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.

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.

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 Analysis of Dynamic Characteristics of the Multistage Planetary Gear Transmission System with Friction Force

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zhengming Xiao ◽  
Fu Chen ◽  
Kongliang Zhang
Keyword(s):  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamical Model ◽  
Tooth Surface ◽  
Time Varying ◽  
Two Stage ◽  
Friction Coefficients ◽  
Planetary Gearbox ◽  
Gear Transmission System

Multistage planetary gear transmission system has been widely utilized in engineering practice due to the salient characteristics, such as high bearing load and large speed ratio. This paper addresses a two-stage planetary gearbox and establishes a system coupling torsional dynamical model which considers the time-varying mesh stiffness, friction forces, and interstage coupling factors. Meanwhile, the friction and lubrication states are classified to comprehensively analyze the calculation of friction coefficients under different conditions. Considering the time-varying influence of friction on the tooth surface under the condition of fluid lubrication, the vibration response under parametric excitation is solved by a numerical method. A multistage planetary transmission test bench is built in the back-to-back form so as to test the vibration of the two-stage planetary gearbox. It shows that the simulation results of the dynamical model are consistent with the test data. Consideration of the calculation of friction on the tooth surface and the friction coefficients is helpful for the establishment of the more accurate dynamical model and lays the foundation for the structural design, fault diagnosis, and dynamic optimization of the multistage planetary gear transmission system.

scholarly journals A Coupling Dynamics Analysis Method for Two-Stage Spur Gear under Multisource Time-Varying Excitation

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Zizhen Qiao ◽  
Jianxing Zhou ◽  
Wenlei Sun ◽  
Xiangfeng Zhang
Keyword(s):  
Dynamic Response ◽  
Spur Gear ◽  
Frequency Component ◽  
Transmission System ◽  
Gear Transmission ◽  
Mode Shapes ◽  
Time Varying ◽  
Two Stage ◽  
Gear Transmission System ◽  
Shaft Flexibility

A new modeling method is proposed to simulate the dynamic response of a two-stage gear transmission system using the finite element method (FEM). The continuous system is divided into four modules: shaft-shaft element, shaft-gear element, shaft-bearing element, and gear-gear element. According to the FEM, the model is built with each element assembled. Meanwhile, the model considers the time-varying mesh stiffness (TVMS), bearing time-varying stiffness (BTVS), and the shaft flexibility. The Newmark integration method (NIM) is used to obtain the dynamic response of the spur gear system. Results show that vibration amplitude and the number of frequency components decrease after considering shaft flexibility through comparing the gear dynamic response under the condition of flexible shaft and rigid shaft. When the effect of bearing stiffness is considered, there will be a bearing passing frequency component in the frequency spectrum. In addition, the result shows that the simulation and experimental test of the frequency component are basically consistent. Furthermore, the theoretical model is validated against an experimental platform of the two-stage gear transmission system and the dynamic responses are compared under the condition of increasing speed. Additionally, the increase of shaft stiffness not only changes some of the dominant mode shapes (torsional mode shapes) but also makes the number of primary resonance speeds added. The method can be used to guide the design of gear systems.

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.

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.

Nonlinear Dynamics of a Multistage Gear Transmission System with Multi-Clearance

2018 ◽  
Vol 28 (03) ◽  
pp. 1850034 ◽  
Author(s):  
Ling Xiang ◽  
Yue Zhang ◽  
Nan Gao ◽  
Aijun Hu ◽  
Jingtang Xing
Keyword(s):  
Nonlinear Dynamics ◽  
Global Bifurcation ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Largest Lyapunov Exponent ◽  
Periodic Motions ◽  
Meshing Stiffness ◽  
Gear Transmission System

The nonlinear torsional model of a multistage gear transmission system which consists of a planetary gear and two parallel gear stages is established with time-varying meshing stiffness, comprehensive gear error and multi-clearance. The nonlinear dynamic responses are analyzed by applying the reference of backlash bifurcation parameters. The motions of the system on the change of backlash are identified through global bifurcation diagram, largest Lyapunov exponent (LLE), FFT spectra, Poincaré maps, the phase diagrams and time series. The numerical results demonstrate that the system exhibits rich features of nonlinear dynamics such as the periodic motion, nonperiodic states and chaotic states. It is found that the sun-planet backlash has more complex effect on the system than the ring-planet backlash. The motions of the system with backlash of parallel gear are diverse including some different multi-periodic motions. Furthermore, the state of the system can change from chaos into quasi-periodic behavior, which means that the dynamic behavior of the system is composed of more stable components with the increase of the backlash. Correspondingly, the parameters of the system should be designed properly and controlled timely for better operation and enhancing the life of the system.

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