Gorbunovich I. The singularly perturbed problems of critical states of deep drill columns

Two point and multipoint boundary value problems on bending bifurcations of drill columns in deep bore holes are stated for different values of characteristic parameters reflecting real conditions of their functioning. It is shown that the constructed system of constitutive differential equations relates to the singularly perturbed type. It was assumed that the drill column length can change in the limits from 500 m till 10000m under different combinations of the longitudinal gravity force value, force of contact interaction of bit with the bore hole bottom, torque, rotational angular velocity and mud velocity as well as under existence of additional intermediate supports. The problems about drill column buckling in rectilinear inclined bore holes are stated with account for frictional interaction of the DC with the bore hole walls; the constitutive equations are deduced, their solution technique is proposed. The critical combinations of characteristic parameters are found, the modes of the DC bucklingare constructed. It is shown that primarily they have shape of spiral wavelets or irregular spirals with predominant bucklings in their lower parts