained in the PGT, thatis, input shaft, floating shaft and as many output shafts asit may have. Fig. 4 shows only one output shaft. Thespeed for each shaft is shown, taking the speed relativeto the input shaft. Thus, on the floating shaft we haveindicated the transmission ratio Rfand on the outputshafts, we have indicated the transmission ratio for thePGT when the shaft is active. If we assume that the speedof the input shaft remains constant, at that shaft the sin-gle point is the unit.In Fig. 4, the distance between the different vertical linesis an arbitrary distance, considering the unitary distancebetween the input and the floating shafts. Vertical lines rep-resenting Rtand Rfare placed at a specific distance fromthe floating shaft. This distance is determined by the lockuptransmission ratio corresponding to the PGT when thisshaft is active.Once the organization of the PGT and the variation ofthe transmission ratio on the floating shaft are known,the point of the input shaft is joined to the ends of the linedefined by the transmission ratio on the floating shaft. Thelines thus obtained correspond to the maximum and mini-mum shaft speeds. The intersection of the two lines withP. Linares et al./Journal of Terramechanics xxx (2010) xxxxxx5ARTICLE IN PRESSPlease cite this article in press as: Linares P et al., Design parameters for continuously variable power-splittransmissions using planetaries with 3 active shafts, J Terramechanics (2010), doi:10.1016/j.jterra.2010.04.004the output shafts provides the transmission ratios. Thelockup line is also represented; it is obtained by joiningthe input shaft point to the corresponding stationary float-ing shaft. We can easily identify the operation status of thetransmission on this diagram. Assuming that Fig. 4 corre-sponds to summing planetary transmission; the differentfields of operation have been represented. For the rangeof variation of the transmission ratio drawn on the floatingshaft, the transmission would operate one half of the rangein the mechanical regenerative zone and the other half inthe non-regen