Three-dimensional free vibration analysis of gears with variable thickness using the Chebyshev-Ritz method
type: Item
instance of: scholarly article
title: Three-dimensional free vibration analysis of gears with variable thickness using the Chebyshev-Ritz method
zbMATH Open document ID: 1427.74057
DOI: 10.1155/2018/9684154
author: Yi Li
author: Ming Lv
author: Shiying Wang
author: Hui-bin Qin
author: Jun-fan Fu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 7019811
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9684154
OpenAlex ID: W2899599990
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description: scientific article; zbMATH DE number 7019811