Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations
Planetary gear is widely used in engineering and usually has symmetrical structure. As the number of teeth in contact changes during rotation, the time-varying mesh stiffness parametrically excites the planetary gear and may cause severe vibrations and instabilities. Taking speed fluctuations into a...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2017/6851903 |
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| _version_ | 1850167844822581248 |
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| author | Xinghui Qiu Qinkai Han Fulei Chu |
| author_facet | Xinghui Qiu Qinkai Han Fulei Chu |
| author_sort | Xinghui Qiu |
| collection | DOAJ |
| description | Planetary gear is widely used in engineering and usually has symmetrical structure. As the number of teeth in contact changes during rotation, the time-varying mesh stiffness parametrically excites the planetary gear and may cause severe vibrations and instabilities. Taking speed fluctuations into account, the time-varying mesh stiffness is frequency modulated, and therefore sideband instabilities may arise and original instabilities are significantly affected. Considering two different speed fluctuations, original and sideband instabilities are numerically and analytically investigated. A rotational lumped-parameter model of the planetary gear is developed, in which the time-varying mesh stiffness, input speed fluctuations, and damping are considered. Closed-form approximations of instability boundaries for primary and combination instabilities are obtained by perturbation analysis and verified by numerical analysis. The effects of speed fluctuations and damping on parametric instability are systematically examined. Because of the frequency modulation, whether a parametric instability occurs cannot be simply predicted by the planet meshing phase which is applicable to constant speed. Besides adjusting the planet meshing phase, speed fluctuation supplies a new thought to minimize certain instability by adjusting the amplitude or frequency of the speed fluctuation. Both original and sideband instabilities are shrunken by damping, and speed fluctuation further shrinks the original instability. |
| format | Article |
| id | doaj-art-dff18e3fb8ea476b8d69faba06f7bb56 |
| institution | OA Journals |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-dff18e3fb8ea476b8d69faba06f7bb562025-08-20T02:21:07ZengWileyShock and Vibration1070-96221875-92032017-01-01201710.1155/2017/68519036851903Investigation of Parametric Instability of the Planetary Gear under Speed FluctuationsXinghui Qiu0Qinkai Han1Fulei Chu2Department of Mechanical Engineering, Tsinghua University, Beijing 100084, ChinaDepartment of Mechanical Engineering, Tsinghua University, Beijing 100084, ChinaDepartment of Mechanical Engineering, Tsinghua University, Beijing 100084, ChinaPlanetary gear is widely used in engineering and usually has symmetrical structure. As the number of teeth in contact changes during rotation, the time-varying mesh stiffness parametrically excites the planetary gear and may cause severe vibrations and instabilities. Taking speed fluctuations into account, the time-varying mesh stiffness is frequency modulated, and therefore sideband instabilities may arise and original instabilities are significantly affected. Considering two different speed fluctuations, original and sideband instabilities are numerically and analytically investigated. A rotational lumped-parameter model of the planetary gear is developed, in which the time-varying mesh stiffness, input speed fluctuations, and damping are considered. Closed-form approximations of instability boundaries for primary and combination instabilities are obtained by perturbation analysis and verified by numerical analysis. The effects of speed fluctuations and damping on parametric instability are systematically examined. Because of the frequency modulation, whether a parametric instability occurs cannot be simply predicted by the planet meshing phase which is applicable to constant speed. Besides adjusting the planet meshing phase, speed fluctuation supplies a new thought to minimize certain instability by adjusting the amplitude or frequency of the speed fluctuation. Both original and sideband instabilities are shrunken by damping, and speed fluctuation further shrinks the original instability.http://dx.doi.org/10.1155/2017/6851903 |
| spellingShingle | Xinghui Qiu Qinkai Han Fulei Chu Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations Shock and Vibration |
| title | Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations |
| title_full | Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations |
| title_fullStr | Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations |
| title_full_unstemmed | Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations |
| title_short | Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations |
| title_sort | investigation of parametric instability of the planetary gear under speed fluctuations |
| url | http://dx.doi.org/10.1155/2017/6851903 |
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