Calculation of Time-Varying Mesh Stiffness Affected by Load Based on FEM

2017 ◽  
Author(s):  
Qian Cheng ◽  
Yimin Shao ◽  
Jing Liu ◽  
Lei Yin ◽  
Minggang Du ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Analytical Method ◽  
Working Condition ◽  
Load Condition ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Behavior Study ◽  
Gear Transmission System ◽  
The Impact ◽  
Line Direction

Time-varying mesh stiffness (TVMS) is a key component of gear transmission system for gear dynamic response. When the machine starts working, stop working or goes into an unstable working condition, the load will be varying. In order to investigate the impact of different loads on TVMS, a numerical method based on FEM is proposed in this paper to study the effect of TVMS. The dynamic mesh forces and dynamic displacements along the action line direction at each mesh point are extracted. The calculated TVMS is validated by comprising with the TVMS calculated by the analytical method (AM). The results show that TVMS increases with the rise of input moment which can be intruded in gear dynamic behavior study under different load condition.

Effect of Mesh Stiffness on the Dynamic Response of Face Gear Transmission System

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Zehua Hu ◽  
Jinyuan Tang ◽  
Siyu Chen ◽  
Duncai Lei
Keyword(s):  
Dynamic Response ◽  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Gear Transmission System ◽  
The Face ◽  
Time Invariant ◽  
Backlash Nonlinearity

The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

Vibration-based fault diagnosis of helical gear pair with tooth surface wear considering time-varying friction coefficient under mixed EHL condition

2021 ◽  
pp. 1-16
Author(s):  
Siyu Wang ◽  
Rupeng Zhu
Keyword(s):  
Dynamic Response ◽  
Hydrodynamic Lubrication ◽  
Helical Gear ◽  
Calculation Model ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Pair ◽  
Surface Wear ◽  
Mesh Stiffness ◽  
Helical Gear Pair

Abstract Based on “slice method”, the improved time-varying mesh stiffness (TVMS) calculation model of helical gear pair with tooth surface wear is proposed, in which the effect of friction force that obtained under mixed elasto-hydrodynamic lubrication (EHL) is considered in the model. Based on the improved TVMS calculation model, the dynamic model of helical gear system is established, then the influence of tooth wear parameters on the dynamic response is studied. The results illustrate that the varying reduction extents of mesh stiffness along tooth profile under tooth surface wear, in addition, the dynamic response in time-domain and frequency-domain present significant decline in amplitude under deteriorating wear condition.

Analytical Solution for the Nonlinear Dynamics of Planetary Gears

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Harmonic Balance ◽  
Gear Tooth ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Mesh Stiffness ◽  
Planetary Gears ◽  
Parallel Finite Element ◽  
The Impact

Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. At resonance, the resulting vibration causes tooth separation leading to nonlinear effects such as jump phenomena and subharmonic resonance. This work examines the nonlinear dynamics of planetary gears by numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. Correlation between the amplitude of response and external torque demonstrates that tooth separation occurs even under large torque. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is evaluated by parallel finite element and numerical integration simulations.

Periodic and Chaotic Dynamic Responses of Face Gear Transmission System

2013 ◽  
Vol 834-836 ◽  
pp. 1273-1280
Author(s):  
Ze Hua Hu ◽  
Jin Yuan Tang ◽  
Si Yu Chen
Keyword(s):  
Periodic Motion ◽  
Chaotic Dynamic ◽  
Rotational Frequency ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Gear Transmission System

The periodic and chaotic dynamic responses of face gear transmission system considering time-varying mesh stiffness and backlash nonlinearity are studied. Firstly, a nonlinear time-varying dynamic model of face gear pair is developed and the motion equations are presented, the real accurate mesh stiffness is obtained by applying Finite element approach. Then, the dynamic equations are solved using Runge-Kutta numerical integral method and bifurcation diagrams are presented and analyzed. The stability properties of steady state responses are illustrated with Floquet multipliers and Lyapunov exponents. The results show that a process of periodic-chaotic-periodic motion exists with the dimensionless pinion rotational frequency as control parameters. The analysis can be a reference to avoid the chaotic motion and unstable periodic motion through choosing suitable rotational frequency.

scholarly journals Influence of Asymmetric Mesh Stiffness on Dynamics of Spiral Bevel Gear Transmission System

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Li Yinong ◽  
Li Guiyan ◽  
Zheng Ling
Keyword(s):  
Dynamic Response ◽  
Transmission System ◽  
Bevel Gear ◽  
Gear Transmission ◽  
Spiral Bevel Gear ◽  
Mesh Stiffness ◽  
Light Load ◽  
Gear Transmission System ◽  
Spiral Bevel ◽  
Asymmetric Mesh

An 8-DOF (degrees-of-freedom) nonlinear dynamic model of a spiral bevel gear pair which involves time-varying mesh stiffness, transmission error, backlash, and asymmetric mesh stiffness is established. The effect of the asymmetric mesh stiffness on vibration of spiral bevel gear transmission system is studied deliberately with numerical method. The results show that the mesh stiffness of drive side has more effect on dynamic response than those of the coast side. Only double-sided impact region is affected considerably by mesh stiffness of coast side while single-sided impact and no-impact regions are unchanged. In addition, the increase in the mesh stiffness of drive side tends to worsen the dynamic response of the transmission system especially for light-load case.

scholarly journals Computation Method of Gear Dynamic Response Using Experimental Strain Data and Application in Pitting Fault Analysis

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Yongzhi Qu ◽  
Haoliang Zhang ◽  
Zechao Wang ◽  
Zude Zhou
Keyword(s):  
Dynamic Response ◽  
Gear System ◽  
Dynamic Strain ◽  
Time Varying ◽  
Tooth Root ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Strain Data ◽  
Experimental Strain ◽  
Fbg Sensors

In this paper, A semi-physical method for calculating time varying mesh stiffness and the dynamic response of gear system based on experimental strain data is studied. In a previous work, it was reported that dynamic strain on gear tooth root can be measured under normal operating condition using fiber Bragg Grating (FBG) sensors. This paper aims to compute gear dynamic response using experimental strain data and give an explanation of the fault propagation process. Using the dynamic strain data from FBG sensors, a method for calculating the dynamic response of gear system is proposed. Based on the theory of potential energy and material mechanics, the relationship between the bending strain of the tooth root and the time varying mesh stiffness is established. The time varying mesh stiffness and dynamic response of healthy gear and pitted gear are then calculated respectively. The force transmission during gear mesh under the condition of surface pitting is analyzed. It is concluded that in the case of pitting fault, there will be a significant loss of torque in the power transmission process due to the loss of contact area. It is further inferred that the loss of meshing force andthedecreasing of Hertzian contact stiffness are the major contributing factors for pitting fault. In addition, the semi-analytical method of computing gear dynamic response is validated with experimental study ofacceleration signal in the perspective of dynamic response.  

scholarly journals Analysis of Dynamic Characteristics of a Fractional-Order Spur Gear Pair with Internal and External Excitations

2021 ◽  
Author(s):  
Jingyu Hou ◽  
Shaopu Yang ◽  
Qiang Li ◽  
Yongqiang Liu
Keyword(s):  
Frequency Response ◽  
Fractional Order ◽  
Dynamic Characteristics ◽  
Spur Gear ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
The Impact ◽  
Ihb Method

Abstract The nonlinear frequency response characteristics of a spur gear pair with fractional-order derivative under combined internal and external excitations are investigated based on the incremental harmonic balance (IHB) method. First, a pure torsional vibration model is proposed that contains various complex factors, such as the time-varying mesh stiffness, transmission error, the fluctuation of input torque, backlash. Then, the IHB method is developed to calculate the higher-order approximate solution of the system and the correctness of the results is verified by comparing with numerical simulation results obtained by the Power Series Expansion (PSE) method. Furthermore, the types of various impact situations and their judgment conditions are discussed, and the different impact behaviors are analyzed in detail when w?[0,1.5] by using phase diagrams and amplitude-frequency response curves. The influence of important parameters on the dynamic characteristics of gear pair is analyzed at last. The results indicate that the analytical solution derived by IHB method is sufficiently precise. Significantly, the dynamic characteristics of the system could be effectively controlled by adjusting time-varying mesh stiffness coefficient, the order and coefficient of fractional-order term and the amplitudes of internal excitation or external excitation. As a part of the theory of fractional-order mechanical system, the impact performance of fractional-order gear pair is approached for the first time by analytical method.

Dynamic Response of Toroidal Drive to Mesh Parametric Excitations

2005 ◽  
Vol 219 (9) ◽  
pp. 889-899 ◽  
Author(s):  
L Xu ◽  
H Jin ◽  
X Hao
Keyword(s):  
Dynamic Response ◽  
Three Dimensional ◽  
Forced Response ◽  
Dynamic Equations ◽  
Dynamic Factor ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Dynamic Factors ◽  
Stiffness Variation ◽  
Model Equations

In this article, a three-dimensional dynamic model of the toroidal drive is given. By the model, equations of the relative displacements between different components and the dynamic equations for the drive are obtained. Changes of the mesh stiffness are analysed and the equation of periodical time-varying mesh stiffness is presented in Fourier series form. Under neglecting nonlinear items, time-varying mesh stiffness is changed into equivalent exciting load and linear dynamic equations of the drive are obtained. Then, the analytical equations of the forced response for the drive to mesh stiffness excitation are obtained, and the equations of the dynamic factors between a planet and worm or stator are given as well. By aforementioned equations, the forced frequency responses of the drive system to mesh stiffness variation are given, the variations of dynamic response for the worm as functions of the main parameters are presented, and the dynamic factor between a planet and worm is given as a function of operating speed.

Noise Radiation Analysis of Structural-Acoustic Coupling System of a Gear Box

2010 ◽  
Vol 37-38 ◽  
pp. 718-722
Author(s):  
Jian Xing Zhou ◽  
Geng Liu ◽  
Shang Jun Ma
Keyword(s):  
Time History ◽  
Noise Spectrum ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Acoustic Coupling ◽  
Noise Radiation ◽  
Coupling System ◽  
Gear Transmission System ◽  
Structure Improvement ◽  
History Of

The dynamic model of the gear transmission system is built in consideration of the time-varying mesh stiffness and the gear errors. Then the time history of the dynamic load of system is calculated. The gearbox structural-acoustic coupling system is built and its noise radiation is calculated by using BEM. The noise spectrum of the gearbox and the panel contribution are obtained. The influence of the gearbox structure improvement, structure damping and different gear style on the noise radiation is analyzed. The study provides useful theoretical guideline to the design of the gearbox.

An Analytical Method to Predict Dynamic Response of Cylindrical Composite Shells Subjected to Internal Blast Loading

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Qi Sun ◽  
Qi Dong ◽  
Sha Yang
Keyword(s):  
Analytical Solution ◽  
Dynamic Response ◽  
Analytical Method ◽  
Composite Shell ◽  
Fiber Composite ◽  
Blast Loading ◽  
Composite Shells ◽  
Element Analysis ◽  
Internal Blast Loading ◽  
The Impact

Abstract The dynamic response of composite explosion containment vessels has been widely reported by experimental observations. In this study, we propose an analytical method to predict the dynamic response of open-ended cylindrical composite shells subjected to internal blast loading. The cylindrical composite shell has an out fiber composite shell with an inner steel liner, in which the outer fiber composite shell is simplified as a single elastic layer by an effective modulus in the hoop direction. Considering the impact between two layers during the dynamic response, the analytical solution for response histories of two layers could be obtained. Finite element analysis on the double-layer model is also conducted by ls-dyna. The analytical solution and the simulation result agree well, which demonstrates that the current analytical method can be employed in the design of this composite structure under blast loading.

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