Stiffness matrix calculation of rolling element bearings using a finite element/contact mechanics model

2012 ◽  
Vol 51 ◽  
pp. 32-45 ◽  
Author(s):  
Yi Guo ◽  
Robert G. Parker
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Stiffness Matrix ◽  
Rolling Element Bearings ◽  
Mechanics Model ◽  
Rolling Element ◽  
Matrix Calculation

scholarly journals Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Emir Gülümser ◽  
Uğur Güdükbay ◽  
Sinan Filiz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Nonlinear Finite Element ◽  
Nonlinear Finite Element Method ◽  
Nonlinear Fem ◽  
Calculation Technique ◽  
Stiffness Matrices ◽  
Matrix Calculation ◽  
Element Method

We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.

A Finite Element Investigation of a Bearing/Cartridge Interface for a Fretting Corrosion Study

1985 ◽  
Vol 107 (2) ◽  
pp. 157-163 ◽  
Author(s):  
R. J. Stover ◽  
H. H. Mabie ◽  
M. J. Furey
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Analytical Study ◽  
Experimental Tests ◽  
Tangential Direction ◽  
Rolling Element Bearings ◽  
Interface Conditions ◽  
Finite Element Technology ◽  
Rolling Element ◽  
Contact Pressures

The bearing/cartridge interfaces of a Ship Service Motor Generator Set (SSMG) were modeled by using finite element technology. The purpose of this analytical study was to verify the results of earlier experimental tests made on an actual SSMG unit. This research is part of a larger research project to examine the important parameters influencing the fretting of rolling element bearings. Models for the bearings at both ends of the unit were developed, and loads simulating the ball pass loads were applied to these models; the contact pressures, radial deformations, and relative displacements at the interface were calculated. The resulting data showed the interface conditions to be extremely complex with the contact pressures varying from zero to a maximum of 55.4 MPa (8030 psi) as the balls passed by. The maximum relative displacements occurred in the tangential direction (2.44 μm) and were independent of the axial boundary conditions.

A 3D Finite Element Study of Fatigue Life Dispersion in Rolling Line Contacts

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Nick Weinzapfel ◽  
Farshid Sadeghi ◽  
Vasilios Bakolas ◽  
Alexander Liebel
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Material Properties ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Critical Shear Stress ◽  
Rolling Contact ◽  
Shear Stresses ◽  
Rolling Element Bearings ◽  
Rolling Element

Rolling contact fatigue of rolling element bearings is a statistical phenomenon that is strongly affected by the heterogeneous nature of the material microstructure. Heterogeneity in the microstructure is accompanied by randomly distributed weak points in the material that lead to scatter in the fatigue lives of an otherwise identical lot of rolling element bearings. Many life models for rolling contact fatigue are empirical and rely upon correlation with fatigue test data to characterize the dispersion of fatigue lives. Recently developed computational models of rolling contact fatigue bypass this requirement by explicitly considering the microstructure as a source of the variability. This work utilizes a similar approach but extends the analysis into a 3D framework. The bearing steel microstructure is modeled as randomly generated Voronoi tessellations wherein each cell represents a material grain and the boundaries between them constitute the weak planes in the material. Fatigue cracks initiate on the weak planes where oscillating shear stresses are the strongest. Finite element analysis is performed to determine the magnitude of the critical shear stress range and the depth where it occurs. These quantities exhibit random variation due to the microstructure topology which in turn results in scatter in the predicted fatigue lives. The model is used to assess the influence of (1) topological randomness in the microstructure, (2) heterogeneity in the distribution of material properties, and (3) the presence of inherent material flaws on relative fatigue lives. Neither topological randomness nor heterogeneous material properties alone account for the dispersion seen in actual bearing fatigue tests. However, a combination of both or the consideration of material flaws brings the model’s predictions within empirically observed bounds. Examination of the critical shear stress ranges with respect to the grain boundaries where they occur reveals the orientation of weak planes most prone to failure in a three-dimensional sense that was not possible with previous models.

Analysis of the Housing Vibration of a Rotorcraft Planetary Gear Using a Finite Element/Contact Mechanics Model

2017 ◽  
Author(s):  
Christopher G. Cooley ◽  
Adrian A. Hood
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Planetary Gear ◽  
Time Instant ◽  
Frequency Content ◽  
Contact Conditions ◽  
Gear Teeth ◽  
Mechanics Model ◽  
Parametric Studies ◽  
Frequency Components

This study investigates the planetary gear housing vibration for rotorcraft systems with equally spaced and diametrically opposed planets using a finite element/contact mechanics model. This approach permits accurate housing deflection calculations at each time instant that result from the changing contact conditions on all gear teeth and elastic deformations of each gear. Planetary gears with diametrically opposed planets have larger amplitude vibrations and more frequency content than those with equally spaced planets. Parametric studies show that although the frequency content does not change with changes in the system’s parameters, the amplitudes of response at these frequencies are meaningfully impacted. The frequency components of the acceleration spectra can have additional content when the planetary gear has manufacturing and assembly errors. Each error case results in different frequency content in the acceleration spectra. Understanding these housing vibrations is beneficial for interpreting measured accelerometer signals to detect and classify damage.

A Study of Gear Root Strains in a Multi-Stage Planetary Wind Turbine Gear Train Using a Three Dimensional Finite Element/Contact Mechanics Model and Experiments

2011 ◽  
Author(s):  
Phillip E. Prueter ◽  
Robert G. Parker ◽  
Frank Cunliffe
Keyword(s):  
Finite Element ◽  
Wind Turbine ◽  
Contact Mechanics ◽  
Three Dimensional ◽  
Gear Train ◽  
Mechanics Model ◽  
Multi Stage ◽  
Dimensional Finite Element ◽  
Advanced Analysis ◽  
Three Dimensional Finite Element

Wind energy has received a great deal of attention in recent years in part due to its minimal environmental impact and improving efficiency. Increasingly complex wind turbine gear train designs, well-known failures in gear train rolling element bearings, and the constant push to manufacture more reliable, longer lasting systems generate the need for more advanced analysis techniques. The objectives of this paper are to examine the mechanical design of an Orbital2 flexible pin multi-stage planetary wind turbine gear train using a three dimensional finite element/contact mechanics model and to compare to full system experiments. Root strain is calculated at multiple locations across the facewidth of ring gears from the computational model and compared to experimental data. Gear misalignment and carrier eccentricity are also considered. Design recommendations for improving load distribution across gear facewidths are also discussed.

Prediction and Experimental Correlation of Tooth Root Strains in Spur Gear Pairs

2015 ◽  
Author(s):  
Xiang Dai ◽  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Gear Tooth ◽  
Strain Curve ◽  
Spur Gear ◽  
Tooth Root ◽  
Contact Conditions ◽  
Tooth Contact ◽  
Mechanics Model ◽  
Large Amplitude Vibration

Spur gear tooth root strains are calculated using a finite element/contact mechanics formulation for varying gear speeds and applied torques. Extensive comparisons with experiments, including those from the literature and new ones, confirm that the finite element/contact mechanics formulation accurately predicts the quasi-static and dynamic tooth root strains. The finite element/contact mechanics model is used to investigate the features of the tooth root strain curves as the gears rotate kinematically and the tooth contact conditions change. Tooth profile modifications are shown to strongly affect the shape of the strain curve. At non-resonant speeds the dynamic tooth root strain curves have similar shapes as the quasi-static strain curves. At resonant speeds, however, the dynamic tooth root strain curves are drastically different because large amplitude vibration causes tooth contact loss.

Transverse Natural Vibrations of a Cracked Beam Loaded with a Constant Axial Force

1993 ◽  
Vol 115 (4) ◽  
pp. 524-528 ◽  
Author(s):  
M. Krawczuk ◽  
W. M. Ostachowicz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Numerical Calculations ◽  
Open Crack ◽  
Natural Vibrations ◽  
Cracked Beam ◽  
Matrix Calculation

The influence of transverse, one-edge open cracks on the natural frequencies of the cantilever beam subjected to vertical loads is analyzed. A finite element method (FE) is used for modelling the beam. A part of the cracked beam is modelled by beam finite elements with an open crack. Parts of the beam without a crack are modelled by standard beam finite elements. An algorithm of a linear stiffness matrix and a geometrical stiffness matrix calculation for a cracked element is presented. The results of numerical calculations obtained for the presented model are compared with the results of analytical calculations given in the literature and also with the results of numerical calculations obtained for a model with geometrical stiffness matrix of uncracked elements.

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