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.

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 Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Zhihui Liu ◽  
Hongzhi Yan ◽  
Yuming Cao ◽  
Yuqing Lai
Keyword(s):  
Excitation Frequency ◽  
Transmission Error ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Torsional Stiffness ◽  
System Response ◽  
Gear Mesh ◽  
Gear Transmission System ◽  
The Impact

A four-degree-of-freedom nonlinear transverse and torsional vibration model of spur gear transmission system for one-way clutch, two-shaft assembly was developed, in which the one-way clutch was modeled as a piecewise nonlinear spring with discontinuous stiffness, considering the factors such as the time-varying gear mesh stiffness, static transmission error, and nonlinearity backlash. With the help of bifurcation diagrams, time domain response diagrams, phase plane diagrams, and Poincaré maps, the effects of the excitation frequency and the torsional stiffness of one-way clutch on the dynamic behavior of gear transmission system for one-way clutch, two-shaft assembly are investigated in detail by using Runge-Kutta method. Numerical results reveal that the system response involves period-1 motion, multiperiodic motion, bifurcation, and chaotic motion. Large torsional stiffness of one-way clutch can increase the impact and lead to instability in the system. The results can present a useful source of reference for technicians and engineers for dynamic design and vibration control of such system.

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.

Effects of directional rotation radius and transmission error on the dynamic characteristics of face gear transmission system

2013 ◽  
Vol 228 (7) ◽  
pp. 1108-1118 ◽  
Author(s):  
Jinyuan Tang ◽  
Zehua Hu ◽  
Siyu Chen ◽  
Duncai Lei
Keyword(s):  
Dynamic Characteristics ◽  
Transmission Error ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Factor ◽  
Gear Pair ◽  
Face Gear ◽  
Amplitude Variation ◽  
Gear Transmission System ◽  
Static Transmission Error

The effects of directional rotation radius and transmission error excitation on the nonlinear dynamic characteristics of face gear transmission system are analyzed. First, the accurate time-varying mesh stiffness is calculated using finite element method, and the nonlinear motion equation of the system under static transmission error excitation is proposed. The frequency response curve, time history curve, dynamic mesh force curve and dynamic factor curve are given, and the phenomena of jump, multiple solutions and tooth impact are observed. The numerical results show that the effect of amplitude variation of directional rotation radius on the dynamic characteristics of face gear pair is less conspicuous than that of transmission error but actually existing. The amplitude of the dynamic response of face gear pair reduces to some extent with the uniform distribution of the loading area through enlarging the amplitude variation of directional rotation radius. The static transmission error excitation should be reduced to perfect the transmission property. The system is in periodic motion most of the time, and tooth impact occurs only near [Formula: see text] . Since its dynamic property at low velocity and high velocity is good, the system should get through the resonant area quickly in work.

Dynamic Analysis of Gear–Shaft–Bearing Coupled System Considering Bearing Waviness Defect

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Huan Bai ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Jianjun Tan ◽  
Xinzi Li
Keyword(s):  
Dynamic Response ◽  
Vibrational Energy ◽  
Coupled Model ◽  
Coupled System ◽  
Transmission Error ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Mesh ◽  
Gear Transmission System ◽  
Dynamic Transmission Error

Abstract Using finite element and lumped parameter methods, a gear–shaft–bearing coupled vibration model was developed for a single-stage gear transmission system considering bearing waviness, bearing clearance, time-varying transmission error excitation, and shaft flexibility. Runge–Kutta algorithm was applied for solving the dynamic response of the coupled model. The influences of rotational speed, the number, and amplitude of bearing waviness on the dynamics were studied. Results show that any change in the number of bearing waviness has an obvious impact on the dominant frequency component of the dynamic transmission error. When the number of bearing waviness is equal to the number or multiples of the rolling element, the dynamic mesh force occurs peak response and the system vibrates violently. At low and medium speeds range, the gear transmission system with bearing waviness has larger vibrational energy than the gear transmission system without bearing waviness, leading to unstable dynamic response, which would potentially cause a significant chaotic response. The dominant frequencies of the dynamic transmission error for the gear transmission system with bearing waviness are the ball passage frequency (BPF) and its harmonic frequency. At high speeds range, the main excitation is the transmission error both for the gear transmission systems with and without bearing waviness. In addition, the increasing amplitude of bearing waviness would enlarge the dynamic mesh force and decrease the number of loaded rolling elements.

scholarly journals Dynamic characteristics analysis of planetary gear system with internal and external excitation under turbulent wind load

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110356
Author(s):  
Hexu Yang ◽  
Xiaopeng Li ◽  
Jinchi Xu ◽  
Zemin Yang ◽  
Renzhen Chen
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Nonlinear Dynamic ◽  
Planetary Gear ◽  
Wind Load ◽  
Transmission System ◽  
Gear Transmission ◽  
Stiffness Ratio ◽  
Gear Transmission System ◽  
Planetary Gear System

According to the working characteristics of a 1.5 MW wind turbine planetary gear system under complex and random wind load, a two-parameter Weibull distribution model is used to describe the distribution of random wind speed, and the time-varying load caused by random wind speed is obtained. The nonlinear dynamic model of planetary gear transmission system is established by using the lumped parameter method, and the relative relations among various components are derived by using Lagrange method. Then, the relative relationship between the components is solved by Runge Kutta method. Considering the influence of random load and stiffness ratio on the planetary gear transmission system, the nonlinear dynamic response of cyclic load and random wind load on the transmission system is analyzed. The analysis results show that the variation of the stiffness ratio makes the planetary gear have abundant nonlinear dynamics behavior and the planetary gear can get rid of chaos and enter into stable periodic motion by changing the stiffness ratio properly on the premise of ensuring transmission efficiency. For the variable pitch wind turbine, the random change of external load increases the instability of the system.

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