scholarly journals Modelling of time-varying meshing stiffness under tooth wear condition for nonlinear dynamics in compound planetary gear set

2021 ◽  
Author(s):  
Haibo Zhang ◽  
Chao Yang
Keyword(s):  
Nonlinear Dynamics ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Time Varying ◽  
Meshing Stiffness ◽  
Wear Condition

Time Varying Meshing Stiffness of Cracked Sun and Ring Gears of Planetary Gear Train

2015 ◽  
Vol 772 ◽  
pp. 164-168
Author(s):  
Arif Abdullah Muhammad ◽  
Guang Lei Liu
Keyword(s):  
Gear Tooth ◽  
Planetary Gear ◽  
Mesh Point ◽  
Gear Train ◽  
Time Varying ◽  
Planetary Gear Train ◽  
Meshing Stiffness ◽  
Face Width ◽  
The Face ◽  
Applied Forces

The time varying meshing stiffness of normal and cracked spur gears of planetary gear train is studied by applying the unit normal forces at mesh point on the face width along the line of action of the single gear tooth in FE based software Ansys Workbench 14.5. The tooth deflections due to the applied forces at one mesh point are noted and a deflection matrix is established which is solved using Matlab to get net deflection and finally the meshing stiffness of gear tooth at particular mesh point. The process is repeated for other mesh points of gear tooth by rotating it to get meshing stiffness for whole gear tooth.

scholarly journals Establishment and analysis of nonlinear frequency response model of planetary gear transmission system

2021 ◽  
Vol 12 (2) ◽  
pp. 1093-1104
Author(s):  
Hao Dong ◽  
Yue Bi ◽  
Zhen-Bin Liu ◽  
Xiao-Long Zhao
Keyword(s):  
Planetary Gear ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Vibration Displacement ◽  
Nonlinear Characteristics ◽  
Planetary Gearbox ◽  
Meshing Stiffness ◽  
Gear Transmission System ◽  
Nonlinear Frequency Response ◽  
Simulation Results

Abstract. Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.

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.

scholarly journals Meshing Stiffness Parametric Vibration of Coaxial Contrarotating Encased Differential Gear Train

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Donglin Zhang ◽  
Rupeng Zhu ◽  
Miaomiao Li ◽  
Wuzhong Tan ◽  
Pingjun Li
Keyword(s):  
Planetary Gear ◽  
Peak Position ◽  
Gear Train ◽  
Parametric Vibration ◽  
Load Factor ◽  
Mechanical Transmission ◽  
Time Varying ◽  
Meshing Stiffness ◽  
Differential Gear ◽  
Combined Resonance

Planetary gears are widely used in mechanical transmission systems, but the vibration and noise affect their reliability and life. In this paper, the torsional dynamic model of an encased differential planetary gear with coaxial contrarotating outputs considering the time-varying meshing stiffness, damping, and phase difference of all gear pairs is established. By solving the equations of the derived system, three types of natural frequencies with different multiplicities of the system are obtained. The multiscale method is used to study the parametric vibration stability caused by the time-varying meshing stiffness, and the results are verified by numerical simulation. The dynamic characteristics of elastic meshing force are analyzed from time domain and frequency domain. The variation of the dynamic load factor of each gear pair with input speed and the relationship between its peak position and the natural frequency of the derived system are discussed. The results show that there is an unequal coupling phenomenon of meshing frequency between the meshing forces of different planetary sets. In the absence of external excitation, the meshing stiffness parameters not only excite the main resonance response of the system but also cause superharmonic resonance, subharmonic resonance, and combined resonance.

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.

Research on dynamic characteristics of gear system considering the influence of temperature on material performance

2021 ◽  
pp. 107754632110026
Author(s):  
Zhou Sun ◽  
Siyu Chen ◽  
Xuan Tao ◽  
Zehua Hu
Keyword(s):  
Elastic Modulus ◽  
Dynamic Characteristics ◽  
Poisson’S Ratio ◽  
Gear System ◽  
Poisson's Ratio ◽  
Effect Of Temperature ◽  
Time Varying ◽  
Influence Of Temperature ◽  
Meshing Stiffness ◽  
Influence Of Temperature On

Under high-speed and heavy-load conditions, the influence of temperature on the gear system is extremely important. Basically, the current work on the effect of temperature mostly considers the flash temperature or the overall temperature field to cause expansion at the meshing point and then affects nonlinear factors such as time-varying meshing stiffness, which lead to the deterioration of the dynamic transmission. This work considers the effect of temperature on the material’s elastic modulus and Poisson’s ratio and relates the temperature to the time-varying meshing stiffness. The effects of temperature on the elastic modulus and Poisson’s ratio are expressed as functions and brought into the improved energy method stiffness calculation formula. Then, the dynamic characteristics of the gear system are analyzed. With the bifurcation diagram, phase, Poincaré, and fast Fourier transform plots of the gear system, the influence of temperature on the nonlinear dynamics of the gear system is discussed. The numerical analysis results show that as the temperature increases, the dynamic response of the system in the middle-speed region gradually changes from periodic motion to chaos.

Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

2016 ◽  
Vol 231 (11) ◽  
pp. 2025-2041 ◽  
Author(s):  
Shijing Wu ◽  
Haibo Zhang ◽  
Xiaosun Wang ◽  
Zeming Peng ◽  
Kangkang Yang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Transmission Error ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Contact Ratio ◽  
The Impact

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

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