Periodic Motions With Impacting Chatter and Stick in a Gear Transmission System

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Albert C. J. Luo ◽  
Dennis O’Connor
Keyword(s):  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Impact Model ◽  
Periodic Motions ◽  
Transmission Systems ◽  
New Model ◽  
Gear Transmission System ◽  
Mapping Structures ◽  
First Time

In this paper, an impact model with possible stick between the two gears is proposed for gear transmission systems, which includes the piecewise backlash model and the traditional impact model for the first time. The new model presented in this paper possesses a time-varying boundary for two dynamical systems either to switch or to impact. Such a model can catch impacting chatter and stick phenomena in gear transmission systems. Based on the new model, periodic impacting chatter and stick in a gear transmission system can be investigated. For doing so, switching sets on the time-varying boundaries are introduced to define basic mappings. Mapping structures based on basic mappings are developed for characterizing motions in gear transmission systems, and from such mapping structures, periodic motions with impacting chatter and stick in such a gear transmission system are predicted analytically. Numerical simulations are performed for illustration of periodic motions with impacting chatter and stick phenomena.

scholarly journals PERIODIC MOTIONS AND CHAOS WITH IMPACTING CHATTER AND STICK IN A GEAR TRANSMISSION SYSTEM

2009 ◽  
Vol 19 (06) ◽  
pp. 1975-1994 ◽  
Author(s):  
ALBERT C. J. LUO ◽  
DENNIS O'CONNOR
Keyword(s):  
Stability Analysis ◽  
Bifurcation Analysis ◽  
Local Stability ◽  
Transmission System ◽  
Gear Transmission ◽  
Periodic Motions ◽  
Local Stability Analysis ◽  
Gear Transmission System ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis

This paper focuses on periodic motions and chaos relative to the impacting chatter and stick in order to find the origin of noise and vibration in such a gear transmission system. Such periodic motions are predicted analytically through mapping structures, and the corresponding local stability and bifurcation analysis are carried out. The grazing and stick conditions presented in [Luo & O'Connor, 2007] are adopted to determine the existence of periodic motions, which cannot be achieved from the local stability analysis. Numerical simulations are performed to illustrate periodic motions and stick motion criteria. Such an investigation may provide some clues to reduce the noise in gear transmission systems.

Nonlinear Dynamics of a Gear Transmission System: Part I — Mechanism of Impacting Chatter With Stick

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Dennis O’Connor
Keyword(s):  
Transmission System ◽  
Gear Transmission ◽  
Impact Model ◽  
Transmission Systems ◽  
Motion Mechanism ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Gear Transmission System ◽  
System Part ◽  
Nonlinear Behaviors

In this paper, an investigation on nonlinear dynamical behaviors of a transmission system with a gear pair is conducted. The transmission system is described through an impact model with possible stick between the two gears. From the theory of discontinuous dynamical systems, the motion mechanism of impacting chatter with stick is investigated. The onset and vanishing conditions of stick motions are developed, and the condition for maintaining the stick motion is achieved as well. The corresponding physics interpretation is given for a better understanding of nonlinear behaviors of gear transmission systems. Furthermore, such an understanding may be very helpful to improve the efficiency of gear transmission systems.

MECHANISM OF IMPACTING CHATTER WITH STICK IN A GEAR TRANSMISSION SYSTEM

2009 ◽  
Vol 19 (06) ◽  
pp. 2093-2105 ◽  
Author(s):  
ALBERT C. J. LUO ◽  
DENNIS O'CONNOR
Keyword(s):  
Transmission System ◽  
Gear Transmission ◽  
Gear Pair ◽  
Impact Model ◽  
Transmission Systems ◽  
Motion Mechanism ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Gear Transmission System ◽  
Nonlinear Behaviors

In this paper, an investigation on nonlinear dynamical behaviors of a transmission system with a gear pair is conducted. The transmission system is described through an impact model with a possible stick between the two gears. From the theory of discontinuous dynamical systems, the motion mechanism of impacting chatter with stick is investigated. The onset and vanishing conditions of stick motions are developed, and the condition for maintaining the stick motion is achieved as well. The corresponding physics interpretation is given for a better understanding of nonlinear behaviors of gear transmission systems. Furthermore, such an understanding may be very helpful to improve the efficiency of gear transmission systems.

Nonlinear Dynamics of a Gear Transmission System: Part II — Periodic Impacting Chatter and Stick

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Dennis O’Connor
Keyword(s):  
Local Stability ◽  
Transmission System ◽  
Gear Transmission ◽  
Periodic Motions ◽  
Motion Mechanism ◽  
Local Stability Analysis ◽  
Gear Transmission System ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis ◽  
System Part

In Part I, the motion mechanism of impacting chatter and stick motion in the gear transmission dynamical system was discussed. This paper focuses on periodic motions relative to the impacting chatter and stick in order to find the origin of noise and vibration in such a gear transmission system. Such periodic motions are predicted analytically through mapping structures, and the corresponding local stability and bifurcation analysis are carried out. The grazing and stick conditions presented in Part I are adopted to determine the existence of periodic motions, which cannot be achieved from the local stability analysis. Numerical simulations are performed to illustrate periodic motions and stick motion criteria. Such an investigation may provide some clues to reduce the noise in gear transmission systems.

Impacting chatter and stick in a transmission system with two oscillators

2009 ◽  
Vol 223 (3) ◽  
pp. 159-188 ◽  
Author(s):  
A C J Luo ◽  
D O'Connor
Keyword(s):  
Local Stability ◽  
Transmission System ◽  
Gear Transmission ◽  
Periodic Motions ◽  
Transmission Systems ◽  
Motion Mechanism ◽  
System Parameters ◽  
Mapping Structures ◽  
Non Linear ◽  
The Relationship

In this article, an investigation on non-linear dynamical behaviours of a transmission system with a gear pair is conducted. The transmission system is described through an impact model with a possible stick between the two gears. From the theory of discontinuous dynamical systems, the motion mechanism of impacting chatter with stick is investigated. The onset and vanishing conditions for stick motions are developed, and the condition for maintaining stick motion is obtained as well. The corresponding physical interpretation is given for a better understanding of non-linear behaviours of gear transmission systems. A parameter map is presented to provide a global picture of the relationship between system parameters and corresponding motion. Grazing and stick conditions are utilized to determine the existence of periodic motions. Such periodic motions are predicted analytically through mapping structures, and the corresponding local stability and bifurcation analyses are carried out. Numerical simulations are performed to illustrate periodic motions and stick motion criteria. A better understanding of the motion mechanism between two gears may be helpful for improving the efficiency of gear transmission systems.

Analysis of dynamic characteristics of a multi-stage gear transmission system

2019 ◽  
Vol 25 (10) ◽  
pp. 1653-1662 ◽  
Author(s):  
Wei Li ◽  
Jingdong Sun ◽  
Jiapeng Yu
Keyword(s):  
Dynamic Characteristics ◽  
Noise Control ◽  
Nonlinear Behavior ◽  
Transmission System ◽  
Gear Transmission ◽  
Transmission Systems ◽  
Multi Stage ◽  
Gear Transmission System ◽  
Characteristics Analysis ◽  
Dynamic Characteristics Analysis

The two-parallel shaft gear transmission system is the most widely used system among the multi-stage gear transmission systems. The dynamic characteristics analysis of the two-parallel shaft gear transmission system is of great significance for nonlinear behavior research and noise control of gear transmission systems. This paper establishes a dynamic model and equations for the two-parallel shaft gear transmission system. According to the solution to the dynamic equations, the effects are studied of parameters such as speed, damping, modulus, and precision on the dynamic characteristics of the system. The results provide the basis for reducing vibration and noise control in multi-stage gear transmission systems.

Periodic and Chaotic Dynamic Responses of Face Gear Transmission System

2013 ◽  
Vol 834-836 ◽  
pp. 1273-1280
Author(s):  
Ze Hua Hu ◽  
Jin Yuan Tang ◽  
Si Yu Chen
Keyword(s):  
Periodic Motion ◽  
Chaotic Dynamic ◽  
Rotational Frequency ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Gear Transmission System

The periodic and chaotic dynamic responses of face gear transmission system considering time-varying mesh stiffness and backlash nonlinearity are studied. Firstly, a nonlinear time-varying dynamic model of face gear pair is developed and the motion equations are presented, the real accurate mesh stiffness is obtained by applying Finite element approach. Then, the dynamic equations are solved using Runge-Kutta numerical integral method and bifurcation diagrams are presented and analyzed. The stability properties of steady state responses are illustrated with Floquet multipliers and Lyapunov exponents. The results show that a process of periodic-chaotic-periodic motion exists with the dimensionless pinion rotational frequency as control parameters. The analysis can be a reference to avoid the chaotic motion and unstable periodic motion through choosing suitable rotational frequency.

scholarly journals Nonlinear characteristics of a multi-degree-of-freedom wind turbine’s gear transmission system involving friction

2021 ◽  
Author(s):  
Qiang Zhang ◽  
Xiaosun Wang ◽  
Shaobo Cheng ◽  
Fuqi Xie ◽  
Shijing Wu
Keyword(s):  
Excitation Frequency ◽  
Transmission System ◽  
Friction Model ◽  
Gear Transmission ◽  
Degree Of Freedom ◽  
Gear System ◽  
Time Varying ◽  
High Frequency Region ◽  
Meshing Stiffness ◽  
Gear Transmission System

Abstract In this study, a 42-degree-of-freedom (42-DOF) translation-torsion coupling dynamics model of the wind turbine’s compound gear transmission system considering time-varying meshing friction, timevarying meshing stiffness, meshing damping, meshing error and backlash is proposed. Considering the different meshing between internal and external teeth of planetary gear, the time-varying meshing stiffness is calculated by using the cantilever beam theory. An improved mesh friction model takes account into the mixing of elastohydrodynamic lubrication (EHL) and boundary lubrication to calculate the time-varying mesh friction. The bifurcation diagram is used to analyze the bifurcation and chaos characteristics of the system under the excitation frequency as bifurcation parameter. Meanwhile, the dynamic characteristics of the gear system are identified from the time domain diagrams, phase diagrams, Poincare maps and amplitude-frequency spectrums of the gear system. The results show that the system has complex bifurcation and chaotic behaviors including periodic, quasi-periodic, chaotic motion. The bifurcation characteristics of the system become complicated and the chaotic region increases considering the effects of friction in the high frequency region.

Investigation on Nonlinear Dynamic Characteristics of a New Rigid-Flexible Gear Transmission With Wear

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Zhibo Geng ◽  
Ke Xiao ◽  
Jiaxu Wang ◽  
Junyang Li
Keyword(s):  
Nonlinear Dynamic ◽  
Operating Time ◽  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Control Parameters ◽  
Nonlinear Dynamic Model ◽  
Meshing Stiffness ◽  
Gear Backlash ◽  
Gear Transmission System

Abstract At present, the mean value of the meshing stiffness and the gear backlash is a fixed value in the nonlinear dynamic model. In this study, wear is considered in the model of the gear backlash and time-varying stiffness. With the increase of the operating time, the meshing stiffness decreases and the gear backlash increases. A six degrees-of-freedom nonlinear dynamic model of a new rigid-flexible gear pair is established with time-varying stiffness and time-varying gear backlash. The dynamic behaviors of the gear transmission system are studied through bifurcation diagrams with the operating time as control parameters. Then, the dynamic characteristics of the gear transmission system are analyzed using excitation frequency as control parameters at four operating time points. The bifurcation diagrams, Poincaré maps, fast Fourier transform (FFT) spectra, phase diagrams, and time series are used to investigate the state of motion. The results can provide a reference for the gear transmission system with wear.

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