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.

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.

A hybrid analytical-numerical method based on Isogeometric Analysis for determination of time varying gear mesh stiffness

2021 ◽  
Vol 160 ◽  
pp. 104291
Author(s):  
Andreas Beinstingel ◽  
Michael Keller ◽  
Michael Heider ◽  
Burkhard Pinnekamp ◽  
Steffen Marburg
Keyword(s):  
Numerical Method ◽  
Isogeometric Analysis ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

scholarly journals Thermo-voltage measurements of atomic contacts at low temperature

2016 ◽  
Vol 7 ◽  
pp. 767-775 ◽  
Author(s):  
Ayelet Ofarim ◽  
Bastian Kopp ◽  
Thomas Möller ◽  
León Martin ◽  
Johannes Boneberg ◽  
...  
Keyword(s):  
Finite Element ◽  
Low Temperature ◽  
Temperature Difference ◽  
Laser Heating ◽  
Laser Source ◽  
Break Junction ◽  
Resistance Change ◽  
Element Simulation ◽  
Novel Method

We report the development of a novel method to determine the thermopower of atomic-sized gold contacts at low temperature. For these measurements a mechanically controllable break junction (MCBJ) system is used and a laser source generates a temperature difference of a few kelvins across the junction to create a thermo-voltage. Since the temperature difference enters directly into the Seebeck coefficient S = −ΔV/ΔT, the determination of the temperature plays an important role. We present a method for the determination of the temperature difference using a combination of a finite element simulation, which reveals the temperature distribution of the sample, and the measurement of the resistance change due to laser heating of sensor leads on both sides next to the junction. Our results for the measured thermopower are in agreement with recent reports in the literature.

Glued-in-rod timber joints: analytical model and finite element simulation

2018 ◽  
Vol 51 (3) ◽  
Author(s):  
A. Hassanieh ◽  
H. R. Valipour ◽  
M. A. Bradford ◽  
R. Jockwer
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Analytical Model ◽  
Element Simulation ◽  
Timber Joints

Time-varying mesh stiffness calculation for gear pairs with misalignment errors in multiple degrees of freedom based on an analytical method

2021 ◽  
pp. 095440622110392
Author(s):  
Qi Wen ◽  
Qi Chen ◽  
Qungui Du ◽  
Yong Yang
Keyword(s):  
Analytical Model ◽  
Contact Line ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Single Pair ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Position Change ◽  
Multiple Degrees Of Freedom ◽  
Effective Contact

Misalignment errors (MEs) in multiple degrees of freedom (multi-DOFs) at the mesh position will lead to a change in the time-varying mesh stiffness (TVMS) and then affect the dynamic behaviour of gear pairs. Therefore, a new, more rapid, three-dimensional analytical model for TVMS calculation for gear pairs with three rotational and three translational MEs is established in this paper, and a new solution method based on potential energy theory is presented. In addition, the correctness of the new model is verified by the finite element method (FEM). Moreover, the effective contact line, uneven distribution of mesh force on the contact line, and mesh position change are taken into account. Finally, the TVMS under different ME conditions is calculated with the new analytical model. The results showed that the different MEs have dissimilar effects on the TVMS, and the relationship between the ME and TVMS is nonlinear. In addition, the region of single-pair and double-pair teeth in contact would also change with ME.

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.

Corner-Filleted Flexure Hinges

2000 ◽  
Vol 123 (3) ◽  
pp. 346-352 ◽  
Author(s):  
Nicolae Lobontiu ◽  
Jeffrey S. N. Paine ◽  
Ephrahim Garcia ◽  
Michael Goldfarb
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Finite Element Simulation ◽  
Analytical Approach ◽  
Flexure Hinge ◽  
Closed Form Solutions ◽  
Flexure Hinges ◽  
Element Simulation ◽  
Model Predictions ◽  
The Right

The paper presents an analytical approach to corner-filleted flexure hinges. Closed- form solutions are derived for the in-plane compliance factors. It is demonstrated that the corner-filleted flexure hinge spans a domain delimited by the simple beam and the right circular flexure hinge. A comparison that is made with the right circular flexure hinges indicates that the corner-filleted flexures are more bending-compliant and induce lower stresses but are less precise in rotation. The finite element simulation and experimental results confirmed the model predictions.

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