Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension

In order to depict the numerical characteristic of the attractor structure in phase space for gear system effectively, a nonlinear dynamical spur gear transmission model including backlash and general transmission error is established, the calculation formula of equispaced gear system correlation di...

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Bibliographic Details
Published inJixie Chuandong Vol. 43; pp. 12 - 16
Main Authors He Lin, Matthias Rätsch, Sanmin Wang, Guangshen Xu
Format Journal Article
LanguageChinese
Published Editorial Office of Journal of Mechanical Transmission 01.07.2019
Subjects
Chaotic attractor
Correlation dimension
Lyapunov exponent
Poincaré section
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ISSN1004-2539

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Summary:In order to depict the numerical characteristic of the attractor structure in phase space for gear system effectively, a nonlinear dynamical spur gear transmission model including backlash and general transmission error is established, the calculation formula of equispaced gear system correlation dimension is deduced based on G-P algorithm. The numerical characteristics are explored quantitatively for both of periodic attractor and chaotic attractor by employing largest Lyapunov exponent as well as correlation dimension, the evolution and migration process of chaotic attractors is analyzed by means of Poincaré section. The evolution of chaotic attractor under the excitation of damping ratio and general transmission error is described by correlation dimension. The results show that the more complex of attractor structure generates the larger correlation dimension values, and causing strong vibration to the system, correlation dimension of chaotic attractor is between integer 1 and 2 with fractal characteristic
ISSN:1004-2539