Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method
Joint Authors
Li, Yi
Lv, Ming
Wang, Shi-ying
Qin, Hui-bin
Fu, Jun-fan
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-11-05
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
To reflect vibration more comprehensively and to satisfy the machining demand for high-order frequencies, we presented a three-dimensional free vibration analysis of gears with variable thickness using the Chebyshev–Ritz method based on three-dimensional elasticity theory.
We derived the eigenvalue equations.
We divided the gear model into three annular parts along the locations of the step variations, and the admissible function was a Ritz series that consisted of a Chebyshev polynomial multiplying boundary function.
The convergence study demonstrated the high accuracy of the present method.
We used a hammering method for a modal experiment to test two annular plates and one gear’s eigenfrequencies in a completely free condition.
We also applied the finite element method to solve the eigenfrequencies.
Through a comparative analysis of the frequencies obtained by these three methods, we found that the results achieved by the Chebyshev–Ritz method were close to those obtained from the experiment and finite element method.
The relative errors of four sets of data were greater than 4%, and the errors of the other 48 sets were less than 4%.
Thus, it was feasible to use the Chebyshev–Ritz method to solve the eigenfrequencies of gears with variable thickness.
American Psychological Association (APA)
Li, Yi& Lv, Ming& Wang, Shi-ying& Qin, Hui-bin& Fu, Jun-fan. 2018. Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1209762
Modern Language Association (MLA)
Li, Yi…[et al.]. Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method. Mathematical Problems in Engineering No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1209762
American Medical Association (AMA)
Li, Yi& Lv, Ming& Wang, Shi-ying& Qin, Hui-bin& Fu, Jun-fan. Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1209762
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209762