Glushakova O. Relaxation wave torsion autovibrations of deep drilling strings

The dissertation is devoted to the statement and solving a new scientific problem about theoretical simulation of torsional self-generated vibrations of seep drilling strings. A wave model of torsional autovibrations of homogeneous drill string is elaborated in the form of a torsional pendulum. On the basis of d'Alembert's solution the wave partial differential equation is reduced to a non-linear singularly perturbed ordinary differential equation with a delayed argument. It is established in the result of the performed analysis that a range of the drill string angular velocity values exists with the boundaries inside which the bit torsional relaxation vibration self-excitation takes place. The transitions through the range boundaries (the states of the limit cycle birth and loss ? the Hopf bifurcations) are investigated, it is found that the autovibrations are attended by existence of fast and slow motions with large scale and small scale discontinuities of the angular velocities. In the phenomena of autovibrations of the mechanical systems, the new effect is found, which consists in existence of additional small scale quantized in time discontinuities of the angular velocities. They occur with the same intervals of time (quanta) equaled the duration of the torsion wave propagation through the doubled length of the drill string (upward and downward). The analysis of the torsion vibration self-excitation in the multilink drill strings is fulfilled, the computer simulation of non-stationary torsion motions of the drill string bits is performed for the cases of the drill string rotations with accelerations. They simulate the effects of the drill string accelerating and braking.