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Research Papers

Investigation on Nonlinear Dynamic Characteristics of a New Rigid-Flexible Gear Transmission With Wear

[+] Author and Article Information
Zhibo Geng

College of Mechanical Engineering;State Key Laboratory of Mechanical Transmission,
Chongqing University,
Chongqing 40044, China
e-mail: zhibo_geng@cqu.edu.cn

Ke Xiao

College of Mechanical Engineering;State Key Laboratory of Mechanical Transmission,
Chongqing University,
Chongqing 40044, China
e-mail: xiaoke993@cqu.edu.cn

Jiaxu Wang

College of Mechanical Engineering;State Key Laboratory of Mechanical Transmission,
Chongqing University,
Chongqing 40044, China
e-mail: jxwang@cqu.edu.cn

Junyang Li

College of Mechanical Engineering;State Key Laboratory of Mechanical Transmission,
Chongqing University,
Chongqing 40044, China
e-mail: lijunyang1982@sina.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received January 17, 2019; final manuscript received April 13, 2019; published online June 5, 2019. Assoc. Editor: Karsten Stahl.

J. Vib. Acoust 141(5), 051008 (Jun 05, 2019) (12 pages) Paper No: VIB-19-1023; doi: 10.1115/1.4043543 History: Received January 17, 2019; Accepted April 15, 2019

At present, the mean value of the meshing stiffness and the gear backlash is a fixed value in the nonlinear dynamic model. In this study, wear is considered in the model of the gear backlash and time-varying stiffness. With the increase of the operating time, the meshing stiffness decreases and the gear backlash increases. A six degrees-of-freedom nonlinear dynamic model of a new rigid-flexible gear pair is established with time-varying stiffness and time-varying gear backlash. The dynamic behaviors of the gear transmission system are studied through bifurcation diagrams with the operating time as control parameters. Then, the dynamic characteristics of the gear transmission system are analyzed using excitation frequency as control parameters at four operating time points. The bifurcation diagrams, Poincaré maps, fast Fourier transform (FFT) spectra, phase diagrams, and time series are used to investigate the state of motion. The results can provide a reference for the gear transmission system with wear.

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Figures

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Fig. 1

The diagram of external involute spur gear pair

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Fig. 2

Nonuniform cantilever beam model of the spur gear tooth with uniform wear

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Fig. 3

The simplified model of the rigid-flexible gear transmission

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Fig. 4

Flowchart of the dynamic model with the consideration of wear in the process of gear transmission

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Fig. 5

Bifurcation diagram of the rigid-flexible gear with operating time w

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Fig. 6

The dynamic response of the transmission system at τ = 20,000: (a) phase diagram, (b) Poincaré map, (c) time series, and (d) FFT spectrum

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Fig. 7

The dynamic response of the transmission system at τ = 38,080: (a) phase diagram, (b) Poincaré map, (c) time series, and (d) FFT spectrum

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Fig. 8

The dynamic response of the transmission system at τ = 46,640: (a) phase diagram, (b) Poincaré map, (c) time series, and (d) FFT spectrum

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Fig. 9

The dynamic response of the transmission system at τ = 70,000: (a) phase diagram, (b) Poincaré map, (c) time series, and (d) FFT spectrum

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Fig. 10

Bifurcation diagram of the rigid-flexible gear with excitation frequency w at (a) τ = 0, (b) τ = 20,000, (c) τ = 40,000, and (d) τ = 60,000

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Fig. 11

Poincaré maps and phase diagrams corresponding to w = 0.638 and different operating time (a) τ = 0, (b) τ = 20,000, (c) τ = 40,000, and (d) τ = 60,000

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Fig. 12

Poincaré maps and time series corresponding to w = 1.045 and different operating time (a) τ = 0, (b) τ = 20,000, (c) τ = 40,000, and (d) τ = 60,000

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Fig. 13

Poincaré maps, phase diagrams, time series, and FFT spectra corresponding to w = 1.1 and different operating time (a) τ = 40,000 and (b) τ = 60,000

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Fig. 14

Poincaré maps and phase diagrams corresponding to different excitation frequency and operating time (a) τ = 0, w = 1.268; (b) τ = 20,000, w = 1.283; (c) τ = 20,000, w = 1.292; (d) τ = 40,000, w = 1.277; (e) τ = 60,000, w = 1.265; and (f) τ = 60,000, w = 1.436

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Fig. 15

Poincaré maps and phase diagrams corresponding to different excitation frequency and operating time (a) τ = 0, w = 1.601; (b) τ = 20,000, w = 1.589; (c) τ = 40,000, w = 1.58; and (d) τ = 60,000, w = 1.571

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Fig. 16

Poincaré maps corresponding to different excitation frequency and operating time (a) τ = 0, w = 2.342; (b) τ = 0, w = 2.345; (c) τ = 0, w = 2.480; (d) τ = 0, w = 2.561; (e) τ = 0, w = 2.588; (f) τ = 20,000, w = 2.303; (g) τ = 20,000, w = 2.318; and (h) τ = 40,000, w = 2.339

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