The quasistatic stability of a rotating drillstring under longitudinal force and torque is analyzed. Constitutive equations are derived, and a technique to solve them is proposed. It is shown that the buckling mode of the drillstring is helical within a section subjected to compressive forces

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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 Introduction. One of the most important engineering tasks in modern mining practice is to develop the technology of drilling deep oil and gas wells. The predominant method in this technology is rotary drilling. It makes it possible to drill wells more than 6 km deep; the next target is to reach depths of 7 km and more.The geometry of wells is of two types [6]: (i) rectilinear vertical (conventional) and (ii) curvilinear (penetrating oil-or gas-bearing strata along their stratified structure).The efficiency of rotary deep-hole drilling can be enhanced by revealing critical modes of drillstrings and developing measures to reduce their adverse effect on the process. Such modes may be accompanied by bifurcational buckling and intensive vibrations of drillstrings when their natural frequencies equal the angular speed of rotation. It is important to not only establish the critical speeds of rotation of drillstrings, but also identify the buckling modes, which would allow finding regions of contact interaction between the string and the well wall and to calculate the reactions of such interactions.So far, however, no methods for physical and mathematical simulation of such effects have been developed. This state of affairs is because (i) it is still impossible to visualize the mechanical state of a drillstring during speedup, steady run, stopping, lowering, and pulling; (ii) there are no reliable methods to record dynamic processes in objects of such configuration and dimensions under full-scale conditions; (iii) drillstrings are so flexible that it is difficult to adequately study their mechanics using large-scale physical models (for example, a drill pipe 7 km in length and 0.3 m in diameter can be modeled by a hollow string 7 m in length and 0.3 mm in diameter that spins, is prestressed by gravity and torque, and contains a fluid); and (iv) there are many factors (length, flexibility, longitudinal force, torque, rotary inertia, internal fluid flow) that make the comprehensive mathematical simulation of the static and dynamic processes difficult.The critical parameters of the drilling process can be identified by mathematical modeling, though this would involve severe computational difficulties. They are due to the combination of the geometry of the drillstring and the forces acting on it during drilling. The former factor is more important because the drillstring is geometrically equivalent to a string with relatively low bending and torsional stiffness, which, however, should be calculated by beam theory to correctly describe edge and local effects of deformation. Therefore, applying this theory to strings se...

V. I. Gulyaev, a V. V. Gaidaichuk, b I. L. Solov'ev, a UDC 539.3:622.24 and I. V. Gorbunovich a We pose the problem of buckling of an elongated twisted rotating rod subjected to tensioncompression and containing an internal flow of homogeneous fluid. We derive the resolving equations capable of modeling the stability of strings for deep drilling, propose a procedure for their solution, and consider typical examples. The critical values of the parameters of the system specifying its elastic equilibrium are determined and the stability loss modes of are established.

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