Modeling and Solution of a Nonlinear Vibration Model of the Bending-Torsion Coupled Spur Gear Transmission System Based on Lumped Mass Method

2014 ◽  
Vol 635-637 ◽  
pp. 172-176
Author(s):  
Chang Li ◽  
Bing Chen Wang ◽  
Xing Han
Keyword(s):  
Nonlinear Vibration ◽  
Optimization Design ◽  
Spur Gear ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Vibration Model ◽  
Gear Transmission System ◽  
Tooth Surfaces ◽  
The Time Domain ◽  
Fifth Order

After comprehensive considerations of the influences of stiffness excitations, deviation excitations, meshing impact excitations, friction of tooth surfaces, gap changes and other kinds of nonlinear factors, it established a nonlinear vibration model of the bending-torsion coupled spur gear driven system based on Lumped Mass Method (LMM). By transforming the model to dimensionless form and using fifth order adaptive variable step (Runge-Kutta) method to solve the nonlinear vibration model of the system, it can get the time domain charts, spectrum charts, phase charts, Poincare charts, FFT charts and the system bifurcation figures. And then it discussed the influence of system parameter vibrations on its dynamic characteristics, and this could provide a foundation for system dynamic optimization design

The Vibration Model Establishment and Solution of Bending-Torsion-Axial-Swing Coupled the Helical Gear Transmission System Based on Lumped Parameter Approximation Method

2014 ◽  
Vol 1061-1062 ◽  
pp. 743-747
Author(s):  
Chang Li ◽  
Bing Chen Wang ◽  
Jun Feng Li
Keyword(s):  
Helical Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Impact Excitation ◽  
Tooth Surface ◽  
Lumped Mass ◽  
Lumped Parameter ◽  
Vibration Model ◽  
Gear Transmission System ◽  
The Time Domain

Based on comprehensive considerations the influences of stiffness excitation, deviation excitation, meshing impact excitation, friction of tooth surface, and other kinds of nonlinear factors, it established a nonlinear coupled vibration model of bending-torsion-axial-swing coupled helical gear transmission system by applying the Lumped Mass Method. After transformed the model to dimensionless form, it used Runge-Kutta method to solve the nonlinear vibration model of the system, and then the time domain chart, spectrum chart, phase chart, Poincare chart, and FFT chart were obtained; it discussed the influence of system parameters on its dynamic characteristics.

Numerical Modelling of the Mooring Line Failure Induced Performance Changes of a Marine Fish Cage in Irregular Waves and Currents

2019 ◽  
Author(s):  
Hung-Jie Tang ◽  
Ray-Yeng Yang ◽  
Chai-Cheng Huang
Keyword(s):  
Marine Fish ◽  
Low Frequency ◽  
Frequency Region ◽  
Irregular Waves ◽  
Mooring Line ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Waves And Currents ◽  
Failure Scenario ◽  
The Time Domain

Abstract This study aims to investigate the performance changes resulted from a mooring line failure of a marine fish cage exposed to irregular waves and current. A numerical model based on the lumped mass method and Morison equation was extended to simulate the mooring line failure scenario. In this study, the failed resulting changes were compared with its normal counterpart in both the time domain and the frequency domain. After one upstream anchor loss, the maximum tension on the remaining anchor has increased significantly, as well as the drift distance of the rearing part (net chamber, floating collar, and tube-sinker) of the fish cage. The resulting changes can also be seen in both the wave-frequency and the low-frequency region in the spectra, including mooring tensions and body motions.

scholarly journals Investigation of the effect of the angle between drive shafts on vibration responses of main reducer

2018 ◽  
Vol 189 ◽  
pp. 06009 ◽  
Author(s):  
Xiaogang Liu ◽  
Zhaoyu Wu ◽  
Weiguang Shu ◽  
Jie Lu
Keyword(s):  
Hypoid Gear ◽  
Force Analysis ◽  
Lumped Mass ◽  
Mesh Stiffness ◽  
Gear Backlash ◽  
Lumped Mass Method ◽  
Vibration Model ◽  
Vibration Responses ◽  
Transfer Error ◽  
Final Drive

The drive shaft arrangement has a considerable influence on the vibration responses of the shaft-final drive system. In this research, a coupled vibration model is developed based on force analysis of hypoid gear and lumped mass method. The effect of time-varying mesh stiffness, gear backlash and transfer error are included to investigate the effect of the angle between drive shafts on vibration responses of main reducer. The vibration responses of main reducer are acquired using this model. The results show that the vibration amplitude of the gears of main reducer increase with the angle between drive shafts. This paper presents an analytical method to determine the value of the angle between drive shafts, so as to control the vibration of main reducer.

scholarly journals Chaos and Stability of Spur Gear Transmission System for Locomotive Based on Energy Method and Floquet Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Junguo Wang ◽  
Bo Lv ◽  
Yongxiang Zhao
Keyword(s):  
Floquet Theory ◽  
Gear Tooth ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Model Parameters ◽  
Lumped Mass ◽  
Mass Model ◽  
Model Parameter ◽  
Gear Transmission System

Considering the internal and external excitations such as time-varying mesh stiffness (TVMS), backlash, transmission error, torque of the traction motor, and load torque of the wheel/rail, a lumped mass model of the spur gear drive system for a railway locomotive is established. Based on Ma models in the relevant literatures, TVMS is calculated by simplifying a gear tooth as a cantilever beam on the root circle, taking into account the effects of extended tooth contact as well as revised foundation stiffness. The bifurcation diagrams and Lyapunov exponent curves of the model parameters are drawn by the numerical method, and the mechanism of chaos evolution of the gear transmission system is analyzed. According to the Floquet theory, variation curves of the maximum Floquet multiplier with pinion speed and support stiffness ratio are drawn by numerical methods. Combined with the bifurcation diagram of the system, the influences of model parameter on the stability of the system are analyzed, and the evolution laws of periodic motion and bifurcation phenomenon are gained. These research results provide the theoretical evidence of model parameter design of the locomotive transmission system.

Analysis on Torsional Vibration of Low-Speed Diesel

2012 ◽  
Vol 562-564 ◽  
pp. 528-531
Author(s):  
Zhong Ming Liu ◽  
Kai Liu ◽  
Xiao Qin Hou
Keyword(s):  
Shear Stress ◽  
Torsional Vibration ◽  
Critical Speed ◽  
Angular Displacement ◽  
Good Condition ◽  
Lumped Mass ◽  
Main Bearing ◽  
Bolt Preload ◽  
Lumped Mass Method ◽  
Vibration Model

In order to analysis the torsional vibration of crankshaft train in various assembly conditions, a 5S60 diesel model is presented based on AVL-EXCITE. A torsional vibration model is established by using the lumped mass method. And the deformation of main bearing is calculated under the bolt preload and outbreak of combustion. In addition to rated conditions, a state of one cylinder out of service is considered in this project. According to the calculation of the critical speed, torsion modes, angular displacement, shear stress in crankpin and minimum oil film thickness, the torsional vibration characteristics are analyzed. The study revealed that this system performs in good condition and the resonance is not obvious.

Theoretical analysis of the vibration modes of the star herringbone gear transmission system

2019 ◽  
Vol 234 (2) ◽  
pp. 358-368
Author(s):  
Feiming Wang ◽  
Sanmin Wang ◽  
Fei Li
Keyword(s):  
Vibration Mode ◽  
Vibration Suppression ◽  
Transmission System ◽  
Gear Transmission ◽  
Vibration Modes ◽  
Lumped Mass ◽  
Coupling Vibration ◽  
Lumped Mass Method ◽  
Gear Transmission System ◽  
Herringbone Gear

The star herringbone gear transmission system has a high load-carrying capacity, and is widely used in aviation, marine power drives, off-road vehicles, and hybrid electric-drive vehicles. Vibration and noise are the key concerns with this transmission system. The lumped mass method was adopted to establish the dynamic model and equations of this system. The modes of the system were analyzed and classified, and the eigenvalues and their multiplicities were determined. The results showed that the system has four typical vibration modes: (1) a lateral-rotational coupled vibration mode (multiplicity m = 1), (2) star gear compound mode (multiplicity m =  N-3, N > 3), (3) center component lateral vibration mode (multiplicity m = 2), and (4) star gear and center gear-coupled mode (multiplicity m = 2). The contribution of this paper lies in the discovery of the coupling vibration modes in the star herringbone gear transmission system and the multiplicities of these modes. This work provides the foundation for further research on vibration suppression for the star herringbone gear transmission system and the theory of planet phasing.

Study on Nonlinear Dynamics of Planetary Reducer

2013 ◽  
Vol 756-759 ◽  
pp. 4616-4620
Author(s):  
Xue Feng Han ◽  
Yang Bai ◽  
Ming Li ◽  
Hong Guang Jia
Keyword(s):  
Nonlinear Dynamics ◽  
Harmonic Balance ◽  
Optimization Design ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Nonlinear Dynamics Model ◽  
Response Variation ◽  
Motor Drive System

Based on nonlinear vibration theory and synthesizing harmonic balance method, numerical analysis method and reducer vibration test, the paper studies the characteristics of traditional systematic nonlinear dynamics. Based on harmonic balance method, the paper deduces the frequency response equation in the range of the whole frequency and studies magnitude-frequency characteristic. The accuracy of the model is verified by comparing with traditional model. Lumped mass method is used to construct nonlinear dynamics model of 2K-H planetary reducer drive mechanism in new hybrid cars double motor drive system. And the paper makes detailed and deeper analysis on response variation rules of the system and meshing stock state of gear pair with different parameters. Through the analysis of the relevant parameters, the planetary reducer is to have a more profound understanding, laid the foundation for future optimization design.

Modeling and Solving of Non-Linear Vibration Model of the Multi-Clearance and Bend and Torsion Coupled Gear-Driven System

2014 ◽  
Vol 1006-1007 ◽  
pp. 280-284
Author(s):  
Xing Han ◽  
Chang Li
Keyword(s):  
Fast Fourier Transformation ◽  
Analysis Model ◽  
Lumped Mass ◽  
Runge Kutta Method ◽  
Lumped Mass Method ◽  
Driven System ◽  
Non Linear ◽  
Phase Map ◽  
Tooth Flank ◽  
Fifth Order

Comprehensively taking the effects of variable rigidities, tooth flank clearances, bearing clearances, contact rigidities, and other multiple non-linear factors into account, it built a bend and torsion coupled gear-driven system’s dynamics analysis model in use of lumped mass method. After dimensionless dealing, it solved this dynamic model by the method of fifth order adaptive variable step (Runge-Kutta) method, and then it obtained system vibratory responses’ time domain diagrams, frequency domain diagrams, phase map, Poincare diagram, fast Fourier transformation (FFT) diagrams, and system branch diagrams under different parameters. All of them analyzed the effects of parameter variations on gearing system’s dynamic characteristics, and it provided a foundation for gearing system dynamic optimum designs.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

Sign in / Sign up

Export Citation Format

Share Document