Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports
Abstract This paper investigates two parameters effect on vibrational responses of the spiral bevel gear. Changing the gear system overall stiffness (GSOS) considering elastic deformation and periodic torques are the two parameters which are represented as the main goals of this study. In order to i...
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| Format: | Article |
| Language: | English |
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Springer
2021-08-01
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| Series: | SN Applied Sciences |
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| Online Access: | https://doi.org/10.1007/s42452-021-04755-6 |
| _version_ | 1818717908911521792 |
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| author | Farhad S. Samani Moein Salajegheh Moslem Molaie |
| author_facet | Farhad S. Samani Moein Salajegheh Moslem Molaie |
| author_sort | Farhad S. Samani |
| collection | DOAJ |
| description | Abstract This paper investigates two parameters effect on vibrational responses of the spiral bevel gear. Changing the gear system overall stiffness (GSOS) considering elastic deformation and periodic torques are the two parameters which are represented as the main goals of this study. In order to investigate the effects of shaft stiffness and elastic deformation, two different cases with different support locations are considered. The first case is presented by locating the support close to the gear, and in the latter one, the distance between gear and support is increased. Besides, to study the effect of torque, two main types are considered: constant and periodic excitation torque. To illustrate the dynamic behavior, the governing differential equations are solved numerically according to the Runge–Kutta method. The equations are nonlinear due to backlash and time-varying coefficients as the results of GSOS variation. Vibrational phenomena are illustrated by means of bifurcation diagrams, RMS, and Poincaré maps. Particular vibrational behaviors such as “chaos” and “period-doubling” phenomena are illustrated with details. By investigating the effect of shaft stiffness, results show that when the support is far away from gear, the vibration response increased by 67.5%. Moreover, while the input torque is constant, the support movement does not cause undesirable responses such as chaotic or period-doubling responses. The periodic torque causes undesirable responses such as chaos and bifurcation and period-doubling responses. Article Highlights What is done in the present paper can be mentioned in three main parts: The nonlinear dynamics of the spiral bevel gear pair under two different support situations is investigated in this paper. To scrutinize the dynamic behavior of the spiral bevel gear-pair in a nearly real situation, the input driver torque is periodically variable. The results show that the spiral bevel gear pair may comprise chaotic response with periodic torque excitation if the bearing supports locate far enough from the gears. |
| first_indexed | 2024-12-17T19:42:38Z |
| format | Article |
| id | doaj.art-807a2d028bff4dd9a13816eeb1ead8ae |
| institution | Directory Open Access Journal |
| issn | 2523-3963 2523-3971 |
| language | English |
| last_indexed | 2024-12-17T19:42:38Z |
| publishDate | 2021-08-01 |
| publisher | Springer |
| record_format | Article |
| series | SN Applied Sciences |
| spelling | doaj.art-807a2d028bff4dd9a13816eeb1ead8ae2022-12-21T21:34:58ZengSpringerSN Applied Sciences2523-39632523-39712021-08-01391910.1007/s42452-021-04755-6Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supportsFarhad S. Samani0Moein Salajegheh1Moslem Molaie2Department of Mechanical Engineering, Shahid Bahonar University of KermanDepartment of Mechanical Engineering, Shahid Bahonar University of KermanDepartment of Engineering “Enzo Ferrari”, InterMech MoRe Centre, University of Modena and Reggio EmiliaAbstract This paper investigates two parameters effect on vibrational responses of the spiral bevel gear. Changing the gear system overall stiffness (GSOS) considering elastic deformation and periodic torques are the two parameters which are represented as the main goals of this study. In order to investigate the effects of shaft stiffness and elastic deformation, two different cases with different support locations are considered. The first case is presented by locating the support close to the gear, and in the latter one, the distance between gear and support is increased. Besides, to study the effect of torque, two main types are considered: constant and periodic excitation torque. To illustrate the dynamic behavior, the governing differential equations are solved numerically according to the Runge–Kutta method. The equations are nonlinear due to backlash and time-varying coefficients as the results of GSOS variation. Vibrational phenomena are illustrated by means of bifurcation diagrams, RMS, and Poincaré maps. Particular vibrational behaviors such as “chaos” and “period-doubling” phenomena are illustrated with details. By investigating the effect of shaft stiffness, results show that when the support is far away from gear, the vibration response increased by 67.5%. Moreover, while the input torque is constant, the support movement does not cause undesirable responses such as chaotic or period-doubling responses. The periodic torque causes undesirable responses such as chaos and bifurcation and period-doubling responses. Article Highlights What is done in the present paper can be mentioned in three main parts: The nonlinear dynamics of the spiral bevel gear pair under two different support situations is investigated in this paper. To scrutinize the dynamic behavior of the spiral bevel gear-pair in a nearly real situation, the input driver torque is periodically variable. The results show that the spiral bevel gear pair may comprise chaotic response with periodic torque excitation if the bearing supports locate far enough from the gears.https://doi.org/10.1007/s42452-021-04755-6Spiral bevel gearNonlinear vibrationShaft stiffnessPeriodic torque |
| spellingShingle | Farhad S. Samani Moein Salajegheh Moslem Molaie Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports SN Applied Sciences Spiral bevel gear Nonlinear vibration Shaft stiffness Periodic torque |
| title | Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports |
| title_full | Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports |
| title_fullStr | Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports |
| title_full_unstemmed | Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports |
| title_short | Nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports |
| title_sort | nonlinear vibration of the spiral bevel gear under periodic torque considering multiple elastic deformation evaluations due to different bearing supports |
| topic | Spiral bevel gear Nonlinear vibration Shaft stiffness Periodic torque |
| url | https://doi.org/10.1007/s42452-021-04755-6 |
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