Strong nonlinearity analysis for gear-bearing system under nonlinear suspension—bifurcation and chaos

Chang‐Jian, Cai‐Wan

doi:10.1016/j.nonrwa.2009.03.027

Cited by 58 publications

(21 citation statements)

References 22 publications

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“…Supposing the internal kinematic excitation in gearing defined by Eqs. (20), (25) and (44) or (45), we can investigate for which operational parameters the gear mesh is constant and we can find a border of interrupted gear mesh.…”

Section: Constant Gear Mesh Conditionsmentioning

confidence: 99%

“…Walha [19] studied nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing flexibility and backlash using the 12-DOF nonlinear system. Similarly, Chang [20] dealt with strong nonlinearity analysis for the gear-bearing system focusing on the influence of nonlinear suspension only. Bonori and Pellicano [21] showed a method for the analysis of nonlinear vibration of spur gears in the presence of manufacturing errors using the 1-DOF model.…”

Section: Introductionmentioning

confidence: 99%

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On modeling and vibration of gear drives influenced by nonlinear couplings

Byrtus

Zeman

2011

Mechanism and Machine Theory

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Section: Constant Gear Mesh Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On modeling and vibration of gear drives influenced by nonlinear couplings

Byrtus

Zeman

2011

Mechanism and Machine Theory

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“…In [10], the frequency responses of a nonlinear geared rotor-bearing system with time-varying mesh stiffness were inspected by the methods of multiplescales and mathematical simulation. In [11], the vibration dynamic responses of a gear transmission system supported by journal bearing were studied; besides the subharmonic, periodic, and chaotic states were examined.…”

Section: Introductionmentioning

confidence: 99%

Nonsmooth Vibration Characteristic of Gear Pair System with Periodic Stiffness and Backlash

Lin

et al. 2018

Discrete Dynamics in Nature and Society

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As the most widely used power transmission device in mechanical equipment, the vibration characteristics of gears have a very important influence on the working performance. It is of great theoretical and practical significance to study the vibration characteristics of gear system. In this paper, a gear transmission system model is set up in a forcefully nonlinear form; the continuity mapping and discontinuity mapping are utilized to analyze the nonsmooth vibration. Then, the sliding dynamics of separation boundaries is studied by using the perturbation method and the differential inclusion theory. In addition, the periodic response of gear pair system is illustrated and Floquet's theory is presented to confirm the stability and bifurcation of periodic response. Concurrently, the maximal Lyapunov exponent is obtained to accurately determine the chaotic state in gear pair system, which is consistent with the bifurcation diagram and Poincare section. Finally, a reasonable explanation is given for the jump phenomenon in bifurcation diagram.

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“…Many factors such as the gear backlash [1][2][3], lubricant [4][5][6][7][8], timevariant meshing stiffness [9][10][11] and the fluctuation of the excitations [12][13][14][15] exert complicated influences on the vibration and noise of gears. Modeling for various gear systems has been conducted [14,16,17], including the interactions between the components [18,19] and also the influence of a particular parameter on the gear noise [8,[20][21][22][23][24]. Meanwhile, various solution techniques, such as analog/digital simulation [25][26][27], numerical integration [2,4,5,28,29], harmonic balance method [30][31][32][33][34], and multiple scale method [35], are used to illustrate the nonlinear characteristics of the gear system including stability of the periodic solution [34,[36][37][38][39], bifurcation and chaos …”

Section: Introductionmentioning

confidence: 99%

“…Modeling for various gear systems has been conducted [14,16,17], including the interactions between the components [18,19] and also the influence of a particular parameter on the gear noise [8,[20][21][22][23][24]. Meanwhile, various solution techniques, such as analog/digital simulation [25][26][27], numerical integration [2,4,5,28,29], harmonic balance method [30][31][32][33][34], and multiple scale method [35], are used to illustrate the nonlinear characteristics of the gear system including stability of the periodic solution [34,[36][37][38][39], bifurcation and chaos [2,19,28,32,40,41]. Suggestions for reducing actual noise are also made [42,43], based on different criteria to evaluate the rattle noise [44,45].…”

Section: Introductionmentioning

confidence: 99%

Stability investigation of velocity-modulated gear system using a new computational algorithm

Liu

Zhang

2017

Nonlinear Dyn

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By considering the lubricant in gear system, one degree-of-freedom model is set up which incorporates the pinion's speed and the drag torque as the excitation sources. By introducing a permissible error (ε), a new computational algorithm using double-changed time steps is proposed in order to reduce the ill-conditioning arising from the numerical stiffness of the gear system and validated by comparison with Runge-Kutta-Fehlberg integration scheme. Then, the influences of the lubricant on the vibration of the gear system are analyzed. The results obtained in this paper indicate that the proposed numerical algorithm not only improves the accuracy of the solution, but also accelerates the calculation speed of the whole system. And according to the collision feature, the contributions of the lubricant on the system are totally different with different pinion's speed and drag torque. Next, by introducing the proposed computational algorithm into the Floquet theory, the stability analyses of the gear system are investigated under the different excitation sources, which demonstrates that the excitation sources significantly affect the operating instability regions. In practice, particular instabilities can be minimized by the proper selection of pinion's speed and drag torque, which can be adjusted according to the working requirements in advance.

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Strong nonlinearity analysis for gear-bearing system under nonlinear suspension—bifurcation and chaos

Cited by 58 publications

References 22 publications

On modeling and vibration of gear drives influenced by nonlinear couplings

On modeling and vibration of gear drives influenced by nonlinear couplings

Nonsmooth Vibration Characteristic of Gear Pair System with Periodic Stiffness and Backlash

Stability investigation of velocity-modulated gear system using a new computational algorithm

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