A review of graph theory application research in gears

2015 ◽  
Vol 230 (10) ◽  
pp. 1697-1714 ◽  
Author(s):  
Hui-Ling Xue ◽  
Geng Liu ◽  
Xiao-Hui Yang
Keyword(s):  
Graph Theory ◽  
Power Flow ◽  
Planetary Gear ◽  
Mechanical Efficiency ◽  
Gear Train ◽  
Synthesis Process ◽  
Epicyclic Gear ◽  
Analysis And Synthesis ◽  
Theory Application ◽  
Gear Trains

Graph theory has been applied to gear train analysis and synthesis for many years, and it is an effective and systematic modeling approach in the design process of gear transmission. Based on more than 100 references listed in this paper, a review about the graph-based method for kinematic and static force analysis, power flow, and mechanical efficiency computation is presented. The method is based on the concept of fundamental circuit corresponding to a basic epicyclic gear train. A 1-dof epicyclic gear train and a two-stage planetary gear train are used to illustrate the application of this method. Besides, isomorphism identification in the synthesis process and enumeration of 1-dof epicyclic gear train graphs are surveyed particularly. Also, the computerized methods for detection of redundant gears and degenerate structures in epicyclic gear trains are reviewed, respectively.

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.

Generation of Epicyclic Gear Trains of One Degree of Freedom

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Y. V. D. Rao ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Planetary Gear Trains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Hamming Matrix

New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

Novel Configurations for Hybrid Transmissions Using a Simple Planetary Gear Train

2015 ◽  
Author(s):  
Huu-Tich Ngo ◽  
Hong-Sen Yan
Keyword(s):  
Hybrid Systems ◽  
Power Flow ◽  
Planetary Gear ◽  
Gear Train ◽  
Design Approach ◽  
Synthesis Process ◽  
Design Constraints ◽  
Planetary Gear Train ◽  
Operation Modes ◽  
Parallel Hybrid

This paper presents a design approach to systematically synthesize feasible configurations for series-parallel and parallel hybrid transmissions subject to design constraints and required operation modes using a simple planetary gear train (PGT). The configuration synthesis process includes two main steps: 1) assign inputs and output powers to the PGT subject to power constraints by the power arrangement process; and 2) assign clutches and brakes to the obtained systems subject to desired operation modes by the clutch arrangement process. By applying the proposed design approach, nine clutchless and 31 clutched configurations for series-parallel and parallel hybrid systems are synthesized, respectively. For each type of the hybrid systems, we analyzed kinematic and power flow of a new configuration to demonstrate the feasibility of the synthesized systems. The design approach can be used to systematically synthesize future hybrid transmissions with different mechanisms, design constraints, and desired operation modes.

New Graph Representation for Planetary Gear Trains

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Wenjian Yang ◽  
Huafeng Ding ◽  
Bin Zi ◽  
Dan Zhang
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Planetary Gear ◽  
Graph Representation ◽  
Synthesis Process ◽  
Planetary Gear Trains ◽  
Computer Aided ◽  
Gear Trains ◽  
Isomorphic Graphs ◽  
Canonical Rotation

Planetary gear trains (PGTs) are widely used in machinery to transmit angular velocity ratios or torque ratios. The graph theory has been proved to be an effective tool to synthesize and analyze PGTs. This paper aims to propose a new graph model, which has some merits relative to the existing ones, to represent the structure of PGTs. First, the rotation graph and canonical rotation graph of PGTs are defined. Then, by considering the edge levels in the rotation graph, the displacement graph and canonical displacement graph are defined. Each displacement graph corresponds to a PGT having the specified functional characteristics. The synthesis of five-link one degree-of-freedom (1DOF) PGTs is used as an example to interpret and demonstrate the applicability of the present graph representation in the synthesis process. The present graph representation can completely avoid the generation of pseudo-isomorphic graphs and can be used in the computer-aided synthesis and analysis of PGTs.

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.

Simplified Kinematic Analysis of Bevel Epicyclic Gear Trains With Application to Power-Flow and Efficiency Analyses

2005 ◽  
Vol 127 (2) ◽  
pp. 278-286 ◽  
Author(s):  
Carl A. Nelson ◽  
Raymond J. Cipra
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Power Flow ◽  
Computer Software ◽  
Input And Output ◽  
Automatic Transmissions ◽  
Epicyclic Gear ◽  
Analysis Technique ◽  
Angular Velocities ◽  
Gear Trains

A kinematic analysis technique is introduced to find the angular velocities of all links in bevel epicyclic gear trains. The method relies on previous work in graph theory. It improves on existing techniques used for analysis of planar geared mechanisms in its ability to accurately solve the kinematics of spatial geared mechanisms, particularly bevel gear trains, in a simpler manner. Usefulness of the method is demonstrated through its application to power-flow and efficiency analyses as well as its implementation in computer software. This discussion is limited to gear trains whose input and output axes are collinear, such as automotive automatic transmissions.

scholarly journals Power-Flow and Mechanical Efficiency Computation in Two-Degrees-of-Freedom Planetary Gear Units: New Compact Formulas

2021 ◽  
Vol 11 (13) ◽  
pp. 5991
Author(s):  
Essam Lauibi Esmail ◽  
Ettore Pennestrì ◽  
Marco Cirelli
Keyword(s):  
Power Flow ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Mechanical Efficiency ◽  
Hybrid Vehicles ◽  
Structural Elements ◽  
Virtual Power ◽  
Two Degrees Of Freedom ◽  
Gear Trains ◽  
The Subject

The mechanical efficiency is a computed value for comparing the performance of the multi degrees-of-freedom geared transmissions of hybrid vehicles. Most of the current methods for estimating gear trains mechanical efficiency require the decomposition of gear transmissions in basic structural elements or planetary gear units (PGU). These are two degrees-of-freedom components whose mechanical efficiency has a deep influence on the overall device. The authors (E.L.E., E.P.) already evidenced that, under certain kinematic conditions, the classic Radzimovsky’s formulas, widely accepted for computing the mechanical efficiency of PGUs, are not adequate. In this paper, more general and reliable formulas for computing the mechanical efficiency are deduced. The proposed formulas herein, exploiting the concept of potential or virtual power, evidence the dependency between kinematics and efficiency. A numerical example compares our results with previous work on the subject.

scholarly journals Mechanical Efficiency of HMCVT under Steady-State Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Guangqing Zhang ◽  
Hengtong Zhang ◽  
Yanyan Ge ◽  
Wei Qiu ◽  
Maohua Xiao ◽  
...  
Keyword(s):  
Steady State ◽  
Mechanical System ◽  
Hydraulic System ◽  
Power Flow ◽  
Ride Comfort ◽  
Mechanical Efficiency ◽  
Gear Train ◽  
Epicyclic Gear ◽  
Physical Prototype ◽  
Variable Transmission

Hydromechanical continuously variable transmission (HMCVT) technology has been widely used due to its advantages of ride comfort and fuel economy. The relatively uniform efficiency expression of HMCVT is obtained by studying torque and transmission ratios to reveal steady-state characteristics and predict the output torque. Mathematical models of torque ratios are derived by analyzing the HMCVT system power flow and calculating the equivalent meshing power of epicyclic gear train and efficiency for the hydraulic system. The relationship between mechanical system transmission and hydraulic system parameters is established using the torque ratios, and a mechanical system demanding surface is proposed. Two numerical examples of the HMCVT system with single and dual variable units are demonstrated to establish an effective and convenient method. The method is validated through a physical prototype TA1-02 test.

Influence of the Operating Conditions of Two-Degree-of-Freedom Planetary Gear Trains on Tooth Friction Losses

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Essam Lauibi Esmail
Keyword(s):  
Power Loss ◽  
Power Flow ◽  
Planetary Gear ◽  
Operating Conditions ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Friction Loss ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Two Degree Of Freedom

In a planetary gear train (PGT), the power loss by tooth friction is a function of the potential power developed within the gear train elements rather than that being transmitted through it. In the present work, we focus on the operating conditions of two-degree-of-freedom (two-DOF) PGTs. Any operating condition induces its own internal power flow pattern; this implies that tooth friction loss depends on the mechanism of power loss developed in the gearing that differs from one case to another over the entire range of operating conditions. The approach adopted in this paper stems from a unification of the kinematics and tooth friction losses of PGTs and is based on potential powers and power ratios. The range of applicability of the power relations is investigated and clearly defined, and tooth friction loss formulas obtained by their use are tabulated. A short comparison with formulas currently available in the literature is also made. The simplicity of the proposed method for analyzing two-input or two-output planetary gear trains is helpful in the design, optimization, and control of hybrid transmissions. It assists particularly in choosing correctly the appropriate operating conditions to the involved application.

A Simplified Approach for Force and Power-Flow Analysis of Compound Epicyclic Spur-Gear Trains

1992 ◽  
Author(s):  
L. Saggere ◽  
D. G. Olson
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Power Flow ◽  
Flow Analysis ◽  
Spur Gear ◽  
Gear Train ◽  
Force Analysis ◽  
Power Flow Analysis ◽  
Torque Analysis ◽  
Gear Trains

Abstract After conceptual design and dimensional synthesis of a compound epicyclic gear train (EGT), its performance evaluation involves kinematic analysis, force analysis, torque analysis, and power-flow analysis. In recent years, graph theory has proven to be a powerful symbolic representation for design of mechanisms. Application of graph theory for the topological representation and kinematic analysis of EGTs is quite well established. However, graph theory based methods for power-flow and force analysis lack certain features, making them unsuitable or difficult to implement in a general purpose program for automatic design of EGTs. The traditional approach has been to perform force and torque analysis first, and then use the results to perform power-flow analysis. This paper presents a novel, systematic approach in which power-flow analysis is performed first, and then the results are used to determine the inter-link forces in epicyclic spur-gear trains. This method is based only on the graph of the gear-train and the angular velocities of the elements, and hence, is more suitable for automatic computation, simpler to implement in a program, and also avoids requiring the formulation of tedious torque equilibrium equations. A numerical example is presented to illustrate the simplicity and generality of the method.

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