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.

Performance Characteristics of a Smart Flexible Beam With Distributed ACLD Elements

2002 ◽  
Author(s):  
L. C. Hau ◽  
Eric H. K. Fung
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Element Model ◽  
Flexible Beam ◽  
Constrained Layer Damping ◽  
Optimal Output ◽  
Modes Of Vibration ◽  
Original Size

The finite element method, in conjunction with the Golla-Hughes-McTavish (GHM) viscoelastic model, is employed to model a clamped-free beam partially treated with active constrained layer damping (ACLD) elements. The governing equations of motion are converted to a state-space form for control system design. Prior to this, since the resultant finite element model has too many degrees of freedom due to the addition of dissipative coordinates, a model reduction is performed to revert the system back to its original size. Finally, optimal output feedback gains are designed based on the reduced models. Numerical simulations are performed to study the effect of different element configurations, with various spacing and locations, on the vibration control performance of a “smart” flexible ACLD treated beam. Results are presented for the damping ratios of the first two modes of vibration. It is found that improvement on the second mode damping can be achieved by splitting a single ACLD element into two and placing them at appropriate positions of the beam.

Modeling Spatial Rigid Multibody Systems Using an Explicit-Time Integration Finite Element Solver and a Penalty Formulation

2004 ◽  
Author(s):  
Tamer Wasfy
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Matrix ◽  
Explicit Time Integration ◽  
Penalty Formulation ◽  
A New Technique ◽  
Rigid Multibody

A new technique for modeling rigid bodies undergoing spatial motion using an explicit time-integration finite element code is presented. The key elements of the technique are: (a) use of the total rotation matrix relative to the inertial frame to measure the rotation of the rigid bodies; (b) time-integration of the rotational equations of motion in a body fixed (material) frame, with the resulting incremental rotations added to the total rotation matrix; (c) penalty formulation for creating connection points (virtual nodes which do not add extra degrees of freedom) on the rigid-body where joints can be placed. The use of the rotation matrix along with incremental rotation updates circumvents the problem of singularities associated with other types of three and four parameter rotation measures. Benchmark rigid multibody dynamics problems are solved to demonstrate the accuracy of the present technique.

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.

Simplified FEM Model of Paper Machine Roll for Multibody Rolling Contact Analyses

2001 ◽  
Author(s):  
Veli-Matti Järvenpää ◽  
Erno K. Keskinen
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Element Model ◽  
Rolling Contact ◽  
Fe Model ◽  
Test Model ◽  
Paper Machine ◽  
Element Analysis ◽  
Computational Costs

Abstract In this paper a finite element model of a rotating paper machine roll for nip unit rolling contact analyses is discussed. This work presented here is based on the earlier work of the authors presented in [1] and [2]. The major motivations for developing a tailored FE-model including the large spin rotation are firstly to include the complex vibration phenomena as the shell vibrations of the roll structure in the analyses and secondly to reduce the computational costs of the numerical simulations due to the large number of degrees of freedom. The approach used is the use of the modal analysis i.e. to express the dynamics of the roll in terms of the lowest eigenmodes. The equations of motion are at first written in the rotating coordinates and then in addition to this the equations are expressed by using the modal coordinates. Numerical tests executed show that this modeling technique reduces computational costs significantly. Furthermore, use of the (semidefinite) eigenmode basis maintains the vibration characteristics of the roll structure. For verification purposes a test model was constructed and these simulation results were compared to the standard geometrically non-linear finite element analysis.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

scholarly journals APPLICATION OF RIGID LINKS IN STRUCTURAL DESIGN MODELS

2017 ◽  
Vol 13 (3) ◽  
pp. 119-137 ◽  
Author(s):  
Sergey Yu. Fialko
Keyword(s):  
Finite Element ◽  
Structural Design ◽  
Stiffness Matrix ◽  
Sparse Matrix ◽  
Element Model ◽  
Rigid Bodies ◽  
Design Models ◽  
Adjacency Graph ◽  
Direct Solvers ◽  
The Finite Element Model

A special finite element modelling rigid links is proposed for the linear static and buckling analysis. Unlike the classical approach based on the theorems of rigid body kinematics, the proposed approach preserves the similarity between the adjacency graph for a sparse matrix and the adjacency graph for nodes of the finite element model, which allows applying sparse direct solvers more effectively. Besides, the proposed approach allows significantly reducing the number of nonzero entries in the factored stiffness matrix in comparison with the classical one, which greatly reduces the duration of the solution. For buckling problems of structures containing rigid bodies, this approach gives correct results. Several examples demonstrate its efficiency.

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