Motion Of String Research Articles

Investigating Drillstring Vibration and Stability in Coring Drilling

Transverse vibration of drillpipe in coring drilling is undesirable. Here, the influence of the core on drillpipe vibration is considered for the first time. Attention is focused on the vibrations of the coring drillpipe as these vibrations lead to contact and collision between drillpipe and core. A reduced-order model of drill string motion is established considering fluid load and core constraints. This model considers fluid action as distributed load and drillpipe as beam structure. The constraint of the core on lateral vibration of the drillpipe is simplified as a nonlinear force. The method of multiple scales is used to analyze the disturbance of the drillpipe’s primary resonance and harmonic resonance, and the influence law of different parameters on the drillpipe resonance is obtained. The results show that damping inhibits resonance vibration, and external excitation determines the resonance type. The existence of the core will aggravate the resonance vibration of the drillpipe. The analysis results are helpful in understanding the resonance of the drillpipe in coring drilling. Some measures to suppress resonance are given in this paper. This study can provide guidance for further research on drillpipe resonance in core drilling.

Global classical solutions of a kind of boundary value problem for quasilinear hyperbolic systems

In this paper, we consider a stability problem of a kind of boundary value problem for quasilinear hyperbolic systems. For small boundary data, we prove that the solution exists globally in time when the system is weakly linearly degenerate. In the special case of linear degeneracy, the smallness assumption on the boundary data is weakened. The error estimate in space between two different solutions with different boundary data is also obtained. In our proof, an important estimate which describes the interaction of different waves is established by constructing a continuous Glimm function. This estimate together with uniform a prior estimates with respect to the time leads to the global‐in‐time existence of smooth solutions. Finally, we apply the stability results to the isentropic Euler equations and the system of the motion of an elastic string.

Numerical analysis of drill string whirl for vertical well based on rolling model and small-strain shell element

Whirl is a kind of serious lateral vibration. Accurate numerical simulation of whirl for drill string is important for drilling engineering. In this study, a new finite element (FE) model using shell element is established, which can accurately describe the whirl and realize the visualization of motion. Rolling model of drill string in the borehole is proposed. Kinematic contact with clearance, Coulomb friction model and initial imperfection are considered in this model. The explicit dynamic method is selected to solve the convergence difficulty caused by complex contact between shell elements. Compared with the experiment results, the accuracy and reliability of the model are verified. Meanwhile, the effects of rotation speed, friction coefficient, weight-on-bit (WOB) and clearance between the drill string and the borehole wall on the whirl of vertical wells are also studied in the numerical simulation. The rotation speed and friction coefficient have an obvious positive effect on the random motion and backward whirl of drill string: The continuous increase of rotation speed or friction coefficient can cause backward whirl, after that, velocity, acceleration of drill string, contact force and friction will increase significantly. When the rotating speed increases from 400 rpm to 800 rpm, the whirling speed increases by 160%, the average friction and contact force increase by 290%, which is much higher than the increase of 100% of the rotating speed. Instead, WOB has little influence on the drilling parameters mentioned-above and the variations of average friction and contact force for different WOB does not exceed 10%. In addition, properly increasing the distance between the drill string and the borehole wall will make backward whirl easily occur. However, when the clearance is large enough, there will be no contact and the drill string will make irregular non-contact forward whirl. What's more, forward whirl has a positive impact on eccentric wear, and backward whirl reduces WOB transmission and increases risk of sticking. Therefore, drill string whirl should be reasonably utilized or its harm should be reduced in practical drilling engineering.

Null cosmic strings: Scattering by black holes, optics, and spacetime content

Equations of motion of null cosmic strings near black holes, or other massive sources, are solved exactly in the weak field approximation. The stress-energy tensor of a null string in a curved spacetime is introduced and used to show how scattering by black holes transforms linear and angular momenta of the string. The corresponding recoil effect of a black hole and change of its angular momentum caused by a null cosmic string are calculated. For a null string, its energy $\mu$ per unit length evolves along the null direction of the string trajectory. The evolution of $\mu$ is connected with a string optical scalar $Z$. Optical properties of null strings are that their energy is concentrated on caustics, where $Z$ has poles. String parameters $\mu$ and $Z$ capture important features of the spacetime where strings move. Explicit dependence of $\mu$ and $Z$ on the strain and Bondi news tensors of gravitational wave background, mass and angular momentum aspects are established, near the future null infinity, up to the 4-th order in expansion in an inverse null parameter in asymptotically flat spacetimes.

A study of the heave-induced surge and swap pressures when a drillstring is in the slips of a floating vessel

This study presents a theory describing surge and swab pressure when a drillstring is hanging in the slips of a heaving vessel. Downhole pressure measurement shows high pressure pulses in these instances, higher than can be explained with simple steady-state calculation. Several factors and parameters affect this pressure, such as annulus geometry, drillstring elasticity, wellbore friction, fluid compressibility, advanced fluid rheology, and fluid inertia. The advanced fluid rheology includes a flow-development phase and a simple fluid thixotropy model. The theoretical model is tested and compared with actual field data recorded at the surface and downhole, both pressure and string acceleration are measured. Key findings from this study are: (1) The annular flow is induced by the axial stick–slip motion of the bottomhole assembly; (2) The surge swab pressure consists of a pressure-loss term and an inertia term, where the latter is the dominating one in this case; (3) The short periods of the axial string motion call for a transient analysis to get an accurate estimate of the pressure amplitude. • Transient surge and swab model. • Stick slip induced pressure pulses. • Fast model for thixotropy and flow pattern development. • High resolution downhole measurements. Both string acceleration and downhole pressure.

Nonintegrability for N=1 SCFTs in 5D

We explore the \emph{Liouvillian} non-integrability criteria for long quiver gauge theories those preserve $ \mathcal{N}=1 $ SUSY in $ 5d $. We probe type IIB solutions with (an $ AdS_6 $ factor) semi-classical strings which capture the strong coupling dynamics of $ \mathcal{N}=1 $ SCFTs in $ 5d $. Our analysis reveals an underlying non-integrable structure within some sub-sector of these $ 5d $ SCFTs. To solidify our claim, we complement our analytic results through numerics. We estimate various chaos indicators for the phase space which confirm the onset of a \emph{chaotic} motion for these type IIB strings.

Toward a physical model of the clavichord.

String excitation by the tangent in the clavichord is a unique mechanism. The tangent, keeping in contact with the string after the initial strike, continuously controls the string tension. Four main flexible subsystems are considered in the clavichord: the tangent/key subsystem, the string subsystem, the bridge-soundboard subsystem, and the string damper subsystem. A modal description of the dynamics of these subsystems is proposed. Parameters of the subsystems are estimated on a copy of a historical instrument by Hubert (1784). The different subsystems and their couplings are modeled using a modal Udwadia-Kalaba formulation. The string-tangent interaction is modeled via the intermittent contact dynamics, using the Kirchoff-Carrier string model. Realistic string, soundboard, and tangent motions are obtained using a time-domain synthesis scheme that computes the dynamics of the uncoupled subsystems and the constraints resulting from coupling between them. Simulated motions of the model in response to a driving force on the key are analyzed. The results are consistent with experimental measurements and published data on the dynamics of the clavichord. The model is able to reproduce the main acoustic features of the instrument: force on the key for intonation control, key velocity for dynamic nuances control, and constant spectral slope for varying dynamic nuances.

From the Galileo Free Fall String to the Principle of Equivalence

We consider the string with the length l, the left end and the right end of which is non relativistically accelerated by the constant acceleration a. We calculate the motion of such string and then the motion of the Galileo free fall string in gravity. The solutions are not identical. So, we distinguish between noninertial field and the gravity field and we discuss the principle of equivalence. In conclusion we suggest to drop charged objects from the very high tower Burj Khalifa in order to say crucial words on the principle of equivalence.

Optimal control of deep petroleum borehole trajectory tracking

• A new problem of optimal tracking of a deep borehole trajectory is posed. • Target functions related to the hole smoothness, cost, and length are considered. • Optimal nonlinear control methods and gradient projection method are jointly used. • Examples of the optimal smoothing of deep projected trajectories are discussed. This paper is concerned with the application of optimal control theory to the problem of tracking deep oil and gas borehole trajectories. Based on the methods of differential geometry, the mathematical model of the trajectory curve with its curvature representing controlling variable is elaborated in the form of ordinary differential equations: The objective functional chosen as integral curvature, length or cost of the borehole are considered. The techniques for the optimization problem solving are developed with the use of the continuous version of the step-by-step anti-gradient projection on the hyper-planes of linearized constraints. At every step of the minimization procedure, the constraints spoilt by the linearization operations are restored through the use of the Newton method. Some examples are considered for a borehole with fixed and shifting boundary positions under conditions of minimizing its total curvature and length. It is shown that it is possible to improve the smoothness of the borehole trajectory using the outlined approach, and in so doing, reduce the friction and resistance forces impeding the drill string motion.

Celestial fields on the string and the Schwarzian action

This paper describes the motion of a classical Nambu-Goto string in three-dimensional anti-de Sitter spacetime in terms of two ‘celestial’ fields on the worldsheet. The fields correspond to retarded and advanced boundary times at which null rays emanating from the string reach the boundary. The formalism allows for a simple derivation of the Schwarzian action for near-AdS2 embeddings.

Invariant analytical solutions for the motion of an elastic string with electric current in a static magnetic field

In this work, the Lie symmetry theory is used to study the propagation of waves in an elastic string with electric currents in a static magnetic field. Both linear and nonlinear cases of the governing equations of string motion are analyzed. The classification problem of finding the principal admitted Lie groups of symmetries is solved. Some invariant analytical solutions are constructed. The physics of invariant solutions is interpreted when it is possible.

Pair-production of cusps on a string in AdS3

The classical motion of a Nambu-Goto string in AdS3 spacetime is governed by the generalized sinh-Gordon equation. It can locally be reduced to the sinh-Gordon (shG), cosh-Gordon (chG), or Liouville equation, depending on the value of the scalar curvature of the induced metric. In this paper, I examine solutions that contain both shG-type and chG-type regions. The boundary between these regions moves with the speed of light. I show that near such boundaries (generalized) solitons can be classically pair-produced. The solitons move subluminally (superluminally) in the shG (chG) region on the worldsheet, and they correspond to cusps on the string. A direct energy cascade is observed at the moment of pair-creation.For the calculations, I use an exact discretization of the equation of motion. The solutions are segmented strings. In this discrete system, pair-production leads to a complete evaporation of the shG region. The final state is a gas of cusps in a chG environment.

유한요소법을 이용한 방향성 시추의 동적 분석과 ROP계산

The motion of the drill string along the excavation trajectory was analyzed using the Lagrangian approach with the finite-element method (FEM). The circular cross section of the drill string was constructed by joining multiple circular axes, each with 12 degrees of freedom (DOF). FEM analysis reveals vibration and dynamic changes of the entire drill string, and comprehensive boundary conditions can be easily applied to reproduce the simulation of the actual drill string. To apply the FEM program to the actual drill trajectory, the dynamic analysis of the curved beam was compared with the actual value, and the dynamic behavior of the beam was verified by comparing the frequency-domain and time-domain analyses. The performance observed after applying FEM dynamic analysis to the operating conditions corresponding to the actual drilling site, was similar to the results observed in related research papers. Therefore, this method can be used as a dynamic model for developing a simulator for drilling control.

Numerical simulation of plane flow field and the force on the inner rod induced by planetary motion of the rod string

In order to a the flow of the plane flow field induced by the inner rod rotates and revolves in the cylinder, the Fluent software is used to numerically simulate the plane flow field of the eccentric annulus generated by the planetary motion of the rod string and based on the superposition principle. The velocity distribution and secondary flow of the two flow fields, as well as the fluid force on the inner rod are analyzed. The calculation results show that the flow field induced by the eccentric rotation of the inner rod and the self-rotation of the outer cylinder is quite different from the planetary motion of the inner rod. When rotation of the inner rod has the same direction with the revolution direction, the fluid velocity distribution near the wall of the inner rod is that the velocity on the narrow space side of the annulus is large, and on the wide space side is small. There is a critical value of eccentricity for secondary flow appears when the eccentricity is greater than this value. When rotation of the inner rod is contrary to the revolution, the fluid velocity distribution near the wall of the inner rod is that the velocity on the wide space side of the annulus is large, on the narrow space side is small. Different eccentricity has obvious secondary flow phenomenon where appears in a wide gap and close to the inner rod. When the inner rod revolves, there is a critical value of eccentricity, the inner rod is pushed outward by the fluid force when the eccentricity is less than this critical value. On the contrary, the inner rod is pushed inward. When rotation and revolution are reversed, the critical value of eccentricity increases, when the rotation and revolution are in the same direction, the critical value of eccentricity decreases.

Расчет нагрузки на штанговую подвеску при неустановившемся колебательном движении штанг скважинной насосной установки

The efficiency of a rod pumping unit is determined by the straightness of its rod string, which is impacted by the load when the rod string is in motion. Determining the dependence of the load impacting the rod suspension on the dynamic forces is one of the major issues in ensuring its straightness. In order to provide equal distribution of the stresses along the entire length of the polished rod under dynamic loading, it is necessary to determine the load on its surface, which is impossible without the equation of unsteady motion of the rod string. To this end, the article examines the issues related to the equation of unstable motion of well pumping unit rods. Formulae for calculating the loads acting on the rod suspension point are derived, and the equation of the rod string motion and load on the polished rod after the initial deformation is obtained.

Dynamic manipulation of unknown string by robot arm: realizing momentary string shapes

We propose a method to realize the dynamic manipulation of a string with unknown characteristics via a high-speed robot arm. We use a mass-spring-damper model for the string and repeat three steps: motion generation, real manipulation, and parameter estimation. Robot motion is given by the joint angular velocities expressed by the Bezier curves. Their control points are randomly positioned to generate various robot motion for dynamic string manipulation. The generated motion is performed by a wire-driven robot arm and, real string movement is captured by the camera. These time-series images are used for the parameter estimation of string. The best parameter set is determined via comparison between real and simulated string movement after changing parameter randomly and logarithmically. This parameter set is not unique, but it simulates the actual string movement well. Since the estimated string parameter is used for the robot motion generation after repeating the above 3 steps, the motion generation reflects string property and motion objective can success without special tests in advance. This is an advantage of our method because it is difficult to know all of string property with very complicated non-linearity beforehand. We focus on realizing the momentary string shape in 2 dimensions in this paper. We confirmed the effectiveness of our proposed method by realizing five momentary shapes and 3 kinds of string properties. We also discussed the reproducibility and compatibility of estimated parameters and motion generation.

Bulk and surface topological indices for a skyrmion string: current-driven dynamics of skyrmion string in stepped samples

The magnetic skyrmion is a topological magnetic vortex, and its topological nature is characterized by an index called skyrmion number which is a mapping of the magnetic moments defined on a two-dimensional space to a unit sphere. In three-dimensions, a skyrmion, i.e., a vortex penetrating though the magnet naturally forms a string, which terminates at the surfaces of the magnet or in the bulk. For such a string, the topological indices, which control its topological stability are less trivial. Here, we study theoretically, in terms of numerical simulation, the dynamics of current-driven motion of a skyrmion string in a film sample with the step edges on the surface. In particular, skyrmion–antiskyrmion pair is generated by driving a skyrmion string through the side step with an enough height. We find that the topological indices relevant to the stability are the followings; (1) skyrmion number along the developed surface, and (2) the monopole charge in the bulk defined as the integral over the surface enclosing a singular magnetic configuration. As long as the magnetic configuration is slowly varying, the former is conserved while its changes is associated with nonzero monopole charge. The skyrmion number and the monoplole charge offer a coherent understanding of the stability of the topological magnetic texture and the nontrivial dynamics of skyrmion strings.

Nonintegrability of La,b,c quiver gauge theories

We show that the $AdS_5 \times L^{a,b,c}$ solution in type IIB theory is non-integrable. To do so, we consider a string embedding and study its fluctuations which do not admit Liouville integrable solutions. We, also, perform a numerical analysis to study the time evolution of the string and compute the largest Lyapunov exponent. This analysis indicates that the string motion is chaotic. Finally, we consider the point-like limit of the string that corresponds to BPS mesons of the quiver theory.

Study the system with innovative rotor control in drilling of deviated and horizontal wells

Controllable rotor systems are the innovation of the drilling tool enabling to manage the well path decreasing failure and complication risk. The rig in this system moves by set path with continuous motion of drill string. The rotation of drilling tool provides the effective well cleaning, reduces the drilling tool sticking and allows drilling deep wells and those with complicated profile compared to the drilling with bottomhole engine. The most complicated circumstance for obtaining required drilling rate is the maintenance of enough load transmission from the earth surface to the rig regardless the boundary conditions between the well and drilling tool.

Investigation of the Helmholtz Motion of a Violin String: A Finite Element Approach

Abstract In the context of this work, a violin string motion is examined using a finite element approach. The string is formulated via ideal string elements and is bowed at one point on the string; hence, there is a nodal contact between the bow and the string. The bow movement induces the stick-slip effect, which is the cause for the violin string sound. The present paper aims at the investigation of the stick-slip phenomenon of bowed strings, considering well-known bowed string effects like the Helmholtz corner modulation, the Schelleng ripples, and the flattening effect. One key element that is used in this work is the Schelleng diagram, which indicates the “perfect” bow force depending on the bowing position. Within these parameters, the Helmholtz motion is carried out. Additionally, different friction characteristic curves are applied in order to study the impact of the rosin on the string motion.