Method of Dynamic Analysis for Rod-in-Hole Buckling

The problem of a postbuckling dynamic behavior of weighted rod, which is inserted into an arbitrary profile hole with some clearance, under the axial compression load is considered. In practice, this analysis is important for calculation of the friction drag of the drillstring in inclined and horizontal wellbores. The mathematical model and numerical method of the rod-in-hole contact interaction are developed. The contact model is based on a nonlinear dependence of the normal-directed contact force on the depth of interpenetration of rod in hole. The tangential interaction of bodies with the contact surfaces is described using a model of “elastic-plastic” friction. The developed system of substantially nonlinear differential equations with partial derivatives of 3-D rod dynamics is approximated by the finite differences and integrated by the Runge-Kutta method. A simplified model for axial motion of rod is suggested to make the process of numerical integration faster. The results of numerical simulation of stress-deformed state of rod in horizontal, inclined and curved holes are presented. The results of numerical simulation are compared with the results of experiment. The effect of the friction factor on the rod buckling has been studied. The effect of local outside bulges of the drillstring on a postbuckling behavior of the drillstring is considered.