摘  要：钻柱力学是关于井眼轨迹设计控制、钻柱设计以及钻进参数优选的基础。从钻柱力学问题的提出、研究目标与分析方法、钻柱运动状况、钻柱力学的基本方程、下部钻具组合受力情况、钻柱振动等一系列方面综合分析了钻柱力学的发展现状。到目前为止钻柱力学已经形成了一套比较完整的理论体系。利用纵横弯曲梁方法研究钻柱，可以有效的控制钻头的实钻轨道，使之尽量靠近预定的理论轨道，准确钻达目标区，从而降低钻井成本，提高固井质量，缩短完井周期。本文就是在纵横弯曲法基本理论的基础上，将下部钻具组合在稳定器处断开并建立简支梁模型，导出其力学模型，再利用边界条件和连续条件求解三弯矩方程组，根据变截面纵横弯曲梁理论所对应的挠曲线微分方程和边界条件及连续条件，能够得出关于梁柱挠度和端部转角的解析计算式，进而应用纵横弯曲理论解决有关的底部钻具组合的受力分析问题。最后在此基础上开发出配套软件系统，对变截面钻具组合的力学特性进行系统分析，并通过数据验证了该理论的正确性。

关键词：  钻柱力学；底部钻具组合；纵横弯曲梁法；变截面；三弯矩方程

Abstract：Drill string mechanics is the basis of the design and control of borehole trajectory,the drill string design,and the drilling parameter optimization.The development of drill string mechanics is discussed from the perspectives of the introduction of the topic,the research objective,the methods employed for the research,the motion behavior of the drill string,the fundamental equation for of drill string dynamics,the stress analysis of the bottom hole assembly,the drill string vibration and so on.A relatively integrated theory has been developed for the drill string mechanics.Through the beam-column theory of drill problems,we can effectively control the actual drilling track,make it nearly orbital track which ever predicted,accurate drill targets,reduce costs,improve the well quality,shorten the completion period.The paper is based on the beam-column theory which is that put bend the lower part of the BHA in the stabilizer root as simply disconnect the number of beams.Then establish the mechanical model,and use the continuity conditions and boundary conditions to solve the three-moment equation.Based on the differential equations of deflection curve and conditions of continuity and boundary of non-uniform stiffness beam-column,the analytical calculation formulae for deflection and slope angles of beam-column are derived.Furthermore,applying beam-column theory principle of superposition,the mechanical force and BHA with variable gauge stabilizer can be solved.At last,On the basis of beam-column theory,deformations of the BHA（Bottom Hole Assembly） of variable cross section are analyzed and the analyzing software system has been developed.The mechanics characters have analyzed to the BHA of variable cross section and theory is proven through the data.

Key words：drill string mechanics；BHA（Bottom Hole Assembly）；beam-column theory；non-uniform beams；three-moment equation