Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

In this article, a discrete model of a drill-string system is developed taking into account stick-slip and time-delay aspects, and this model is used to study the nonlinear motions of this system. The model has eight degrees-of-freedom and allows for axial, torsional, and lateral dynamics of both the drill pipes and the bottom-hole assembly. Nonlinearities that arise due to dry friction, loss of contact, and collisions are considered in the development. State variable dependent time delays associated with axial and lateral cutting actions of the drill bit are introduced in the model. Based on this original model, numerical studies are carried out for different drilling operations. The results show that the motions can be self-exited through stick-slip friction and time-delay effects. Parametric studies are carried out for different ranges of friction and simulations reveal that when the drill pipe undergoes relative sticking motion phases, the drill-bit motion is suppressed by absolute sticking. Furthermore, the sticking phases observed in this work are longer than those reported in previous studies and the whirling state of the drill pipe periodically alternates between the sticking and slipping phases. When the drive speed is used as a control parameter, it is observed that the system exhibits aperiodic dynamics. The system response stability is seen to be largely dependent upon the driving speed. The discretized model presented here along with the related studies on nonlinear motions of the system can serve as a basis for choosing operational parameters in practical drilling operations.     

井下多股淹没射流水力清岩能力分析

研究石油钻井井下射流的水力清岩能力对钻井业有重要意义。本文借助于预处理方法和多块网格对接技术由计算机数值模拟了形状复杂的钻井PDC钻头井底下的多股淹没射流流场。为体现井底有岩屑时射流场对其的清洗作用。文中借助河流泥沙运动理论，分析了岩屑在井下的受力与运动以考虑固相的作用。因岩屑主要为推移运动。在井底除环空外的大部分地方可简化视为二维运动。提出了钻头井底水力清岩能力的体现参数-水力挟岩力。并通过数值模拟显示了井下流场，描述了转速，射流流量，喷嘴面积，射流雷诺数及井下过流空间等流场控制参数对井底水力清岩能力的不同影响，指出相关水力参数在射流时的优化方向。为复杂的井底流场控制和钻头的合理设计做探索基础。     

Quantized attractors in wave models of torsion vibrations of deep-hole drill strings

We pose the problem of self-excitation of elastic wave torsional vibrations of a rotating drill string, which arise as a result of frictional interaction of the drill bit with the rock at the bottom of the deep hole. We use d’Alembert’s solution of the wave equation to construct a mathematical model of the wave torsion pendulum in the form of a nonlinear ordinary differential equation with retarded argument. We show that there exists a range of variation in the angular velocity of the drill string rotation, where, along with the unstable stationary solution characterized by the absence of vibrations, there are oscillatory solutions in the form of a stable limit cycle (attractor). The self-excitation of these vibrations is soft, and the self-oscillations themselves belong to the class of relaxation vibrations, because their period can be divided into several separated intervals corresponding to slow and fast variations in the state of the system. The velocities of the drill bit elastic motions on each of these time intervals remain constant, and the durations of all of them are the same and equal to the time interval (quantum) of the twist mode propagation from the drill bit to the drill string top and conversely.     

Influence of Drilling Parameters on the Accuracy of Hole-drilling Residual Stress Measurements

Multiple measurements using the hole drilling method were made in samples with a “known” state of residual stress. Drilling parameters were independently varied (bit rotation speed, bit diameter, and hole depth) to determine the effect on accuracy and repeatability. The study showed that accurate results can be achieved without ultra-high drill rotation speeds and that, in aluminum and stainless steel, speeds over 5 krpm and 10 krpm (respectively) were sufficient. Inaccuracies were evident in the stainless steel at speeds below 10 krpm and were attributed to non-circular holes, which may have been the result of bit vibration. There were no significant trends associated with altering the hole depth and only a slight trend associated with bit diameter variation.     

Torsional vibration analysis of push-the-bit rotary steerable drilling system

Ordinary drillstring torsional vibration is a very common phenomenon that has been attracted great interesting. Through Measurement data, a series of studies and analysis of torsional vibration characteristics of the bottom hole assembly (BHA) have been developed. However, for rotary steerable system (RSS), especially push-the-bit mode, its drill torsional vibration phenomenon will demonstrate the new properties, because that the underground implementing agencies will generate cycle torque and drag to the BHA in the orientation process. This process is completely different to the previous. A set of “strap-down” measurement system was developed in this paper, and the triaxial accelerometer and triaxial fluxgate were installed near the bit. Proposed a method of solver drill bit rotation speed using real-time downhole measurement data (sampling frequency 100 Hz), and the torsional vibration mathematical model of push-the-bit RSS was established. We found that the torsional vibration phenomenon of push-the-bit RSS is more serious than the ordinary drilling system by downhole measurement data analysis, even in most cases manifested as stick-slip. The torsional vibration was divided into five different modes, which showing different statistical regularities. Corresponding analysis of the angular displacement and speed, we found that the drill bit always appears low-speed in the position of oriented. This is a strong proof of that the RSS implementing agencies pushing the BHA caused the drill bit torsional vibration more serious. This work is supplemented and development of the drill string torsional vibration studies. Contribute to the better understanding of the dynamics of the push-the-bit RSS. Put forward a new way of analysis the rotary steerable drillstring fatigue damage predicted, steering ability and the torsional vibration control.     

钻进速度对钻屑温度影响的实验研究

利用钻屑温度预测冲击地压时,钻进速度是影响钻屑温度的一个重要因素。本文利用自行研制的钻头温度测试装置,对钻头温度变化进行监测,分析不同钻进速度对钻头温度变化的影响规律。实验结果表明:钻孔时,钻进速度减慢,钻头与孔壁之间的摩擦时间增长,摩擦产生的热量增多,使钻头温度升高。钻进速度对钻屑温度有较大影响,使用钻屑温度法预测冲击地压时,应制定统一的钻进速度指标,增加预测准确性。     

Three-Dimensional Nonlinear Analysis of Drill String Structurein Annulus

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电梯轮轨耦合高频振动计算模型研究

电梯导轮和导轨相互作用产生的高频振动是电梯噪音的主要来源之一,本文基于导轨、导轮和电梯框架等各柔性构件的频响函数,建立了耦合振动系统的频域计算模型。分析了导轨表面粗糙度、导轮偏心和扁疤等激励对电梯高频振动的影响。通过与实测数据进行比较．验证了计算模型的有效性．从而为电梯的减振降噪设计提供了有用的分析工具。     

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.     

弹性力学中Fredholm积分方程组解法的表达通式及其讨论

本文采用覆盖域的概念,给出受外力作用的任意形状弹性体采用Fredhikm积分方程组解法的统一表达式,而且就含洞的无限大体且远场应力不为零,边界上有集中力作用等特殊情况进行讨论并给出相应的表达式,对边界上作用力和覆盖域边界上作用力之间在合力和合力矩上的关系也作了讨论,文中给出的算例表明,对于一些简单情况可以求得解析解。而对于需要采用数值解的问题,本文工作具有精度高、收敛快的优点。     

波动钻压下阶梯钻柱系统稳定性研究

处于狭长井筒中的钻柱,其动力响应受到钻具组合、内外钻井液流动以及钻井参数等因素的影响,钻柱动力失稳导致的剧烈振动是井壁坍塌和钻具失效的重要原因。考虑到钻杆和钻铤在刚度和线密度上存在很大的差别,论文将钻柱简化为单阶梯输液管柱,钻井液沿着钻柱内部向下泵入并从环空返回地面。耦合考虑钻柱自重、随时间简谐变化的波动钻压、稳定器以及钻井液的水动力和阻尼力,建立了直井中钻柱横向振动的解析模型。利用有限单元法离散为四阶常微分方程后,采用Bolotin法得到临界频率方程确定系统的不稳定区范围,研究了钻压、钻杆长度、稳定器安装位置、钻井液的流速和密度等参数对系统稳定性影响的机理。研究表明：钻压的平均值和波动幅值都是钻柱失稳的驱动因素,而系统的稳定性对处于受拉状态的钻杆的长度变化不敏感。在论文所研究的参数范围内,降低钻井液流速和密度、下移稳定器的安装位置均有助于增强系统的稳定性。     

PROGRESS IN MEASUREMENT TECHNOLOGY FOR DRILL STRING VIBRATION

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.     

求解中短半径弯螺杆钻具的纵横弯曲法

介绍了一种求解中短半径($K=1^\circ$/m$ \sim 3^\circ$/m)弯螺杆 钻具的纵横弯曲法, 以指导弯螺杆钻具的设计和使用. 采用变刚度梁柱理论, 并应用等效载荷法对具有初始结构弯角的梁柱进行等效处理, 根据钻具组合支座连续条件及 边界条件建立了中短半径水平井造斜螺杆钻具组合的力学模型, 进而求得钻头侧向力, 依此 预测弯螺杆钻具的造斜能力. 这种分析方法得到了成功应用.     

流体动力干扰对单排圆柱桩列波浪力的影响

多物体之间的流体动力干扰特性对超大型海洋结构物的设计和研究十分重要用波动源在截面周线上分布的方法，就垂直桩柱间三维流体动力干扰对波浪力的影响进行了系统的研究，桩柱的数目可达１００余根得到了柱间流体动力干扰力学机理的若干新的特性尤应指出的是，当桩柱根数超过某一数量后，桩柱上的受力表现出有规律的连续依赖性当柱数很大时，无论柱数是奇数还是偶数，中间大部分的桩柱都将表现出均匀的受力特征这些特性的发现对其他形式多体结构物流体动力干扰的研究也有重要的借鉴和指导意义     

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.     

Method and apparatus for on-line estimation of soil parameters during excavation

Time-varying forces from soil–machine interactions cause stresses in the components of earthmoving machinery, which may cause damage to the machine. It is not always possible to know all the characteristics of a soil sample prior to excavation; however, by estimating necessary soil parameters, it is possible to predict the soil–machine interaction forces in a practical manner. This article presents the development of a simple apparatus and method for estimating the soil parameters from the cutting force measured by the novel bench-scale excavating tool, validation of the soil model, and comparison with other available techniques. The apparatus used to collect data of soil forces on a tool consists of an instrumented crank-slider mechanism equipped with a thin plate to fragment the soil, which is contained in a sample box. Using the Mohr-Coulomb earth pressure model to predict failure force during the interaction, two methods are used to minimize the error between the predicted and measured failure force, that allows to estimate soil parameters: First, the Newton–Raphson Method (NRM) is used to minimize the error, which allows estimation of two soil parameters (interface friction angles) on non-cohesive soil samples. Additionally, a new estimation scheme based on the NRM is presented, that uses an auxiliary equation, and allows estimation of up to three soil parameters, including interface friction angles and cohesion. Comparing the results obtained from the presented apparatus, it is confirmed that the friction angles are successfully estimated for two non-cohesive particulate materials. Additionally, it is shown that the new scheme demonstrates smaller error in estimating soil parameters for cohesive and non-cohesive soil samples than previously reported methods. The parameter estimation method is subsequently applied to determine the properties of highly cohesive oil sand, and delivers promising results.     

The interaction of a screw dislocation with a circular inhomogeneity near the free surface

The interaction of a screw dislocation with a circular inhomogeneity near the free surface is discussed in this paper. By using the complex potential and conformal mapping technique, an explicit series solution is obtained. Then, the solution is cast into a new expression to separate the interaction effects between the dislocation, inhomogeneity, and free surface. The new expression is not only convenient to reveal the coupling interaction effects, but also helpful to improve the convergence of the solution. As an application of the new expression, a simple approximate formula is presented with high accuracy. Finally, the full-field interaction energy and image force are evaluated and studied graphically. It is found that when the screw dislocation, inhomogeneity, and free surface are close to each other, their interaction effects strongly and intricately couple in the near field. In the case of a soft inhomogeneity or a hole, there is an unstable equilibrium point of the screw dislocation between the inhomogeneity and free surface, whereas in the case of a hard or rigid inhomogeneity, there is an unstable equilibrium point on the opposite side of the inhomogeneity.     

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.