The Vibration Model Establishment and Solution of Bending-Torsion-Axial-Swing Coupled the Helical Gear Transmission System Based on Lumped Parameter Approximation Method

2014 ◽  
Vol 1061-1062 ◽  
pp. 743-747
Author(s):  
Chang Li ◽  
Bing Chen Wang ◽  
Jun Feng Li
Keyword(s):  
Helical Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Impact Excitation ◽  
Tooth Surface ◽  
Lumped Mass ◽  
Lumped Parameter ◽  
Vibration Model ◽  
Gear Transmission System ◽  
The Time Domain

Based on comprehensive considerations the influences of stiffness excitation, deviation excitation, meshing impact excitation, friction of tooth surface, and other kinds of nonlinear factors, it established a nonlinear coupled vibration model of bending-torsion-axial-swing coupled helical gear transmission system by applying the Lumped Mass Method. After transformed the model to dimensionless form, it used Runge-Kutta method to solve the nonlinear vibration model of the system, and then the time domain chart, spectrum chart, phase chart, Poincare chart, and FFT chart were obtained; it discussed the influence of system parameters on its dynamic characteristics.

Nonlinear Dynamic Analysis of Helical Gear Considering Meshing Impact

2012 ◽  
Vol 201-202 ◽  
pp. 135-138 ◽  
Author(s):  
Feng Wang ◽  
Zong De Fang ◽  
Sheng Jin Li
Keyword(s):  
Dynamic System ◽  
Nonlinear Dynamic ◽  
Helical Gear ◽  
Transmission System ◽  
Contact Analysis ◽  
Gear Transmission ◽  
Impact Excitation ◽  
Tooth Contact Analysis ◽  
Meshing Stiffness ◽  
Gear Transmission System

Comprehensive meshing stiffness and single tooth meshing stiffness are calculated by tooth contact analysis and load tooth contact analysis program. The corner meshing impact model is proposed. Nonlinear dynamic model of helical gear transmission system is established in this paper considering time-varying meshing stiffness excitation, transmission error excitation, corner meshing impact excitation, and the backlash excitation. Take the ship’s helical gear transmission system as an example, the mesh impact force is derived and the primary factors that produce noises are discussed. The effects which the mesh impact brings to vibration characteristics of the gear dynamic system are concluded. Meshing impact has an inevitable effect on the vibration of the dynamic system. Impact excitation costs 8.5% in maximum of vibration acceleration response, 31% in maximum of instantaneous acceleration, and 4.9% in maximum of spectral component amplitude.

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.

Analysis of Dynamic Characteristics of Gear Transmission System Based on Wind Turbine Gearbox

2013 ◽  
Vol 321-324 ◽  
pp. 9-12
Author(s):  
Wen Jun Yang ◽  
Hui Qun Yuan ◽  
Zhi Min Huang ◽  
Li Se Yang
Keyword(s):  
Wind Turbine ◽  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Transmission System ◽  
Gear Transmission ◽  
Parameter Method ◽  
Wind Turbine Gearbox ◽  
Vibration Direction ◽  
Lumped Parameter ◽  
Gear Transmission System

Based on gear transmission system of 1.5MW wind turbine, dynamic characteristics are analyzed under the effect of both external and internal incentives. Using lumped parameter method, the dynamic model involving 6 degrees of freedom for every helical gear is established with taking the time-varying mesh stiffness and error into account. The results show that the transmission system is quasi-periodic under the operating speed, and the vibration direction of gear with a large amplitude is obtained. This study can be referred to the engineering applications.

Study of the Dynamic Behavior of Face Gear Transmission System

2012 ◽  
Vol 268-270 ◽  
pp. 1063-1066 ◽  
Author(s):  
Zhi Wang ◽  
Qing Chen ◽  
Jia Chun Lin ◽  
Li Li Yang
Keyword(s):  
Mathematical Model ◽  
Static Load ◽  
Transmission System ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Cyclic Loads ◽  
Face Gear ◽  
Static Loads ◽  
Gear Transmission System ◽  
The Mathematical Model

According to the gear meshing theory, the tooth surface equation of orthogonal face gear is derived and the mathematical model is established. Also the model was provided for simulating the bevel gear transmission system concerning the time variant stiffness and face gears errors under static load and cyclic loads. Through the model the computerized analysis of speed, angle and acceleration of gear real tooth surface could be accomplished. Rattle as discussed under condition of different static loads and the constant cyclic loads.

Dynamic Analysis of Offset Printing Press Gear-Cylinder-Bearing System under Time-Varying Meshing Stiffness Effect

2015 ◽  
Vol 656-657 ◽  
pp. 658-663
Author(s):  
Tian Cheng Ou Yang ◽  
Nan Chen ◽  
Cui Cui Ju ◽  
Cheng Long Li ◽  
Jiang Hu Li
Keyword(s):  
Equations Of Motion ◽  
Transmission System ◽  
Gear Transmission ◽  
Printing Press ◽  
Time Varying ◽  
Offset Printing ◽  
Meshing Stiffness ◽  
Lumped Parameter ◽  
Gear Transmission System ◽  
Bearing System

This study propose a new nonlinear model for offset printing press gear-cylinder-bearing system by the lumped parameter approach. The multi-DOF model consists of helical gear pairs and spur gear pairs with time-varying meshing stiffness. Bearing and shaft flexibilities are include in the model as well. The equations of motion are obtained by Darren Bell principle and Runge-Kutta numerical method is used to slove the equations of motion. The results show that meshing stiffness and bearing stiffness significantly affect critical speed, vibration acceleration and meshing force. Multi-body dynamics software are applied to compare with lumped parameter model. The results show that there are many similarities in different aspects. Results of experimental study on offset printing press are also presented for validation of different models. After Discrete Fourier Transform, the graphics display that acceleration peaks frequencies are an integer multiple of the gear mesh frequency. It demonstrate that mechanical vibration is mainly from gear transmission system at high printing speed and gear transmission system lead to nonlinear vibration. This work provide a foundation for further improvement of the dynamics of gear system.

Modeling and Solution of a Nonlinear Vibration Model of the Bending-Torsion Coupled Spur Gear Transmission System Based on Lumped Mass Method

2014 ◽  
Vol 635-637 ◽  
pp. 172-176
Author(s):  
Chang Li ◽  
Bing Chen Wang ◽  
Xing Han
Keyword(s):  
Nonlinear Vibration ◽  
Optimization Design ◽  
Spur Gear ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Vibration Model ◽  
Gear Transmission System ◽  
Tooth Surfaces ◽  
The Time Domain ◽  
Fifth Order

After comprehensive considerations of the influences of stiffness excitations, deviation excitations, meshing impact excitations, friction of tooth surfaces, gap changes and other kinds of nonlinear factors, it established a nonlinear vibration model of the bending-torsion coupled spur gear driven system based on Lumped Mass Method (LMM). By transforming the model to dimensionless form and using fifth order adaptive variable step (Runge-Kutta) method to solve the nonlinear vibration model of the system, it can get the time domain charts, spectrum charts, phase charts, Poincare charts, FFT charts and the system bifurcation figures. And then it discussed the influence of system parameter vibrations on its dynamic characteristics, and this could provide a foundation for system dynamic optimization design

Dynamic Analysis on the Bend-Torsion-Shaft-Pendulum Coupling Vibration Model of Helical Gear

2016 ◽  
Vol 851 ◽  
pp. 273-278
Author(s):  
Bao Sen Yan ◽  
Rui Yang Li ◽  
Chao Hong Liu
Keyword(s):  
Nonlinear Dynamic ◽  
Piecewise Linear ◽  
Helical Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Production Operation ◽  
Coupling Vibration ◽  
Nonlinear Dynamic Equations ◽  
Gear Transmission System ◽  
Meshing Characteristics

Based on the condition of comprehensively considering the nonlinear factors, such as backlash helical gear transmission, time-varying meshing stiffness and composition error, a coupled nonlinear dynamics model of the multi-DOF bending - torsion - axis - pendulum helical gear is built in this paper, and on the basis of the "piecewise linear" backlash function, getting backlash function that is fitting for helical gear transmission system meshing characteristics through high order fitting. The Runge-Kutta method of the variable step is used to solve the nonlinear dynamic equations of the helical gear transmission system which is deduced and non-dimensional, and the result of the nonlinear dynamic response of the helical gear transmission system is obtained. After comparison, the response results are consistent with the actual situation, which can provide reference for the production operation, etc in the actual conditions, there is practical guiding significance.

Theoretical analysis of the vibration modes of the star herringbone gear transmission system

2019 ◽  
Vol 234 (2) ◽  
pp. 358-368
Author(s):  
Feiming Wang ◽  
Sanmin Wang ◽  
Fei Li
Keyword(s):  
Vibration Mode ◽  
Vibration Suppression ◽  
Transmission System ◽  
Gear Transmission ◽  
Vibration Modes ◽  
Lumped Mass ◽  
Coupling Vibration ◽  
Lumped Mass Method ◽  
Gear Transmission System ◽  
Herringbone Gear

The star herringbone gear transmission system has a high load-carrying capacity, and is widely used in aviation, marine power drives, off-road vehicles, and hybrid electric-drive vehicles. Vibration and noise are the key concerns with this transmission system. The lumped mass method was adopted to establish the dynamic model and equations of this system. The modes of the system were analyzed and classified, and the eigenvalues and their multiplicities were determined. The results showed that the system has four typical vibration modes: (1) a lateral-rotational coupled vibration mode (multiplicity m = 1), (2) star gear compound mode (multiplicity m =  N-3, N > 3), (3) center component lateral vibration mode (multiplicity m = 2), and (4) star gear and center gear-coupled mode (multiplicity m = 2). The contribution of this paper lies in the discovery of the coupling vibration modes in the star herringbone gear transmission system and the multiplicities of these modes. This work provides the foundation for further research on vibration suppression for the star herringbone gear transmission system and the theory of planet phasing.

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