Effect of an Original Gear Mesh Modeling on the Gearbox Dynamic Behavior

2007 ◽  
Author(s):  
Emmanuel Rigaud ◽  
Joe¨l Perret-Liaudet ◽  
Mohamed-Salah Mecibah
Keyword(s):  
Load Distribution ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Elastic Coupling ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Face Width ◽  
Building Process ◽  
Coupling Terms

Prediction of the vibratory and acoustical behavior of gearboxes is generally based on characterization of the excitation sources, overall modeling of the gearbox, modal analysis and solving of the parametric equations of motion generated by these models. On the building process of such large degrees of freedom models, the elastic coupling induced by the gear mesh is generally described by the parametric meshing stiffness k(t) along the line of action. This kind of model is not able to take into account the load distribution along the tooth face width, even though the resulting moment can constrain rotational angles associated to wheels tilting and flexural deformation of shafts. The scope of this study is to introduce the coupling terms between wheels associated to these phenomena. Some examples show how they can influence the gear modal characteristics and dynamic response and, consequently, the vibratory and acoustical response of the gearbox.

Dynamic Characteristics of Double Helical Planetary Gear Train With Tooth Friction

2015 ◽  
Author(s):  
Fengxia Lu ◽  
Rupeng Zhu ◽  
Haofei Wang ◽  
Heyun Bao ◽  
Miaomiao Li
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Step Size ◽  
Planetary Gear Train ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Nonlinear Dynamics Model

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.

Closed-Form Calculation of Lead Flank Modification Proposal for Spur and Helical Gear Stages

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Uwe Weinberger ◽  
Michael K. Otto ◽  
Karsten Stahl
Keyword(s):  
Load Distribution ◽  
Degrees Of Freedom ◽  
Best Practice ◽  
Equation System ◽  
Constant Load ◽  
Calculation Model ◽  
Computing Power ◽  
Gear Mesh ◽  
A Value ◽  
Linear Equation System

Abstract Due to the growing need for gearboxes to be as lightweight and efficient as possible, it is most important that the gear mesh’s potential is utilized as well as possible. One way of doing that is to define a flank modification that optimally distributes the load over the flank. Best practice for defining a flank modification is to manually check out the load distribution and to define a value of the flank modification. In general, this is an iterative method to get an optimally distributed load. This method can also be automated. To do this, the deformations of the gearbox (shafts, bearings, gear mesh) are calculated. With those results, a modification proposal is calculated and applied to the calculation model. As soon as the values for the next additional modification proposal drop under a certain limit, the iteration is finished. This method consumes time and computing power. Additionally, since it is an iteration, it does not always converge. A new method for calculating the lead flank modification for all gear stages in the gearbox to be calculated is presented in this paper. The method shown in this paper uses additional degrees of freedom and equations, which are integrated into the linear equation system of the gearbox model. Those degrees of freedom and the equations apply the boundary condition to the model of a constant load distribution. By introducing additional factors in the equations, it is possible to calculate a lead flank modification for an arbitrary load distribution. By integrating these additional degrees of freedom and the equations, only one additional calculation is needed to get a modification proposal. Examples throughout this paper show the results of this method.

Closed Form Calculation of Lead Flank Modification Proposal for Spur and Helical Gear Stages

2019 ◽  
Author(s):  
Uwe Weinberger ◽  
Michael K. Otto ◽  
Karsten Stahl
Keyword(s):  
Load Distribution ◽  
Degrees Of Freedom ◽  
Best Practice ◽  
Equation System ◽  
Constant Load ◽  
Calculation Model ◽  
Computing Power ◽  
Gear Mesh ◽  
A Value ◽  
Linear Equation System

Abstract Due to the growing need for gearboxes to be as lightweight and efficient as possible, it is most important that the gear mesh’s potential is utilized as well as possible. One way of doing that is to define a flank modification that optimally distributes the load over the flank. Best practice for defining a flank modification is to manually check out the load distribution and to define a value of the flank modification. In general, this is an iterative method to get an optimally distributed load. This method can also be automated. To do this, the deformations of the gearbox (shafts, bearings, gear mesh) are calculated. With those results a modification proposal is calculated and applied to the calculation model. As soon as the values for the next additional modification proposal drop under a certain limit, the iteration is finished. This method consumes time and computing power. Additionally, since it is an iteration, does not always converge. A new method for calculating the lead flank modification for all gear stages in the gearbox to be calculated is presented in this paper. The method shown in this paper uses additional degrees of freedom and equations, which are integrated into the linear equation system of the gearbox model. Those degrees of freedom and the equations apply the boundary condition to the model of a constant load distribution. By introducing additional factors in the equations, it is possible to calculate a lead flank modification for an arbitrary load distribution. By integrating these additional degrees of freedom and the equations, only one additional calculation is needed to get a modification proposal. Examples throughout this paper show the results of this method.

Coupling of In-Plane Flexural, Tangential, and Shear Wave Modes of a Curved Beam

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
B. Kang ◽  
C. H. Riedel
Keyword(s):  
Shear Wave ◽  
Equations Of Motion ◽  
High Order ◽  
Curved Beam ◽  
Beam Model ◽  
Elastic Coupling ◽  
Dynamic Coupling ◽  
Frequency Spectra ◽  
Coupling Terms ◽  
Wave Modes

In this paper, the coupling effects among three elastic wave modes, flexural, tangential, and radial shear, on the dynamics of a planar curved beam are assessed. Two sets of equations of motion governing the in-plane motion of a curved beam are derived, in a consistent manner, based on the theory of elasticity and Hamilton’s principle. The first set of equations retains all resulting linear coupling terms that includes both static and dynamic coupling among the three wave modes. In the derivation of the second set of equations, the effects of Coriolis acceleration and high-order elastic coupling terms are neglected, which leads to a set of equations without dynamic coupling terms between the tangential and shear wave modes. This second set of equations of motion is the one most commonly used in studies on thick curved beams that include the effects of centerline extensibility, rotary inertia, and shear deformation. The assessment is carried out by comparing the dynamic behavior predicted by each curved beam model in terms of the dispersion relations, frequency spectra, cutoff frequencies, natural frequencies and mode shapes, and frequency responses. In order to ensure the comparison is based on accurate results, the wave propagation technique is applied to obtain exact wave solutions. The results suggest that the contributions of the dynamic and high-order elastic coupling terms to the response of a thick curved beam are quite significant and that these coupling terms should not be neglected for an accurate analysis of a thick curved beam with a large curvature parameter.

Vibration Modes of Helical Planetary Gears

2009 ◽  
Author(s):  
Tugan Eritenel ◽  
Robert G. Parker
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Lumped Parameter Model ◽  
Vibration Modes ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Modal Properties ◽  
Lumped Parameter

This paper examines the vibration modes of single stage helical planetary gears in three dimensions with equally spaced planets. A lumped-parameter model is formulated to obtain the equations of motion. The gears and shafts are modeled as rigid bodies with compliant bearings at arbitrary axial locations on the shafts. A translational and a tilting stiffness account for the force and moment transmission at the gear mesh interface. The modal properties generalize those of two-dimensional spur planetary gears; there are twice as many degrees of freedom and natural frequencies due to the added tilting and axial motion. All vibration modes are categorized as planet, rotational-axial, and translational-tilting modes. The modal properties are shown to hold even for configurations that are not symmetric about the gear plane, due to, for example, shaft bearings not being equidistant from the gear plane. Computational modal analysis are performed to numerically verify the findings.

Dynamic Analysis of Mechanical Systems With Elastic Telescopic Members

1994 ◽  
Author(s):  
B. O. Al-Bedoor ◽  
Y. A. Khulief
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Vibrational Motion ◽  
Dynamic Coupling ◽  
Gravitational Effects ◽  
Coupling Terms ◽  
Tip Mass ◽  
Stiffening Effect

Abstract A dynamic model for the vibrational motion of an elastic beam-like telescopic member is presented. In addition to translation, the elastic member is allowed to execute large reference rotation. The Lagrangian approach in conjunction with the assumed modes technique are employed in deriving the equations of motion. The developed model accounts for all the dynamic coupling terms, as well as the stiffening effect due to the beam reference rotation. The tip mass dynamics is included together with the associated dynamic coupling between the modal degrees of freedom. In addition, the devised dynamic model takes into account the gravitational effects, thus permitting motions in either vertical or horizontal planes. Numerical simulation of a mechanical system with an elastic telescopic member is presented.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

Experimental Investigation of Laser Sintering of Conductive Adhesive for Functional Prototypes Produced by Embedding Stereolithography

2014 ◽  
Vol 1038 ◽  
pp. 75-81
Author(s):  
Bernd Niese ◽  
Philipp Amend ◽  
Uwe Urmoneit ◽  
Stephan Roth ◽  
Michael Schmidt
Keyword(s):  
Thermal Damage ◽  
Laser Sintering ◽  
Conductive Adhesive ◽  
Flexible Production ◽  
Sintering Process ◽  
Building Process ◽  
In Situ Generation ◽  
Functional Components

Embedding stereolithography (eSLA) is an additive, hybrid process, which provides a flexible production of 3D components and the ability to integrate electrical and optical conductive structures and functional components within parts. However, the embedding of conductive circuits in stereolithography (SLA) parts assumes usage of process technologies, which enables their direct integration of conductive circuits during the layer-wise building process. In this context, a promising method for in-situ generation of conductive circuits is dispensing of conductive adhesive on the current surface of the SLA part and its subsequent sintering. In this paper, the laser sintering (λ = 355 nm) of conductive adhesive mainly consisting of silver nanoparticles is investigated. The work intends to evaluate the curing behavior of the conductive adhesive, the beam-matter-interactions and the thermal damage of the SLA substrate. The investigations revealed a fast and flexible laser sintering process for the generation of conductive circuits with sufficient electrical conductivity and sufficient current capacity load. In this context, a characterization of the conductive structures is done by measuring their electrical resistance and their potential current capacity load.

scholarly journals Lattice-shifted nematic quantum critical point in FeSe1−xSx

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
S. Chibani ◽  
D. Farina ◽  
P. Massat ◽  
M. Cazayous ◽  
A. Sacuto ◽  
...  
Keyword(s):  
Transition Temperature ◽  
Critical Point ◽  
Degrees Of Freedom ◽  
Quantum Critical Point ◽  
Substantial Effect ◽  
Low Energy ◽  
Elastic Coupling ◽  
Superconducting Transition ◽  
Local Moments ◽  
Quantum Critical

AbstractWe report the evolution of nematic fluctuations in FeSe1−xSx single crystals as a function of Sulfur content x across the nematic quantum critical point (QCP) xc ~ 0.17 via Raman scattering. The Raman spectra in the B1g nematic channel consist of two components, but only the low energy one displays clear fingerprints of critical behavior and is attributed to itinerant carriers. Curie–Weiss analysis of the associated nematic susceptibility indicates a substantial effect of nemato-elastic coupling, which shifts the location of the nematic QCP. We argue that this lattice-induced shift likely explains the absence of any enhancement of the superconducting transition temperature at the QCP. The presence of two components in the nematic fluctuations spectrum is attributed to the dual aspect of electronic degrees of freedom in Hund’s metals, with both itinerant carriers and local moments contributing to the nematic susceptibility.

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