A Frequency Domain Finite Element Approach for Three-Dimensional Gear Dynamics

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker ◽  
Sandeep M. Vijayakar
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Frequency Domain ◽  
Dynamic Models ◽  
Three Dimensional ◽  
Static Solution ◽  
System Level ◽  
Element Formulation ◽  
Lumped Parameter ◽  
Element Approach

A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides an accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.

A Frequency Domain Finite Element Approach for Three-Dimensional Gear Dynamics

2009 ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker ◽  
Sandeep M. Vijayakar
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Frequency Domain ◽  
Dynamic Models ◽  
Three Dimensional ◽  
Transmission Error ◽  
System Level ◽  
Element Formulation ◽  
Lumped Parameter ◽  
Static Transmission Error

A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static transmission error is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides superior calculation of static transmission error and average mesh stiffness that is used in the dynamic simulation. The frequency domain finite element calculation of dynamic response correlates to numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, and housing structures.

A Nonclassical Finite Element Approach for the Nonlinear Analysis of Micropolar Plates

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
R. Ansari ◽  
A. H. Shakouri ◽  
M. Bazdid-Vahdati ◽  
A. Norouzzadeh ◽  
H. Rouhi
Keyword(s):  
Finite Element ◽  
Plate Theory ◽  
Nonlinear Modeling ◽  
Three Dimensional ◽  
Mindlin Plate ◽  
Small Scale ◽  
Element Formulation ◽  
Nonlinear Bending ◽  
Finite Element Approach ◽  
Element Approach

Based on the micropolar elasticity theory, a size-dependent rectangular element is proposed in this article to investigate the nonlinear mechanical behavior of plates. To this end, a novel three-dimensional formulation for the micropolar theory with the capability of being used easily in the finite element approach is developed first. Afterward, in order to study the micropolar plates, the obtained general formulation is reduced to that based on the Mindlin plate theory. Accordingly, a rectangular plate element is developed in which the displacements and microrotations are estimated by quadratic shape functions. To show the efficiency of the developed element, it is utilized to address the nonlinear bending problem of micropolar plates with different types of boundary conditions. It is revealed that the present finite element formulation can be efficiently employed for the nonlinear modeling of small-scale plates by considering the micropolar effects.

Consistent Hydrodynamic Mass for Parallel Prismatic Beams in a Fluid-Filled Container

1984 ◽  
Vol 106 (3) ◽  
pp. 270-275
Author(s):  
J. F. Loeber
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Incompressible Fluid ◽  
Finite Element Methods ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Beam Length ◽  
Step Process ◽  
Beam Bending

In this paper, representation of the effects of incompressible fluid on the dynamic response of parallel beams in fluid-filled containers is developed using the concept of hydrodynamic mass. Using a two-step process, first the hydrodynamic mass matrix per unit (beam) length is derived using finite element methods with a thermal analogy. Second, this mass matrix is distributed in a consistent mass fashion along the beam lengths in a manner that accommodates three-dimensional beam bending plus torsion. The technique is illustrated by application to analysis of an experiment involving vibration of an array of four tubes in a fluid-filled cylinder.

scholarly journals Polygonal finite elements for three-dimensional Voronoi-cell-based discretisations

2012 ◽  
Author(s):  
Kaliappan Jayabal ◽  
Andreas Menzel
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Three Dimensional ◽  
Specific Property ◽  
Voronoi Cell ◽  
Polycrystalline Materials ◽  
Element Formulation ◽  
Hybrid Finite Element ◽  
Grain Structures ◽  
Polygonal Elements

Hybrid finite element formulations in combination with Voronoi-cell-based discretisation methods can efficiently be used to model the behaviour of polycrystalline materials. Randomly generated three-dimensional Voronoi polygonal elements with varying numbers of surfaces and corners in general better approximate the geometry of polycrystalline microor rather grain-structures than the standard tetrahedral and hexahedral finite elements. In this work, the application of a polygonal finite element formulation to three-dimensional elastomechanical problems is elaborated with special emphasis on the numerical implementation of the method and the construction of the element stiffness matrix. A specific property of Voronoi-based discretisations in combination with a hybrid finite element approach is investigated. The applicability of the framework established is demonstrated by means of representative numerical examples.

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