Journal ArticleDOI
Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems
TLDR
In this paper, the global homoclinic bifurcation and transition to chaotic behavior of a nonlinear gear system are studied by means of Melnikov analytical analysis, where the threshold values of the control parameter for the occurrence of homocallinic Bifurcation and onset of chaos are predicted.Abstract:
The global homoclinic bifurcation and transition to chaotic behavior of a nonlinear gear system are studied by means of Melnikov analytical analysis. It is also an effective approach to analyze homoclinic bifurcation and detect chaotic behavior. A generalized nonlinear time varying (NLTV) dynamic model of a spur gear pair is formulated, where the backlash, time varying stiffness, external excitation, and static transmission error are included. From Melnikov method, the threshold values of the control parameter for the occurrence of homoclinic bifurcation and onset of chaos are predicted. Additionally, the numerical bifurcation analysis and numerical simulation of the system including bifurcation diagrams, phase plane portraits, time histories, power spectras, and Poincare sections are used to confirm the analytical predictions and show the transition to chaos.read more
Citations
More filters
Journal ArticleDOI
Nonlinear dynamics analysis of the spur gear system for railway locomotive
TL;DR: In this article, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter.
Journal ArticleDOI
Dynamic analysis of a planetary gear system with multiple nonlinear parameters
Ling Xiang,Nan Gao,Aijun Hu +2 more
TL;DR: Analysis results show that the variation of meshing frequency as the external excitation could transit the states of the system and the higher damping coefficient and suitable backlash could suppress the region of chaos.
Journal ArticleDOI
Effects of polygonal wear of wheels on the dynamic performance of the gearbox housing of a high-speed train:
TL;DR: The results of the analysis show that polygonal wear can significantly influence the vibration of the gearbox housing, and the maximum amplitude of the acceleration of vibration is more than 200 g.
Journal ArticleDOI
An analytical study of controlling chaotic dynamics in a spur gear system
TL;DR: In this paper, a control system for eliminating the chaotic behaviors in a gear dynamic transmission system is presented, and the numerical simulations are considered to check the validity of theoretical predictions, and also to investigate the efficiency of the proposed control system to eliminate the homoclinic bifurcation and chaos.
Journal ArticleDOI
Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis
TL;DR: In this article, a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error is established, based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model are predicted.
References
More filters
Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Book
Introduction to Applied Nonlinear Dynamical Systems and Chaos
TL;DR: The Poincare-Bendixson Theorem as mentioned in this paper describes the existence, uniqueness, differentiability, and flow properties of vector fields, and is used to prove that a dynamical system is Chaotic.
Journal ArticleDOI
Mathematical models used in gear dynamics—A review
TL;DR: A comprehensive survey of the studies involved in mathematical modelling of gears for dynamic analysis is made in this paper, where the basic characteristics of each class of dynamic models along with the objectives and different parameters considered in modeling are discussed.
Related Papers (5)
Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: sub-harmonic motions
Ahmad Al-Shyyab,Ahmet Kahraman +1 more