Model and Method for a Time-Efficient Analysis of Lateral Drillstring Dynamics

2015 ◽  
Author(s):  
Ilja Gorelik ◽  
Marcus Neubauer ◽  
Jörg Wallaschek ◽  
Oliver Höhn
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Element Model ◽  
Steady State Solution ◽  
Contact Forces ◽  
Lumped Parameter Model ◽  
Computational Time ◽  
Operational Parameters ◽  
Real Time Analysis ◽  
Inclined Boreholes

The lumped parameter model and numerical method proposed in this paper aim at gaining a better understanding of the mechanisms leading to harmful lateral drillstring vibrations in inclined boreholes. The shooting method is applied to the equations of motion in order to skip transients and to arrive quickly at a steady state solution. In combination with a sequential continuation technique, parameter maps are generated that show regions where harmful vibrations can be avoided. Comparisons to a finite element model show that the steady state is predicted accurately, while consuming only a fraction of the computational time. The proposed model is experimentally validated on a test rig. Special emphasis is put upon the evaluation of contact forces and the frequency content of the signals. The presented investigations create the basis for real-time analysis of drillstring dynamics and can be used to give recommendations to adjust operational parameters.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

Investigation of Damping Potential of Strip Damper on a Real Turbine Blade

2016 ◽  
Author(s):  
M. Afzal ◽  
I. Lopez Arteaga ◽  
L. Kari ◽  
V. Kharyton
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Element Model ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Bladed Disk ◽  
Different Types

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-free and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

Deformation Index–Based Modeling of Transient, Thermo-mechanical Rolling Resistance for a Nonpneumatic Tire

2013 ◽  
Vol 41 (2) ◽  
pp. 82-108 ◽  
Author(s):  
James M. Gibert ◽  
Balajee Ananthasayanam ◽  
Paul F. Joseph ◽  
Timothy B. Rhyne ◽  
Steven M. Cron
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Finite Element Model ◽  
Rolling Resistance ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Structural Deformation ◽  
Elastic Response ◽  
Full Potential ◽  
Deformation Index

ABSTRACT When competing in performance with their pneumatic counterparts, nonpneumatic tires should have several critical features, such as low energy loss when rolling over obstacles, low mass, low stiffness, and low contact pressure. In recent years, a nonpneumatic tire design was proposed to address each of these critical issues [1]. In this study, the steady state and transient energy losses due to rolling resistance for the proposed nonpneumatic tire are considered. Typically, such an analysis is complex because of the coupling of temperature on the structural deformation and the viscoelastic energy dissipation, which requires an iterative procedure. However, researchers have proposed a simplified analysis by using the sensitivity of the tire's elastic response to changes in material stiffness through a deformation index [2–4]. In the current study, the method is exploited to its full potential for the nonpneumatic tire due to the relatively simple nature of deformation in the tire's flexible ring and the lack of several complicating features present in pneumatic tires, namely, a heated air cavity and the complex stress state due to its composite structure. In this article, two models were developed to predict the transient and steady-state temperature rise. The first is a finite element model based on the deformation index approach, which can account for thermo-mechanical details in the tire. Motivated by the simplicity of the thermo-behavior predicted by this finite element model, a simple lumped parameter model for temperature prediction at the center of the shear band was developed, which in many cases compares very well with the more detailed finite element approach due to the nature of the nonpneumatic tire. The finite element model can be used to, for example, explore the design space of the nonpneumatic tire to reach target temperatures by modifying heat transfer coefficients and/or material properties.

A Computational Investigation of the Disk-Housing Impacts of Accelerating Rotors Supported by Hydrodynamic Bearings

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Jaroslav Zapoměl ◽  
Petr Ferfecki
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Angular Speed ◽  
Contact Forces ◽  
Computational Time ◽  
Radial Clearance ◽  
Lagrange Equations ◽  
Time Step ◽  
Hydrodynamic Bearings ◽  
Nonlinear Force

As the radial clearance between disks and the casing of rotating machines is usually very narrow, excessive lateral vibration of accelerating rotors passing critical speeds can produce impacts between the disks and the housing. The computer modeling method is an important tool for investigating such events. In the developed procedure, the shaft is flexible and the disks are absolutely rigid. The hydrodynamic bearings and the impacts are implemented in the mathematical model by means of nonlinear force couplings. Most of the publications and computer codes from the field of rotor dynamics are referred only in the case when the rotor turns at a constant angular speed and in simple cases of disk-housing impacts. Moreover, if the disks turning at variable speed are investigated, the resulting form of the equations of motion derived by different authors slightly differs and the differences depend on the method used for their derivation. Therefore, particular emphasis in this article is given to the derivation of the motion equations of a continuous rotor turning with variable revolutions to explain the mentioned differences, to develop a computer algorithm enabling the investigation of cases when impacts between an arbitrary number of disks and the stationary part take place, and to analyze the mutual interaction between the impacts and the fluid film bearings. The Hertz theory is applied to determine the contact forces. Calculation of the hydrodynamic forces acting on the bearings is based on solving the Reynolds equation and taking cavitation into account. Lagrange equations of the second kind and the principle of virtual work are used to derive equations of motion. The Runge–Kutta method with an adaptive time step is applied for their solution. The applicability of the developed procedure was tested by computer simulations. The results show that it can be used for the modeling of complex rotor systems and that the short computational time enables carrying out calculations for a number of design and operation parameters.

Comparison of Transient and Steady-State Behaviors in Unwinding Mechanism

2011 ◽  
Author(s):  
Wan-Suk Yoo ◽  
Kun-Woo Kim ◽  
Deuk-Man An ◽  
Jae-Wook Lee
Keyword(s):  
Steady State ◽  
Tensile Force ◽  
Equations Of Motion ◽  
Finite Difference Methods ◽  
Nonlinear Partial Differential Equations ◽  
Inertial Force ◽  
Steady State Solution ◽  
State Solution ◽  
Resistance Force ◽  
Transient Solution

In this study, the transient analysis of a cable unwinding from a cylindrical spool package is first studied and compared to experiment. Then, a steady-state solution is also compared to transient solution. Cables are assumed to be withdrawn with a constant velocity through a fixed point which is located along the axis of the package. When the cable is flown out of the package, several dynamic forces, such as inertial force, Coriolis force, centrifugal force, tensile force, and fluid-resistance force are acting on the cable. Consequently, the cable becomes to undergo very nonlinear and complex unwinding behavior which is called unwinding balloon. In this paper, to prevent the problems during unwinding such as tangling or cutting, unwinding behaviors of cables in transient state were derived and analyzed. First of all, the governing equations of motion of cables unwinding from a cylindrical spool package were systematically derived using the extended Hamilton’s principles of an open system in which mass is transported at each boundary. And the modified finite difference methods are suggested to solve the derived nonlinear partial differential equations. Time responses of unwinding cables are calculated using Newmark time integration methods. The transient solution is compared to physical experiment, and then the steady-state solution is compared to transient solution.

The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 1: Steady-State Response

1996 ◽  
Vol 118 (3) ◽  
pp. 277-284 ◽  
Author(s):  
S. F. Felszeghy
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
State Solution ◽  
Actual Problem ◽  
State Response ◽  
Particular Solution

The response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions are developed in Part 1 of this article for all load speeds greater than zero. It is shown that a steady-state solution which is identically zero ahead of the load front exists at every load speed, in the sense of generalized functions, including the critical speeds when the load travels at the minimum phase velocity of propagating harmonic waves and the sonic speeds. The solution to the homogeneous equations of motion is developed in Part 2 where the two solutions in question are summed and numerical results are presented as well.

A Computational Investigation of the Steady State Vibrations of Unbalanced Flexibly Supported Rigid Rotors Damped by Short Magnetorheological Squeeze Film Dampers

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Jaroslav Zapoměl ◽  
Petr Ferfecki ◽  
Paola Forte
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Steady State Solution ◽  
Squeeze Film ◽  
Damping Force ◽  
Lateral Vibrations ◽  
Lubricating Layer ◽  
Squeeze Film Dampers ◽  
Rigid Rotors

Unbalance is the principal cause of excitation of lateral vibrations of rotors and generation of the forces transmitted through the rotor supports to the foundations. These effects can be significantly reduced if damping devices are added to the constraint elements. To achieve their optimum performance, their damping effect must be controllable. The possibility of controlling the damping force is offered by magnetorheological squeeze film dampers. This article presents an original investigation of the dynamical behavior of a rigid flexibly supported rotor loaded by its unbalance and equipped with two short magnetorheological squeeze film dampers. In the computational model, the rotor is considered as absolutely rigid and the dampers are represented by force couplings. The pressure distribution in the lubricating layer is governed by a modified Reynolds equation adapted for Bingham material, which is used to model the magnetorheological fluid. To obtain the steady state solution of the equations of motion, a collocation method is employed. Stability of the periodic vibrations is evaluated by means of the Floquet theory. The proposed approach to study the behavior of rigid rotors damped by semi-active squeeze film magnetorheological dampers and the developed efficient computational methods to calculate the system steady state response and to evaluate its stability represent new contributions of this article.

Experimental and numerical study of friction and .giffness characteristics of small rolling tires

2011 ◽  
Vol 39 (1) ◽  
pp. 5-19 ◽  
Author(s):  
R. van der Steen ◽  
I. Lopez ◽  
H. Nijmeijer
Keyword(s):  
Steady State ◽  
Numerical Study ◽  
Complex Structure ◽  
Element Model ◽  
Steady State Solution ◽  
Experimental Results ◽  
Small Scale ◽  
The Road ◽  
Rubber Compounds ◽  
Complex Measurement

Abstract Virtual testing is nowadays the standard in the design process of new tires. Besides modeling the static response of the tire itself, the dynamics of a rolling tire in contact with the road needs to be incorporated. Due to the uncontrollable environmental conditions and the complex structure of the tires, it is advantageous to use small-scale testing under more controlled conditions. Experimental characterization of frictional properties of rubber compounds is, however, limited due to the necessity of complex measurement systems. In this paper a commercially available laboratory abrasion and skid tester is used to ide.gify both friction and .giffness characteristics of the same rubber compound. The obtained friction properties are implemented in a finite element model of the setup, and different validation steps are presented. Finally, a steady-state transport approach is used to efficiently compute a steady-state solution, which is compared with the experimental results. The numerical results show a good qualitative agreement with the experimental results.

Stability of Motion of Elastic Planar Linkages With Application to Slider Crank Mechanism

1982 ◽  
Vol 104 (4) ◽  
pp. 698-703 ◽  
Author(s):  
I. G. Tadjbakhsh
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
Critical Values ◽  
Length Ratio ◽  
Viscous Damping ◽  
Stability Of Motion ◽  
Start Up ◽  
Planar Linkages ◽  
Crank Mechanism

The problem of stability of motion of elastic planar linkages is considered in the context of the classical Euler-Bernoulli equations of motion. The case of slider-crank mechanism is considered in detail and the critical values of the dimensionless parameters measuring slenderness, speed, and length ratio which may cause instability are determined. The start-up and the steady-state solution of the mechanism without viscous damping and the effects of flexibility on piston force and efficiency is evaluated.

scholarly journals Performant and Simple Numerical Modeling of District Heating Pipes with Heat Accumulation

Energies ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 633 ◽  
Author(s):  
Libor Kudela ◽  
Radomir Chylek ◽  
Jiri Pospisil
Keyword(s):  
Numerical Modeling ◽  
Method Of Lines ◽  
Time Integration ◽  
District Heating ◽  
Steady State Solution ◽  
Computational Time ◽  
Distribution Grid ◽  
Operational Parameters ◽  
Heat Accumulation ◽  
Physical Phenomena

This paper compares approaches for accurate numerical modeling of transients in the pipe element of district heating systems. The distribution grid itself affects the heat flow dynamics of a district heating network, which subsequently governs the heat delays and entire efficiency of the distribution. For an efficient control of the network, a control system must be able to predict how “temperature waves” move through the network. This prediction must be sufficiently accurate for real-time computations of operational parameters. Future control systems may also benefit from the accumulation capabilities of pipes. In this article, the key physical phenomena affecting the transients in pipes were identified, and an efficient numerical model of aboveground district heating pipe with heat accumulation was developed. The model used analytical methods for the evaluation of source terms. Physics of heat transfer in the pipe shells was captured by one-dimensional finite element method that is based on the steady-state solution. Simple advection scheme was used for discretization of the fluid region. Method of lines and time integration was used for marching. The complexity of simulated physical phenomena was highly flexible and allowed to trade accuracy for computational time. In comparison with the very finely discretized model, highly comparable transients were obtained even for the thick accumulation wall.

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