Recirculation is expected to be identified for its possibility to dramatically decrease the efficiency of planetary gear trains (PGTs). However, it exhibits an unexplained connection with the structure, making it challenging to identify without tedious computation through tooth and speed ratios, thus complicating the design process. This study employs a generic model utilizing the mechanical balance principle and reveals the fundamental laws of the previously unexplained connection for parallel-connected ring-sun-type PGTs. Two necessary and sufficient conditions, torque and structure, were proven for multi-stage and two-stage PGTs without recirculation, respectively. This shows that the structure, specifically whether the links are central gears or carriers, and the connections between them directly impact the recirculation of these PGTs. A geometric model representing the structure and kinematics was developed to visualize the power flow. Thus, the recirculation of parallel-connected ring-sun-type PGTs can be predicted without calculations. Our results provide the underlying insights to understanding recirculation from the structural connection viewpoint, thereby contributing to the conceptual design phase where the task is to select the kinematic structure and the gear size is unknown.
Hong Chen
,
Xiao-An Chen
. Recirculation of Parallel-Connected Planetary Gear Trains[J]. Chinese Journal of Mechanical Engineering, 2022
, 35(2)
: 27
-27
.
DOI: 10.1186/s10033-022-00703-6
Recirculation is expected to be identified for its possibility to dramatically decrease the efficiency of planetary gear trains (PGTs). However, it exhibits an unexplained connection with the structure, making it challenging to identify without tedious computation through tooth and speed ratios, thus complicating the design process. This study employs a generic model utilizing the mechanical balance principle and reveals the fundamental laws of the previously unexplained connection for parallel-connected ring-sun-type PGTs. Two necessary and sufficient conditions, torque and structure, were proven for multi-stage and two-stage PGTs without recirculation, respectively. This shows that the structure, specifically whether the links are central gears or carriers, and the connections between them directly impact the recirculation of these PGTs. A geometric model representing the structure and kinematics was developed to visualize the power flow. Thus, the recirculation of parallel-connected ring-sun-type PGTs can be predicted without calculations. Our results provide the underlying insights to understanding recirculation from the structural connection viewpoint, thereby contributing to the conceptual design phase where the task is to select the kinematic structure and the gear size is unknown.
[1] E Pennestrì, L Mariti, P P Valentini, et al. Efficiency evaluation of gearboxes for parallel hybrid vehicles: Theory and applications. Mechanism and Machine Theory, 2012, 49: 157–176.
[2] J M del Castillo. The analytical expression of the efficiency of planetary gear trains. Mechanism and Machine Theory, 2002, 37(2): 197–214.
[3] E Pennestrì, F Freudenstein. A systematic approach to power-flow and static-force analysis in epicyclic spur-gear trains. Journal of Mechanical Design, 1993, 115(3): 639–644.
[4] C Chen. Power flow analysis of compound epicyclic gear transmission: simpson gear train. Journal of Mechanical Design. 2011, 133(9): 945021–945025.
[5] A K Gupta, C P Ramanarayanan. Analysis of circulating power within hybrid electric vehicle transmissions. Mechanism and Machine Theory, 2013, 64: 131–143.
[6] G White. Derivation of high efficiency two-stage epicyclic gears. Mechanism and Machine Theory, 2003, 38(2): 149–159.
[7] A Kahraman, H Ligata, K Kienzle, et al. A Kinematics and power flow analysis methodology for automatic transmission planetary gear trains. Journal of Mechanical Design, 2004, 126(11): 1071–1081.
[8] F Yang, J Feng, H Zhang. Power flow and efficiency analysis of multi-flow planetary gear trains. Mechanism and Machine Theory, 2015, 92: 86–99.
[9] E L Esmail, S S Hassan. An approach to power-flow and static force analysis in multi-input multi-output epicyclic-type transmission trains. Journal of Mechanical Design, 2010, 132(1): 0110091–01100910.
[10] R A Lloyd. Power flow and ratio sensitivity in differential systems. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 1991, 205(1): 59–67.
[11] D R Salgado, J M del Castillo. Selection and design of planetary gear trains based on power flow maps. Journal of Mechanical Design, 2005, 127(1): 120–134.
[12] T Ciobotaru, D Frunzeti, I Rus, et al. Method for analysing multi-path power flow transmissions. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2010, 224(9): 1447–1454.
[13] D R Salgado, J M del Castillo. Analysis of the transmission ratio and efficiency ranges of the four-, five-, and six-link planetary gear trains. Mechanism and Machine Theory, 2014, 73: 218–243.
[14] G Del Pio, E Pennestrì, P P Valentini. Kinematic and power-flow analysis of bevel gears planetary gear trains with gyroscopic complexity. Mechanism and Machine Theory, 2013, 70: 523–537.
[15] E Pennestrì, F Freudenstein. The mechanical efficiency of epicycle gear trains. Journal of Mechanical Design, 1993, 115(3): 645–651.
[16] D Yu, N Beachley. On the mechanical efficiency of differential gearing. Journal of Mechanisms Transmissions and Automation in Design, 1985, 107(1): 61–67.
[17] L C Hsieh, H C. Tang. On the meshing efficiency of 2K-2H type planetary gear reducer. Advances in Mechanical Engineering, 2015, 5(5): 686187.
[18] C Chen. Power flow and efficiency analysis of epicyclic gear transmission with split power. Mechanism and Machine Theory, 2013, 59: 96–106.
[19] C Chen, T T Liang. Theoretic study of efficiency of two-DOFs of epicyclic gear transmission via virtual power. Journal of Mechanical Design, 2011, 133(3): 0310071–0310077.
[20] Z Lévai. Structure and analysis of planetary gear trains. Journal of Mechanisms, 1968, 3: 131–148.
[21] X A Chen, H Chen. Analytical geometry method of planetary gear trains. Science China Technological Sciences, 2012, 55(4): 1007–1021.
[22] R Mathis, Y Remond. Kinematic and dynamic simulation of epicyclic gear trains. Mechanism and Machine Theory, 2009, 44(2): 412–424.
[23] C S Ross, W D Route. A method for selecting parallel-connected, planetary gear train arrangements for automotive automatic transmissions. SAE Technical Paper Series, 1991, 911941.
[24] F Buchsbaum, F Freudenstein. Synthesis of kinematic structure of geared kinematic chains and other mechanisms. Journal of Mechanisms, 1970, 5(3): 357–392.
[25] R J Willis. On the kinematics of the closed epicyclic differential Gears. Journal of Mechanical Design, 1982, 104(4): 712–719.
[26] T L Xie, J B Hu, Z X Peng, et al. Synthesis of seven-speed planetary gear trains for heavy-duty commercial vehicle. Mechanism and Machine Theory, 2015, 90(8): 230–239.
