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Nonlinear dynamics of a spur gear pair with tooth root crack based on an amplitude modulation function

Nan Gao (School of Mechanical Engineering, Tianjin University, Tianjin, PR China) (Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, PR China) (Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, PR China)
Shiyu Wang (School of Mechanical Engineering, Tianjin University, Tianjin, PR China) (Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, PR China) (Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, PR China)
Muhammad Asad Ur Rehman Bajwa (School of Mechanical Engineering, Tianjin University, Tianjin, PR China) (Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, PR China) (Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, PR China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 23 November 2021

Issue publication date: 24 March 2022

185

Abstract

Purpose

Gear transmissions are widely utilized in practice. This paper aims to uncouple the crack feature from the cracked time-varying mesh stiffness (TVMS) and investigate the effects of the crack on the nonlinear dynamics of a spur gear pair.

Design/methodology/approach

An approximate method to simulate the cracked TVMS is proposed by using an amplitude modulation function. The ratio of mesh stiffness loss is introduced to estimate the TVMS with different crack depths and angles. The dynamic responses are obtained by solving a torsional model which takes the non-loaded static transmission error, the backlash and the cracked TVMS into account. By using the bifurcation diagram, the largest Lyapunov exponent (LLE) and dynamic mesh force, the influences of crack on nonlinear behaviors are examined. The dynamic characteristics are identified from the phase diagram, Poincaré map, dynamic mesh force, time series and FFT spectra.

Findings

The comparison between the healthy and cracked gear pairs indicates that the crack affects the system motions, such as the obvious changes of impact force and unpredictable instability. Besides, the additive and difference combination frequencies can be found in periodic-1 and -2 motions, but they are covered in periodic-3 and chaotic motions. Deeper crack is an important determinant of the nonlinear behaviors at a higher speed.

Originality/value

The research provides an interesting perspective on cracked TVMS and reveals the connection between crack and nonlinear behaviors of the gear pairs.

Keywords

Acknowledgements

This study received financial supports from the National Key R&D Program of China through Grant no. 2018YFB2001300 and the National Natural Science Foundation of China through Grant nos. 51675368 and 51705519.

Declaration of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Citation

Gao, N., Wang, S. and Bajwa, M.A.U.R. (2022), "Nonlinear dynamics of a spur gear pair with tooth root crack based on an amplitude modulation function", Engineering Computations, Vol. 39 No. 4, pp. 1575-1596. https://doi.org/10.1108/EC-06-2020-0334

Publisher

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Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited

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