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.

Bifurcation and Chaos of a Spur Gear Transmission System With Non-Uniform Wear

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Zhibo Geng ◽  
Ke Xiao ◽  
Junyang Li ◽  
Jiaxu Wang
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Operating Time ◽  
Spur Gear ◽  
Gear Transmission ◽  
Nonlinear Dynamic Model ◽  
Gear Backlash ◽  
Gear Transmission System ◽  
Nonlinear Dynamic Characteristics

Abstract In this study, a nonlinear dynamic model of a spur gear transmission system with non-uniform wear is proposed to analyze the interaction between surface wear and nonlinear dynamic characteristics. A quasi-static non-uniform wear model is presented, with consideration of the effects of operating time on mesh stiffness and gear backlash. Furthermore, a nonlinear dynamic model with six degrees-of-freedom is established considering surface friction, time-varying gear backlash, time-varying mesh stiffness, and eccentricity, and the Runge–Kutta method applied to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found that surface wear is generated with a change in operating time and affects the nonlinear dynamic characteristics of the spur gear system. This study provides a better understanding of nonlinear dynamic characteristics of gear transmission systems operating under actual conditions.

Influence of the Random System Parameters on the Nonlinear Dynamic Characteristics of Gear Transmission System

2017 ◽  
Vol 18 (7-8) ◽  
pp. 619-630
Author(s):  
Jingyue Wang ◽  
Haotian Wang ◽  
Huan Wang ◽  
Lixin Guo
Keyword(s):  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Damping Ratio ◽  
Transmission System ◽  
Gear Transmission ◽  
Random Parameters ◽  
Meshing Stiffness ◽  
Gear Backlash ◽  
Gear Transmission System ◽  
Nonlinear Dynamic Characteristics

AbstractIn order to analyze the influence of the random parameters of the system on the nonlinear dynamic characteristics of the gear transmission system, considering the random perturbation of damping ratio, gear backlash, meshing frequency, meshing stiffness and the low frequency excitation caused by torque fluctuation, the random vibration equations of three-degree-of-freedom gear transmission system are established according to the Newton’s law. The motion differential equations are solved by the Runge–Kutta method. The effects of different random parameters such as load ratio, tooth frequency ratio, damping ratio, gear backlash and meshing stiffness on the dynamic response of the gear transmission system are analyzed in light and heavy loads and low and high speeds.

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.

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 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.

A Model of Nonlinear Dynamic Modeling for Planetary Gear Transmission System with Backlash

2011 ◽  
Vol 86 ◽  
pp. 510-513
Author(s):  
Fa Jia Li ◽  
Ru Peng Zhu ◽  
He Yun Bao ◽  
Xiao Zhen Li
Keyword(s):  
Nonlinear Dynamic ◽  
Planetary Gear ◽  
Horizontal Displacement ◽  
Load Sharing ◽  
Relative Displacement ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Equations ◽  
Nonlinear Dynamic Model ◽  
Gear Transmission System

The (4+N) DOFs (degrees of freedom) nonlinear dynamic model of the planetary gear transmission system has been established which include the horizontal displacement, vertical displacement of sun gear, eccentricity error excitation of the sun gear and planetary gear, and gear backlash. The nonlinear dynamic equations was dealt with non-dimensional. Non-dimensional relative displacement of sun gear with planet gears and planet gears with internal gear were solved by using the method of numerical integration. Load sharing coefficients of every planet gear was got by dealt with the result of dynamic equations. The differences of non-dimensional relative displacement and load sharing coefficient were contrasted.

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.

scholarly journals Study on Dynamics of a Two-Stage Gear Transmission System with and without Tooth Breakage

Processes ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 2141
Author(s):  
Deyi Fu ◽  
Shiqiao Gao ◽  
Haipeng Liu
Keyword(s):  
Numerical Simulation ◽  
Periodic Motion ◽  
Domain Analysis ◽  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Two Stage ◽  
Meshing Stiffness ◽  
Vibration Condition ◽  
Gear Transmission System

This paper studies the dynamics of a two-stage gear transmission system in both the normal state and the fault state with tooth breakage. The torsional vibration model of the two-stage parallel shaft gear was developed by using the lumped parameter method. The time-varying meshing stiffness of the gear transmission system is described by Fourier series which is determined by the periodical meshing characteristics of the gears with both the single-tooth and the double-tooth contacts. By introducing the pulse into the regular time-varying meshing stiffness, the tooth breakage existing in the gear transmission system is mimicked. Based on the numerical simulation of the developed dynamic model, both the time domain analysis and the frequency domain analysis of the gear transmission system under both the normal condition and the tooth breakage are compared accordingly. The influence of the tooth breakage on the dynamic characteristics of the gear transmission system is analyzed comprehensively. Furthermore, based on the developed test bench of a two-stage gear transmission system, the experimental research was carried out, and the experimental results show great agreements with the results of numerical simulation, and thus the validity of the developed mathematical model is demonstrated. By comparing the periodic motion with the chaotic motion, the fault identification for the gear transmission system is verified to be tightly related to its vibration condition, and the control of the vibration condition of the gear transmission system as periodic motion is of great significance to the fault diagnosis.

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.

Dynamical Analysis of Planetary Gear Transmission System Under Support Stiffness Effects

2020 ◽  
Vol 30 (06) ◽  
pp. 2050080
Author(s):  
Ling Xiang ◽  
Zeqi Deng ◽  
Aijun Hu
Keyword(s):  
Excitation Frequency ◽  
Global Bifurcation ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Dynamical Analysis ◽  
Largest Lyapunov Exponent ◽  
Meshing Stiffness ◽  
Gear Transmission System

The transverse-torsional nonlinear model of multistage gear transmission system which is comprised of a planetary gear set and two parallel gear stages is proposed with time-varying meshing stiffness, comprehensive gear errors and gear backlash. The nonlinear dynamic responses are analyzed by applying excitation frequency and support stiffness as the bifurcation parameters. The motions of the system are identified through global bifurcation diagram, largest Lyapunov exponent (LLE) and Poincaré map. The numerical results demonstrate that the support stiffness affects the system, especially on planetary gear set. The motions of the system with the changes of the support stiffness are diverse including some different multiperiodic motions. Also, the state of the system undergoes 2T-periodic motion, chaos, quasi-periodic behavior and multiperiodic motion. For the support stiffness or other nonlinear factors of the gear system, the suitable range of working frequencies could make the system stable. Correspondingly, parameters of the system should be designed properly and controlled for the better operation and enhancing the life of the system.

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