斜井段钻柱混沌运动的数学模型与参数

基于现代动力系统理论，对斜井段钻柱的复杂动力学行为进行研究．通过考虑由于弯曲变形而产生的附加轴向力，得到描述井孔约束下斜井段钻柱在周期性钻压作用下的非线性参数激励系统，利用Melnikov-Holmes方法得到钻柱发生混沌运动的判据，并结合具体工程实例分析了倾斜井钻柱混沌运动的参数激励阈值，所得结论在钻井工程中具有较强的可操作性．

Mathematical Model and Parameters of Drill String's Chaotic Motion in Slant Hole Interval

Based on theory of modem dynamic system, complicated dynamic behaviors of drill string were studied. Considering the extra axial force aroused by the lateral deformation, a non-linear parametrically excited system was established to describe the action of drill string （leashed by the wellbore in slant hole） under periodical weight-on bit. Then making use of Melnikov-Holmes method, the threshold value of the parameter excitation that can trigger chaotic motion of the drill string was obtained. In addition, relevant conclusions of parametric excitation threshold were obtained by analyzing the chaotic motion of slant drill string in engineering practice. The achieved conclusions have more practicable operability in drilling project.