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 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.

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.

On the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Three-Dimensional Gear Systems

2015 ◽  
Author(s):  
Nina Sainte-Marie ◽  
Philippe Velex ◽  
Guillaume Roulois ◽  
Franck Marrot
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
Test Rig ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Dynamic Transmission Error ◽  
Time Variations ◽  
The Relationship

A three-dimensional dynamic model is presented to simulate the dynamic behavior of single stage gears by using a combination of classic shaft, lumped parameter and specific 2-node gear elements. The mesh excitation formulation is based on transmission errors whose mathematical grounding is briefly described. The validity of the proposed methodology is assessed by comparison with experimental evidence from a test rig. The model is then employed to analyze the relationship between dynamic transmission errors and dynamic tooth loads or root stresses. It is shown that a linear dependency can be observed between the time variations of dynamic transmission error and tooth loading as long as the system can be assimilated to a torsional system but that this linear relationship tends to disappear when the influence of bending cannot be neglected.

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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