Abstract

Planetary gear set (PGS) has been one of the best components to constitute a transmission configuration, including the dedicated hybrid transmission (DHT). Using different synthesis approaches, the DHT configurations can be obtained through algorithms. However, different synthesis results correspond to different connection states of the planetary gear system. There are a certain number of results that violate the motion requirements of the mechanical principal need to be detected and removed. Therefore, this paper presents a novel modeling method to systematically remove the interference structures, with graph theory in structural synthesis. Based on the original graph theory, this paper proposes an equivalent replacement modeling method to convert the motor graph model into a brake-like graph model. Based on the conversion, avoid the appearance of the hanging points in the graph model. By applying the proposed approach, a DHT structure proves the feasibility of the method. The proposed detection approach can systematically detect all the PGS-based transmission with multi-PGSs, multi-shifting elements, and multi-power sources.

References

1.
Mingyue
,
M.
,
Yanfang
,
L.
,
Xiangyang
,
X.
, and
Dianting
,
L.
,
2014
, “
Structure Synthesis of 4-DOF Planetary Transmission
,”
J. Mech. Transm.
,
38
(
9
), pp.
34
38
.
2.
Raghavan
,
M.
,
2010
, “
The Analysis of Planetary Gear Trains
,”
ASME J. Mech. Robot.
,
2
(
2
), p.
021005
. 10.1115/1.4001092
3.
Xu
,
X.
,
Dong
,
P.
,
Liu
,
Y.
, and
Zhang
,
H.
,
2018
, “
Progress in Automotive Transmission Technology
,”
Automot. Innov.
,
1
(
3
), pp.
187
210
. 10.1007/s42154-018-0031-y
4.
Shanmukhasundaram
,
V. R.
,
Rao
,
Y. V. D.
, and
Regalla
,
S. P.
,
2021
, “Review of Structural Synthesis Algorithms for Epicyclic Gear Trains,”
Mechanism and Machine Science
,
Springer
,
Singapore
, pp.
351
375
.
5.
Chan
,
C. C.
,
2002
, “
The State of the Art of Electric and Hybrid Vehicles
,”
Proc. IEEE
,
90
(
2
), pp.
247
275
. 10.1109/5.989873
6.
Yang
,
W.
,
Ding
,
H.
, and
Kecskeméthy
,
A.
,
2018
, “
A New Method for the Automatic Sketching of Planar Kinematic Chains
,”
Mech. Mach. Theory
,
121
, pp.
755
768
. 10.1016/j.mechmachtheory.2017.11.028
7.
Yang
,
W.
, and
Ding
,
H.
,
2019
, “
The Complete Set of One-Degree-of-Freedom Planetary Gear Trains With Up to Nine Links
,”
ASME J. Mech. Des.
,
141
(
4
), p.
043301
. 10.1115/1.4041482
8.
Hopcroft
,
J.
, and
Tarjan
,
R.
,
1974
, “
Efficient Planarity Testing
,”
J. ACM
,
21
(
4
), pp.
549
568
. 10.1145/321850.321852
9.
Pei
,
H.
,
Hu
,
X.
,
Yang
,
Y.
,
Tang
,
X.
,
Hou
,
C.
, and
Cao
,
D.
,
2018
, “
Configuration Optimization for Improving Fuel Efficiency of Power Split Hybrid Powertrains With a Single Planetary Gear
,”
Appl. Energy
,
214
, pp.
103
116
. 10.1016/j.apenergy.2018.01.070
10.
Bilinski
,
M.
,
Kwon
,
Y. S.
, and
Yu
,
X.
,
2007
, “
On the Reconstruction of Planar Graphs
,”
J. Comb. Theory. Ser. B
,
97
(
5
), pp.
745
756
. 10.1016/j.jctb.2006.12.005
11.
Cortese
,
P. F.
,
Di Battista
,
G.
,
Patrignani
,
M.
, and
Pizzonia
,
M.
,
2009
, “
On Embedding a Cycle in a Plane Graph
,”
Discrete Math.
,
309
(
7
), pp.
1856
1869
. 10.1016/j.disc.2007.12.090
12.
Hsu
,
C. H.
, and
Huang
,
R. H.
,
2009
, “
Systematic Design of Six-Speed Automatic Transmissions With an Eight-Link Two-DOF Ravigneaux Gear Mechanism
,”
ASME J. Mech. Des.
,
131
(
1
), p.
011004
. 10.1115/1.3013346
13.
Lempel
,
A.
,
Even
,
S.
, and
Cederbaum
,
I.
,
1975
, “
An Algorithm for Planarity Testing of Graphs
,”
Theory Graphs (International Symposium, Rome, 1966)
,
C-24
(
2
), pp.
113
121
.
14.
Stamm-Wilbrandt
,
H.
,
1993
, “
A Simple Linear-Time Algorithm for Embedding Maximal Planar Graphs
,”
ALCOM International Workshop on Graph Drawing
,
Pairs
.
15.
Weinberg
,
L.
,
1966
, “
A Simple and Efficient Algorithm for Determining Isomorphism of Planar Triply Connected Graphs
,”
IEEE Trans. Circuit Theory
,
CT-13
(
2
), pp.
142
148
. 10.1109/TCT.1966.1082573
16.
Whitney
,
H.
,
1933
, “
A Set of Topological Invariants for Graphs
,”
Am. J. Math.
,
55
(
1/4
), p.
231
. 10.2307/2371125
17.
Hwang
,
W. M.
, and
Huang
,
Y. L.
,
2011
, “
Connecting Clutch Elements to Planetary Gear Trains for Automotive Automatic Transmissions via Coded Sketches
,”
Mech. Mach. Theory
,
46
(
1
), pp.
44
52
. 10.1016/j.mechmachtheory.2010.08.013
18.
Hsu
,
C. H.
, and
Hsu
,
J. J.
,
1997
, “
An Efficient Methodology for the Structural Synthesis of Geared Kinematic Chains
,”
Mech. Mach. Theory
,
32
(
8
), pp.
957
973
. 10.1016/S0094-114X(96)00081-X
19.
Del Castillo
,
J. M.
,
2002
, “
Enumeration of 1-DOF Planetary Gear Train Graphs Based on Functional Constraints
,”
ASME J. Mech. Des.
,
124
(
4
), pp.
723
732
. 10.1115/1.1514663
20.
Salgado
,
D. R.
, and
Del Castillo
,
J. M.
,
2005
, “
A Method for Detecting Degenerate Structures in Planetary Gear Trains
,”
Mech. Mach. Theory
,
40
(
8
), pp.
948
962
. 10.1016/j.mechmachtheory.2004.12.019
21.
Mingqi
,
R.
,
1999
, “
A Method for Geometric Compatibility Judgement of the Synthesization Diagram of the Planetary Transmission
,”
Vehicle & Power Technology
,
1
, pp.
39
43
.
22.
Shanmukhasundaram
,
V. R.
,
Rao
,
Y. V. D.
, and
Regalla
,
S. P.
,
2019
, “
Algorithms for Detection of Degenerate Structure in Epicyclic Gear Trains Using Graph Theory
,”
J. Brazilian Soc. Mech. Sci. Eng.
,
41
(
11
), p.
496
. 10.1007/s40430-019-2003-5
23.
Skerritt
,
B.
,
2018
,
Graph Theory
,
American Mathematical Society
.
24.
Xu
,
X.
,
Sun
,
H.
,
Liu
,
Y.
, and
Dong
,
P.
,
2019
, “
Automatic Enumeration of Feasible Configuration for the Dedicated Hybrid Transmission With Multi-Degree-of-Freedom and Multiplanetary Gear Set
,”
ASME J. Mech. Des.
,
141
(
9
), p.
093301
. 10.1115/1.4042846
25.
Pennestri
,
E.
,
Mariti
,
L.
,
Valentini
,
P. P.
, and
Mucino
,
V. H.
,
2012
, “
Efficiency Evaluation of Gearboxes for Parallel Hybrid Vehicles: Theory and Applications
,”
Mech. Mach. Theory
,
49
, pp.
157
176
. 10.1016/j.mechmachtheory.2011.10.012
26.
Shanmukhasundaram
,
V. R.
,
Rao
,
Y. V. D.
, and
Regalla
,
S. P.
,
2019
, “
Enumeration of Displacement Graphs of Epicyclic Gear Train From a Given Rotation Graph Using Concept of Building of Kinematic Units
,”
Mech. Mach. Theory
,
134
, pp.
393
424
. 10.1016/j.mechmachtheory.2019.01.005
27.
Li
,
Jianying
,
Xu
,
Zhiyong
, and
Zhu
,
Tianjun
,
2019
, “
Transmission Efficiency Study of Planetary Gears Transmission Based on Directed Digraph and Screw Theories
,”
Proceedings of International Conference on Mechatronics and Intelligent Robotics
,
Kunming, China
.
28.
Yang
,
W.
,
Ding
,
H.
,
Zi
,
B.
, and
Zhang
,
D.
,
2018
, “
New Graph Representation for Planetary Gear Trains
,”
ASME J. Mech. Des.
,
140
(
1
), p.
012303
. 10.1115/1.4038303
29.
Yang
,
W.
, and
Ding
,
H.
,
2018
, “
The Perimeter Loop-Based Method for the Automatic Isomorphism Detection in Planetary Gear Trains
,”
ASME J. Mech. Des.
,
140
(
12
), p.
123302
. 10.1115/1.4041572
30.
Fu
,
S.
,
Li
,
S.
, and
Luo
,
N.
,
2018
, “
Topological Transformation and Transmission Characteristics Analysis of Vehicle Auto Transmission Based on Graph Theory
,”
Shanghai Jiaotong Daxue Xuebao
,
52
(
3
), pp.
348
355
.
31.
Xu
,
X.
,
Sun
,
H.
,
Liu
,
Y.
, and
Dong
,
P.
,
2020
, “
Matrix-Based Operation Method for Detecting Structural Isomorphism of Planetary Gear Train Structures
,”
ASME J. Mech. Des.
,
142
(
6
), p.
063301
. https://doi.org/10.1115/1.4044916
32.
Holmes
,
A.
,
Liu
,
J.
,
Ames
,
D.
,
Neelakantan
,
V.
,
Rahman
,
K.
, and
Grewe
,
T.
,
2016
, “
General Motors Electric Variable Transmission for Cadillac CT6 Sedan
,”
SAE 2016 World Congress and Exhibition
,
SAE International in United States
.
33.
Demoucron
,
G.
,
Malgrange
,
Y.
, and
Pertuiset
,
R.
,
1964
, “
Graphes Planaires: Reconnais-sance et Construction de Representations Planaires Topologiques
,”
Rev. Franc. Rech. Oper.
,
8
, pp.
33
34
.
34.
Sharma
,
M. B.
,
Iyengar
,
S. S.
, and
Mandyam
,
N. K.
,
1989
, “
An Efficient Distributed Depth-First-Search Algorithm
,”
Inf. Process. Lett.
,
32
(
4
), pp.
183
186
. 10.1016/0020-0190(89)90041-0
You do not currently have access to this content.