scholarly journals Dynamic Modeling and Chaotic Analysis of Gear Transmission System in a Braiding Machine with or without Random Perturbation

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Zhang Yujing ◽  
Meng Zhuo ◽  
Sun Yize
Keyword(s):  
Degrees Of Freedom ◽  
Random Perturbation ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Gear System ◽  
Random Disturbance ◽  
Nonlinear Phenomenon ◽  
Gear Transmission System ◽  
Clifford System

This paper is aimed at analyzing the dynamic behavior of the gear transmission system in a braiding machine. In order to observe the nonlinear phenomenon and reveal the time-varying gear meshing mechanism, a mathematical model with five degrees-of-freedom gear system under internal and external random disturbance of gear system is established. With this model, bifurcation diagrams, Poincare maps, phase diagrams, power spectrum, time-process diagrams, and Lyapunov exponents are used to identify the chaotic status. Meanwhile, by these analytical methods, spur gear pair with or without random perturbation are compared. The numerical results suggest that the vibration behavior of the model is consistent with that of Clifford system. The chaotic system associated parameters are picked out, which can be helpful to the design and control of braiding machines.

Analysis of Stochastic Nonlinear Dynamics in the Gear Transmission System with Backlash

2015 ◽  
Vol 16 (2) ◽  
pp. 111-121 ◽  
Author(s):  
Jingyue Wang ◽  
Haotian Wang ◽  
Lixin Guo
Keyword(s):  
Time Course ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Period Doubling ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Stochastic Dynamic ◽  
Random Disturbance ◽  
Gear Transmission System

AbstractIn order to study the different backlash, gear damping ratio and random disturbance on dynamic behavior of gear transmission system, stochastic dynamic equations of the three-degree-of-freedom spur gear transmission system are established considering random disturbances of a low-frequency external excitation induced by torque fluctuation, gear damping ratio, gear backlash, excitation frequency and meshing stiffness. Using bifurcation diagram, phase diagram, time course diagram, Poincaré map and power spectrum of the system, the dynamic characteristics of the gear transmission system with different backlash under gear damping ratio changing, and the influence of the random disturbance of gear damping ratio on the bifurcation characteristic of system are analyzed. Numerical simulation shows that the gear transmission system will be from periodic motion with a noisy disturbance to chaotic-like motion by period-doubling bifurcation with decreasing gear damping ratio. In the small damping ratio range, the backlash has great effect on the motion characteristics. Random disturbance has an important effect on the bifurcation characteristics.

scholarly journals Investigation of Nonlinear Characteristics of a Gear Transmission System in a Braiding Machine with Multiple Excitation Factors

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Lingling Yao ◽  
Zhuo Meng ◽  
Jianqiu Bu ◽  
Yize Sun
Keyword(s):  
Degrees Of Freedom ◽  
Surface Friction ◽  
Transmission System ◽  
Gear Transmission ◽  
Gear System ◽  
Considerable Influence ◽  
Nonlinear Characteristics ◽  
Six Degrees Of Freedom ◽  
Gear Transmission System ◽  
And Control

In this study, we attempt to analyze the influence of different excitation factors on the dynamic behavior of a gear transmission system in a braiding machine. In order to observe nonlinear characteristics, a mathematical model is established with a six-degrees-of-freedom gear system for consideration of multiple excitation factors. Iterative results are used to study the nonlinear characteristics of the gear system with respect to contact temperature, varying levels of friction, and disturbance of yarn tension using bifurcation diagrams, maximum Lyapunov exponents, phase diagrams, Poincare maps, and the power spectrum. The numerical results show that excitation factors such as temperature and surface friction, among others, have considerable influence on the nonlinear characteristics of the gear system in a braiding machine, and the model is evaluated to show the key regions of sensitivity. The analysis of associated parameters can be helpful in the design and control of braiding machines.

scholarly journals Nonlinear Dynamic Characteristic Analysis of a Coated Gear Transmission System

Coatings ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Yangyi Xiao ◽  
Liyang Fu ◽  
Jing Luo ◽  
Wankai Shi ◽  
Minglin Kang
Keyword(s):  
Dynamic Characteristic ◽  
Time History ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Phase Curve ◽  
Gear Pair ◽  
Characteristic Analysis ◽  
Mesh Stiffness ◽  
Gear Transmission System

Coatings can significantly improve the load-carrying performance of a gear surface, but how they affect the vibration characteristic of the system is an urgent issue to be solved. Taking into account the nonlinear factors like the variable mesh stiffness, friction, backlash, and transmission error, a six-degree-of-freedom spur gear transmission system with coatings is presented. Meanwhile, the finite element method is applied to acquire the time-varying mesh stiffness of the coated gear pair in the engagement process. With the support of the time-history curve, phase curve, Poincare map, and fast Fourier transform spectrum, the dynamic characteristics and the effects of the coating elastic modulus on vibration behaviors of a gear transmission system are minutely dissected by using a numerical integration approach. Numerical cases illustrate that the dynamic characteristic of a gear transmission system tends toward a one-period state under the given operating condition. They also indicate that, compared with softer coatings, stiffer ones can properly enhance the transmission performance of the coated gear pair. Numerical results are also compared with previous studies, and can establish a theoretical basis for dynamic design and vibration control of the coated gear transmission system.

scholarly journals Non-Linear Dynamic Feature Analysis of a Multiple-Stage Closed-Loop Gear Transmission System for 3D Circular Braiding Machine

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1788
Author(s):  
Lingling Yao ◽  
Zhuo Meng ◽  
Jianqiu Bu ◽  
Yize Sun
Keyword(s):  
Closed Loop ◽  
Transmission Error ◽  
Mean Value ◽  
Transmission System ◽  
Gear Transmission ◽  
Random Disturbance ◽  
Symmetrical Structure ◽  
Linear Dynamic ◽  
Gear Transmission System ◽  
The Mean

Aiming at the particularity of a multiple-stage closed-loop gear transmission system for 3D circular braiding machine, the model of gear transmission system in radial braiding machine was simplified. The non-linear dynamic equations of a n-elements closed-loop gear transmission system with symmetrical structure including static transmission error, the random disturbance of meshing damping and backlash were considered. For convenience of calculation n = 3, the equations were solved numerically by using Runge-Kutta. The dynamic transmission error(DTE) with different backlash, dynamic meshing forces with and without the random disturbance of meshing damping, the amplitude of dynamic transmission error at n = 1000 r/min and b = 2.65 × 10−5 m, root mean square(RMS) of DTE and the mean value of DTE of the first pair of gears were analyzed. The simulation results show that different backlash and the random disturbance of meshing damping have a great influence on the dynamic displacement error and meshing force of the gear pair, and RMS and the mean value of DTE changes at different rotational speeds. The results will provide a reference for realizing the smoothness of the closed-loop gear transmission system with symmetrical structure for 3D braiding machine and have great practical significance for improving the braiding quality.

The Gap Nonlinear Characteristics of Gear Transmission System under External Excitation

2012 ◽  
Vol 215-216 ◽  
pp. 1067-1070
Author(s):  
Kang Huang ◽  
Jue Li ◽  
Xin Jin ◽  
Qi Chen
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Transmission System ◽  
Gear Transmission ◽  
Engineering Practice ◽  
Nonlinear Dynamic Model ◽  
Gear Transmission System ◽  
Nonlinear Dynamic Characteristics ◽  
Domain Of Parameters

For the study of nonlinear dynamic characteristics of a pair of gears in an external torque under gear meshing error excitation, we will establish two degrees of freedom nonlinear torsional vibration model. The use of Matlab / Simulink for numerical simulation solves the nonlinear dynamic model of the gear gap. Study the dynamic characteristics of the system in a certain domain of parameters on external incentive conditions, as well as external motivation of gear transmission system dynamic characteristics influence. The results have important practical value for future engineering practice on gear transmission system's dynamic design, and have important theoretical significance for complex gear transmission system dynamics study.

scholarly journals Chaos and Stability of Spur Gear Transmission System for Locomotive Based on Energy Method and Floquet Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Junguo Wang ◽  
Bo Lv ◽  
Yongxiang Zhao
Keyword(s):  
Floquet Theory ◽  
Gear Tooth ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Model Parameters ◽  
Lumped Mass ◽  
Mass Model ◽  
Model Parameter ◽  
Gear Transmission System

Considering the internal and external excitations such as time-varying mesh stiffness (TVMS), backlash, transmission error, torque of the traction motor, and load torque of the wheel/rail, a lumped mass model of the spur gear drive system for a railway locomotive is established. Based on Ma models in the relevant literatures, TVMS is calculated by simplifying a gear tooth as a cantilever beam on the root circle, taking into account the effects of extended tooth contact as well as revised foundation stiffness. The bifurcation diagrams and Lyapunov exponent curves of the model parameters are drawn by the numerical method, and the mechanism of chaos evolution of the gear transmission system is analyzed. According to the Floquet theory, variation curves of the maximum Floquet multiplier with pinion speed and support stiffness ratio are drawn by numerical methods. Combined with the bifurcation diagram of the system, the influences of model parameter on the stability of the system are analyzed, and the evolution laws of periodic motion and bifurcation phenomenon are gained. These research results provide the theoretical evidence of model parameter design of the locomotive transmission system.

The Fault Characteristics of Planetary Gear System with Tooth Breakage

2013 ◽  
Vol 569-570 ◽  
pp. 489-496 ◽  
Author(s):  
Yong Gui ◽  
Qin Kai Han ◽  
Zheng Li ◽  
Zhi Ke Peng ◽  
Fu Lei Chu
Keyword(s):  
Dynamic Response ◽  
Wind Turbine ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Gear System ◽  
Operation Conditions ◽  
Gear Transmission System ◽  
Planetary Gear System ◽  
Two Parameters

Tooth breakage is a typical failure form of wind-turbine planetary gear transmission system, it is important to study the influence of tooth breakage on vibration characteristics of planetary gear transmission system. In this paper, considering the tooth breakage defect, a lumped parameter vibration model of a planetary gear system with time-periodic mesh stiffness is established. Effects of the length and width of tooth breakage on meshing stiffness and dynamic response are discussed in detail. The relation between characteristic frequency of the tooth breakage fault and rotating speeds is pointed out. Several statistical indicators are utilized to show the influence of two parameters (length of planet tooth breakage and input speed) on the dynamic response of the system. Experiments are carried out to verify the simulation results. These results would be useful for fault diagnosis of wind turbine transmission system at different operation conditions.

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