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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| Format: | Article |
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Editorial Office of Journal of Mechanical Transmission
2019-07-01
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| Series: | Jixie chuandong |
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| Online Access: | http://www.jxcd.net.cn/thesisDetails#10.16578/j.issn.1004.2539.2019.07.003 |
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| author | He Lin Matthias Rätsch Sanmin Wang Guangshen Xu |
| author_facet | He Lin Matthias Rätsch Sanmin Wang Guangshen Xu |
| author_sort | He Lin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-87d27fc1299c466cab638d9a16c00d32 |
| institution | Kabale University |
| issn | 1004-2539 |
| language | zho |
| publishDate | 2019-07-01 |
| publisher | Editorial Office of Journal of Mechanical Transmission |
| record_format | Article |
| series | Jixie chuandong |
| spelling | doaj-art-87d27fc1299c466cab638d9a16c00d322025-01-10T13:58:36ZzhoEditorial Office of Journal of Mechanical TransmissionJixie chuandong1004-25392019-07-0143121630648806Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation DimensionHe LinMatthias RätschSanmin WangGuangshen XuIn 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.http://www.jxcd.net.cn/thesisDetails#10.16578/j.issn.1004.2539.2019.07.003Correlation dimensionLyapunov exponentPoincaré sectionChaotic attractor |
| spellingShingle | He Lin Matthias Rätsch Sanmin Wang Guangshen Xu Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension Jixie chuandong Correlation dimension Lyapunov exponent Poincaré section Chaotic attractor |
| title | Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension |
| title_full | Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension |
| title_fullStr | Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension |
| title_full_unstemmed | Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension |
| title_short | Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension |
| title_sort | numerical characteristic of gear system attractor in phase space based on g p algorithm of correlation dimension |
| topic | Correlation dimension Lyapunov exponent Poincaré section Chaotic attractor |
| url | http://www.jxcd.net.cn/thesisDetails#10.16578/j.issn.1004.2539.2019.07.003 |
| work_keys_str_mv | AT helin numericalcharacteristicofgearsystemattractorinphasespacebasedongpalgorithmofcorrelationdimension AT matthiasratsch numericalcharacteristicofgearsystemattractorinphasespacebasedongpalgorithmofcorrelationdimension AT sanminwang numericalcharacteristicofgearsystemattractorinphasespacebasedongpalgorithmofcorrelationdimension AT guangshenxu numericalcharacteristicofgearsystemattractorinphasespacebasedongpalgorithmofcorrelationdimension |