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Research Papers

Gear Dynamics Analysis With Turbulent Journal Bearings Under Quadratic Damping and Nonlinear Suspension—Bifurcation and Chaos

[+] Author and Article Information
Cai-Wan Chang-Jian

Department of Mechanical
and Automation Engineering,
I-Shou University,
1, Section 1, Hsueh-Cheng Rd.,
Ta-Hsu District, Kaohsiung City,
Taiwan 840, Republic of China
e-mail: cwchangjian@mail.isu.edu.tw

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 18, 2011; final manuscript received February 16, 2012; published online June 22, 2012. Assoc. Editor: Albert C.J. Luo.

J. Comput. Nonlinear Dynam 8(1), 011013 (Jun 22, 2012) (10 pages) Paper No: CND-11-1067; doi: 10.1115/1.4006203 History: Received May 18, 2011; Revised February 16, 2012

This study performs a systematic analysis of the dynamic behavior of the gear for the gear-bearing system with the turbulent flow effect, quadratic damping effect, nonlinear suspension effect, nonlinear oil-film force, and complicated gear mesh force. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimension of the gear-bearing system. The ignorance of quadratic damping effect for turbomachineries especially in turbulent cases may cause significant errors. The proposed simulation model and theory may provide some useful information for engineers in designing or controlling some turbomachineries particularly in turbulent flow cases.

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Figures

Grahic Jump Location
Fig. 1

Schematic illustration of the gear-bearing system under nonlinear suspension

Grahic Jump Location
Fig. 2

Model of force diagram for pinion and gear

Grahic Jump Location
Fig. 3

Bifurcation diagram of the gear using dimensionless unbalance coefficient β as bifurcation parameter

Grahic Jump Location
Fig. 4

Simulation results obtained for gear-bearing system with β=0.57 (yg)

Grahic Jump Location
Fig. 5

Simulation results obtained for gear-bearing system with β=0.95 (yg)

Grahic Jump Location
Fig. 6

Bifurcation diagram of the gear using dimensionless rotational speed ratio s as bifurcation parameter ( s = 1.21–3.19)

Grahic Jump Location
Fig. 7

Simulation results obtained for gear-bearing system with s = 1.21 (yg)

Grahic Jump Location
Fig. 8

Simulation results obtained for gear-bearing system with s = 3.19 (yg)

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