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.

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.

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.

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.

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.

Topological Analysis of Single-Degree-of-Freedom Planetary Gear Trains

1991 ◽  
Vol 113 (1) ◽  
pp. 10-16 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Topological Analysis ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Graph Representation ◽  
Straightforward Manner ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Gear Trains

Graph theory has been demonstrated by many researchers to be useful during the conceptual phase of mechanism design. For the particular class of mechanisms known as planetary gear trains, the graph representation has been used primarily for “topological synthesis,” the enumeration of kinematic chains satisfying the requirements for planetary gear trains. The subsequent “topological analysis” steps resulting in the specification of ground, input, and output links, have received very little attention in the literature, perhaps because the conventional graph representation for topological analysis, and utilizes a new graph representation which enables these steps to be performed in a straightforward manner. It is shown that among the thirteen distinct displacement graphs representing planetary geared kinematic chains with five links and one degree-of-freedom, only four distinct planetary gear trains result after assigning the ground, input, and output links subject to meaningful topological requirements.

Reliability Model for Planetary Gear Trains

1983 ◽  
Vol 105 (3) ◽  
pp. 291-297 ◽  
Author(s):  
M. Savage ◽  
C. A. Paridon ◽  
J. J. Coy
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Reliability Model ◽  
The Sun ◽  
Dynamic Capacity ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Gear Trains ◽  
The Individual ◽  
Input Torque

A reliability model is presented for planetary gear trains in which the ring gear is fixed, the sun gear is the input, and the planet arm is the output. The input and output shafts are coaxial and the input and output torques are assumed to be coaxial with these shafts. Thrust and side loading are neglected. This type of gear train is commonly used in main rotor transmissions for helicopters and in other applications which require high reductions in speed. The reliability model is based on the Weibull distribution of the individual reliabilities of the transmission components. The transmission’s basic dynamic capacity is defined as the input torque which may be applied for one million input rotations of the sun gear. Load and life are related by a power law. The load-life exponent and basic dynamic capacity are developed as functions of the component capacities.

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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