Bifurcation observation of combining spiral gear transmission based on parameter domain structure analysis
type: Item
instance of: scholarly article
title: Bifurcation observation of combining spiral gear transmission based on parameter domain structure analysis
zbMATH Open document ID: 1400.70008
DOI: 10.1155/2016/3738508
author: He Lin
author: Jincheng Dong
author: Sanmin Wang
author: E. H. Dowell
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: This study considers the bifurcation evolutions for a combining spiral gear transmission through parameter domain structure analysis. The system nonlinear vibration equations are created with piecewise backlash and general errors. Gill's numerical integration algorithm is implemented in calculating the vibration equation sets. Based on cell-mapping method (CMM), two-dimensional dynamic domain planes have been developed and primarily focused on the parameters of backlash, transmission error, mesh frequency and damping ratio, and so forth. Solution demonstrates that \textit{Period}-doubling bifurcation happens as the mesh frequency increases; moreover nonlinear discontinuous jump breaks the periodic orbit and also turns the periodic state into chaos suddenly. In transmission error planes, three cell groups which are \textit{Period}-1, \textit{Period}-4, and \textit{Chaos} have been observed, and the boundary cells are the sensitive areas to dynamic response. Considering the parameter planes which consist of damping ratio associated with backlash, transmission error, mesh stiffness, and external load, the solution domain structure reveals that the system step into chaos undergoes \textit{Period}-doubling cascade with \textit{Period}-\(2^m\) (\(m\): integer) periodic regions. Direct simulations to obtain the bifurcation diagram and largest Lyapunov exponent (LE) match satisfactorily with the parameter domain solutions.
Mathematics Subject Classification ID: 70B15
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 6953094
Wikidata QID: Q59130931
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3738508
OpenAlex ID: W2381885303
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description: scientific article; zbMATH DE number 6953094