scholarly journals Random Vibration and Dynamic Analysis of a Planetary Gear Train in a Wind Turbine

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Jianming Yang ◽  
Ping Yang
Keyword(s):  
Random Vibration ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Gear Train ◽  
Premature Failure ◽  
Shaping Filter ◽  
Vibration Responses ◽  
Gear Trains ◽  
Dynamic Meshing

Premature failure of gearboxes is a big challenge facing the wind power industry. It highly depends on fully understanding the embedded dynamics to solve this problem. To this end, this paper investigates the random vibration and dynamics of planetary gear trains (PGTs) in wind turbines under the excitation of wind turbulence. The turbulence is represented by the Von Karmon spectrum and implemented by passing white noise through a 2nd-order shaping filter. Then, extra equations are formed and added to the original governing equations of motion. With this augmented equation set, a recursive numerical algorithm based on stochastic Newmark scheme is applied to solve for the statistics of the responses starting from initial conditions. After simulation, the variances of the vibration responses and the dynamic meshing forces at gear meshes are obtained.

Signal Flow Graphs for Spatial Gear Trains

1994 ◽  
Vol 116 (1) ◽  
pp. 326-331 ◽  
Author(s):  
R. Ma ◽  
K. C. Gupta
Keyword(s):  
Operations Research ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Gear Train ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
System Variables ◽  
Flow Graphs

Signal flow graphs (SFG) have been applied in many areas such as circuit analysis, controls, mechanical vibrations, statistics, and operations research. They have also been applied to the analysis of planetary gear trains which are planar, i.e., where all of the gear axes are parallel. In this paper, signal flow graphs are applied to spatial planetary gear trains. Some additional terminology and rules which are needed for this important application are developed in this paper and illustrated by examples. The significance of applying SFG to a gear system is that the graph describes the interrelationship among the system variables by linking causes and effects, offers the information about the topology of system connection, and the kinematic equations of motion can be written easily by inspection. In this way, it helps use to visualize and understand spatial gear train systems better.

Symbolic Notation and Kinematic Equations of Motion of the Twenty-Two Basic Spur Planetary Gear Trains

1984 ◽  
Vol 106 (3) ◽  
pp. 333-340 ◽  
Author(s):  
D. Gibson ◽  
S. Kramer
Keyword(s):  
Equations Of Motion ◽  
Planetary Gear ◽  
Equation Of Motion ◽  
Gear Train ◽  
Kinematic Equation ◽  
Planetary Gear Trains ◽  
Symbolic Notation ◽  
Planet Gear ◽  
Gear Trains ◽  
Simple Notation

This paper introduces a symbolic notation for describing two degree-of-freedom spur planetary gear trains with the configuration of two central gears, one carrier or arm, and at least one planet gear. This simple notation is then used to write the kinematic equation of motion for this type of planetary gear train without the need to develop any intermediate equations. It is also shown that, there are exactly 22 basic spur planetary gear trains with this configuration and not 34 as Levai [1] previously found. These 22 planetary gear trains are illustrated along with their symbolic notation and kinematic equation of motion.

A New Technique Based on Loops to Investigate Displacement Isomorphism in Planetary Gear Trains

2002 ◽  
Vol 124 (4) ◽  
pp. 662-675 ◽  
Author(s):  
V. V. N. R. Prasad Raju Pathapati ◽  
A. C. Rao
Keyword(s):  
Graph Isomorphism ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Graph Representations ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
A New Technique

The most important step in the structural synthesis of planetary gear trains (PGTs) requires the identification of isomorphism (rotational as well as displacement) between the graphs which represent the kinematic structure of planetary gear train. Previously used methods for identifying graph isomorphism yielded incorrect results. Literature review in this area shows there is inconsistency in results from six link, one degree-of-freedom onwards. The purpose of this paper is to present an efficient methodology through the use of Loop concept and Hamming number concept to detect displacement and rotational isomorphism in PGTs in an unambiguous way. New invariants for rotational graphs and displacement graphs called geared chain hamming strings and geared chain loop hamming strings are developed respectively to identify rotational and displacement isomorphism. This paper also presents a procedure to redraw conventional graph representation that not only clarifies the kinematic structure of a PGT but also averts the problem of pseudo isomorphism. Finally a thorough analysis of existing methods is carried out using the proposed technique and the results in the category of six links one degree-of-freedom are established and an Atlas comprises of graph representations in conventional form as well as in new form is presented.

Conceptual Design of Gear Differentials for Automotive Vehicles

1994 ◽  
Vol 116 (2) ◽  
pp. 565-570 ◽  
Author(s):  
Hong-Sen Yan ◽  
Long-Chang Hsieh
Keyword(s):  
Conceptual Design ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear Train ◽  
Design Constraints ◽  
Two Degrees Of Freedom ◽  
Design Concepts ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Gear Differential

An automotive gear differential is a joint-fractionated planetary gear train with two degrees-of-freedom. We summarize the characteristics of planetary gear trains and the design constraints of noncoupled automotive gear differentials to synthesize their corresponding kinematic graphs. Based on these graphs and the proposed respecializing process, we generate the atlas of design concepts for automotive gear differentials with any types of gear pairs. As a result, there are 4, 25, and 156 design concepts for five-, six-, and seven-bar automotive gear differentials, respectively.

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.

The Kinematic Design of 2K-2H Planetary Gear Reducers with High Reduction Ratio

2013 ◽  
Vol 319 ◽  
pp. 610-615 ◽  
Author(s):  
Long Chang Hsieh ◽  
Hsiu Chen Tang
Keyword(s):  
Planetary Gear ◽  
Reduction Ratio ◽  
Gear Train ◽  
Design Algorithm ◽  
Kinematic Design ◽  
Planetary Gear Trains ◽  
Kinematic Relationship ◽  
Gear Trains ◽  
High Reduction ◽  
Relationship Of

The power system equipped in machinery contains power source (motor or engine) and gear reducer to get large output torque. The rotation speed of motor is made higher and higher to obtain high power with the same volume. Hence, the reduction ratio of gear reducer is required to be higher and higher. Planetary gear trains can be used as the gear reducers with high reduction ratio. However, the planetary gear train with high reduction ratio is compound gear system. The purpose of this paper is to propose 2K-2H type planetary gear reducers with high reduction ratio. Based on the concept of train value equation, we propose a new representation to present the kinematic relationship of the members of the train circuit. According to this representation graph, we propose an algorithm for the kinematic design of planetary simple gear trains with high reduction ratio. Some 2K-2H type planetary gear reducers are designed to illustrate the design algorithm.

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