Dynamic behavior of the spur gear system with time varying stiffness by gear positions in the backlash

2020 ◽  
Vol 34 (2) ◽  
pp. 565-572 ◽  
Author(s):  
Chan Il Park
Keyword(s):  
Dynamic Behavior ◽  
Spur Gear ◽  
Gear System ◽  
Time Varying

Dynamic analysis of nonlinear time-varying spur gear system subjected to multi-frequency excitation

2018 ◽  
Vol 25 (6) ◽  
pp. 1210-1226 ◽  
Author(s):  
Yi Yang ◽  
Mengjuan Xu ◽  
Yang Du ◽  
Pan Zhao ◽  
Yiping Dai
Keyword(s):  
Spur Gear ◽  
Numerical Results ◽  
Gear System ◽  
Working Environment ◽  
Single Frequency ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Varying ◽  
Harmonic Excitations ◽  
Frequency Excitation

Due to the complex working environment, gear systems always suffer from multiple excitations in actual engineering. This paper concerns the frequency response characteristics of a nonlinear time-varying spur gear system subjected to multi-frequency excitation. Firstly, a single degree-of-freedom gear pair model is established with consideration of the gear backlash, time-varying mesh stiffness and multiple harmonic excitations. Then, using the multiple time scales method, a comprehensive theoretical study is conducted to analyze various resonant cases including primary, parametric and combination resonances. Besides, parametric studies are accomplished to reveal the effects of the multi-frequency excitation on gear dynamics and to provide some useful references for reducing the vibration level. With the help of the fifth-order Runge–Kutta method, the numerical results are obtained to verify the validity of the analytical solutions and to emphasize the significances of the multi-frequency excitation. In addition, a comparison is performed between the numerical results and the published experimental results to validate the proposed gear model. Results show that the presence of the multi-frequency excitation will introduce the interaction between different harmonic excitations, which significantly affects the nonlinear vibration characteristics of a spur gear system. The proposed gear model with multi-frequency excitation could be more reliable and universal than that with single-frequency excitation. In addition, the results of parametric study could provide some suggestions to designers and researchers attempting to obtain desirable dynamic behaviors of a gear system subjected to multi-frequency excitation.

Torsional Vibration of a Spur Gear System With Time-Varying and Square Nonlinearities

2013 ◽  
Author(s):  
Qian Ding ◽  
Wei Zhang
Keyword(s):  
Torsional Vibration ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Spur Gear ◽  
Gear System ◽  
Phase Portraits ◽  
Resonant Peak ◽  
Time Varying ◽  
Frequency Spectra ◽  
Input Torque

This paper investigates the torsional vibration of a spur gear system with time-varying and square nonlinearities, by both the analytical method and numerical simulation. First, the equations of motion of a rotating spur gear system are established. Then a single-dof equivalent system is induced to describe the relative motion or torsional vibration of the gears. The harmonic balance method is used to obtain the steady-state response. Influence of the input torque on the response is discussed and a phenomenon, one resonant peak split up into two peaks when the input torque is high enough is revealed. Last, numerical simulations are carried out and bifurcation diagrams and amplitude-frequency curve is given by taking the excitation frequency as control parameter. Selected typical motions are also presented in detail by time-histories, phase portraits, Poincaré map and frequency spectra.

scholarly journals Time-varying Response Analysis of Spur Gear System

2021 ◽  
Vol 276 ◽  
pp. 01007
Author(s):  
Chao Li ◽  
Hongwei Liu
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
High Load ◽  
Gear System ◽  
Theoretical Formula ◽  
Response Analysis ◽  
Time Varying ◽  
System A ◽  
Drive Systems ◽  
Return Difference

In this paper, a space-driven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. Considering the high load characteristics of the space drive system and the time-varying stiffness and tooth clearance of the gear system, a nonlinear dynamic response analysis was performed. The characteristics of the vibration acceleration, shock and transmission error of the gear system are studied in this paper. This paper analyzes the relationship between backlash and return difference, and derives the theoretical formula between the two. The time-varying stiffness was corrected to make the theoretical model closer to reality. The research in this paper enriches the study on space drive systems and high load gear systems.

Effects of gear eccentricity on time-varying mesh stiffness and dynamic behavior of a two-stage gear system

2019 ◽  
Vol 33 (3) ◽  
pp. 1019-1032 ◽  
Author(s):  
Xiuzhi He ◽  
Xiaoqin Zhou ◽  
Zhen Xue ◽  
Yixuan Hou ◽  
Qiang Liu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Gear System ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Two Stage

A polynomial chaos method to the analysis of the dynamic behavior of spur gear system

2015 ◽  
Vol 53 (4) ◽  
pp. 819-831 ◽  
Author(s):  
A. Guerine ◽  
A. El Hami ◽  
T. Fakhfakh ◽  
M. Haddar
Keyword(s):  
Dynamic Behavior ◽  
Polynomial Chaos ◽  
Spur Gear ◽  
Gear System

TORSION VIBRATION AND PARAMETRIC INSTABILITY ANALYSIS OF A SPUR GEAR SYSTEM WITH TIME-VARYING AND SQUARE NONLINEARITIES

2014 ◽  
Vol 06 (01) ◽  
pp. 1450007 ◽  
Author(s):  
WEI ZHANG ◽  
QIAN DING
Keyword(s):  
Equations Of Motion ◽  
Parametric Instability ◽  
Harmonic Balance Method ◽  
Period Doubling ◽  
Spur Gear ◽  
Gear System ◽  
System Response ◽  
Time Varying ◽  
Contact Ratio ◽  
Resonant Condition

This paper investigates the dynamics of a spur gear system with time-varying and square nonlinearities, by both analytical method and numerical simulation. First, the equations of motion of a 2 degree-of-freedom system are established and the harmonic balance method is used to analyze the stability and the steady-state response of the system under the main resonant condition. Then the perturbation method is used to analyze the parameter instability under the main, subharmonic and nonresonance conditions. Finally, the interactions between the main and subharmonic resonant amplitudes and the nonlinearity and the contact ratio are analyzed. The results reveal that the system response contains various frequency components, such as meshing frequency and its higher harmonic terms due to the nonlinearity and the time-varying stiffness. The existence of the time-varying meshing stiffness can also result in the subharmonic resonance, and even chaos through period-doubling bifurcations as the input torque increases.

scholarly journals Generation Mechanism and Evolution of Five-state Meshing Behavior of a Spur Gear System Considering Gear-tooth Time-varying Contact Characteristics

2021 ◽  
Author(s):  
Shi Jian-Fei ◽  
Xiang-feng Gou ◽  
Ling-yun Zhu
Keyword(s):  
Chaotic Behavior ◽  
Gear Tooth ◽  
Time History ◽  
Spur Gear ◽  
Gear System ◽  
Generation Mechanism ◽  
Load Factor ◽  
Back Side ◽  
Time Varying ◽  
Dynamic Meshing

Abstract Teeth disengaging or back-side teeth meshing induced by backlash reduces the transmission quality and dynamic performance of gear systems, and accurate interpretation of multi-state meshing behavior can provide guidance for structural optimization and performance evaluation. Therefore, the multi-state meshing behavior of the gear system is elaborated. A new nonlinear dynamic model of a spur gear system with five-state meshing behavior is proposed based on time-varying backlash and contact ratio. The time-varying meshing stiffness and time-varying backlash considering the elastic contact of gear teeth, gear temperature rise and lubrication are included in the model. The five-state meshing behavior is clearly characterized by constructing five Poincaré maps, and its generation mechanism is studied using dynamic meshing force time history, teeth relative displacement time history and phase portrait. The bifurcation and evolution of five-state meshing behavior are analyzed under the effects of load factor, meshing frequency and error coefficient. The results show that the mutation in the direction of dynamic meshing force leads to teeth disengaging and back-side single or double teeth contact, forming multi-state meshing behavior. Bifurcation caused by parameter changes greatly affects the evolution of five-state meshing behavior, particularly grazing bifurcation can decrease the number of teeth disengagement. Chaotic behavior or trajectory expansion inspires multi-state meshing vibration of the system. Previous gear system models could not reveal these phenomena due to ignoring the multi-state meshing behavior.

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.

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