Transmission Analysis—Automatic Derivation of Relationships

1993 ◽  
Vol 115 (4) ◽  
pp. 1031-1037 ◽  
Author(s):  
A. Hedman
Keyword(s):  
Computer Program ◽  
Planetary Gear ◽  
Mechanical Transmission ◽  
Transmission Systems ◽  
Human Errors ◽  
Planetary Gear Trains ◽  
Computer Aided Analysis ◽  
Analysis And Synthesis ◽  
Gear Trains ◽  
Overall Efficiency

A method for derivation of relationships for general mechanical transmission systems is given. It is adapted for computer-aided analysis and synthesis of the kinematics, loads, and power flows. Losses are included. All relationships are handled by a computer program. No manual dealing with equations is necessary. The user only describes the transmission systems: (1) The transmission units, e.g., gear transmissions, planetary gear trains, clutches and input shafts. (2) How the shafts of those units are connected. Then, the computer program formulates the relationships, and a computer algebra program performs algebraic eliminations. Symbolic, non-numerical, relationships between speeds and torques of two arbitrary shafts can be derived, e.g., the overall efficiency. Special algorithms handle the power flows in split-power transmissions. The method saves time and eliminates the risk for human errors.

Transmission Analysis: Automatic Derivation of Relationships

1992 ◽  
Author(s):  
Anders Hedman
Keyword(s):  
Computer Program ◽  
Planetary Gear ◽  
Mechanical Transmission ◽  
Human Errors ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Computer Aided Analysis ◽  
Analysis And Synthesis ◽  
Commercial Program ◽  
Gear Trains

Abstract A method for derivation of relationships for general mechanical transmission systems is given. The method is adapted for computer aided analysis and synthesis of the kinematics, loads and power flows. Losses are included. All relationships are handled by a computer program. No manual formulation and elimination of equations are necessary. The user only needs to describe the transmission system: 1. The transmission units, e.g. gear transmissions, planetary gear trains, clutches, input and output shafts. 2. How the shafts of those units are connected. Then, the computer program formulates and arranges the relationships. After that, a commercial program, “Maple”, performs the algebraic eliminations. Relationships between the speeds and/or torques of two arbitrary shafts can be derived, e.g. an algebraic relationship for the overall efficiency. Different power flows are possible in split-power transmissions. Special algorithms handle that. The method is a useful tool. It saves time and eliminates the risk for human errors.

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.

Automatic Analysis of Kinematic Structure of Planetary Gear Trains

1993 ◽  
Vol 115 (3) ◽  
pp. 631-638 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Kin-Tak Lam
Keyword(s):  
Computer Program ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Automatic Analysis ◽  
Kinematic Structure ◽  
Identification Number ◽  
Interactive Computer Program ◽  
Planetary Gear Trains ◽  
Gear Trains

This paper presents a systematic algorithm for the automatic analysis of the kinematic structure of planetary gear trains with any number of degrees of freedom. The canonical displacement graphs and rotation graphs are introduced to represent the kinematic structure of planetary gear trains. Next, a single identification number method is presented to identify the displacement isomorphism of planetary gear trains. Then, nonfractionated multi-DOF planetary gear trains can be identified from their rotation graphs. Finally, an interactive computer program is developed for the automatic analysis of the kinematic structure of planetary gear trains. The result of this work is beneficial to the development of the new planetary gear trains.

The Systematic Design of Multi-Speed Internal Gear Hub for a Bicycle

2011 ◽  
Vol 199-200 ◽  
pp. 431-435 ◽  
Author(s):  
Long Chang Hsieh ◽  
Tzu Hsia Chen
Keyword(s):  
Design Methodology ◽  
Planetary Gear ◽  
Systematic Design ◽  
Transmission Systems ◽  
Kinematic Design ◽  
Planetary Gear Trains ◽  
Kinematic Relationship ◽  
Gear Trains ◽  
Relationship Of ◽  
Internal Gear

The bicycle is invented so far more than 200 years. Now, bicycles are used as exercising equipments 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 multi-speed internal gear hubs with planetary gear trains for bicycles. Based on the concept of train value equation and the kinematic relationship of the members between the train circuit, we propose a design methodology for the kinematic design of multi-speed gear hubs. One multi-speed internal gear hubs is designed to illustrate the design methodology. Based on the proposed methodology, all multi-speed gear hubs with planetary gear trains can be synthesized.

scholarly journals An Analysis of the Gear Meshing Characteristics of the Main Planetary Gear Trains of Helicopters Undergoing Shafting Position Changes

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Li Xuejun ◽  
Jiang Lingli ◽  
Hua Dengrong ◽  
Yin Daoxuan ◽  
Yang Dalian
Keyword(s):  
Planetary Gear ◽  
The Sun ◽  
Mass Center ◽  
Main Rotor ◽  
Transmission Systems ◽  
Planetary Gears ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Meshing Characteristics ◽  
Helicopter Transmission

The complex three-shaft three-reducer structural designs of helicopter transmission systems are prone to changes in the relative positions of shafting under the conditions of main rotor and tail rotor loads. These changes will affect the transmission characteristics of the entire transmission system. In this study, the planetary gear trains of helicopters were examined. Due to the fact that these structures are considered to be the most representative structures of the main reducers of helicopters, they were selected as the study objects for the purpose of examining the meshing characteristics of planetary gear trains when the relative positions of the shafting changed due to the position changes of the main rotor shafts under variable load conditions. It was found that by embedding the comprehensive time-varying meshing stiffness values of the main rotor shafts at different positions, a dynamic model of the relative position changes of the planetary gear trains could be established. Then, combined with the multibody dynamics software, the meshing characteristics of the sun gears, and the planetary gears, the planetary gears and the inner ring gears were simulated and analyzed under different inclinations and offsets of the shafting. The results obtained in this study revealed the following: (1) the average meshing force of the gears increased with the increases in the angle inclinations, and the meshing force between the sun gears and the planetary gears increased faster than the meshing force between the planetary gears and the inner ring gears. It was observed that during the changes in the shafting tilt positions, obvious side frequency signals had appeared around the peak of the meshing frequency in the spectrum. Then, with the continuous increases in the tilt position, the peak was gradually submerged; (2) the average meshing force of the gears increased with the increases in the offset, and the increasing trend of the meshing force between the sun gears and the planetary gears was similar to that observed between the planetary gears and the inner ring gears. It was found that when the shafting offset position changed, there were obvious first and second frequency doubling in the spectrum; (3) the mass center orbit radii of the sun gears increased with the increases in the shafting position changes, and the changes in the angular tilt position were found to have greater influencing effects on the mass center orbit radii of the sun gears than the changes in the offset positions. This study’s research findings will provide a theoretical basis for future operational status monitoring of the main transmission systems of helicopters and are of major significance for improvements in the operational stability of helicopter transmission systems, which will potentially ensure safe and efficient operations.

Automatic Detection of Embedded Structure in Planetary Gear Trains

1997 ◽  
Vol 119 (2) ◽  
pp. 315-318 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Yi-Chang Wu
Keyword(s):  
Computer Program ◽  
Automatic Detection ◽  
Planetary Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Structural Synthesis ◽  
Planetary Gear Train ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Embedded Structure

The detection of embedded structure is one of important steps in the structural synthesis of planetary gear trains. The purpose of this paper is to develop a computer program for the automatic detection of embedded structure in planetary gear trains. First, the graph representation of a planetary gear train is used to clarify the kinematic structure. Next, the concept of fundamental circuit is applied to derive an algorithm for the detection of embedded structure in a planetary gear train. Using the notation of adjacency matrix, an interactive computer program has been developed such that embedded structure in a planetary gear train can be automatically analyzed by only entering the corresponding graph.

The Detection of Embedded Structure in Planetary Gear Trains

1996 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Jin-Juh Hsu ◽  
Yi-Chang Wu
Keyword(s):  
Computer Program ◽  
Planetary Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Structural Synthesis ◽  
Planetary Gear Train ◽  
Interactive Computer Program ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Embedded Structure

Abstract The detection of embedded structure is one of important steps in the structural synthesis of planetary gear trains. The purpose of this paper is to develop a computer program for the automatic detection of embedded structure in planetary gear trains. First, the graph representation of planetary gear trains are used to clarify the kinematic structure. Next, a method which is based on the concept of fundamental circuits for the detection of embedded structure in a planetary gear train. Using the notation of adjacency matrix, an interactive computer program has been developed such that embedded structure in a planetary gear train can be automatically analyzed by only entering the corresponding graph.

The Perimeter Loop-Based Method for the Automatic Isomorphism Detection in Planetary Gear Trains

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Wenjian Yang ◽  
Huafeng Ding
Keyword(s):  
Computer Program ◽  
Present Method ◽  
Planetary Gear ◽  
Previous Method ◽  
Important Process ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
The Future ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in transmission systems. The structural synthesis of PGTs is an effective way to create novel and excellent transmissions. In the structural synthesis of PGTs, the isomorphism detection (ID) is an essential and especially important process. The ID aims to avoid duplication and guarantee the uniqueness of each PGT. The reliability of the ID method directly determines the accuracy of the synthesis result. Unfortunately, when the existing ID methods are used to synthesize PGTs, the synthesis results are not consistent with each other. A very important reason is that the ID methods fail to work in some cases. This fact gives rise to the need of an extremely reliable ID method, which may resolve the contradiction in the existing synthesis results in the future. In this paper, our previous perimeter loop-based ID method, which is applicable for linkage kinematic chains and has been proved to be reliable and efficient, is improved to detect isomorphic PGTs. The improvements relative to our previous method are discussed in detail. The present method is fully automated with the aid of a computer program, and verified by the atlas of PGTs with up to six links, as well as some PGTs with seven, eight, and ten links.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

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.

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