Criticality of bifurcation in the tuned axial–torsional rotary drilling model

We study the bifurcation characteristics of a lumped-parameter model of rotary drilling with 1:1 internal resonance between the axial and the torsional modes which leads to the largest stability thresholds. For this special case, the two-degree-of-freedom model for the drill-string reduces to an effectively single-degree-of-freedom system facilitating further analysis. The regenerative effect of the cutting action due to the axial vibrations is incorporated through a delayed term in the cutting force with the delay depending on the torsional oscillations. This state dependency of the delay introduces nonlinearity in the current model. Steady drilling loses stability via a Hopf bifurcation, and the nature of the bifurcation is determined by an analytical study using the method of multiple scales. We find that both subcritical and supercritical Hopf bifurcations are present in this system depending on the choice of operating parameters. Hence, the nonlinearity due to the state-dependent delay term could both be stabilizing or destabilizing in nature, and the self-interruption nonlinearity is essential to capture the global behavior. Numerical bifurcation analysis of a global axial–torsional model of rotary drilling further confirms the analytical results from the method of multiple scales. Further exploration of the rotary drilling dynamics unravels more complex phenomena including grazing bifurcations and possibly chaotic solutions.     

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.     

旋转导向钻具组合力学分析

旋转导向系统代表了当今定向钻井的先进水平,是井眼轨道控制技术的发展方向. 为了解决旋转导向钻井轨道控制问题,进行了旋转导向钻具组合(rotary steering bottom hole assembly, RS-BHA) 力学分析. 应用纵横弯曲法建立了典型的柔性RS-BHA 三维力学分析模型,得到了钻头侧向力和导向参数间的相互关系,进而根据极限曲率法可预测旋转导向工具的造斜能力,并计算设计井眼轨道需要的导向参数. 通过力学分析,可以优化RS-BHA,了解井眼轨道控制规律,为旋转导向工具设计和定向钻井自动控制提供理论依据.     

Dynamics of milling processes with variable time delays

A milling-process model with a variable time delay associated with each cutting tooth is presented in this article. The source of this variable time delay is the feed rate. The effect of the feed motion on the entry cutting angle, the exit cutting angle, and the amplitude of feed mark is also discussed. Loss-of-contact effects are also considered. The system dynamics is described by a set of delay differential equations with periodic coefficients and variable time delays. A semi-discretization scheme is presented for analyzing the stability of periodic orbits of this system. The analysis provides evidence of period-doubling bifurcations and secondary Hopf bifurcations. Good agreement is found between the numerical results obtained from this work and the results of related experimental studies.     

Self-excited stick–slip oscillations of drill bitsOscillations stick–slip auto-entretenues d'un outil de forage

This Note studies the self-excited stick–slip oscillations of a rotary drilling system with a drag bit, using a discrete model which takes into consideration the axial and torsional vibration modes of the bit. Coupling between these two vibration modes takes place through a bit-rock interaction law which accounts for both frictional contact and cutting processes at the bit-rock interface. The cutting process introduces a delay in the equations of motion which is ultimately responsible for the existence of self-excited vibrations, exhibiting stick–slip oscillations under certain conditions. To cite this article: T. Richard et al., C. R. Mecanique 332 (2004).     

Understanding root cause of stick–slip vibrations in deep drilling with drag bits

In search for the root cause of stick–slip, a mode of torsional vibrations of a drilling assembly, a linear stability analysis of coupled axial–torsional vibrations has been carried out. It has been shown that in a rotary drilling system with axial and torsional degree of freedom two distinct modes of self-excited vibrations are present: axial and torsional. These axial (torsional) modes of vibrations are due to resonance between the cutting forces acting at the bit and the axial (torsional) natural modes of drillstring vibrations. It has been demonstrated that although axial and torsional modes of vibrations do affect each other the underlying mechanisms driving these modes of vibrations are completely different. In particular, the only driving mechanism of the axial vibrations is the regenerative effect, while there are two distinct mechanisms that drive the torsional vibrations: (i) the cutting action of the bit, and (ii) the wearflat/rock interaction. Moreover, in the case of the torsional vibrations the regenerative effect plays only a secondary role. The results of the present study indicate that the axial compliance can play a stabilizing role. In particular, the stabilizing role of the axial compliance increases as the ratio of the torsional to the axial natural frequency of the drillstring vibrations decreases.     

Numerical investigation on dynamic characteristics of drilling shaft in deep hole drilling influenced by minimal quantity lubrication

The dynamic characteristics of drilling shaft in deep hole drilling influenced by minimal quantity lubrication (MQL) is investigated. According to the features of the compressible fluid Reynolds equation in oil/air feature, a time-dependent mathematical model is established to describe the pressure distribution of cutting fluid with nonlinearity in MQL deep hole drilling. By introducing the differential transformation approach, the time-dependent pressure equation arising from cutting fluid is solved by the use of direct integral method. The influences of the rotational speed, the transverse displacement ratio, and radial clearance on the hydrodynamic pressure distribution of cutting fluid are obtained. The advantage of this method is to overcome much of the computational cost and has its rapid convergence rate. Furthermore, the nonlinear responses of drilling shaft influenced by MQL are analyzed, and the instability rotational speeds of drilling tool are discussed while the design parameters of drilling shaft system changing.     

Evaluation for energy-saving effect of hybrid drilling rig system based on the logic threshold method

A simulation model of the current rotary drilling rig (RDR) system was built according to the basic configuration of the TR160D-type rotary drilling rig, and the test-rig based on the working principle of the RDR system was built. The results show that simulation model of the RDR system was accurate and reasonable by means of comparative analysis between theoretical computation and test data. The working principle and logic threshold control method of the HDR system were presented to reduce the fuel consumption and improve energy-saving efficiency via the analysis of energy flow of the RDR system, which mainly includes engine, electric motor/generator, super capacitor, AC–DC rectifier/DC–AC inverter and torque coupler, etc. Finally, the comparative analysis of the fuel economy between the RDR and the hybrid drilling rig (HDR) system was completed in the same overall typical operating conditions. The results show that energy-saving efficiency of HDR system is at 18.8% and total fuel economy efficiency of HDR reaches 15.9% relatively in a typical operating condition.     

Developing an excavation torque model for dense cohesionless soils

Torque encountered during the rotary excavation of soils (e.g., when using the DJM method for deep soft ground improvement) poses a serious detrimental effect not only to the excavating machines but also to the viability of a project as a whole. Consequently, this research investigates ways and means of realizing the reduction of torque encountered during the excavation of cohesionless soils. In this paper, the development of a torque model for a rotary excavation of cohesionless soils is proposed. Whereas in most of the soil tillage theories (i) the cutting tool is usually partially exposed at the surface, and (ii) excavation is generally longitudinal, this model is significant because; (i) the excavation process is radial, and (ii) the blade is completely immersed in the excavated medium. Various theories for the prediction of forces acting during the interaction of cutting tools and soils in conjunction with localized modeling of all the other forces, applied and adopted to suit this excavation geometry, have been applied in the development of the torque model. Experimental data was obtained from excavation experiments performed on compacted completely saturated sand samples. Within the experimental and theoretical limitations, the results showed that this model represented the excavation process.     

A Mechanics Based Model for Study of Dynamics of Milling Operations

A unified mechanics based model with multiple degrees of freedom is developed and numerically simulated to study workpiece-tool interactions during milling of ductile workpieces with helical tools. A refined orthogonal cutting model is used at each section of the tool, and the milling forces are determined by using a spatial integration scheme along the axis of the tool. Both regenerative and loss of contact effects are considered in determining the cutting forces, which makes the model well suited for a wide range of milling operations. The model also allows for partial engagement of a tool with a workpiece, which is an important feature needed for milling operations with helical tools. Time domain simulations are carried out by using the developed model to predict the stability boundaries in the space of the tool spindle speed and the axial depth of cut. Poincaré sections are used to determine loss of stability from period-one motions to other motions such as two-period quasiperiodic motions, as a control parameter is varied.     

Torsional Vibration Control and Cosserat Dynamics of a Drill-Rig Assembly

Aspects of drill-string vibrations in the context of a recently developed integrated model of a drill-rig assembly based on the Cosserat theory of rods are discussed. Computer simulations are used to compare existing rotary feedback strategies currently in use to optimise drilling performance where torsional slip-stick vibrations are a hazard. Guided by the wave nature of axial and torsional vibrations in axially symmetric drill-string configurations, we present a new control mechanism, torsional rectification, and compare its performance with existing controllers within the context of the model. The practical guidelines for the improvement of drilling rates in a wide variety of circumstances are discussed.     

The mechanics of soil cutting by a rotating wire

The cutting of soil by a rotating wire analogous to the tip of a rotary tiller blade while cutting a two-dimensional soil slice over a range of ‘fetch-ratios’ (bite length/depth-ratios) in a quasi-static condition is presented. A theoretical models based on Mohr-Coloumb soil mechanics has been proposed to predict forces on the wire (tip). The model is dependent upon observed passive general shear failure of the soil slice towards the curved free surface of a previous cut and the lateral local shear failure towards the undeformed soil. The predicted forces in a frictional soil and in a pure cohesive medium (artificial clay) agreed well with experimental results.     

井内流动与传热的三维耦合数值模型

钻井过程中,井内的压力、流场及温度分布是钻井作业必需的重要参数。本文提出了一个描述井内流动和传热的三维数学模型,用SIMPLER方法获得了该数学模型的数值解。该数值模型考虑了温度、压力对钻井液的流变性、密度以及各种介质的热物理参数的影响。现场试验数据与数值模拟结果的对比表明：本文提出的数学模型及采用的数值计算方法是可行的。     

State-dependent delay in regenerative turning processes

Stability of a two degrees of freedom model of the turning process is considered. An accurate modeling of the surface regeneration shows that the regenerative delay, determined by the combination of the workpiece rotation and the tool vibrations, is in fact state-dependent. For that reason, the mathematical model considered in this paper is a delay-differential equation with state-dependent time delay. In order to study linearized stability of stationary cutting processes, an associated linear system, corresponding to the state-dependent delay equation, is derived. Stability analysis of this linear system is performed analytically. A comparison between the state-dependent delay model and the previously used constant or time-periodic delay models shows that the incorporation of the state-dependent delay into the model slightly affects the linear stability properties of the system in certain parameter domains.     

Soil-blade dynamics in reverse-rotational rotary tillage

Soil cutting and the clod crack formation process during reverse-rotational rotary tillage in a heavy clay soil were investigated. Of particular interest was the relationship between clod crack formation and tillage resistance during sequential rotations of the tillage blade. Investigation of the crack formation process is helpful to develop and to design more effective and high performance tillage methods. This paper describes two new discoveries. The first is that the tillage resistance showed a higher cross-correlation between sequential rotations within a certain distance of tilling, while there was little or no cross-correlation between different tillage plots that were separated more than 0.4 m. The forward distance of untilled soil that was disturbed by the tillage blade was estimated to be 36.4 mm. This is the distance of two tillage pitches. The second discovery involved the blade frequencies during tilling. Fluctuation in tillage resistance frequencies of a single blade was nearly equal to the predicted occurrence of crack intervals on the tilled clod's surface. This frequency was 120 Hz. When these frequencies were translated into the distance along the trochoid trajectory of the blade cutting edge, they were the same as the length of the clods tilled by the reverse-rotational rotary tiller. These minute vibrations in the tillage resistance were considered the important indexes for recognizing the tilled soil conditions and the tilled clod failure on the reverse-rotational rotary tiller. The analytical results of this paper will be utilized for the active occurrence of the cracks regarding with natural frequency of the blade and the operation condition of the reverse-rotational rotary tiller.     

石油钻井旋转导向实验转台测试系统设计

设计了一种实验转台测试系统,主要用于在实验室环境下验证石油钻井旋转导向工具可行性并测试其性能参数。提出了总体方案,设计并完成了系统的关键组成部分：两轴手动转台、合力测试仪、惯性测量模块、信号处理系统,完成了计算参数和姿态误差角测试实验。实验结果表明,所设计的各部分工作正常,满足系统的总体要求。这为将来石油钻井导向工具的井下实验打下很好的基础。     

Fluid-solid coupling model for studying wellbore instability in drilling of gas hydrate bearing sediments

As the oil or gas exploration and development activities in deep and ultra- deep waters become more and more, encountering gas hydrate bearing sediments （HBS） is almost inevitable. The variation in temperature and pressure can destabilize gas hydrate in nearby formation around the borehole, which may reduce the strength of the formation and result in wellbore instability. A non-isothermal, transient, two-phase, and fluid-solid coupling mathematical model is proposed to simulate the complex stability performance of a wellbore drilled in HBS. In the model, the phase transition of hydrate dissociation, the heat exchange between drilling fluid and formation, the change of mechanical and petrophysical properties, the gas-water two-phase seepage, and its interaction with rock deformation are considered. A finite element simulator is developed, and the impact of drilling mud on wellbore instability in HBS is simulated. Results indicate that the re- duction in pressure and the increase in temperature of the drilling fluid can accelerate hydrate decomposition and lead to mechanical properties getting worse tremendously. The cohesion decreases by 25% when the hydrate totally dissociates in HBS. This easily causes the wellbore instability accordingly. In the first two hours after the formation is drilled, the regions of hydrate dissociation and wellbore instability extend quickly. Then, with the soaking time of drilling fluid increasing, the regions enlarge little. Choosing the low temperature drilling fluid and increasing the drilling mud pressure appropriately can benefit the wellbore stability of HBS. The established model turns out to be an efficient tool in numerical studies of the hydrate dissociation behavior and wellbore stability of HBS.     

机床非线性颤振的分段线性化及其数学模型

通过引入非线性调制环节N(S),本文实现了非线性颤振的分段线性化,建立了统一的切削动力学系统模型。这一模型使线性颤振理论、非线性颤振理论趋于统一,并使超声振动切削抑制颤振的机理从理论上得到解释。     

Effect of the length of a rotating drillstring on the stability of its quasistatic equilibrium

A mathematical model is proposed to describe the critical quasistatic equilibrium of long rotating drillstrings. The prestress of drillstrings by the gravity and torsion forces, the gyroscopic interaction of rotary and linear motions, and the destabilizing effect of the internal flow of the drilling fluid are taken into account. The phenomena accompanying the drilling to different depths are studied numerically __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 83–92, September 2007.     

Modeling and experimental investigation of drilling into lunar soils

Dry drilling only with the assistance of an auger is a reliable and realistic approach to remove abundant soils from the side of a bit in the harsh, dry conditions on the Moon. Based on an elementary analysis, using Janssen's model to reflect the coupling effect among the different components of the stress, the present paper models the conveying dynamics along the helical groove and the sampling mechanism in the centering hole of the stem for an auger drilling into lunar soil simulant. Combining the two parts as well as a simple cutting model for the bit, a whole drilling model is established to investigate the complicated relation among the conveying ability of the auger, the coring rate, and drilling parameters such as the penetration and rotation speeds. The relation is revealed by the complicated transition between different sub-models with the help of the physical transition conditions. A series of experiments with constant penetration and rotation speeds are conducted to verify the model. Three aspects of characteristics of the drilling dynamics are manifested,(i) the loads on the bit are almost independent of penetration;(ii) three obvious drilling stages with respect to cut per revolution are grouped;(iii) a linear relationship is found between the coring rate and the revolution per penetration.