Bifurcation and chaos analysis of multistage planetary gear train

Li, Sheng; Wu, Qingming; Zhang, Zhi-Qiang

doi:10.1007/s11071-013-1060-z

Cited by 74 publications

(33 citation statements)

References 19 publications

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“…However, the mesh stiffness will be varied due to the variation of contact position in the mesh process. The mesh stiffness, which is modeled as an internal parametric excitation in numerous studies [3][4][5][6], is generally neglected in the geared rotor dynamics analysis, especially in the gear whirling analysis. In the present section, the effects of mesh stiffness on the critical speed of the geared rotor system are illustrated in Fig.…”

Section: Effect Of Time Varying Mesh Stiffnessmentioning

confidence: 99%

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Rotordynamics analysis of a double-helical gear transmission system

Chen

Tang

et al. 2015

Meccanica

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The rotordynamics of a double-helical gear transmission system is investigated. The equation of motion of the system with bearing and gyroscopic effect is derived by using the finite element method, in which Timoshenko beam finite element is used to represent the shaft, a rigid mass for the gear. Natural frequencies, mode shapes and Campbell diagrams are illustrated to indicate the effects of gear input speed and time varying mesh stiffness. Besides, effects of mesh stiffness on the critical speed of the gear transmission system are analyzed. The numerical results show that the axial force has significant influence on the natural frequency and the mode shape of the double-helical gear transmission system, for which the mix whirling motion dominates the natural characteristics. There are two higher critical speed curves which increase with the mesh stiffness, but one of them is related to the gyroscopic effect.

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Section: Effect Of Time Varying Mesh Stiffnessmentioning

confidence: 99%

“…In this case, the effects of shaft and bearing flexibility are simplified or neglected with an underlying assumption. The nonlinear phenomena [3][4][5][6] (such as chaos and bifurcation) and parametric resonance [2,[7][8][9] due to time varying mesh stiffness, gear backlash and friction dominate in the gear dynamic analysis.…”

Section: Introductionmentioning

confidence: 99%

Rotordynamics analysis of a double-helical gear transmission system

Chen

Tang

et al. 2015

Meccanica

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“…As key ingredients of a transmission, gears also suffer from multiple nonlinearities. ough plenty of research studies have been published on nonlinear dynamics of PGT [16][17][18][19][20], most of them have one element of the PGT fixed to construct a single-input single-output transmission, and OWCs are not commonly considered because of their application limitations in the past days. Gill-Jeong [21] validated OWCs' function of reducing vibration and pointed out that stiffness of the OWC had great effects on the behavior of a gear pair.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of a Power-Split Transmission Unit with a Planetary Gear Train and Selectable One-Way Clutches

Jia

2020

Complexity

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A Planetary Gear Train (PGT) can be used in series-parallel transmission to redistribute powers. Selectable one-way clutches (SOWCs), compared with traditional friction clutches, can simplify controls and diversify patterns especially for hybrid transmissions. In this paper, a nonlinear torsional model of a power-split PGT coupled with three SOWCs is proposed. Piecewise nonlinearities of SOWCs as well as clearance, time-varying mesh stiffness, and synthetic transmission error of the PGT are considered. With a specified group of comprehensive evaluation indices, influences of piecewise nonlinearities of SOWCs are explored. Simulation results show that the piecewise nonlinearities of SOWCs can diminish collision range and reduce resonances of the PGT. Further research studies on parameter configurations of each SOWC reveal that of the three SOWCs, stiffness and radius of the SOWC connected to the sun gear of the PGT are dominant factors. Large stiffness and effective radius of the SOWC render the PGT fall into chaos on lower meshing frequencies; however, enormous impact vibrations occur to the SOWC if it gets too soft. Additionally, the increase of the damping ratio of the SOWC connected to sun gear can distinctly reduce the vibration and maximum dynamic load of the system on the entire working range.

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“…Wang [12] analyzed the bifurcation and chaos of the gear train by investigating the maximum Lyapunov exponents and Poincare section. Li [13] evaluated the bifurcation and chaos in spur gears system. Sheng [14] provided an understanding of strong nonlinearity in a gear-bearing system, including nonlinear oil-film force and nonlinear gear mesh force.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations and chaos in a gear assembly with clearances for solar array drive assembly

Wei¹,

Li²,

Li³

2017

J. vibroeng.

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Solar array drive assembly is an important part of the spacecraft. It is used to rotate the solar panels. The gear assembly in solar array drive assembly plays a key role in transferring power safely. Nonlinear behavior of gear assembly, like the chaotic motion, can highly affect the stability and operating life of solar array drive assembly. Clearances in gear assembly which were neglected for simplification in past years have increased the risk of failure and become a problem in accurate control. To investigate the clearances effect on nonlinear behavior, this paper establishes a new dynamic model of the gear assembly with bilateral clearances. The main difference comparing to general spur gears is its unique hysteresis stiffness may also influence the clearance effects. Transformation of the hysteresis loop is observed from theoretical equations using different parameters. Bifurcations and chaotic analysis of the system are carried out by numerical simulations in this study. The results show that the variation of clearances may induce the chaotic behavior into gear transmission even when the primary response is stable. When the system step into the chaotic region, it has a high risk of unstable vibration and fuzzy output. The influence of excitation frequency on the chaotic motion of the system is also provided. Chaos thresholds are calculated to avoid nonlinear behavior of the system in design and control. This study makes it possible to predict the unstable clearance interval in this system and avoid the system stepping into chaotic motion. Analyzing and predicting the chaotic behaviors can contribute to the further studies on design and control of the solar array drive assembly.

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Bifurcation and chaos analysis of multistage planetary gear train

Cited by 74 publications

References 19 publications

Rotordynamics analysis of a double-helical gear transmission system

Rotordynamics analysis of a double-helical gear transmission system

Nonlinear Dynamics of a Power-Split Transmission Unit with a Planetary Gear Train and Selectable One-Way Clutches

Bifurcations and chaos in a gear assembly with clearances for solar array drive assembly

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