The problem about identification of elastic bending deformation of a drill string in a curve wells based on the theory of flexible curved rods and the direct inverse problems of drill string bending in the channels of curvilinear bore-holes is stated. The problem is solved which determines the resistance forces and moments during performing ascending-descending operations in curvilinear bore-holes with trajectories of the second order curve shapes. The sensitivity of the resistance forces relative to geometric parameters of the bore-hole axial line trajectories is analyzed.

This paper deals with the theoretic simulation of a drill bit whirling under conditions of its contact interaction with the bore-hole bottom rock plane. The bit is considered to be an absolutely rigid ellipsoidal body with uneven surface. It is attached to the lower end of a rotating elastic drill string. In the perturbed state, the bit can roll without sliding on the bore-hole bottom, performing whirling vibrations (the model of dynamic equilibrium with pure rolling when maximum cohesive force does not exceed the ultimate Coulombic friction). To describe these motions, a nonholonomic dynamic model is proposed, constitutive partial differential equations are deduced. With their use, the whirling vibrations of oblong and oblate ellipsoidal bits are analyzed, the functions of cohesive (frictional) forces are calculated. It is shown that the system of elastic drill string and ellipsoidal bit can acquire stable or unstable whirl modes with approaching critical Eulerian values by the parameters of axial force, torque and angular velocity. The analogy of the found modes of motions with ones of the Celtic stones is established. It is shown that the ellipsoidal bits can stop their whirling vibrations and change directions of their circumferential motions in the same manner as the ellipsoidal Celtic stones do. As this takes place, the trajectories of the oblate ellipsoidal bits are characterized by more complicated paths and irregularities.

This article deals with the use of an interdisciplinary approach to modelling and creation of a complex technical system of different physical nature in relation to the kinematics of cutting and shaping. The professor of the National Technical University of Ukraine, Kuznetcov Iu. N., proposed the approach based on generalization of knowledge, methodological basis of which is the theory of evolution of the systems and methods of genetic analysis and synthesis. For generalization of the knowledge in the fundamental sciences is based on the principles of a limited number of elementary generic structures with the introduction of the gene concept. The modelling and synthesis of kinematic cutting schemes are providing the efficiency and viability of genetic and morphological approach. The material point, which can interact with other material points in space and time, simulating anthropogenic system of different origin, is introduced as a material object.

The research work deals with the torsional vibration of a drill string in a vertical cylindrical cavity of a borehole with liquid medium. The mechanical interaction models of the drill string with viscous liquid are investigated, Also this paper describes the vibrations of the drill string bit with allowance made for viscous friction, the nonlinear deferential equation with partial derivatives is used. The oscillation scheme of torsional auto-vibration of homogeneous drill string in the form of oscillation pendulum is stated. It was found that the properties of the liquid medium in whichthe rotating column, lead to a small range of angular velocity value, which are generated during the self-oscillation.

This paper solves the basis of the ray-path method, the problem about the wave propagation and transformation, which are generated by the shock pressure field in the spherical enclosure of the transversely isotropic elastic medium with the non-uniform density and non-uniform parameters. The techniques for construction of evolving system of the fronts and rays are proposed. The geometric singularity forms on the front surfaces for the different values of the both anisotropy and heterogeneity elastic medium are analyzed The problem about propagation and transformation of discontinuous wave fronts in transversely isotropic heterogeneous elastic media is investigated.