井筒内受压杆管后屈曲能量法分析与实验研究

目前不少理论力学教材都涉及刚体平面运动动力学方程的教学内容,但有些教材在叙述上有许多值得商榷之处.对这一重要的基本概念,本文提出作者的思考,供理论力学教学的教师与学过此内容的学生讨论.     

Critical states of drill strings in the channels of inclined boreholes

The problem of determining the critical states and the postbuckling deformation of drill strings in the cavities of curvilinear boreholes is posed. The process of elastic bending of the drill string is associated with the motion of its axial line along the corresponding channel surface. On the basis of the theory of flexible curvilinear rods, a specially chosen moving system of axes is used to construct nonlinear ordinary differential equations describing the contact interaction between the drill string tube and the borehole wall. Themoving reference system allows us to separate the desired variables and decrease the order of the resolving equations. As an example, we solve the problem of stability of drill strings lying at the bottom of a cylindrical cavity in a rectilinear inclined borehole. The critical values of the axial forces are determined and the buckling modes are constructed. It is also shown that they have the form of edge effects typical of singularly perturbed equations. The developedmethods can be used in design of a curvilinear borehole and its possible driving conditions to determine the admissible values of the axial force and the torque at the point of the drill string suspension so as to prevent its bifurcation buckling.     

铅直圆筒内细长杆柱在屈曲位移激励下的横向振动仿真1)

对于铅直圆筒内受交变拉压轴向载荷作用的细长杆柱,当杆柱底端所受到的轴向压力大于杆柱屈曲的临界载荷时,细长杆柱在圆筒内将产生螺旋屈曲,杆柱的屈曲变形将激励杆柱在圆筒内产生横向振动。以细长杆在圆筒内的瞬时屈曲构型作为杆柱横向振动的位移激励,建立了屈曲位移激励下的细长杆在圆筒内横向振动与杆管碰撞规律的仿真模型。采用有限差分法对井深进行离散,Newmark 法对时间进行离散,以恢复系数法建立了细长杆和圆筒的碰撞条件,对细长杆在圆筒内的横向振动数学模型进行了数值仿真。仿真结果表明,细长杆和圆筒内壁的碰撞现象主要发生在细长杆底端受压发生屈曲后,且几乎沿整个圆筒都有发生,从圆筒顶部至底部的碰撞力峰值逐渐增大;而在杆柱底端受拉时碰撞现象很少,碰撞力也较小。     

Controlling torsional vibrations of drill strings via decomposition of traveling waves

Torsional vibrations in drill strings, especially stick-slip vibrations, are detrimental to the drilling process as they slow down the rate of penetration and may lead to failure of the drilling equipment. We present a method for controlling these vibrations by exactly decomposing the drill string dynamics into two traveling waves traveling in the direction of the top drive and in the direction of the drill bit. The decomposition is derived from the wave equation governing the string vibrations and is achieved with only two sensors that can be placed directly at the top drive and at a short distance below the top drive (e.g., 5 m). Therefore, downhole measurements along the string and at the bit are not necessary, which is a major advantage compared to other control concepts for drill string dynamics. The velocity of the top drive is then controlled in order to absorb the wave traveling in the direction of the top drive, thus achieving a reflection coefficient of zero for the frequency range of the undesired torsional vibrations. The proposed algorithm is implemented for both a numerical example and an experimental setup; results show that the control concept works very effectively.     

Dynamics of rotating conveying mud drill string subjected to torque and longitudinal thrust

In the view of fluid-structure interactions and rotor dynamics, this paper models the lateral vibration of a vertical downward rotating elastic drill string conveying mud subjected to supporting stabilizers, bit torque and longitudinal thrust. The dynamic model involves the rotational inertia of the drill string tube cross section, the gyroscopic effect caused by rotation, the damping due to friction with the surrounding fluid, the gravity force and mud buoyancy. Damped natural frequency, stability and resonance of the drill string system are determined by quadratic eigenvalue problem and investigated at influences of the stabilizer, rotational angular speed, mud flowing velocity, bit torque and thrust. As a result, the drill string can lose stability both at simultaneous and separate influences of the mud conveying, bit torque and thrust, whereas the rotation, stabilizer and gravity of the drill string can improve system stability; the rotational angular speed causing system resonance decreases with the increase of the mud flowing velocity, bit torque and thrust.     

钻柱振动信息测量技术研究进展

随着深井、超深井数量的快速增加, 钻柱振动导致的钻具失效问题更加突出. 针对钻柱振动的研究可分为理论与数值模拟、测量分析两种方法. 由于钻柱振动具有复杂的非线性特征, 使得理论与数值模拟研究受到了很大限制, 因此井下振动测量技术的研究显得尤为重要. 本文比较全面和系统地介绍了国内外钻柱振动测量技术研究现状和进展情况, 并对几个应用较为成熟的国外测量系统的工作原理、分析方法及应用技术进行了详细的综述. 所得结论可为我国井下振动测量技术的发展提供重要参考.     

Ball spin generation for oblique impacts with a tennis racket

In this paper, we describe an experimental investigation of the oblique impact between a tennis ball and head clamped tennis racket. It was found that the magnitude of the ball rebound spin was not a function of the material, gage or tension of the string used in the tennis racket. Furthermore, it was concluded that all strings exhibit a sufficiently large friction coefficient that the ball begins to roll during impact. There is anecdotal evidence from tennis players that suggests that a high string tension or a rough string surface enable them to impart more spin to the ball. For example, players have been quoted as saying that a high string tension makes the strings “bite” into the ball, giving more spin. The data reported in this study do not support these observations. Analysis of the experimental data has shown that the balls are rebounding from the surface with more spin than would typically be associated with rolling. A second experiment showed that the balls commenced rolling at the mid-point of the impact. This information was used in a theoretical model to show that the spin that acts on the ball during the impact can be higher than the value of the rolling spin at the end of the impact.     

Non-linear buckling analysis of inclined circular cylinder-in-cylinder by the discrete singular convolution

The lateral buckling and helical buckling problem of a circular cylinder constrained by an inclined circular cylinder under a compressive force, torsion, and its own weight is complicated and difficult to obtain an exact analytical solution. Thus, the non-linear differential equation is solved incrementally using the discrete singular convolution (DSC) algorithm together with the Newton–Raphson method. Detailed formulations are worked out. A simple way to numerically simulate the helical buckling is proposed and solution procedures are given. Four examples with various inclined angles, weights per unit length of the inner cylinder, axial applied loads, and boundary conditions are investigated. To verify the formulations and solution procedures, comparisons are firstly made with data obtained using the finite element method. It is verified that under certain circumstance, only lateral or helical buckling alone will occur. On some other circumstance, both lateral buckling and helical buckling may occur and the critical helical buckling loads are higher than the critical lateral buckling loads if frictions are not considered. Some conclusions are made based on the results presented herein.     

Spatially complex localisation in twisted elastic rods constrained to a cylinder

We consider the problem of a long thin weightless rod constrained to lie on a cylinder while being held by end tension and twisting moment. Applications of this problem are found, for instance, in the buckling of drill strings inside a cylindrical hole. In a previous paper the general geometrically exact formulation was given and the case of a rod of isotropic cross-section analysed in detail. It was shown that in that case the static equilibrium equations are completely integrable and can be reduced to those of a one-degree-of-freedom oscillator whose non-trivial fixed points correspond to helical solutions of the rod. A critical load was found where the rod coils up into a helix.Here the anisotropic case is studied. It is shown that the equations are no longer integrable and give rise to spatial chaos with infinitely many multi-loop localised solutions. Helices become slightly modulated. We study the bifurcations of the simplest single-loop solution and a representative multi-loop as the aspect ratio of the rod's cross-section is varied. It is shown how the anisotropy unfolds the `coiling bifurcation'. The resulting post-buckling behaviour is of the softening–hardening–softening type typically seen in the cellular buckling of long structures, and can be interpreted in terms of a so-called Maxwell effective failure load.     

液压作用下套管柱临界屈曲载荷计算的能量法

推导了内外液压作用下套管柱微弯时的能量平衡公式,并计算了其屈曲临界载荷计算公式。得到的结果低于目前已发表的结果。内外液压对套管稳定性的影响相当于在套管底端作用一个附加的轴向力和一个沿轴线均布的线载荷。对含有内压的两端封堵的细长管柱,内压对临界屈曲载荷没有影响。结果可供油井设计及作业参考。     

Energetics and conserved quantity of an axially moving string undergoing three-dimensional nonlinear vibration

Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quantity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invariance of the conserved quantity.     

井下管柱力学与控制方法若干研究进展

关于井下管柱力学的研究迄今已有七十多年的历程, 取得了许多重要的研究成果, 并主要在油气井工程中获应用实效. 然而, 由于井眼约束和作业工况的复杂性, 目前仍未能够全面而准确地揭示井下管柱在狭长井眼内的复杂力学行为, 导致相关工程设计控制方法难以解决好实际遇到的许多复杂问题. 本文回顾了井下管柱力学的整体发展脉络, 重点讨论井下管柱的静力学变形控制方程, 然后针对井下管柱力学中的几个重要科学问题, 包括井下管柱屈曲、井下管柱摩阻磨损、井下管柱安全作业极限和底部钻具组合力学特性及其相应的设计控制方法等, 分别简要介绍了相关研究进展、最新研究成果及存在的一些问题等, 并在一定程度上进行了总结与展望, 以期为井下管柱力学与控制方法的创新发展并促进油气井工程技术进步提供有益参考.      

复合材料结构力学分析CAE软件现状

复合材料结构分析软件是用以分析、设计复合材料结构的重要工具,常用的复合材料结构分析软件包括基于CAD软件发展而来的复合材料分析工具、通用有限元软件自带复合材料分析工具和以Digimat等为代表的专业化复合材料结构分析软件。本文对常用的复合材料分析软件进行了综述,介绍其主要功能,从学术、应用等多方面探讨相关产品的优点及不足;论述了专业化复合材料结构分析软件的特点及功能;分析了复合材料结构分析软件的现状和发展趋势;探讨了复合材料结构力学分析CAE软件在国产化方面所需进一步解决的问题。     

隔水管弯曲对钻柱振动影响的计算与分析

海洋油气资源钻探中隔水管的弯曲对钻柱振动以及钻进特性有特别的影响。为得到隔水管弯曲对钻柱振动的影响规律,对南海已钻深水井使用非线性有限元软件建立全井钻井数值计算模型,研究获得了不同垂深时隔水管弯曲对钻柱振动特性的影响规律。研究表明:隔水管弯曲会加剧钻柱的振动,钻柱振动加剧会导致钻井能耗上升、钻头切削能力下降并且会加快钻柱疲劳;当隔水管的弯曲达到某临界值,钻柱与隔水管间的接触力会陡增;井口的钩载越大,隔水管弯曲带来的井口钩载波动量越大;井越深,隔水管弯曲对全井钻柱最大弯矩和钻头切削能力的影响越小。     

水平圆管中受压扭作用管桩屈曲后的解析解

首先建立了考虑自重、受水平圆管约束的管柱在压担组合作用下的屈曲方程：此方程为四阶强非线性常微分方程,难以直接精确求解;通过管柱的正弦屈由分析,找到了方程中的小参数;利用小参数摄动法求解了强非线性屈曲方程,得到了管柱螺旋屈曲后的实际屈曲构形解析解,由此可进一步得到管柱发生螺旋屈曲的临界载荷;所得解析结果与数值计算结果及本文结果退化后与文献中的相关结果比较都有良好的一致性．     

基于颗粒物质力学的铁粉末压制中摩擦特性对力链演化影响

结合颗粒物质力学理论,通过离散元法实现铁粉末压制过程模拟并通过压制方程进行验证,针对粉末体系中的力链演化问题,提出力链特征定量分析方式,进一步通过分析不同颗粒间摩擦系数、侧壁摩擦系数与颗粒运动状态转变的方式,探讨摩擦特性对力链量化特征的影响,从而建立摩擦行为与力链演化间的联系. 研究结果表明:随颗粒间摩擦系数增大,整体力链数目变少,力链方向系数、承载不均匀度及单位屈曲度均变大,而随侧壁摩擦系数增大,力链特征差异较小,则颗粒间摩擦系数较侧壁摩擦系数对力链特征演化具有更显著影响. 同时发现,颗粒接触状态的改变与力链特征演化间具有对应性. 研究成果将进一步拓展粉末压制中考虑摩擦行为及力链演化过程在内的粉体致密化行为理论.      

Free vibration/buckling analyses of noncylindrical initially compressed helical composite springs

This article presents the use of the stiffness matrix method based on the first-order shear deformation theory to predict the fundamental natural frequencies and buckling loads of noncylindrical unidirectional composite helical springs subjected to initial static axial force and moment. This theoretical study about such springs with circular/rectangular cross-sections and large pitch angles is performed for the first time in the literature. The validity of the present results is verified by the benchmark studies related with initially compressed isotropic cylindrical springs.     

气体钻井中接触非线性问题的数值算法研究

根据动量守恒和钻柱力学的基本理论,建立了气体钻井三维弯曲井眼钻柱动力学模型和钻柱与井壁接触碰撞模型;提出了一种求解钻柱与井壁接触非线性有限元方程的元胞自动机算法。该方法具有编程简单、收敛速度快等优点,以实际工况为例进行仿真模拟,选取有代表性节点的仿真计算结果并加以分析。仿真结果表明:该方法较好地解决了三维弯曲井眼中钻柱与井壁接触碰撞的复杂边界条件问题,在解决气体钻井钻柱与井壁接触非线性问题的研究中具有良好的应用前景。     

井筒内杆管柱双层接触有限元分析及应用

构造双层多向接触间隙元描述细长油管柱与内外杆管柱的随机接触摩擦问 题,与空间梁单元相结合,采用变刚度与等刚度交替方式求解,得出抽油杆柱与油管柱以及 油管柱与套管柱的接触状态、接触位置、摩阻力大小以及抽油杆柱与油管柱在任意井深处的 广义内力、应力和变形. 三口井算例表明,抽油杆柱与油管柱的井口悬重误差低 于10{\%}, 能够为抽油杆和油管柱设计和失效分析提供可靠的计算方法和理论依据.     

A Material Momentum Balance Law for Rods

A material momentum balance law is presented in this paper where it is also specialized for a variety of rod and string theories. The local form of the law is assumed to be identically satisfied, while the jump condition provides an extra equation which is often needed to solve problems involving the application of rod and string theories. The balance law is also related to several existing conservation laws for strings and rods, including Kelvin’s circulation theorem. A novel identity for the singular sources at a discontinuity is also established. Dedicated to James N. Flavin, my friend and mentor, on the occasion of his 70th Birthday.