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.

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.

Effects of the Gear Tooth Modification on the Nonlinear Dynamics of Gear Transmission System

2010 ◽  
Vol 97-101 ◽  
pp. 2764-2769
Author(s):  
Si Yu Chen ◽  
Jin Yuan Tang ◽  
C.W. Luo
Keyword(s):  
Nonlinear Dynamics ◽  
Gear Tooth ◽  
Simulation Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Meshing Stiffness ◽  
Gear Transmission System ◽  
Tooth Modification ◽  
Static Transmission Error ◽  
Misalignment Error

The effects of tooth modification on the nonlinear dynamic behaviors are studied in this paper. Firstly, the static transmission error under load combined with misalignment error and modification are deduced. These effects can be introduced directly in the meshing stiffness and static transmission error models. Then the effect of two different type of tooth modification combined with misalignment error on the dynamic responses are investigated by using numerical simulation method. The numerical results show that the misalignment error has a significant effect on the static transmission error. The tooth crowning modification is generally preferred for absorbing the misalignment error by comparing with the tip and root relief. The tip and root relief can not resolve the vibration problem induced by misalignment error but the crowning modification can reduce the vibration significantly.

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.

scholarly journals Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Qilin Huang ◽  
Yong Wang ◽  
Zhipu Huo ◽  
Yudong Xie
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Dynamic Model ◽  
Total Mass ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Gear Transmission System

A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM). Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

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.

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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