Stochastic and Deterministic Vibration Analysis on Drill-String With Finite Element Method

2013 ◽  
Author(s):  
Hongyuan Qiu ◽  
Jianming Yang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Element Model ◽  
Random Excitation ◽  
Drill String ◽  
Mitigation Measures ◽  
Stick Slip ◽  
Drilling Performance ◽  
Mc Simulation

Using Euler-Bernoulli beam theory, a finite element model with six degrees of freedom per node is developed for a drill-string assembly. The drill-string is driven by a DC motor on the top and is subjected to distributed loads due to its own weight as well as bit/formation interaction. The model is axial-torsional, lateral-torsional coupled. Under deterministic excitations, the model captures stick-slip behavior in drilling operation. Analysis on its negative effect on drilling performance are made, and potential mitigation measures are also discussed. In random model, the excitations to the drill-bit are modeled as combination of deterministic and random components. Monte Carlo (MC) simulation is employed to obtain the statistics of the response. Two cases of random excitation with different intensities are investigated. The results from MC simulation are compared against that from deterministic case.

scholarly journals Stick-Slip Analysis of a Drill String Subjected to Deterministic Excitation and Stochastic Excitation

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Hongyuan Qiu ◽  
Jianming Yang ◽  
Stephen Butt
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Element Model ◽  
Random Excitation ◽  
Time Instant ◽  
Drill String ◽  
Stochastic Excitation ◽  
Stick Slip ◽  
Probabilistic Distribution ◽  
Noise Simulation

Using a finite element model, this paper investigates the torsional vibration of a drill string under combined deterministic excitation and random excitation. The random excitation is caused by the random friction coefficients between the drill bit and the bottom of the hole and assumed as white noise. Simulation shows that the responses under random excitation become random too, and the probabilistic distribution of the responses at each discretized time instant is obtained. The two points, entering and leaving the stick stage, are examined with special attention. The results indicate that the two points become random under random excitation, and the distributions are not normal even when the excitation is assumed as Gaussian white noise.

Flexible Multibody Approaches for Dynamical Simulation of Beam Structures in Drilling

2014 ◽  
Author(s):  
Gennady Mikheev ◽  
Dmitry Pogorelov ◽  
Oleg Dmitrochenko ◽  
Raju Gandikota
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Element Model ◽  
Drill String ◽  
Rigid Bodies ◽  
Nonlinear Finite Element ◽  
Beam Structures ◽  
Modal Approach ◽  
Large Rotation

Two approaches for simulation of dynamics of complex beam structures such as drill strings are considered. In the first approach, the drill string is presented as a set of uniform beams connected via force elements. The beams can undergo arbitrary large displacements as absolutely rigid bodies but its flexible displacements due to elastic deformations are assumed to be small. Flexibility of the beams is simulated using the modal approach. Thus, each beam has at least twelve degrees of freedom: six coordinates define position and orientation of a local frame and six modes are used for modeling flexibility. The second approach is dynamic simulation of the drill string using nonlinear finite element model. The proposed beam finite element uses Cartesian coordinates of its nodes and node rotation angles around axis of Cartesian coordinate system as generalized coordinates. The nonlinear finite element is developed based on method of large rotation vectors. Rotation angles in the nodes can be arbitrary large. Equations of motion of beam structure are derived in the paper. The number of degrees of freedom is decreased by factor two as compared with the modal approach. Thereby, computational efficiency under simulation of dynamics of long drill strings is considerably increased. The features of creating the models and numerical methods as well as results obtained by applying both approaches are discussed in the paper.

A Finite Element Method With Full Bit-Force Modeling to Analyze Drillstring Vibration

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Tianheng Feng ◽  
Madhu Vadali ◽  
Zheren Ma ◽  
Dongmei Chen ◽  
Jason Dykstra
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Normal Operation ◽  
Force Model ◽  
Modeling Framework ◽  
Stick Slip ◽  
Rock Interaction ◽  
Drilling Performance ◽  
Element Method

Drillstring vibration is detrimental to drilling operations. It is crucial to understand the underlying mechanisms to circumvent these vibrations and to help improve drilling performance. This paper presents a six degrees-of-freedom (DOF) finite element method (FEM) model to characterize the drillstring dynamics. In addition, a comprehensive bit-force model is developed and included as a boundary condition to the model, corresponding to the vibrations in axial, lateral, and torsional directions. This bit-force model considers the bottom hole assembly (BHA) eccentricity, mud damping, bit–rock interaction, and their coupling mechanisms. Simulation results have shown good agreement with field observations and experimental data in the literature. The utility of this modeling framework is demonstrated in the paper through case studies for normal operation, stick–slip vibration, and whirl vibration.

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.

A Parallel Solution Strategy for Finite Element Models

1996 ◽  
Author(s):  
Jordan J. Cox ◽  
Jeffrey A. Talbert ◽  
Eric Mulkay
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Decomposition Methods ◽  
Finite Element Models ◽  
Unique Contribution ◽  
Matrix Equations ◽  
Parallel Solution ◽  
The Finite Element Model ◽  
Parallel Fashion

Abstract This paper presents a method for naturally decomposing finite element models into sub-models which can be solved in a parallel fashion. The unique contribution of this paper is that the decomposition strategy comes from the geometric features used to construct the solid model that the finite element model represents. Domain composition and domain decomposition methods are used to insure global compatibility. These techniques reduce the N2 behavior of traditional matrix solving techniques, where N is the number of degrees of freedom in the global set of matrix equations, to a sum of m matrices with n2 behavior, where n represents the number of degrees of freedom in the smaller sub-model matrix equations.

Finite Element Model of the Human Knee Joint to Study Tibio-Femoral Contact Mechanics

2000 ◽  
Author(s):  
Tammy Haut Donahue ◽  
Maury L. Hull ◽  
Mark M. Rashid ◽  
Christopher R. Jacobs
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Soft Tissues ◽  
Element Model ◽  
Human Knee ◽  
Human Knee Joint ◽  
Solid Models ◽  
Flexion Extension ◽  
A New Technique

Abstract A finite element model of the tibio-femoral joint in the human knee was created using a new technique for developing accurate solid models of soft tissues (i.e. cartilage and menisci). The model was used to demonstrate that constraining rotational degrees of freedom other than flexion/extension when the joint is loaded in compression markedly affects the load distribution between the medial and lateral sides of the joint. The model also was used to validate the assumption that the bones can be treated as rigid.

A finite element model to study the effect of porosity location on the elastic modulus of a cantilever beam

2019 ◽  
Vol 43 (4) ◽  
pp. 443-453
Author(s):  
Stephen M. Handrigan ◽  
Sam Nakhla
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Focused Ion Beam ◽  
Mechanical Response ◽  
Ion Beam ◽  
Three Dimensional ◽  
Beam Theory ◽  
Element Model ◽  
Fe Model ◽  
Three Dimensional Finite Element

An investigation to determine the effect of porosity concentration and location on elastic modulus is performed. Due to advancements in testing methods, the manufacturing and testing of microbeams to obtain mechanical response is possible through the use of focused ion beam technology. Meanwhile, rigorous analysis is required to enable accurate extraction of the elastic modulus from test data. First, a one-dimensional investigation with beam theory, Euler–Bernoulli and Timoshenko, was performed to estimate the modulus based on load-deflection curve. Second, a three-dimensional finite element (FE) model in Abaqus was developed to identify the effect of porosity concentration. Furthermore, the current work provided an accurate procedure to enable accurate extraction of the elastic modulus from load-deflection data. The use of macromodels such as beam theory and three-dimensional FE model enabled enhanced understanding of the effect of porosity on modulus.

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

2012 ◽  
Vol 04 (01) ◽  
pp. 1250010 ◽  
Author(s):  
V. P. VALLALA ◽  
G. S. PAYETTE ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Beam Theory ◽  
Element Model ◽  
Higher Order ◽  
Time Step ◽  
Third Order ◽  
The Third

In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

Finite Element Model Based Full Spectrum Response Analysis of a Cracked Rotor With Internal and External Damping

2019 ◽  
Author(s):  
Dipendra Kumar Roy ◽  
Rajiv Tiwari
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Rotor System ◽  
Response Analysis ◽  
Stable Operation ◽  
Internal Damping ◽  
Full Spectrum ◽  
Fault Parameters ◽  
Spectrum Response

Abstract The ratio of internal and external damping is one of the important fault parameters and it leads to instability of a rotor shaft at higher spin speeds. The crack in a rotor is one of the sources of its instability due to the crack internal damping. A rotor with crack internal damping that originates from the rubbing action between the two crack faces. For a sustained stable operation of the rotor, it is imperative to analyze rotor parameters such as the internal and external damping and other parameters, like the additive crack stiffness and disc eccentricity. Therefore, the present work considers a full spectrum response analysis of a transverse cracked shaft based on the finite element method. The rotary and translations of inertia are considered including of gyroscopic effect in the rotor system. The transverse crack is modeled based on the switching crack assumption. The crack in the rotor gives forcing with multiple harmonics with the forward and backward. The equation of motion has been developed for the rotor system having four degrees of freedom at each node and using MATLAB™ Simulink the responses are generated for a numerical example.

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