Study of the Modeling of the Gear Dynamics Considering Mesh Stiffness and Sliding Friction

2010 ◽  
Vol 29-32 ◽  
pp. 618-623
Author(s):  
Cheng Zhong Gu ◽  
Xin Yue Wu
Keyword(s):  
Fourier Transform ◽  
Sliding Friction ◽  
Approximate Analytical Solution ◽  
Friction Torque ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Friction Modeling ◽  
Period Function ◽  
Stiffness Variation

Time- varying mesh stiffness and sliding friction between teeth are the great excitation for vibration and noise in gears system. But, there are rarely studies on this topic. This paper proposes a new dynamic modeling of gear system, which is effect of mesh stiffness variation, sliding friction and distribution of load. Firstly, the expression of time-varying mesh stiffness is gained, which is a period function. Secondly, a new friction modeling has the same period as mesh stiffness, is proposed. Thirdly, friction torque of each gear pair is calculated respectively, which is considering the distribution of load and time-varying friction arm. Finally, because all parameter have the same cycle, it is easy to get the approximate analytical solution to non-line model of gear dynamic by fourier transform.

Dynamic Analysis of Sliding Friction in a Gear Pair

2003 ◽  
Author(s):  
Rajendra Gunda ◽  
Rajendra Singh
Keyword(s):  
Load Distribution ◽  
Sliding Friction ◽  
Spur Gear ◽  
Time Instant ◽  
Friction Torque ◽  
Speed Ratio ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Static Mode

Chief objective of this article is to evaluate the role of sliding friction in gear dynamics, and more specifically the effect of the periodic variations in mesh stiffness, load distribution and friction torque during a mesh cycle. A non-unity speed ratio spur gear is considered. Only the torsional degree of freedom of the gear pair, with ideal Coulomb friction law, is analyzed. Previous studies by Vaishya and Singh [1–3] make idealized assumptions about temporal (or spatial) variation of mesh stiffness and load sharing in order to obtain more tractable analytical solutions. In our formulation, an accurate Finite Element/Contact Mechanics analysis code [4] is run in the static mode to compute the mesh stiffness and load distribution at every time instant of the mesh. The computed parametric variation of stiffness is then incorporated into our dynamic formulation that includes frictional torques. Next, we use appropriate numerical techniques to solve for the dynamic response in time domain. This study, though preliminary in nature, examines the effects of pinion speed, coefficient of friction and mean input torque. This, along with work in progress, should yield further insights into the role of friction sources in gear vibro-acoustics.

Influence of simultaneous time-varying bearing and tooth mesh stiffness fluctuations on spur gear pair vibration

2019 ◽  
Vol 97 (2) ◽  
pp. 1403-1424 ◽  
Author(s):  
Guanghui Liu ◽  
Jun Hong ◽  
Robert G. Parker
Keyword(s):  
Spur Gear ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness

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.

Nonlinear Dynamic Analysis of a Multi-Gear Train With Time-Varying Mesh Stiffness Including Modification Coefficient Effect

2011 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
K. H. Huang ◽  
C. J. Cheng ◽  
C. R. Wang
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Gear Train ◽  
Work Piece ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Harmonic Motion ◽  
Gear Profile

The nonlinear dynamic analysis of a multi-gear train with time-varying mesh stiffness on account of the modification coefficient effect is in vestigated in this paper. The proposed application of the modification coefficient will revise the center distance of the gear pair, avoid undercut and raise the mesh stiffness of the designed gear system. In this study, the gear profile is generated from the relationship between the rack cutter and the gear work piece by using the envelope theory. The rack cutter with the modification coefficient increases the mesh stiffness and thus enhances the strength of the gear tooth. Then the time-varying mesh stiffness at the contact position of the gear pair is calculated from the tooth deflection analysis using the generated gear profile. With the obtained time-varying mesh stiffness, the nonlinear dynamic behavior of multi-gear train is investigated by using Runge-Kutta integration method. The numerical results of the studied examples show the harmonic motion, sub-harmonic motion, chaotic motion and bifurcation phenomenon of the gear train.

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.

Dynamic Behavior of Helical Gears with Effects of Shaft and Bearing Flexibilities

2011 ◽  
Vol 86 ◽  
pp. 26-29
Author(s):  
Kai Feng ◽  
Shigeki Matsumura ◽  
Haruo Houjoh
Keyword(s):  
Experimental Tests ◽  
Time Varying ◽  
Gear Pair ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Shaft System ◽  
Proposed Model ◽  
Center Distance ◽  
Good Agreement

This study presents a numerical model of helical gears to consider the effects of shaft and bearing flexibility. A primary feature of this study is that the time-varying mesh stiffness is not just determined by the geometry of gear pair but also updated for each iteration according to the change of center distance. The effects of shaft and bearing flexibilities are discussed by comparing the dynamic response of gear pairs supported with a rigid and a flexible bearing-shaft system. The results show that the pressure angle and contact ratio are significantly changed due to the center-distance variation of gears and the gear pair with a flexible bearing-shaft system has much larger vibration. Finally, experimental tests are conducted to validate the proposed model. The predicted results show good agreement with the experimental data.

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