Analytical Investigations on the Mesh Stiffness Function of Solid Narrow Faced Spur and Helical Gears

2015 ◽  
Author(s):  
Xiaoyu Gu ◽  
Philippe Velex ◽  
Philippe Sainsot ◽  
Jérôme Bruyère
Keyword(s):  
Finite Element ◽  
Analytical Approach ◽  
Finite Element Models ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Software Codes

Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid narrow-faced spur and helical gears. The corresponding results compare very well with those obtained by using 2D finite element models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modelling of gear body deflections.

Analytical Investigations on the Mesh Stiffness Function of Solid Spur and Helical Gears

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
X. Gu ◽  
P. Velex ◽  
P. Sainsot ◽  
J. Bruyère
Keyword(s):  
Finite Element ◽  
Analytical Approach ◽  
Time Varying ◽  
Two Dimensional ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Software Codes

Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid spur and helical gears. The corresponding results compare very well with those obtained by using two-dimensional (2D) finite element (FE) models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modeling of gear body deflections.

scholarly journals Determination of Mesh Stiffness of Gear—Analytical Approach vs. FEM Analysis

2021 ◽  
Vol 11 (11) ◽  
pp. 4960
Author(s):  
Jan Flek ◽  
Martin Dub ◽  
Josef Kolář ◽  
František Lopot ◽  
Karel Petr
Keyword(s):  
Finite Element ◽  
Analytical Model ◽  
Analytical Approach ◽  
Dynamic Models ◽  
Fem Analysis ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Element Simulation ◽  
Internal Excitation

This paper focuses on modeling the time-varying stiffness of spur gearings, which in dynamic models of transmission systems acts as an important element of the internal excitation of the dynamic system. Here are introduced ways to approach the modeling of gear stiffness using analytical calculations, which allow to model the course of mesh stiffness depending on its rotation. For verification of used analytical model were created five different gearings, and based on their geometry, the respective stiffness curves were analytically determined. Subsequently, a finite element simulation was performed in the Abaqus CAE software. Due to this software, it was possible to identify and objectively compare the stiffness curves and further determine the suitability of using the analytical model to determine the mesh stiffness of gearing.

Coupled Dynamic and Vibration Analysis of Beveloid Geared System

2012 ◽  
Vol 215-216 ◽  
pp. 917-920
Author(s):  
Rong Fan ◽  
Chao Sheng Song ◽  
Zhen Liu ◽  
Wen Ji Liu
Keyword(s):  
Transmission Error ◽  
Time Varying ◽  
Spur Gears ◽  
Dynamic Coupling ◽  
Nonlinear Dynamic Model ◽  
Mesh Stiffness ◽  
Hypoid Gears ◽  
Helical Gears ◽  
Beveloid Gears ◽  
Vibration Model

Dynamic modeling of beveloid gears is less developed than that of spur gears, helical gears and hypoid gears because of their complicated meshing mechanism and 3-dimsional dynamic coupling. In this study, a nonlinear systematic coupled vibration model is created considering the time-varying mesh stiffness, time-varying transmission error, time-varying rotational radius and time-varying friction coefficient. Numerical integration applying the explicite Runge-Kutta formula and the implicit direct integration is used to solve the nonlinear dynamic model. Also, the dynamic characteristics of the marine gear system are investigated.

Effects of tip relief on vibration responses of a geared rotor system

2013 ◽  
Vol 228 (7) ◽  
pp. 1132-1154 ◽  
Author(s):  
Hui Ma ◽  
Jian Yang ◽  
Rongze Song ◽  
Suyan Zhang ◽  
Bangchun Wen
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Spur Gear ◽  
Rotor System ◽  
Time Varying ◽  
Frequency Range ◽  
Mesh Stiffness ◽  
Resonance Frequencies ◽  
Vibration Responses

Considering tip relief, a finite element model of a spur gear pair in mesh is established by ANSYS software. Time-varying mesh stiffness under different amounts of tip relief is calculated based on the finite element model. Then, a finite element model of a geared rotor system is developed by MATLAB software considering the effects of time-varying mesh stiffness and constant load torque. Emphasis is given to the effects of tip relief on the lateral–torsional coupling vibration responses of the system. The results show that as the amount of tip relief increases, the saltation of time-varying mesh stiffness reduces at the position of approach action and transition mesh region from the single tooth to double tooth. A number of primary resonances and some super-harmonic of gears 1 and 2 are excited by time-varying mesh stiffness in amplitude frequency responses. As the amount of tip relief increases, some super-harmonic responses change due to the variation in the higher frequency components of time-varying mesh stiffness. After tip relief, the vibration and meshing force decrease obviously at lower mesh frequency range except at some resonance frequencies; however, tip relief is not effective in reducing the vibration at higher mesh frequency range. The amplitude fluctuation of the vibration acceleration reduces evidently after considering tip relief, which is not remarkable with the increase of meshing frequency.

Study on the Effect of Ways of Gear Relief on Contact Force of Teeth Face

2011 ◽  
Vol 415-417 ◽  
pp. 66-70
Author(s):  
Yong Ma ◽  
Qi Huang ◽  
Tian Ji ◽  
Zhi Feng Lou
Keyword(s):  
Finite Element ◽  
Contact Force ◽  
Contact Analysis ◽  
Finite Element Models ◽  
Contact Method ◽  
Helical Gears ◽  
Profile Modification ◽  
Involute Gears ◽  
Main Basis ◽  
Better Than

An accurate finite element contact analysis of helical gears was done directly under ANSYS, while the integrated elastic deformation of the meshed teeth was extracted directly from the finite element contact analysis results, and considered as the main basis of the amount of tooth profile modification. Linear, conic, cubic, and sine relief curve are compiled and established in MATLAB, on which gear models of two ways of modified gear are built. Under the same modified parameters, contact method is used on the proposed finite element models of gears by software LS-DYNA, and the effect of the two ways of gear relief on contact force on teeth face is analyzed. The results show that the effect of a pair of gears relief is better than one gear relief for linear and conic relief curve, and the effect of one gear relief is better than a pair of gears relief for cubic and sine relief curve. So dynamic simulation on modified involute gears has great significance for reducing contact force of teeth face of gears.

scholarly journals A Model for Analysis of Time-Varying Mesh Stiffness of Helical Gears with Misalignment Errors

2021 ◽  
Vol 45 (2) ◽  
pp. 59-73
Author(s):  
Zeyin He ◽  
Weiyi Tang ◽  
Shizheng Sun
Keyword(s):  
Time Varying ◽  
Mesh Stiffness ◽  
Helical Gears

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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