A Novel Algorithm for Enumeration of the Planetary Gear Train Based on Graph Theory

2011 ◽  
Vol 199-200 ◽  
pp. 392-399 ◽  
Author(s):  
Ming Yue Ma ◽  
Xiang Yang Xu
Keyword(s):  
Graph Theory ◽  
Mechanism Design ◽  
Planetary Gear ◽  
Gear Train ◽  
Enumeration Algorithm ◽  
Planetary Gear Train ◽  
The Core ◽  
Planet Gear ◽  
Gear Trains ◽  
Novel Algorithm

As well known, graph theory is a powerful tool for mechanism design. The enumeration of planet gear trains can be converted the synthesis of graphs while a planetary gear train is converted to a graph. During the enumeration of graphs, the problem of isomorphism should be solved. This paper proposes a novel algorithm used to generate non-isomorphism graphs and thereby omits the part of isomorphism detection. The vertex characteristic is firstly defined in this paper that is the core of the enumeration algorithm. This paper also gives an example of the application for the algorithm.

Investigation of Power Transmission Mechanism Under Three-Axis Driving Planetary Gear Train Based on the Mechanism

2016 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Power Transmission ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Gear Train ◽  
Experimental Result ◽  
Planetary Gear Train ◽  
Planetary Gear Trains ◽  
Planet Gear ◽  
Gear Trains ◽  
Driving Condition

Planetary gear trains are presently widely used in various machines owing to their many advantages. They, however, suffer from problems of noise and vibration due to their structural complexity. Moreover, their dynamic characteristics are yet to be fully understood. Although several studies have been conducted on two-axis driving and displacement of planet gear, none has considered three-axis driving. In the present study, the general driving conditions of a planetary gear train, including during three-axis driving, were investigated based on the theory of instant center. Ideal driving condition is proposed based on the experimental result on three-axis driving which was tested on an original fully wireless test stand.

Conditions for Self-Locking in Planetary Gear Trains

2006 ◽  
Vol 129 (9) ◽  
pp. 960-968 ◽  
Author(s):  
David R. Salgado ◽  
J. M. del Castillo
Keyword(s):  
Planetary Gear ◽  
Degree Of Freedom ◽  
The Self ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Analytical Expression ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Approximate Relationship ◽  
Gear Trains

The objective of the present work is to determine the conditions that have to be satisfied for a planetary gear train of one degree of freedom to be self-locking. All planetary gear trains of up to six members are considered. As a result, we show the constructional solutions of planetary gear trains exhibiting self-locking. Unlike other studies, the self-locking conditions are obtained systematically from the analytical expression for the product of the efficiency of a given train by the efficiency of the train resulting from interchanging its input and output axes. Finally, a proof is given of an approximate relationship between these two efficiencies.

Investigation of Planet Gear Motion in a Planetary Gear Train With Direct High Speed Monitoring

2018 ◽  
Author(s):  
Tomoki Fukuda ◽  
Masao Nakagawa ◽  
Syota Matsui ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
High Speed ◽  
Planetary Gear ◽  
Gear Train ◽  
Improved Method ◽  
Lighting Conditions ◽  
Planetary Gear Trains ◽  
Low Weight ◽  
Torque Capacity ◽  
Planet Gear ◽  
Gear Trains

Planetary gear trains (PGTs) are widely applied in various machines owing to their advantages, such as compactness, low weight, and high torque capacity. However, they experience the problems of vibration due to the structural and motional complexities caused by planet gears. In a previous study, it was shown that high speed monitoring is effective for evaluating the motion of planet gears under steady conditions and transient conditions including the influence of backrush. However graphical investigation was conducted manually, and improvement in accuracy is required. In this report, an improved method is proposed, which includes lighting conditions and measurement conditions. Throughout these improvement processes, instant center of rotation is calculated automatically with detected coordinates using software. This makes it possible to estimate the transient response of PGTs with planet gear motion.

Tooth Contact Analysis of Planetary Gear Trains with Equally Spaced Planets

2010 ◽  
Vol 43 ◽  
pp. 279-282
Author(s):  
Kai Xu ◽  
Xiao Zhong Deng ◽  
Jian Jun Yang ◽  
Guan Qiang Dong
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Spur Gear ◽  
Contact Analysis ◽  
Gear Train ◽  
Tooth Contact Analysis ◽  
Planetary Gear Train ◽  
Tooth Contact ◽  
Gear Trains ◽  
Equal Space

Based on Tooth Contact Analysis (TCA), a feasible approach for Transmission Error (TE) of planetary gear train is proposed in this paper. With a view to getting the total TE curve of the planetary gear train, a specific analysis of the TE from the planetary gear train with only one planet should be proceed firstly, the second step is to calculate each phase difference of planets in the gear train. The applicable conditions for the simplified calculation are spur gear or involute gear pairs in the gear train. Due to equal space between them, planets have the same phase angle.

The Analysis of Planetary Gear Trains

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Madhusudan Raghavan
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Compact Representation ◽  
Planetary Gear Train ◽  
Traditional Concept ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Large Families ◽  
Case Basis

The generalized lever is a new tool in gear train representation. It extends the traditional concept of a lever representation of a planetary gear set to 1 that includes negative lever ratios. This allows an exhaustive permutation of the nodes of a lever, thereby leading to all possible topological arrangements of a planetary gear train. Consequently, we achieve a compact representation of large families of planetary gear trains, which would otherwise have to be dealt with on a case-by-case basis.

The Kinematics of Eight-Speed Planetary Gear Hubs for Bicycles

2012 ◽  
Vol 232 ◽  
pp. 955-960 ◽  
Author(s):  
Long Chang Hsieh ◽  
Hsiu Chen Tang
Keyword(s):  
Design Methodology ◽  
Planetary Gear ◽  
Design Concept ◽  
Gear Train ◽  
Transmission Systems ◽  
Planetary Gear Train ◽  
Kinematic Design ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Internal Gear

Recently, bicycles are used as exercising machines and traffic vehicles. Planetary gear trains can be used as the transmission systems with multi-speed for bicycles. The purpose of this work is to propose a design methodology for the design of eight-speed internal gear hubs with planetary gear trains for bicycles. First, we propose a design concept for the design of eight-speed planetary gear hub. Then, based on this design concept and train value equation of planetary gear train, the kinematic design of eight-speed planetary gear hub is accomplished. One eight-speed planetary gear hub is synthesized to illustrate the design methodology. Based on the proposed design methodology, many eight-speed internal gear hubs with planetary gear trains can be synthesized.

scholarly journals Work of the planetary gear trains as differentials and their capabilities

2019 ◽  
Vol 287 ◽  
pp. 04001
Author(s):  
Kiril Arnaudov ◽  
Stefan Petrov ◽  
Emiliyan Hristov
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Gear Train ◽  
Motor Drive ◽  
Planetary Gear Train ◽  
Maximum Security ◽  
Single Carrier ◽  
Planetary Gear Trains ◽  
Gear Trains

Planetary gear trains can work differently, namely, with F=1 degree of freedom, i.e. as reducers or multipliers, and also with F=2 degrees of freedom, i.e. as differentials. Moreover, with a two-motor drive they work as a summation planetary gear train and with a one-motor drive, they work as a division planetary gear train. The most popular application of planetary gear trains is as a differential which is bevel and is produced globally in millions of pieces. Some of the cylindrical planetary gear trains can also be used as differentials. Although less often, they are used in heavy wheeled and chain vehicles such as trailer trucks, tractors and tanks. They are also very suitable for lifting machines with a two-motor drive which provides maximum security for the most responsible cranes, such as the metallurgical ones. Initially the paper presents some simple, i.e. single-carrier cylindrical planetary gear trains, both with external and internal meshing, driven by 2 motors. Their kinematic capabilities and velocity, respectively, are considered to realize the necessary gear ratio. Finally, the case of a compound two-carrier planetary gear train is considered, which is composed of 2 simple planetary gear trains. This shows that not only the simple planetary gear trains, i.e. the single-carrier ones, can work as differentials.

A Method for the Identification of Displacement Isomorphism of Planetary Gear Trains

1992 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Kin-Tak Lam
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Mathematical Representation ◽  
Automatic Identification ◽  
Planetary Gear Train ◽  
Rotational Displacement ◽  
Interactive Computer Program ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Structural Code

Abstract The purpose of this paper is to present an efficient method for the identification of the displacement isomorphism of planetary gear trains. For every planetary gear train, the kinematic structure is characterized by its displacement graph and rotation graph. A mathematical representation, called the Structural Code, is introduced to represent the topological structure of the displacement graph and rotation graph of a planetary gear train. Based on the Structural Codes of displacement graphs and rotation graphs, the linear and rotational displacement isomorphism of planetary gear trains can be identified in an unambiguous way. Finally, an interactive computer program is developed for the automatic identification of the displacement isomorphism of planetary gear trains.

A PLANETARY GEAR TRAIN WITH RING-INVOLUTE TOOTH

2008 ◽  
Vol 32 (2) ◽  
pp. 251-266
Author(s):  
Shyue-Cheng Yang ◽  
Tsang-Lang Liang
Keyword(s):  
Planetary Gear ◽  
Conjugate Problem ◽  
Gear Ratio ◽  
Gear Train ◽  
Tooth Surface ◽  
The Sun ◽  
Ring Gear ◽  
Planetary Gear Train ◽  
Envelope Method ◽  
Planet Gear

This paper proposes a planetary gear train with ring-involute tooth profile. Inherent in a planetary gear train is the conjugate problem among the sun, the planet gears and the ring gear. The sun gear and the planet gear can be obtained by applying the envelope method to a one-parameter family of a conical tooth surface. The conical tooth rack cutter was presented in a previous paper [5]. The obtained planet gear then becomes the generating surface. The double envelope method can be used to obtain the envelope to the family of generating surfaces. Subsequently the profile of a ring gear of the planetary gear trains can be easily obtained, and using the generated planet gear and applying the gear theory, the ring gear is generated. To illustrate, the planetary gear train with a gear ratio of 24:10:7 is presented. Using rapid prototyping and manufacturing technology, a sun gear, four planet gears, and a ring gear are designed. The RP primitives provide an actual full-size physical model that can be analyzed and used for further development. Results from these mathematical models are applicable to the design of a planetary gear train.

Research on Calculation of Unloaded Transmission Error of Planetary Gear Train Caused by Eccentricity

2017 ◽  
Author(s):  
Shuaidong Zou ◽  
Guangjian Wang ◽  
Li Yu
Keyword(s):  
Curve Fitting ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear Train ◽  
Computational Formula ◽  
Planetary Gear Train ◽  
Ratio Error ◽  
Load Transmission ◽  
Planet Gear ◽  
Load Conditions

In this paper, calculation of no-load transmission error (TE) of planetary gear train is studied. The theory computational model of the eccentric planetary gear train with single planet gear (SPG) under no-load conditions is constructed initially for acquiring the formulas of no-load transmission ratio error and unloaded transmission error (UTE) of internal and external gear pairs. Then computational formula of the UTE of planetary gear train with SPG caused by eccentricity is presented. Through simulation TE and the developed formula of UTE, the eccentricities and initial phasing are uncoupled by curve fitting. Simultaneously, formula of UTE of planet gear train with SPG is validated. At the same time, different groups of initial phasing are analyzed to acquire the relatively good initial phasing group. In addition, the UTE of planetary gear train with multiple planet gears (MPG) caused by eccentricity is developed.

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