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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

References

[1]. Z. Levai, (1968). “Structure and Analysis of Planetary Gear Trains”. Jnl. Mechanisms, Vol. 3, pp: 131-148.

[2]. Buchsbaum F., and Frudenstein F., (1970). “Synthesis of Kinematic Structure of Geared Kinematic Chains and other Mechanisms”. Journal of Mechanisms, Vol. 5, No. 3, pp. 357-392.

[3]. Frudenstein, (1971). “An application of Boolean Algebra to the Motion of Epicyclic drives”. ASME Journal of Engineering for Industry, Vol. 93(1), pp. 176-182, doi:10.1115/1.3427871.

[4]. R. Ravisankar and T.S. Mruthyunjaya, (1985). “Computerized Synthesis of the Structure of Geared Kinematic chains”. Mechanism and Machine Theory, Vol. 20, pp. 367-387.

[5]. L.W. Tsai, (1987). “An application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains”. ASME Journal of Mechanisms, Transactions and Automation in Design, Vol.109(3), pp. 329-336.

[6]. Jae Uk Kim, and Byung Man Kwak, (1990). “Application of Edge Permutation Group to Structural Synthesis of Epicyclic Gear Trains”. Mechanism and Machine Theory , Vo l .25 ,No. 5 , pp. 563 - 574.

[7]. D.G Oslon, Erdman A.G and Riley D.R, (1991). “Topological Analysis of Single Degree of Freedom Planetary Gear Trains”. ASME Journal of Mechanical Design, Vol. 113(1), pp. 10-16.

[8]. Cheng-Ho Hsu, and Kin-Tak Lam, (1992). “A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur Gear Trains”. ASME Journal of Mechanical Design, Vol. 114, pp. 196-200.

[9]. Cheng-Ho Hsu, and Kin-Tak Lam, (1993). “Automatic Analysis of Kinematic Structure of Planetary Gear Trains”. Journal of Mechanical Design, ASME, Vol.115, pp. 631- 638.

[10]. Cheng-Ho Hsu, and Jin-Juh Hsu, (1997). “An Efficient methodology for the structural synthesis of Geared Kinematic Chains”. Mech. Mach. Theory, Vol. 32, No. 8, pp. 957-973.

[11]. Cheng-Ho Hsu, (2002). “An Analytic Methodology for the Kinematic Synthesis of Epicyclic Gear Mechanisms”. Journal of Mechanical Design, Vol. 124, No. 3, pp. 574- 589.

[12]. Cheng-Ho Hsu, “Displacement Isomorphism of Planetary Gear Trains”. Mech. Mach. Theory, Vol. 29, pp. 513-523.

[13]. JK Shin, and S Krishnamurty, (1993). “Standard Code Technique in the Enumeration of Epicyclic Gear Trains”, Mechanism and Machine Theory, Vol. 28, No. 3, pp. 347- 355.

[14]. AC Rao, (1996). “Topological Characteristic of Planetary Gear Trains”. Journal of Institution of Engineers (India), Vol. 77, pp. 7-12

[15]. AC Rao, (2000a). “A Genetic Algorithm for Epicyclic gear trains”. Mech. Mach. Theory, Vol. 38, pp.135-147.

[16]. AC Rao, (2000). “Application of Fuzzy Logic for the study of Isomorphism, Inversions, Symmetry, parallelism and mobility in kinematic chains”. Mech. Mach. Theory, Vol. 35, pp. 1103-1116.

[17]. AC Rao, and VVNR Prasad Raju Pathapati, (2002). “A New Technique Based on Loops to Investigate Displacement Isomorphism in Planetary Gear Trains”. Journal of Mechanical Design, ASME, Vol.124, pp. 662- 675.

[18]. AC Rao and D Varada Raju, (1991). “Application of the Hamming number technique to detect isomorphism among kinematic chains and inversions”. Mech. Mach. Theory, Vol. 26, pp. 55-75.

[19]. YVD Rao, and AC Rao, (2008). “Generation of Epicyclic Gear Trains of One Degree of Freedom”. Journal of Mechanical Design, Vol.130.

[20]. J.M Del Castillo, (2002). “Enumeration of 1- DOF Planetary Gear Train Graphs Based on Functional Constraints”. ASME Journal of Mechanical Design, Vol. 124, pp. 723-732.

[21]. L. Xue, Y. Wang, and H. Wang R Liu, (2005). “Classification and Synthesis of Planetary Gear Trains”. Proceedings of IDETC/CIE 2005 ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, pp. 24-28.

[22]. MS El-Gayyar, HM El-Eashy, and M Zaki, (2006). “Structural Synthesis and Enumeration of Epicyclic Gear Mechanisms up to 12 links using Acyclic Graph Method”. Proceedings of GT2006,ASME Turbo Expo 2006, May 8-11, Spain, pp. 711-717.

[23]. Ming Yue Ma, and Xiang Yang Xu, (2011). “A Novel algorithm for Enumeration of the Planetary Gear Train Based on Graph Theory”. Advanced Materials Research, Vol.199-200, pp. 392-399

[24]. Ettore Pennestri, and Nicola Pio Belfiore, (2015). “On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains”. Mechanism and Machine Theory, Vol. 89, pp. 92–106.

A Novel Method to Detect Isomorphism in Epicyclic Gear Trains

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