Harmonic Resonance Frequency Factor of Spur Gear System and Oscillation Reduction Approaches

2007 ◽  
Author(s):  
Jianping Wang ◽  
Pengfei Li ◽  
Ziying Wu ◽  
Minghong Zhang
Keyword(s):  
Parametric Excitation ◽  
Linear Time ◽  
Primary Resonance ◽  
Frequency Factor ◽  
Multiple Scale ◽  
Transmission Error ◽  
Spur Gear ◽  
High Order ◽  
Time Varying ◽  
Harmonic Resonance

In this study, a non-linear time-varying dynamic model of a spur gear pair system is used to investigate the dynamic behavior of the system by means of multiple scale approach. Both time-varying stiffness, transmission error and tooth backlash clearance of the system are taken into account in the model. The mesh stiffness fluctuation is developed as high order Fourier series and tooth backlash clearance is fitted by high order polynomial function. The frequency factors of the system are investigated and the frequency-response equations at the case of internal and external excitation, parametric excitation and combined excitation are obtained. The peak value of the amplitude of the primary resonance, super and sub harmonic resonance and combination harmonic under internal, external and parametric excitation are researched. The approaches of vibration reduction are investigated. Finally an example is investigated using the presented process and the results indicate the sensitivity and correctness of the presented analysis approaches.

Construction of Semianalytical Solutions to Spur Gear Dynamics Given Periodic Mesh Stiffness and Sliding Friction Functions

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Song He ◽  
Todd Rook ◽  
Rajendra Singh
Keyword(s):  
Dynamic Models ◽  
Sliding Friction ◽  
Linear Time ◽  
Transmission Error ◽  
Spur Gear ◽  
Degree Of Freedom ◽  
System Model ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Friction Forces

Gear dynamic models with time-varying mesh stiffness, viscous mesh damping, and sliding friction forces and moments lead to complex periodic differential equations. For example, the multiplicative effect generates higher mesh harmonics. In prior studies, time-domain integration and fast Fourier transform analysis have been utilized, but these methods are computationally sensitive. Therefore, semianalytical single- and multiterm harmonic balance methods are developed for an efficient construction of the frequency responses. First, an analytical single-degree-of-freedom, linear time-varying system model is developed for a spur gear pair in terms of the dynamic transmission error. Harmonic solutions are then derived and validated by comparing with numerical integration results. Next, harmonic solutions are extended to a six-degree-of-freedom system model for the prediction of (normal) mesh loads, friction forces, and pinion/gear displacements (in both line-of-action and off-line-of-action directions). Semianalytical predictions compare well with numerical simulations under nonresonant conditions and provide insights into the interaction between sliding friction and mesh stiffness.

Time-varying output formation control for high-order linear time-invariant swarm systems

2015 ◽  
Vol 298 ◽  
pp. 36-52 ◽  
Author(s):  
Xiwang Dong ◽  
Zongying Shi ◽  
Geng Lu ◽  
Yisheng Zhong
Keyword(s):  
Formation Control ◽  
Linear Time ◽  
High Order ◽  
Time Varying ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Invariant

Study on Effect of Surface Friction on the Dynamic Behaviours of Cylindrical Gear Transmission

2010 ◽  
Vol 139-141 ◽  
pp. 2316-2321
Author(s):  
Jin Yuan Tang ◽  
Qi Bo Wang ◽  
Cai Wang Luo
Keyword(s):  
Sudden Change ◽  
Surface Friction ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Time Varying ◽  
Cylindrical Gear ◽  
Static Transmission Error ◽  
Effect Of Surface

The effect of surface friction on the dynamic response of spur gear pair is investigated in this paper. Firstly, surface friction during the mesh is described briefly, and realistic time-varying tooth stiffness and realistic static transmission error are introduced. Subsequently, the differential equation of the torsional vibration of gear transmission is developed in which the realistic time-varying stiffness and realistic static transmission error are incorporated. Finally, using the numerical simulation method, the solutions in time domain and spectrum graphs of the nonlinear system are obtained. Results show that surface friction has great influences on the dynamic responses nearby the pitch point but less influences far away the pitch point. Surface friction may also bring sudden change to the dynamic responses at pitch point when the rotational speed is low.

scholarly journals Dynamic Model of Spur Gear Pair with Modulation Internal Excitation

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Wang ◽  
Lei Zhang ◽  
Yuan-Qing Luo ◽  
Chang-Zheng Chen
Keyword(s):  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Experimental Result ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Internal Excitation ◽  
Modulation Sideband

In the actual measurements, vibration and noise spectrum of gear pair often exhibits sidebands around the gear mesh harmonic orders. In this study, a nonlinear time-varying dynamic model of spur gear pair was established to predict the modulation sidebands caused by the AM-FM modulation internal excitation. Here, backlash, modulation time-varying mesh stiffness, and modulation transmission error are considered. Then the undamped natural mode was studied. Numerical simulation was made to reveal the dynamic characteristic of a spur gear under modulation condition. The internal excitation was shown to exhibit obvious modulation sideband because of the modulation time-varying mesh stiffness and modulation transmission error. The Runge-Kutta method was used to solve the equations for analyzing the dynamic characteristics with the effect of modulation internal excitation. The result revealed that the response under modulation excitation exhibited obvious modulation sideband. The response under nonmodulation condition was also calculated for comparison. In addition, an experiment was done to verify the prediction of the modulation sidebands. The calculated result was consistent with the experimental result.

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.

NN approach to state-feedback control of high-order non-linear time-delay systems with time-varying control coefficient

2016 ◽  
Vol 40 (1) ◽  
pp. 163-170 ◽  
Author(s):  
Min Huifang ◽  
Duan Na
Keyword(s):  
Neural Network ◽  
Feedback Control ◽  
State Feedback ◽  
Linear Time ◽  
High Order ◽  
State Feedback Control ◽  
Delay Systems ◽  
Time Varying ◽  
Control Coefficient ◽  
Non Linear

This paper considers the adaptive state-feedback control problem for a class of high-order non-linear systems with unknown control coefficient and time delays. By applying the neural network approximation method and the Nussbaum function approach, the restrictions on non-linear functions and the conditions on the time-varying control coefficient are largely relaxed. In addition, an adaptive neural network state-feedback controller with only one adaptive parameter is successfully constructed by introducing proper Lyapunov–Krasovskii functionals and using the backstepping technique. The proposed scheme guarantees the closed-loop system to be semi-globally uniformly ultimately bounded. Finally, a simulation example demonstrates the effectiveness of the controller.

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