Dynamic Characteristics on the Dual-Power State of Flow in Hydro-Mechanical Transmission Jibin Hu and Shihua Yuan Xiaolin Guo School of Mechanical and Vehicular Engineering Department of Automotive Engineering Beijing Institute of Technology Tsinghua University Beijing 100081, China Beijing 100084, China hujibin & Abstract In order to study the dynamic characteristics of a hydro-mechanical transmission (HMT) system, a bond graph model of the dual-power state of flow of the two ranges HMT system is established based on the bond graph theory. Taking the elements at the state variables, the state equations of the system are deduced. Based on this model, dynamic response of the HMT system is simulated. The response characteristics of output speed and systemic pressure of the HMT are given when the load, input speed and angle of slope plate of the pump change by their respective rules, and the influence of fluid volume is analyzed. The results of analysis illustrates that the HMT system needs less than 0.5s to attain the steady state in its dynamic response and will take longer when the fluid volume is increased. Index Terms Hydro-mechanical transmission, Bond graph, Dynamic characteristic I. INTRODUCTION Hydro-mechanical transmission (HMT) system is composed of hydrostatic transmission and mechanical transmission. The power flow in the hydrostatic transmission branch and the opposite in the mechanical branch are transmitted to the system output shaft through the differential mechanism in the form of power conflux. Continuously variable ratio will be obtained as the displacement of variable displacement hydrostatic unit is altered. As a type of continuously variable transmission (CVT), Hydro-mechanical transmission (HMT) system has been in use in the direct propulsion and steering system of military tracked vehicles. But, recent researches on Hydro-mechanical transmission are mainly focused on structures and static characteristics. With the application of the theory of power bond graph, we built a bond graph model of a two ranges hydro-mechanical transmission system, and simulated its dynamic characteristics. II. MODEL OF THE HMT SYSTEM A. Schematic of the HMT system The basic components of a two ranges Hydro-mechanical continuously variable transmission system are shown in Fig.1. The system consists of several components: three clutches, four planetary gear trains (PGT), a variable displacement hydrostatic unit and a fixed displacement hydrostatic unit. Planetary gear train P2and P3will work alone on conditions that clutch CLengaged and CH, CRdisengaged. It characterizes the dual-power flow mode of the two ranges HMT system. Meanwhile, the power input at gear Z1is split into two paths by gear Z21and Z22. One power input is transmitted to the hydrostatic transmission units through gear Z3. Another is transmitted to the mechanical transmission units through gear Z4. These two power flow are finally united at planetary gear train P2and transmitted to the downstream components of driveline through gears Z5, Z6and Z7. Fig. 1 Schematic of the HMT system B. System modeling According to the analyses of power flows of the hydro-mechanical transmission (HMT) system showed in Fig.1, a bond graph model of the dual-power state of flow of the system is established (shows in Fig.2), based on the bond graph theory. In Fig.2, all bonds have been numbered. Variables in different bonds can be identified by corresponding serial numbers as suffixes. For instance, effect variable and flow variable in bond 25 can be respectively denoted as e25and f25. Symbols in bond graph can be defined as follows: n0stands for power source and can be taken for a flow source, because it is speed input source of the system. Tbis load of the system and can be taken for an effect source, because it is torque input source of the system. pdlis a compensator, it is taken for a effect source here in order to keep invariable pressure in low pressure oil pipe of the hydrostatic loop. io is InputOutput1-4244-0828-8/07/$20.00 2007 IEEE. 890Proceedings of the 2007 IEEEInternational Conference on Mechatronics and AutomationAugust 5 - 8, 2007, Harbin, Chinatransmission ratio from gear Z1to Z21; ijzis the mechanical path ratio. ipis the transmission ratio from gear Z22to Z3. ihzis the conflux ratio of mechanical path. ihyis the conflux ratio of hydrostatic path. ibis the transmission ratio from gear Z5to Z7. MTF1is the variable displacement hydrostatic unit and can be describe as a variable gyrator. The modulus of the gyrator is decided by parameter qpof the signal generator. qmand qmlstand for conversion gain coefficient of the fixed displacement hydrostatic unit, furthermore, qm qml=1. 1-junction is a co-flow node in which flow variables is equal. 0-junction is a co-effect node in which effect variables is equal. 10 2019181716151413121129 28 27 26 25 24 2322219 8 7 6 5 4 3 2 1 5958575650 55 553 52 51 4847 46 4544434249 4140393837363534333231301 I Io R g541o MTF MTF1 010 TFqmSfno SeTbRRpCCpIIglCCmRRm1 R g541fmRg541bIIbI Im10 C Co 0 C CbRRgl1TF ihy 10 1TFqm1RRdlIIdlTF io R g541fp I Ip 1 Se pdl TFip 1 TF ib 0 0 1 TFihzRg541jz1IIjz1C Cjz1 011TFijzRg541jz3CCjz2IIjz3IIjz2Rg541jz2qp Fig.2 Bond graph model of the HMT system g1000is coefficient of viscous friction on input shaft (Ns/m). g100fpis coefficient of viscous friction counteracting the rotation of the variable displacement hydrostatic unit. g100fmis coefficient of viscous friction counteracting the rotation of the fixed displacement hydrostatic unit. g100bis coefficient of viscous friction on output shaft. Rglis leakage fluid resistance of oil in high pressure hydrostatic loop (Ns/m5). Rdlis leakage fluid resistance of oil in low pressure hydrostatic loop. Rpis leakage fluid resistance of oil in the variable displacement hydrostatic unit. Rmis leakage fluid resistance of oil in the fixed displacement hydrostatic unit. g100jz1is coefficient of viscous friction in drive shafting of the mechanical path transmission. g100jz2is coefficient of viscous friction in driven shafting of the mechanical path transmission. g100jz3is coefficient of viscous friction in conflux shafting. Cois coefficient of pliability of the input shaft (m/N). Cbis coefficient of pliability of the output shaft. Cpis the fluid capacitance of inner oil in the variable displacement hydrostatic unit (m5/N). Cmis the fluid capacitance of inner oil in the fixed displacement hydrostatic unit. Cjz1is coefficient of pliability of the drive shafting of the mechanical path transmission. Cjz2is coefficient of pliability of the driven shafting of the mechanical path transmission. Iois the moment of inertia of the input shaft. Ipis the moment of inertia of the variable displacement hydrostatic unit. Imis the moment of inertia of the fixed displacement hydrostatic unit. Ibis the moment of inertia of the output shaft. Iglis the fluid inductance in high pressure oil loop (Ns/m5). Idlis the fluid inductance in low pressure oil loop. Ijz1is the moment of inertia of the drive shafting of the mechanical path transmission. Ijz2is the moment of inertia of the driven shafting of the mechanical path transmission. Ijz3is the moment of inertia of the conflux shafting. C. State equations of the HMT system Analyzing the dynamic characteristic of system using bond graph methods need to choose state variables of system reasonably and establish state equation of the system according to the known bond graph model of system. In a general way, the generalized momentum p of inertial unit and the generalized displacement of capacitive unit are introduced as state variables of system 510. If causalities of the bond graph are annotated according to principle of priority of the integral causality, some energy storage elements in bond graph maybe have differential causality on occasion. Under the circumstances, the amount of state variables of the system is equal to the counterpart of energy storage elements which have the integral causality. Energy variables of the energy storage elements which have the differential causality depend upon state variables of the system. These variables are dependent variables. Algebraic loop problem will occur while establishing state equation of 891these kinds of bond graph. The bond graph model of the HMT system established as above belongs to these kinds. In Fig.2, energy variables in inertial elements Io, Ijz2and Imhave differential causalities. The resolution is to express the generalized momentum and the generalized displacement of energy storage elements which have the differential causality with involved state variables and to work out the first derivative of these equations toward time. The expressions of the inertial elements Io, Ijz2and Imare derived as follows: 274pIIiippopog6g6 g32(1) 111215pIiIpjzjzjzg6g6 g32(2) 43149pIqIpdlmmg6g6 g32(3) Therefore, the amount of state variables of the HMT system is just 12: )(2tq, )(9tq, )(11tp,)(18tq,)(20tp, )(27tp, )(31tq,)(34tp, )(37tq, )(43tp, )(55tq, )(58tp. The input state vector: U g62g64TbdloTpng32 . According to the structural characteristics of the system shown by bond graph, the differentials of state variables can be describe as functions of state variables related to input variables. 12 state equations can be formulated as follows: 272pIiinqppoog16g32g6(4) 2711191pIipIqppjzg14g16g32g6(5) 1821112112129111111qCiCpiICiqCCpjzjzjzjzjzjzjzjzg16g14g16g32g80g80g6(6) 2031111811pIpIiqjzjzjzg16g32g6(7) 5520331822011qCiipIqCpbbhzjzjzjzg16g16g32g80g6 (8) 272229122227pICliqCCiqCCiippopofpjzpopog80g80 g14g16g16g32g6dlppppCqtqCCqt2312)()( g72g72g14g16(9) 3431273111)(pIqCRpIqtqglppppg16g16g32g72g6 (10) 3734313411qCpIRqCpmglglpg16g16g32g6(11) 43373437111pIqCRpIqdlmmglg16g16g32g6(12) 43232373431pIqCRqqCCpdlmdlmfmmg14g16g32g80g6dlbbhympCqCiiqC355311g16g16(13) 584320355111pIpIqiipIiiqbdlmbhyjzbhzg16g14g32g6(14) bbbbTpIqCp g14g16g325855581 g80g6(15) Where, 121211jzjzjzIiIC g14g32, popoIIiiC2221g14g32, 231mdlmqIIC g14g32. III. SIMULATION RESULTS In these equations above, with the structural and calculative parameters of the known HMT system, dynamic simulation can be done in computer. In the process of simulation, initial values are given primarily. After the system stabilized, input signal is stimulated. Meanwhile, the results of dynamic response of the system are recorded. The response curves of the output speed of system and the oil pressure in main pipe of the bump-motor system under varied input signals are shown from Fig.3 to Fig.8. Fig.3 shows the pulsed response curves of the output speed and the oil pressure of the system as the load change instantaneously. The rising time of the oil pressure response is 22ms. The control time is 445ms. The overshoot is equal to 86%. Times (s) Fig. 3 Pulsed response of the system as load changing Pressure Output speed Speed response (rpm)Pressure response (MPa) 892 Fig.4 shows the pulsed response curves of the output speed and the oil pressure of the system as the speed changes instantaneously. The rising time of the speed response is 17ms. The control time is 479ms. The overshoot is equal to 65%. Times (s) Fig. 4 Pulsed response of the system as speed changing Fig.5 shows a group of slope response curves as the angle of swing plate of the variable displacement bump is a ramp excitation. In this figure, the ascending gradients of the angle of swing plate whose range is from 0 to its maximum (correspondingly, relative rate of changing displacement is from 0 to 1, i.e. 10g32g72 ) are assigned some values respectively, such as 50, 20, 8, 4 (corresponding rising time for ramp excitation are 0.04, 0.10, 0.25, 0.50s). The rising times of response of the output speed are 43, 108, 255, 505 ms. Overshoot are respectively 47%, 12%, 4%, 2%. Times (s) Fig. 5 Slope response of the system as angle of swing plate changing Fig.6 shows the pulsed response curves of the output speed and the main oil pressure of the system as the angle of swing plate changes instantaneously. The rising time of the speed response is 22ms. The control time is 420ms. The overshoot is equal to 73%. The bond graph model of the two range HMT system established by the author is a linear system. The results of simulation demonstrate that the speed of response of the system is quite fast and the stability is satisfactory, but the overshoot of step response is too large. On condition that the input signal is ramp type and the gradients is greater than 8 (the time interval in which the angle of swing plate changed from 0 to the maximum is not less than 0.25s), the transition process of the system whose overshoot will not exceed 5% will approach steady state. Times (s) Fig. 6 Pulsed response of the system as angle of swing plate changing The results of simulation indicated by Fig.3 Fig.6 is acquired on condition that the fluid capacitances Cmand Cpin the model denoted in Fig.2 are set to 0.0085. As other conditions are invariable, response curves indicated by Fig.7 and Fig.8 can be obtained for Cmand Cpare set to 0.0850. Fig.7 shows the slope response curves of the rotation speed and the pressure as the angle of swing plate changes on the principle of ramp excitation. The rising times of response of the output speed are 87, 121, 204, 519 ms. Overshoot are respectively 52%, 38%, 11%, 5%. Times (s) Fig. 7 Slope response of the system when Cmand Cpare set to 0.0850 Pressure Output speed Speed response (rpm)Pressure response (MPa) Pressure Output speed Speed response (rpm)Pressure response (MPa) Pressure Output speed Speed response (rpm)Pressure response (MPa) PressureOutput speed Speed response (rpm)Pressure response (MPa) 893 Fig.8 shows the pulsed response curves of the rotation speed and the pressure. The rising time of response of the output speed is 68ms. Overshoot is 57%. Compared with the results of simulation indicated in Fig.5 and Fig.6, the speed of response of the system is slowing down and the time interval needed to reach the steady state is delayed. At the same time, the number of oscillations of the response and fluctuating quantity of the pressure is decreasing. The overshoot of the pulsed response increased a little, but the overshoot of the slope response increased a bit as well. Times (s) Fig. 8 Pulsed response of the system when Cmand Cpare set to 0.0850 IV. CONCLUSIONS A bond graph model of the dual-power state of flow of the two ranges HMT system is established based on the bond graph theory. The model can be applied to simulate and study the dynamic characteristics of a hydro-mechanical transmission (HMT) system. On conditions that the displacement of the hydrostatic bump is constant, the system focused in this article can be simplified to a linear stationary system. On conditions that the displacement of the hydrostatic bump changes along with time, the system is a linear time varying system; the transition of the system approaches to stable state while the ramp input signal draws 8s. The value of the fluid capacitance in the hydrostatic system affects the dynamic response performance of the system. A further study on the influence of the fluid capacitance and the fluid resistance will be done. REFERENCES 1 X. Liu, Analysis of Vehicular Transmission System, Beijing: Natio