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.

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.

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.

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.

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.

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.

Power Analysis of Epicyclic Transmissions Based on Constraints

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Chao Chen
Keyword(s):  
Power Analysis ◽  
Power Flow ◽  
Flow Analysis ◽  
Total Efficiency ◽  
Power Losses ◽  
Virtual Power ◽  
Contour Maps ◽  
System A ◽  
Epicyclic Gear ◽  
Electrical Vehicles

Epicyclic gear transmissions have many applications. The internal power flow of epicyclic systems is highly related to the power loss of the system. A systematic method and generic formulas based on kinematic constraints are derived to conduct the power flow analysis, by means of Lagrange multipliers and newly introduced selection matrices. The method and formulas can be readily applied to complicated epicyclic systems. The graphic representation of the power flow of two examples verifies the balance of the power flow and virtual power flow. In the example of the Dual-E powertrain for hybrid electrical vehicles, an estimation of the total efficiency is derived. The pattern of contour maps of the total efficiency indicates the operational ranges of the powertrain with relatively low power losses.

Power Flow Analysis of Compound Epicyclic Gear Transmission: Simpson Gear Train

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Chao Chen
Keyword(s):  
Power Flow ◽  
Flow Analysis ◽  
Gear Transmission ◽  
Gear Train ◽  
Total Efficiency ◽  
Virtual Power ◽  
Speed Reduction ◽  
Power Flow Analysis ◽  
Epicyclic Gear ◽  
The Individual

An analytical expression for the total efficiency of the Simpson gear train is derived using virtual power analysis. This expression is consistent with intuition when the total efficiency is 100%. Power flow analysis shows that there are no internal power circulation and amplification in the Simpson gear train. Analysis based on the derived efficiency formula shows that the total efficiency of the Simpson gear transmission is more sensitive to the individual gear efficiencies when the speed reduction is higher.

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.

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.

Theoretic Study of Efficiency of Two-DOFs of Epicyclic Gear Transmission via Virtual Power

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Chao Chen ◽  
Teck Teh Liang
Keyword(s):  
Design Optimization ◽  
Fundamental Form ◽  
Degrees Of Freedom ◽  
Gear Transmission ◽  
Gear Train ◽  
Mechanical Transmission ◽  
Virtual Power ◽  
Two Degrees Of Freedom ◽  
Analytical Expression ◽  
Epicyclic Gear

Epicyclic gear train is a fundamental form of mechanical transmission with broad applications. Efficiency study of these trains is critical to design, optimization, and operation. It is known that the efficiencies of these systems are highly related to the internal power flows. We apply the concept of virtual power to find analytical expression of the efficiency of a two degrees of freedom train, with associated applicable ranges. The results are verified by an example.

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