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.

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.

The Torque Responses in Spur Gearing

1998 ◽  
Author(s):  
Ah-Der Lin ◽  
Jao-Hwa Kuang
Keyword(s):  
Fourier Expansion ◽  
Spur Gear ◽  
Time Varying ◽  
Gear Pair ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Frequency Spectra ◽  
Stiffness Model ◽  
Close Form ◽  
Input Torque

Abstract In this study, the frequency spectra of a meshing spur gear pair are derived. A two-step mesh stiffness model is assumed to account for the time varying stiffness during the teeth engagement. The analytic load of this simplified gear pair system is used to derive the corresponding Fourier expansion series of the transmitted torque in close form solutions. Numerical results have shown that the frequency spectra of the transmitted torque are dominated by the mesh stiffness alternation and the contact ratio of a gear pair. Furthermore, the amplitude modulation introduced by a harmonic input torque has also been investigated.

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.

Nonlinear dynamic analysis of a microsegment gear system with a time-varying base circle

2020 ◽  
Vol 44 (2) ◽  
pp. 279-293
Author(s):  
Kang Huang ◽  
Fengwei Xu ◽  
Yangshou Xiong ◽  
Meng Sang ◽  
Yong Yi
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
High Speed ◽  
Operating Conditions ◽  
Gear System ◽  
Resonant Peak ◽  
Time Varying ◽  
Heavy Load ◽  
Involute Gear ◽  
Base Circle

A systematic dynamic analysis of a microsegment gear system with a time-varying base circle, time-varying mesh stiffness, and gear backlash is carried out in this paper. By discretizing the meshing process, a six degree-of-freedom nonlinear dynamic model of a microsegment gear pair is established. To study the dynamic response of the microsegment gear and involute gear under various operating conditions, the numerical integration method is adopted. The dynamic transmission error (DTE) of the two gears is analysed in terms of time history charts, phase diagrams, fast Fourier transformation spectra, and Poincaré maps. The effects of support damping and support stiffness on radial vibration are also investigated. Results reveal that, compared with the involute gear system, the microsegment gear system is more stable at the high-speed condition and has a smaller amplitude of DTE under medium-speed and heavy-load, high-speed, and heavy-load conditions. The support damping and support stiffness have great effects on the resonant peak in the radial direction of the microsegment gear. Both the proposed model and numerical results are expected to provide a useful source of reference for the dynamic design of the microsegment gear system.

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.

scholarly journals Dynamic Characteristics Analysis of the Coupled Lateral-Torsional Vibration with Spur Gear System

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Shihua Zhou ◽  
Zhaohui Ren ◽  
Guiqiu Song ◽  
Bangchun Wen
Keyword(s):  
Dynamic Characteristics ◽  
Torsional Vibration ◽  
Variable Stiffness ◽  
Transmission Error ◽  
Spur Gear ◽  
Rotational Frequency ◽  
Gear System ◽  
Bearing Clearance ◽  
Rotor Bearing ◽  
Bearing System

A sixteen-degree-of-freedom (16-DOF) lumped parameter dynamic model taking into account the gravity, eccentricity, bearing clearance, transmission error, and coupled lateral-torsional vibration is established. Based on the dynamical equation, the dynamic behaviors of the spur gear rotor bearing system are investigated by using Runge-Kutta method. The research focuses on the effect of rotational speed, eccentricity, and bearing clearance and nonlinear response of the coupled multibody dynamics is presented by vibration waveform, spectrum, and 3D frequency spectrum. The results show that the rotational frequency of the driven gear appears in the driving gear, and the dynamic characteristics of gears have obvious differences due to the effects of the gear assembly and the coupled lateral-torsional vibration. The bearing has its own resonance frequency, and the effect of the variable stiffness frequency of the bearings should be avoided during the system design. The results presented in this paper show an analysis of the coupled lateral-torsional vibration of the spur gear system. The study may contribute to a further understanding of the dynamic characteristics of such a spur gear rotor bearing system.

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.

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