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Research Papers: Design of Mechanisms and Robotic Systems

Kinematic Analysis of Planetary Gear Trains Based on Topology

[+] Author and Article Information
Ming-Fei Gao

National Key Laboratory of Vehicular Transmission,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: gaomingfei@bit.edu.cn

Ji-Bin Hu

National Key Laboratory of Vehicular Transmission,
Beijing Institute of Technology,
Beijing 100081, China

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 28, 2017; final manuscript received September 20, 2017; published online November 9, 2017. Assoc. Editor: Dar-Zen Chen.

J. Mech. Des 140(1), 012302 (Nov 09, 2017) (12 pages) Paper No: MD-17-1513; doi: 10.1115/1.4038072 History: Received July 28, 2017; Revised September 20, 2017

Planetary gear trains (PGTs) are used in automatic transmission to achieve any desired speed ratios. At present, the study on the relationship between speed ratio and topology is not significant. Therefore, this paper focuses on studying the speed ratio based on topology. For this purpose, the graph theory is used to represent PGTs, and a concept of the speed topological graph is introduced. Based on the proposed graph representation, the relationship between the speed ratio and topology is studied. Three types of topological graphs are analyzed, which includes path, tree, and unicyclic graph, and necessary results are presented. The results reveal the relationship between speed ratio and topology, which helps in understanding the PGTs further. The result can help engineers to arrange the clutches and brakes to achieve desired speed ratio during the conceptual design phase, which can greatly improve the design efficiency of PGTs. The presented kinematics analysis method can be extended to analyze multi-input and multi-output planetary transmission.

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References

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Figures

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Fig. 2

Planetary gear train and graph representation

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Fig. 3

Gear pair and graph representation

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Fig. 4

Braking and graph representation: (a) ring gear is braked and (b) x3 is braked

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Fig. 5

Fixed connection: (a) fixed connection with input and output and (b) fixed connection between components of PGTs

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Fig. 6

Speed topological graph

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Fig. 7

Tree topology: (a) PGT, (b) P1, and (c) P2

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Fig. 8

Speed with tree topology: (a) topological graph of speed, (b) speed path P1, (c) speed path P2, and (d) speed path Pn

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Fig. 9

Speed with unicyclic topology: type one

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Fig. 10

Speed with unicyclic topology: type two: (a) speed topological graph, (b) speed path P1, and (c) speed path P2

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Fig. 12

Toyota hybrid system

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Fig. 13

Speed design based on tree and path: (a) basic speed, (b) higher speed, (c) lower speed, and (d) reverse speed

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Fig. 14

Speed design based on unicyclic graph: (a) basic speed, (b) higher speed, (c) lower speed, and (d) reverse speed

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Fig. 15

Design based on original scheme

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Fig. 16

Allison TX-100 transmission scheme

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Fig. 17

Three speeds and topological graphs: (a) the first speed, (b) the second speed, and (c) the reverse speed

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Fig. 18

ZF 8HP transmission scheme

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Fig. 19

Four speeds and topological graphs: (a) the first speed, (b) the second speed, (c) the third speed, and (d) the reverse speed

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Fig. 20

Two speeds and topological graphs: (a) the fourth speed and (b) the eighth speed

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