Three Kinds of Gear Transmission Nonlinear Dynamics Models

2013 ◽  
Vol 787 ◽  
pp. 765-770
Author(s):  
Li Juan Wu ◽  
Jin Yuan Tang ◽  
Si Yu Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Time Domain ◽  
Rotation Angle ◽  
Dynamic Responses ◽  
Relative Rotation ◽  
Dissipation Energy ◽  
Motion Equations ◽  
Low Speed ◽  
Dynamics Models

Based on the Lagranges equations, a new nonlinear dynamic gear model is established by introducing two variables of relative rotation angleand mean rotation angle. The motion equations derived with Lagranges equation exhibit nonlinear terms which are absent in the equations derived on Newtons equations. Combining with the numerical simulation, the dynamic responses in time domain and frequency domain are deduced, and it can be concluded that the responses at low speed of three different models are different. However, they are similar at the designed speed without the consideration of dissipation energy. On the contrary, the dynamic responses are similar at low speed and the simplified Newtons equation differs at the designed speed including dissipation energy.

Numerical Simulation of Single Box Floating Breakwater in Time Domain

2011 ◽  
Vol 250-253 ◽  
pp. 3634-3637
Author(s):  
Yan Na Zheng ◽  
Guo Hai Dong ◽  
Ben Chao Guo ◽  
Chang Ping Chen
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Time Domain ◽  
Regular Wave ◽  
Dissipation Energy ◽  
Numerical Result ◽  
Floating Breakwater ◽  
Numerical Program ◽  
Mooring Chain

Based on boundary element method, a mathematical model of single box floating breakwater with mooring chain under regular wave is developed in time domain. From the comparison with the experimental data, the numerical program can simulate the transmission coefficient variaty tendency well, while on the aspect of the quantity, the numerical result is always larger than the experimental one, for the ignorance of the friction and dissipation energy.

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.

Nonlinear Dynamics Behavior of Tethered Submerged Buoy under Wave Loadings

2020 ◽  
Vol 21 (1) ◽  
pp. 11-21
Author(s):  
Lin Zhao ◽  
Weihao Meng ◽  
Zhongqiang Zheng ◽  
Zongyu Chang
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Behavior ◽  
Coupling Factor ◽  
Dynamic Responses ◽  
Mooring Line ◽  
Second Law ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Characteristic ◽  
Runge Kutta Method ◽  
Marine Engineering

AbstractTethered submerged buoy is used extensively in the field of marine engineering. In this paper considering the effect of wave, the nonlinear dynamics behavior of tethered submerged buoy is debated under wave loadings. According to Newton’s second law, the dynamic of the system is built. The coupling factor of the system is neglected, the natural frequency is calculated. The dynamic responses of the system are analyzed using Runge–Kutta method. Considering the variety of the steepness kA, the phenomenon of dynamic behavior can be periodic, double periodic and quasi-periodic and so on. The bifurcation diagram and the largest Lyapunov exponent are applied to judge the nonlinear characteristic. It is helpful to understand the dynamic behavior of tethered submerged buoy and design the mooring line of tethered submerge buoy.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

Experimental and Numerical Analysis for Two Kinds of Impact Vibration of Gear

2011 ◽  
Vol 141 ◽  
pp. 43-48 ◽  
Author(s):  
Lin Yu Su ◽  
Yi Qiang Sun ◽  
Jian Ming Wen
Keyword(s):  
Numerical Analysis ◽  
Experimental Analysis ◽  
Dynamic Responses ◽  
Elastic Model ◽  
Motion Equations ◽  
Elastic Boundary ◽  
Mechanical Models ◽  
Impact Vibration ◽  
Dynamic Bifurcation ◽  
Impact Models

In this paper, there are two kinds of impact vibration models: rigid impact model and elastic model. The dynamic responses of the two kinds of gear impact models are compared by experimental and numerical analysis. Firstly, establish the motion equations of the two models. Secondly, verify the correctness of the mechanical models through experimental analysis. Comparing the results of the numerical and experimental analysis, we can find that the intensity noise of gear vibration is reduced by the elastic boundary. Finally, the dynamic bifurcation characteristic of dimensionless excitations magnitude and backlash will be analyzed as well.

Focusing Technique for Holographic Subsurface Radar Based on Image Entropy

2021 ◽  
Vol 36 (4) ◽  
pp. 373-378
Author(s):  
Haewon Jung ◽  
Dal-Jae Yun ◽  
Hoon Kang
Keyword(s):  
Numerical Simulation ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Software Package ◽  
Reconstruction Algorithm ◽  
Simulation Software ◽  
Material Information ◽  
Difference Time ◽  
Actual Depth ◽  
Good Agreement

An image focusing method for holographic subsurface radar (HSR) is proposed herein. HSR is increasingly being utilized to survey objects buried at shallow depths and the acquired signals are converted into an image by a reconstruction algorithm. However, that algorithm requires actual depth and material information or depends on human decisions. In this paper, an entropy-based image focusing technique is proposed and validated by numerical simulation software package based on finite-difference time-domain method and experiment. The resulting images show good agreement with the actual positions and shapes of the targets.

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