Modeling and Finite Element Analysis of Drill Bit Vibrations

1989 ◽  
Vol 111 (2) ◽  
pp. 148-155 ◽  
Author(s):  
O. Tekinalp ◽  
A. G. Ulsoy
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Helix Angle ◽  
Drill Bit ◽  
Element Analysis ◽  
Cross Sectional ◽  
Various Boundary Conditions ◽  
Drill Bits ◽  
Euler Bernoulli Beam

Drill bit vibrations are modeled using the Euler-Bernoulli beam theory. The model includes the most important properties of drill bits and of the drilling operation. These are: the drill bit cross sectional geometry, the drill helix angle, rotational speed of the drill bit, the thrust force, torque, and cutting forces generated during drilling. Equations of motion are derived in an inertial frame and then transformed to a rotating fluted frame for convenience in the solution. The transformed equations are discretized using finite element techniques. The finite element code developed is capable of solving the eigenvalue problem for various boundary conditions and drill cross sectional geometries. Finite element solutions are compared to known analytical, numerical, and experimental results from the literature and good agreement is obtained.

Finite element analysis of a Timoshenko beam traversed by a moving vehicle

2009 ◽  
Vol 223 (3) ◽  
pp. 231-243
Author(s):  
M Moghaddas ◽  
R Sedaghati ◽  
E Esmailzadeh ◽  
P Khosravi
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Weak Form ◽  
Element Formulation ◽  
Governing Equations ◽  
Element Analysis ◽  
Moving Vehicle ◽  
The Difference

In this study the finite element formulation for the dynamics of a bridge traversed by moving vehicles is presented. The vehicle including the driver and the passenger is modelled as a half-car planner model with six degree of freedom, travelling on the bridge with constant velocity. The bridge is modelled as a uniform beam with simply supported end conditions that obeys the Timoshenko beam theory. The governing equations of motion are derived using the extended Hamilton principle and then transformed into the finite element format by using the weak-form formulation. The Newmark-β method is utilized to solve the governing equations and the results are compared with those reported in the literature. Furthermore, the maximum values of deflection for the Timoshenko and Euler—Bernoulli beams have been compared. The results illustrated that as the velocity of the vehicle increases, the difference between the maximum beam deflections in the two beam models becomes more significant.

Effects of Geometric and Process Parameters on Drill Transverse Vibrations

1990 ◽  
Vol 112 (2) ◽  
pp. 189-194 ◽  
Author(s):  
O. Tekinalp ◽  
A. Galip Ulsoy
Keyword(s):  
Finite Element ◽  
Process Parameters ◽  
Rotational Speed ◽  
Cutting Forces ◽  
Thrust Force ◽  
Helix Angle ◽  
Drill Bit ◽  
Cross Sectional ◽  
Transverse Vibrations ◽  
Simulation Results

Finite element solutions are used to analyze the effects of geometric and process parameters on the drill bit transverse vibrations. The effects of cross sectional geometry, of the flute helix angle, the drill rotational speed, and the thrust force generated during drilling on the drill transverse frequencies are investigated. Simulation results also show the transient vibrations of a drill bit under transverse cutting forces at the drill tip.

NONCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS

2011 ◽  
Vol 08 (03) ◽  
pp. 349-368 ◽  
Author(s):  
WOORAM KIM ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Mixed Models ◽  
Mixed Model ◽  
Mixed Finite Element ◽  
Beam Theory ◽  
Finite Element Models ◽  
Various Boundary Conditions ◽  
Beam Bending ◽  
Displacement Based ◽  
Euler Bernoulli Beam

In this study, mixed finite element models of beam bending are developed to include the membrane forces and shear forces in addition to the bending moments and displacements. Mixed finite element models were developed based on the weighted residual statements of governing equations. The Euler–Bernoulli beam theory (EBT) and the Timoshenko beam theory (TBT) are used. The effectiveness of the new mixed models is evaluated in light of other mixed models to show the advantages. Each newly developed model is examined and compared with other models to verify its performance under various boundary conditions. In the linear analysis, solutions are compared with available analytical solutions and solutions of existing models. In the nonlinear case, direct and Newton–Raphson methods are used to solve the nonlinear equations. The converged solutions are compared with available solutions of the displacement models. Post-processed data of the mixed model developed herein shows better accuracy than the conventional displacement-based model.

Damping Improvement in Layered and Jointed Beams by Finite Element Analysis

2012 ◽  
Vol 505 ◽  
pp. 501-505 ◽  
Author(s):  
D.N. Thatoi ◽  
R.C. Mohanty ◽  
A.K. Acharya ◽  
B.K. Nanda
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Element Model ◽  
Damping Capacity ◽  
Bernoulli Beam ◽  
Element Analysis ◽  
Linear Elastic ◽  
Mass Matrices ◽  
Euler Bernoulli Beam

Damping in built-up structures is produced by the energy dissipation due to micro-slip along the frictional interfaces. A finite element model of the linear elastic system has been formulated using the Euler-Bernoulli beam theory to investigate the damping phenomena in riveted connections. The discrete element system having two degrees of freedom per node representing v and has been used for the analysis. The generalized stiffness and mass matrices for this element has been derived. Extensive experiments have been conducted for the validation of the analysis. From this study, it is established that the damping capacity increases and the natural frequency decreases due to the joint effects.

scholarly journals Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones

2013 ◽  
Vol 10 (79) ◽  
pp. 20120823 ◽  
Author(s):  
Charlotte A. Brassey ◽  
Lee Margetts ◽  
Andrew C. Kitchener ◽  
Philip J. Withers ◽  
Phillip L. Manning ◽  
...  
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Beam Theory ◽  
Maximum Principal Stress ◽  
Long Bones ◽  
Element Analysis ◽  
Cross Sectional ◽  
Computed Tomographic ◽  
Slender Beams ◽  
Stress Behaviour

Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress ( σ min ) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r 2 = 0.56). Under bending, FEA values of maximum principal stress ( σ max ) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r 2 = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ torsion were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

Mechanical Design, Additive Manufacturing, and Performance of Equal Volume Metamaterials

2021 ◽  
Author(s):  
Richárd Horváth ◽  
Vendel Barth ◽  
Viktor Gonda ◽  
Mihály Réger ◽  
Imre Felde
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Absorption ◽  
Mechanical Design ◽  
Area Under The Curve ◽  
Cell Number ◽  
Element Analysis ◽  
Cross Sectional ◽  
Unit Cells ◽  
And Performance

Abstract In this paper, we study the energy absorption of metamaterials composed of unit cells whose special geometry makes the cross-sectional area and the volume of the bodies generated from them constant (for the same enclosing box dimensions). After a parametric description of such special geometries, we analyzed by finite element analysis the deformation of the metamaterials we have designed during compression. We 3D printed the designed metamaterials from plastic to subject them to real compression. The results of the finite element analysis were compared with the real compaction results. Then, for each test specimen, we plotted its compaction curve. By fitting a polynomial to the compaction curves and integrating it (area under the curve), the energy absorption of the samples can be obtained. As a result of these investigations, we drew a conclusion about the relationship between energy absorption and cell number.

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