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.

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.

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.

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.

A Framework for Efficiency Evaluation of Multi-Degree-of-Freedom Gear Trains

1996 ◽  
Vol 118 (4) ◽  
pp. 556-560 ◽  
Author(s):  
C. Innocenti
Keyword(s):  
Experimental Data ◽  
Finite Number ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Efficiency Evaluation ◽  
Suggested Approach ◽  
New Approach ◽  
Gear Trains ◽  
Two Degree Of Freedom

The paper proposes a new approach to the efficiency evaluation of any one- or multi-degree-of-freedom gear trains. The suggested approach generalizes the known procedures developed for two-degree-of-freedom gear trains. It is based on the determination of a vector whose components are the torques delivered to the shafts of the gear train. Furthermore the paper shows that, for a notable category of gear trains, such a vector can have only a finite number of directions, which implies that a limited number of experimental data suffices for estimating the efficiency at any operational condition. Examples of application of the proposed methodology are provided.

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.

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.

The Creation of Nonfractionated, Two-Degree-of-Freedom Epicyclic Gear Trains

1989 ◽  
Vol 111 (4) ◽  
pp. 524-529 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Chen-Chou Lin
Keyword(s):  
Degree Of Freedom ◽  
Kinematic Structure ◽  
Walking Machines ◽  
Epicyclic Gear ◽  
Systematic Methodology ◽  
Gear Trains ◽  
The Creation ◽  
Two Degree Of Freedom

To date, most of the multi-DOF (degree-of-freedom) epicyclic gear trains have been used as a series of one-DOF devices. Comparatively little is known with regard to the existence and synthesis of nonfractionated, epicyclic gear trains. This paper presents a systematic methodology for the identification and enumeration of the kinematic structure of nonfractionated, two-DOF epicyclic gear trains. It has been shown that there exists no such gear trains with five or less links. It has also been shown that there exist two nonisomorphic rotation graphs of six vertices and twenty nonisomorphic rotation graphs of seven vertices. An atlas of nonisomorphic displacement graphs which can be used to construct nonfractionated, two-DOF epicyclic gear trains with six and seven links has been developed. It is hoped that this atlas will lead to more optimum and efficient designs of machines with multiple actuating requirements such as robotic wrists, grippers, and walking machines.

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.

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.

Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

1992 ◽  
Author(s):  
Sridhar Kota ◽  
Srinivas Bidare
Keyword(s):  
Degrees Of Freedom ◽  
Building Blocks ◽  
Degree Of Freedom ◽  
Differential Systems ◽  
Practical Applications ◽  
Epicyclic Gear ◽  
Differential Mechanism ◽  
Long Time ◽  
Gear Trains ◽  
Drive Systems

Abstract A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and four output differential systems and some of their practical applications.

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