Creative Design of Epicyclic Gear Trains Using Number Synthesis

1967 ◽  
Vol 89 (2) ◽  
pp. 309-314 ◽  
Author(s):  
R. C. Johnson ◽  
K. Towfigh
Keyword(s):  
Initial Step ◽  
Gear Train ◽  
Creative Design ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Associated Linkage ◽  
Number Synthesis

The following paper applies the theory of number synthesis to the creative design of epicyclic gear trains. First, the associated linkage of an existing epicyclic gear train is derived as an initial step of analysis. Next, the requirements for an acceptable associated linkage are established. Finally, epicyclic gear trains are derived by number synthesis from acceptable associated linkages up to and including the degree of complexity of eight links.

Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
High Velocity ◽  
Mechanical Energy ◽  
Gear Train ◽  
Recursive Method ◽  
Gear Pair ◽  
Simple Method ◽  
Epicyclic Gear ◽  
Thick Line ◽  
Gear Trains ◽  
Isomorphic Graphs

Epicyclic gear trains (EGTs) are used in the mechanical energy transmission systems where high velocity ratios are needed in a compact space. It is necessary to eliminate duplicate structures in the initial stages of enumeration. In this paper, a novel and simple method is proposed using a parameter, Vertex Incidence Polynomial (VIP), to synthesize epicyclic gear trains up to six links eliminating all isomorphic gear trains. Each epicyclic gear train is represented as a graph by denoting gear pair with thick line and transfer pair with thin line. All the permissible graphs of epicyclic gear trains from the fundamental principles are generated by the recursive method. Isomorphic graphs are identified by calculating VIP. Another parameter “Rotation Index” (RI) is proposed to detect rotational isomorphism. It is found that there are six nonisomorphic rotation graphs for five-link one degree-of-freedom (1-DOF) and 26 graphs for six-link 1-DOF EGTs from which all the nonisomorphic displacement graphs can be derived by adding the transfer vertices for each combination. The proposed method proved to be successful in clustering all the isomorphic structures into a group, which in turn checked for rotational isomorphism. This method is very easy to understand and allows performing isomorphism test in epicyclic gear trains.

Meshing Efficiency Analysis of Two Degree-of-Freedom Epicyclic Gear Trains

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Essam Lauibi Esmail
Keyword(s):  
Reference Frame ◽  
Power Efficiency ◽  
Power Flow ◽  
Flow Direction ◽  
Efficiency Analysis ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Two Degree Of Freedom

The concept of potential power efficiency is introduced as the efficiency of an epicyclic gear train (EGT) measured in any moving reference frame. The conventional efficiency can be computed in a carrier-moving reference frame in which the gear carrier appears relatively fixed. In principle, by attaching the reference frame to an appropriate link, torques can be calculated with respect to each input, output, or (relatively) fixed link in the EGT. Once the power flow direction is obtained from the potential power ratio, the torque ratios are obtained from the potential power efficiencies, the particular expression of the efficiency of the EGT is found in a simple manner. A systematic methodology for the efficiency analysis of one and two degree-of-freedom (DOF) EGTs is described, and 14 ready-to-use efficiency formulas are derived for 2DOF gear pair entities (GPEs). This paper includes also a discussion on the redundancy of the efficiency formulas used for 1DOF GPEs. An incomplete in the efficiency formulas in previous literature, which make them susceptible to wrong application, is brought to light.

A New Method of Design of Epicyclic Gear Trains

2013 ◽  
Vol 457-458 ◽  
pp. 707-712
Author(s):  
Pei Wen An ◽  
Zhong Liang Lv
Keyword(s):  
New Method ◽  
Combination Method ◽  
Engineering Practice ◽  
Type Number ◽  
Practical Application ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Number Synthesis ◽  
Method Of Design

Epicyclic gear trains have been broadly applied in engineering practice. In this paper, kinematic chains (K.C.) with single-joint (S.J.) were applied to innovative synthesis of the epicyclic gear trains. The method of the innovative synthesis of the epicyclic gear trains was presented. Not only the epicyclic gear trains in common uses were obtained, but some new types of epicyclic gear trains that are got difficultly by means of conventional combination method were gained. Thereby, a new way has been offered for the innovative synthesis of the epicyclic gear trains, at the same time, a way has also been offered for practical application of some multi-link kinematic chains gained by using the theory of type-number synthesis of the K.C. with S.J.. Examples show that the method presented in this paper is right and feasible, and the method is efficient and practical for the innovative synthesis of the epicyclic gear trains.

A Study of the Duality Between Epicyclic Gear Trains and Beam Systems

2006 ◽  
Author(s):  
Gordon P. Pennock ◽  
Jeremiah J. Alwerdt
Keyword(s):  
Gear Train ◽  
Specific Design ◽  
Beam System ◽  
Dual Beam ◽  
Epicyclic Gear ◽  
Angular Velocities ◽  
Gear Trains ◽  
Design Requirements ◽  
Primary Contribution ◽  
Insight Into

This paper provides geometric insight into the duality between the kinematics of epicyclic gear trains and the statics of beam systems. The two devices have inherent geometrical relationships that allow the angular velocities of the gears in a gear train to be investigated from a knowledge of the forces acting on the dual beam system, and vice-versa. The primary contribution of the paper is the application of this duality to obtain the dual beam system for a given compound epicyclic gear train. The paper develops a systematic procedure to transform between the first-order kinematics of a gear train and the statics of the dual beam system. This provides a simple and intuitive approach to study the speed ratios of an epicyclic gear train and the force ratios of the dual beam system. The speed ratios are expressed in terms of kinematic coefficients, which are a function of the position of the input gear and provide insight into the gear train geometry. Several numerical examples of simple and compound epicyclic gear trains are presented to demonstrate the simplicity of the proposed approach. The analytical equations that are developed in the paper can be incorporated, in a straightforward manner, into a spreadsheet that is oriented towards an epicyclic gear train satisfying specific design requirements.

Nomographs for Kinematics, Statics and Power Flow Analysis of Epicyclic Gear Trains

2009 ◽  
Author(s):  
Essam L. Esmail ◽  
Hamed A. Hussen
Keyword(s):  
Electric Motor ◽  
Power Flow ◽  
Automatic Transmission ◽  
Flow Analysis ◽  
Gear Train ◽  
Innovative Design ◽  
Epicyclic Gear ◽  
Power Split ◽  
Gear Trains ◽  
Flow Through

A new methodology for constructing multi-axes nomographs is developed. Using this methodology, a unified general formulation for computing velocities and torques of any epicyclic-type transmission train is presented. To demonstrate and apply the new technique, Ravigneaux automatic transmission is used to show how the velocities, the torques and the power flow through the train can be simultaneously visualized on a single nomograph. The present methodology is judged to be more efficient than other methods and than the three-ax nomograph methodology. Using this methodology an innovative design of two-input transmission with only one electric motor/generator (MG) and without any rotating clutches is presented. The proposed design provides some of the benefits and flexibility of a power-split design by using the conventionally available Ravigneaux gear train in a simpler mechanical layout which makes the design compact, mechanically simple, and operationally flexible.

Fault Tree Approach for the Reliability Analysis of Gear Trains: Part I — Basic Theory

1987 ◽  
Author(s):  
T. S. Pan ◽  
S. S. Rao
Keyword(s):  
Fault Tree ◽  
Gear Train ◽  
System Failure ◽  
Fault Trees ◽  
Minimal Cut Sets ◽  
Logic Diagram ◽  
Epicyclic Gear ◽  
Total Failure ◽  
Gear Trains ◽  
Tree Approach

Abstract The application of fault tree techniques to the analysis of gear trains is considered. The techniques involve the decomposition of the system into a logic diagram or fault tree in which certain basic or primary events lead to a specified top event which signifies the total failure of the system. The fault trees are used to obtain minimal cut sets from which the modes of system failure and, hence, the reliability measure for the top event can be calculated. The method of constructing fault trees and the subsequent estimation of reliability of the system is illustrated through a nine speed compound gear train and a five speed epicyclic gear train.

Fault Tree Approach for the Reliability Analysis of Gear Trains

1988 ◽  
Vol 110 (3) ◽  
pp. 348-353 ◽  
Author(s):  
T. S. Pan ◽  
S. S. Rao
Keyword(s):  
Fault Tree ◽  
Gear Train ◽  
System Failure ◽  
Fault Trees ◽  
Minimal Cut Sets ◽  
Logic Diagram ◽  
Epicyclic Gear ◽  
Total Failure ◽  
Gear Trains ◽  
Tree Approach

The application of fault tree techniques to the analysis of gear trains is considered. The techniques involve the decomposition of the system into a logic diagram or fault tree in which certain basic or primary events lead to a specified top event which signifies the total failure of the system. The fault trees are used to obtain minimal cut sets from which the modes of system failure and, hence, the reliability measure for the top event can be calculated. The method of constructing fault trees and the subsequent estimation of reliability of the system is illustrated through a nine speed compound gear train and a five speed epicyclic gear train.

Complete Efficiency Analysis of Epicyclic Gear Train With Two Degrees of Freedom

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Kieran Davies ◽  
Chao Chen ◽  
Bernard K. Chen
Keyword(s):  
Optimal Design ◽  
Power Flow ◽  
Degrees Of Freedom ◽  
Efficiency Analysis ◽  
Operating Conditions ◽  
Gear Train ◽  
Virtual Power ◽  
Two Degrees Of Freedom ◽  
Epicyclic Gear ◽  
Gear Trains

Epicyclic gear trains (EGTs) are important mechanical transmissions with many applications. For optimal design and operation of these gear trains, it is necessary to obtain complete efficiency maps of such transmissions. The efficiency of a two degrees of freedom (two-dof) EGT is derived based on the internal power flow and virtual power flow patterns. Expressions for the efficiencies in different operating conditions are obtained and verified by three special conditions.

Virtual-Power Flow and Mechanical Gear-Mesh Power Losses of Epicyclic Gear Trains

2006 ◽  
Vol 129 (1) ◽  
pp. 107-113 ◽  
Author(s):  
Chao Chen ◽  
Jorge Angeles
Keyword(s):  
Power Loss ◽  
Power Flow ◽  
Gear Train ◽  
Power Losses ◽  
Virtual Power ◽  
Noninertial Frame ◽  
Gear Mesh ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
The Subject

The concept of virtual power is first defined as the power measured, in a noninertial frame, in an epicyclic gear train. We then introduce the concept of virtual-power ratio, an invariant related to the power loss in an epicyclic system. It is shown that virtual-power flow and balance exist in an epicyclic gear train, based on which a novel algorithm to compute the gear-mesh powerloss and the train efficiency is formulated. This algorithm is general enough to be applied to any given epicyclic gear train. Our results are compared with previous work on the subject.

Fault Tree Approach for the Reliability Analysis of Gear Trains: Part II — Example Applications

1987 ◽  
Author(s):  
T. S. Pan ◽  
S. S. Rao
Keyword(s):  
Fault Tree ◽  
Gear Train ◽  
System Failure ◽  
Fault Trees ◽  
Minimal Cut Sets ◽  
Logic Diagram ◽  
Epicyclic Gear ◽  
Total Failure ◽  
Gear Trains ◽  
Tree Approach

Abstract The application of fault tree techniques to the analysis of gear trains is considered. The techniques involve the decomposition of the system into a logic diagram or fault tree in which certain basic or primary events lead to a specified top event which signifies the total failure of the system. The fault trees are used to obtain minimal cut sets from which the modes of system failure and hence the reliability measure for the top event can be calculated. The method of constructing fault trees and the subsequent estimation of reliability of the system is illustrated through a nine speed compound gear train and a five speed epicyclic gear train.

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