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.

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.

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.

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.

Period-Doubling Bifurcation and Non-Typical Route to Chaos of a Two-Degree-Of-Freedom Vibro-Impact System

2000 ◽  
Vol 68 (4) ◽  
pp. 670-674 ◽  
Author(s):  
G. L. Wen and ◽  
J. H. Xie
Keyword(s):  
Finite Number ◽  
Period Doubling ◽  
Degree Of Freedom ◽  
Period Doubling Bifurcation ◽  
Periodic Response ◽  
Impact System ◽  
Route To Chaos ◽  
Two Degree Of Freedom ◽  
Impact Motion ◽  
Period Doubling Bifurcations

A nontypical route to chaos of a two-degree-of-freedom vibro-impact system is investigated. That is, the period-doubling bifurcations, and then the system turns out to the stable quasi-periodic response while the period 4-4 impact motion fails to be stable. Finally, the system converts into chaos through phrase locking of the corresponding four Hopf circles or through a finite number of times of torus-doubling.

Kinematic Analysis of Robotic Bevel-Gear Trains

1984 ◽  
Vol 106 (3) ◽  
pp. 371-375 ◽  
Author(s):  
F. Freudenstein ◽  
R. W. Longman ◽  
C.-K. Chen
Keyword(s):  
Kinematic Analysis ◽  
Industrial Robot ◽  
General Procedure ◽  
Bevel Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
End Effector ◽  
Gear Trains ◽  
Three Degree Of Freedom

A general procedure has been developed for the kinematic analysis of complex bevel-gear trains in which the motion of the arm can be of mobility two or greater (i.e. the arm can rotate about two or more nonparallel, intersecting axes). The analysis of a three-degree-of-freedom gear train used in guiding the motion of the end effector of a recently developed industrial robot is described in detail.

scholarly journals Kinematic Analysis of Spatial Geared Mechanisms

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Julie Penaud ◽  
Daniel Alazard ◽  
Alexandre Amiez
Keyword(s):  
Adjacency Matrix ◽  
Kinematic Analysis ◽  
Polar Coordinates ◽  
Constraint Matrix ◽  
New Approach ◽  
Bevel Gears ◽  
Gear Trains ◽  
Complex Coefficients ◽  
Two Degree Of Freedom ◽  
General Method

In this paper, a general method for kinematic analysis of complex gear mechanisms, including bevel gear trains and noncollinear input and output axes, is presented. This new approach is based on the nullspace of the kinematic constraint matrix computed from the mechanism graph or its adjacency matrix. The novelty is that the elements of the adjacency matrix are weighted with complex coefficients allowing bevel gears to be taken into account and the angular velocity of each link to be directly expressed using polar coordinates. This approach is illustrated on a two-degree-of-freedom car differential and applied to a helicopter main gear box. A MATLAB open source software was developed to implement this method.

Experimental Determination of the Complete Dynamical Properties of a Two-Degree-Of-Freedom Model Having Nearly Coincident Natural Frequencies

1967 ◽  
Vol 9 (5) ◽  
pp. 402-413 ◽  
Author(s):  
R. W. Traill-Nash ◽  
G. Long ◽  
C. M. Bailey
Keyword(s):  
Experimental Investigation ◽  
Experimental Determination ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Influence Coefficients ◽  
Stiffness Properties ◽  
Modes Of Vibration ◽  
Dynamical Properties ◽  
Two Degree Of Freedom

Existing techniques of resonance testing have shown a marked inability to find the principal modes, natural frequencies and levels of damping in a structure which possesses two or more close natural frequencies (1)§. This paper describes an experimental investigation on a two-degree-of-freedom model of a technique which makes use of dynamical influence coefficients (or receptances) measured at a number of stations on the structure (2) (3) (4) (5). The measured coefficients are used to calculate natural frequencies and modes of vibration, and the mass, damping and stiffness properties of the system. Several model configurations having different natural frequency separations were tested and no special difficulty resulted when natural frequencies were close or even coincident.

Numerical Investigation of Vortex-Induced Vibration of a Circular Cylinder Close to a Plane Boundary

2010 ◽  
Author(s):  
Ming Zhao ◽  
Liang Cheng
Keyword(s):  
Experimental Data ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Degree Of Freedom ◽  
Plane Boundary ◽  
Structural Dynamic ◽  
Vortex Induced Vibration ◽  
Two Degree Of Freedom ◽  
Bounce Back

Two-degree of freedom vortex-induced vibration (VIV) of a circular cylinder close to a plane boundary is investigated numerically. Two-dimensional (2D) Reynolds-Averaged Navier-Stokes Equations (RANS) and structural dynamic equation are solved using a finite element method (FEM). If the cylinder is initially very close to the plane boundary, it will be bounced back after it collides with boundary. It is assumed that the bouncing back only alters the cylinder’s velocity component perpendicular to the boundary. After it is bounced back, the cylinder’s velocity are determined by Uc = Uc′, Vc = −bVc′, where Uc and Vc are the cylinder’s velocity parallel to the boundary and that perpendicular to the boundary respectively, Uc′ and Vc′ are the velocities before cylinder is bounced back, b is the bounce back coefficient which is between 0 and 1. Numerical results of the vibration amplitude and frequency of a one-degree-of-freedom vibration (transverse to flow direction) of a circular cylinder close to a plane boundary are compared with the experimental data by Yang et al. [1]. The overall trends of the variation of the VIV amplitude with the reduced velocity were found to be in agreement with the experimental results. The calculated amplitude is smaller than the measured data. The frequency of the vibration increases with the increase of reduced velocity. The calculated vibrating frequency agrees well with the experimental data. It was found in this study that vortex-induced vibration (VIV) occurs even when the gap between the cylinder and the plane boundary is zero. This contradicts a perception that VIV would not occur for a pipeline close to the seabed with a gap ratio smaller than 0.3, this is because it was understood that vortex shedding would have been suppressed if the gap between the cylinder and the plane boundary is less than about 0.3 times of cylinder diameter for a fixed cylinder. Two-degree-of-freedom VIV of a circular cylinder close to a plane boundary is studied. The XY-trajectories, the frequency and the amplitude of the vibration are studied. The effects of the cylinder-to-boundary gap and the bounce back coefficient on VIV and the link between the vortex shedding mode and the VIV are discussed.

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