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A Novel Method to Detect Isomorphism in Epicyclic Gear Trains

V.V. Kamesh*, K. Mallikarjuna Rao**, A.B. Srinivasa Rao***

* Ph.D Scholar, Jawaharlal Nehru Technological University, Andhra Pradesh, India.

** Professor, Department of Mechanical Engineering, College of Engineering, JNTUK, Kakinada, Andhra Pradesh, India..

*** Principal, Sri Vasavi Institute of Engineering & Technology, Nandamuru, Andhra Pradesh, India

Periodicity:August - October'2016
DOI : https://doi.org/10.26634/jfet.12.1.8211

Abstract

Graph theory is an effective tool in the Structural synthesis of Epicyclic Gear Trains (EGTs) widely used in Automatic transmission system, Overdrives, Gas turbine engines, Machine tool gearboxes, etc. Enumeration of EGTs with different links with varying degrees of freedom were studied by many researchers earlier. In recursive method of enumeration, starting with 3-link EGT having one gear pair and two transfer pairs, higher link EGTs are generated by adding one transfer pair and one gear pair to the base level gear train. As large numbers of topological structures are generated, many of them are identical in structure and behaviour, i.e., isomorphous. In this paper, a simple method is proposed to detect isomorphism in epicyclic gear trains by estimating influence of every link over the other links and vice versa. A new parameter 'Functional Value of Gear Train' defined in the method assess the overall influence of all links on a single link and vice versa. All the 4-link, 5-link and 6-link 1-dof epicyclic gear trains are studied by the proposed method. Structural Isomorphism in EGTs explained by calculating 'Functional Value of Gear Train' are proposed in the method taking two 5- link 1-DOF graphs and two 6-link 1-DOF graphs. The distinct structural non-isomorphic graphs of 4-link 1-DOF are checked for Rotational Isomorphism. The number of computations is less in the proposed method. The proposed method can be extended to check isomorphism in EGTs with higher linkage and DOF.

Keywords

Adjacency Matrix, Epicyclic Gear Train, Isomorphism, Enumeration, Functional Schematic, Rotation Graph, Functional Value.

How to Cite this Article?

Kamesh, V.V., Rao, K..M., and Rao, A. B S. (2016). A Novel Method to Detect Isomorphism in Epicyclic Gear Trains. i-manager’s Journal on Future Engineering and Technology, 12(1), 28-35. https://doi.org/10.26634/jfet.12.1.8211

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