Bifurcation and chaos analysis of spur gear pair with and without nonlinear suspension

Chang‐Jian, Cai‐Wan; Chang, Shiuh-Ming

doi:10.1016/j.nonrwa.2010.08.021

Cited by 57 publications

(20 citation statements)

References 24 publications

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“…The chaotic motion was identified from the largest Lyapunov exponents, Poincaré maps, and the phase diagrams of the system. Chang-Jian and Chang [14] studied the dynamic orbits of a singledegree-of-freedom spur gear system by using bifurcation diagrams with the dimensionless damping coefficient and the dimensionless rotational speed ratio as control parameters. Gou et al [15] used the simple cell mapping method and escape time algorithm to examine the bifurcation dynamic characteristics of the multiparameter coupling in torsionvibration gear system.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

Liu¹,

Yan²,

Cao³

et al. 2017

Shock and Vibration

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A four-degree-of-freedom nonlinear transverse and torsional vibration model of spur gear transmission system for one-way clutch, two-shaft assembly was developed, in which the one-way clutch was modeled as a piecewise nonlinear spring with discontinuous stiffness, considering the factors such as the time-varying gear mesh stiffness, static transmission error, and nonlinearity backlash. With the help of bifurcation diagrams, time domain response diagrams, phase plane diagrams, and Poincaré maps, the effects of the excitation frequency and the torsional stiffness of one-way clutch on the dynamic behavior of gear transmission system for one-way clutch, two-shaft assembly are investigated in detail by using Runge-Kutta method. Numerical results reveal that the system response involves period-1 motion, multiperiodic motion, bifurcation, and chaotic motion. Large torsional stiffness of one-way clutch can increase the impact and lead to instability in the system. The results can present a useful source of reference for technicians and engineers for dynamic design and vibration control of such system.

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Section: Introductionmentioning

confidence: 99%

Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

Liu¹,

Yan²,

Cao³

et al. 2017

Shock and Vibration

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show abstract

“…Some domestic and foreign experts [2][3][4][5][6] have done the related research work in the principle of gear engagement, tooth surface contact strength, tooth root bending strength, tooth profile machining and profile modification. Due to the gear transmission system includes parameters of gear backlashes [7], time-varying mesh stiffness [8], mesh damping [9], transmission errors [10], tooth surface friction [11], the system is a strongly nonlinear system and the vibration properties of the gear system will directly affect the stability and reliability of the system [12]. In the nonlinear dynamics of gear system, the author [13] did some research relevantly and analyzed the effect of speed ratios, backlashes and load on the dynamic response of gear system.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Analysis of Helical Face-Gear Transmission System with Multi-Factor

et al. 2016

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Abstract.A systematic analysis of the dynamics of a helical face-gear system with 8 degree of freedom is performed in this study under complex excitation. The nonlinear dynamic system is solved by the Runge-Kutta method. The bifurcation and dynamic load characteristics of the system is identified from a series of diagrams. The effect of multi-factor on bifurcation diagrams is also analysed. The results real that with the increase of dimensionless frequency, the system undergoes the process of periodic, chaotic and periodic motions. The amplitude of the dynamic load gradually increases in a certain range and begins to decrease at a certain value. A higher mesh damping coefficient or a higher input torque or a lower gear backlash can reduce the vibration or eliminate chaotic responses.

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“…The interest in the nonlinear behavior of the gear system vibration with backlash nonlinearity in terms of transmission error is reflected in recent studies [1][2][3]. Moradi and Salarieh [1] investigated primary, super-harmonic and sub-harmonic resonances of spur gear pairs including the backlash nonlinearity using multiple scale method.…”

Section: Introductionmentioning

confidence: 99%

“…Moradi and Salarieh [1] investigated primary, super-harmonic and sub-harmonic resonances of spur gear pairs including the backlash nonlinearity using multiple scale method. Chang-Jian and Chang [2] presented the nonlinear dynamic behavior of spur gear pair with nonlinear suspension system. Si-Yu and Jin-Yuan [3] investigated the parameter stability of a strong nonlinear parametric excitation system for primary resonance by using the Multiple-scales method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Analysis of Spur Gear Pair with Time-varying Mesh Stiffness

Rao

Awang

Lias

et al. 2014

MATEC Web of Conferences

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Abstract. This study presents nonlinear analysis of single degree of freedom spur gear pair with time-varying mesh stiffness. The backlash is approximated using nonlinear term. The periodic steady-state solutions of the nonlinear system are obtained by closed-form expressions using the method of multiple scales. The stability and forced vibration response of the gear system are analyzed. The effect of mesh stiffness variation on the amplitude parameter of nondimensional dynamic transmission error for primary resonance is presented. The closed-form solutions in terms of mesh stiffness variations provide design guidelines for dynamic analysis of spur gear.

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Bifurcation and chaos analysis of spur gear pair with and without nonlinear suspension

Cited by 57 publications

References 24 publications

Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

Nonlinear Vibration Analysis of Helical Face-Gear Transmission System with Multi-Factor

Nonlinear Analysis of Spur Gear Pair with Time-varying Mesh Stiffness

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