scholarly journals Nonlinear Frequency Response Analysis of Double-helical Gear Pair Based on the Incremental Harmonic Balance Method

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Hao Dong ◽  
Libang Wang ◽  
Haoqin Zhang ◽  
Xiao-long Zhao
Keyword(s):  
Frequency Response ◽  
Harmonic Balance Method ◽  
Transmission Error ◽  
Time Varying ◽  
Incremental Harmonic Balance Method ◽  
Meshing Stiffness ◽  
Amplitude Frequency Response ◽  
Incremental Harmonic Balance ◽  
Static Transmission Error ◽  
Helical Gear Pair

The torsional dynamic model of double-helical gear pair considering time-varying meshing stiffness, constant backlash, dynamic backlash, static transmission error, and external dynamic excitation was established. The frequency response characteristics of the system under constant and dynamic backlashes were solved by the incremental harmonic balance method, and the results were further verified by the numerical integration method. At the same time, the influence of time-varying meshing stiffness, damping, static transmission error, and external load excitation on the amplitude frequency characteristics of the system was analyzed. The results show that there is not only main harmonic response but also superharmonic response in the system. The time-varying meshing stiffness and static transmission error can stimulate the amplitude frequency response of the system, while the damping can restrain the amplitude frequency response of the system. Changing the external load excitation has little effect on the amplitude frequency response state change of the system. Compared with the constant backlash, increasing the dynamic backlash amplitude can further control the nonlinear vibration of the gear system.

Bending-torsional-axial-pendular nonlinear dynamic modeling and frequency response analysis of a marine double-helical gear drive system considering backlash

2021 ◽  
pp. 146134842110657
Author(s):  
Hao Dong ◽  
Yue Bi ◽  
bo Wen ◽  
Zhen-bin Liu ◽  
Li-bang Wang
Keyword(s):  
Frequency Response ◽  
Dynamic Modeling ◽  
External Load ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear System ◽  
Time Varying ◽  
Vibration Displacement ◽  
Meshing Stiffness ◽  
Nonlinear Dynamic Modeling

The double-helical gear system was widely used in ship transmission. In order to study the influence of backlash on the nonlinear frequency response characteristics of marine double-helical gear system, according to the structural characteristics of double-helical gear transmission, considering the time-varying meshing stiffness, backlash, damping, comprehensive transmission error, external load excitation, and other factors, a three-dimensional bending-torsional-axial-pendular coupling nonlinear dynamic modeling and dynamic differential equation of 24-DOF double-helical gear transmission system were established. The Runge–Kutta numerical method was used to analyze the influence of backlash, time-varying meshing stiffness, damping, error and external load excitation on the amplitude frequency characteristics. The results show that the backlash can cause the runout of the double-helical gear system, and the system has first harmonic and second harmonic response. With the increase of backlash, the amplitude of the system increases and the jumping phenomenon remains unchanged. The amplitude frequency response of the system is stimulated by time-varying meshing stiffness and comprehensive transmission error, and restrained by damping and external load excitation. The vibration displacement amplitude of the system increases with the increase of vibration displacement and has little effect on the state change of the system. The vibration test of double-helical gear is carried out. The frequency response components obtained by numerical simulation are basically consistent with the experimental results, which proves the correctness of the theoretical calculation. It provides a technical basis for the study of vibration and noise reduction performance of double-helical gear.

Nonlinear and Time-Varying Dynamics of High-Dimensional Models of a Translating Beam With a Stationary Load Subsystem

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
G. Y. Xu ◽  
W. D. Zhu
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
High Dimensional ◽  
Structural Systems ◽  
Time Varying ◽  
Incremental Harmonic Balance Method ◽  
Included Trial ◽  
Incremental Harmonic Balance ◽  
Dimensional Models ◽  
Low Dimensional

Nonlinear vibration and dynamic stability analyses of distributed structural systems have often been conducted for their low-dimensional spatially discretized models, and the results obtained from the low-dimensional models may not accurately represent the behaviors of the distributed systems. In this work the incremental harmonic balance method is used to handle a variety of problems pertaining to determining periodic solutions of high-dimensional models of distributed structural systems. The methodology is demonstrated on a translating tensioned beam with a stationary load subsystem and some related systems. With sufficient numbers of included trial functions and harmonic terms, convergent and accurate results are obtained in all the cases. The effect of nonlinearities due to the vibration-dependent friction force between the translating beam and the stationary load subsystem, which results from nonproportionality of the load parameters, decreases as the number of included trial functions increases. A low-dimensional spatially discretized model of the nonlinear distributed system can yield quantitatively and qualitatively inaccurate predictions. The methodology can be applied to other nonlinear and/or time-varying distributed structural systems.

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 of the Bouc–Wen Nonlinear Isolation System

2021 ◽  
Vol 11 (13) ◽  
pp. 6106
Author(s):  
Zhiying Zhang ◽  
Xin Tian ◽  
Xin Ge
Keyword(s):  
Dynamic Characteristics ◽  
Seismic Isolation ◽  
Influence Factors ◽  
Harmonic Balance Method ◽  
Control Parameters ◽  
Hysteretic Model ◽  
Incremental Harmonic Balance Method ◽  
Isolation System ◽  
Nonlinear Dynamic Characteristics ◽  
Incremental Harmonic Balance

The Bouc–Wen nonlinear hysteretic model has many control parameters, which has been widely used in the field of seismic isolation. The isolation layer is the most important part of the isolation system, which can be effectively simulated by the Bouc–Wen model, and the isolation system can reflect different dynamic characteristics under different control parameters. Therefore, this paper mainly studies and analyzes the nonlinear dynamic characteristics of the isolation system under different influence factors based on the incremental harmonic balance method, which can provide the basis for the dynamic design of the isolation system.

scholarly journals Comparison of Common Methods in Dynamic Response Predictions of Rotor Systems with Malfunctions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongliang Yao ◽  
Qian Zhao ◽  
Qi Xu ◽  
Bangchun Wen
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Newmark Method ◽  
Incremental Harmonic Balance Method ◽  
Rotor Systems ◽  
Double Frequency ◽  
Frequency Domain Methods ◽  
Incremental Harmonic Balance

The efficiency and accuracy of common time and frequency domain methods that are used to simulate the response of a rotor system with malfunctions are compared and analyzed. The Newmark method and the incremental harmonic balance method are selected as typical representatives of time and frequency domain methods, respectively. To improve the simulation efficiency, the fixed interface component mode synthesis approach is combined with the Newmark method and the receptance approach is combined with the incremental harmonic balance method. Numerical simulations are performed for rotor systems with single and double frequency excitations. The inherent characteristic that determines the efficiency of the two methods is analyzed. The results of the analysis indicated that frequency domain methods are suitable single and double frequency excitation rotor systems, whereas time domain methods are more suitable for multifrequency excitation rotor systems.

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