Incipient Regimes of Drill Bit Whirlings on Uneven Bottoms of Deep Bore-Holes

This paper studies the problem of whirl vibrations of rotating drill string bit under conditions of its contact interaction with the bore-hole bottom surface. The destructive effects of whirl vibrations of drill bits and drill strings have long been recognized. The backward whirling is believed to randomly happen to some degree in 40% of all wells. It is shown that the situation is essentially associated with enlargement of the compressive thrust force and its approaching to the Eulerian critical value. Then, the bending stiffness of the drill string reduces, it hogs and the diamond impregnations existing in the bit surface penetrate into the rock medium. As this takes place, the bit axis tilts and nutates. It should be particularly emphasized that at this stage, the bit is under action of the vertical force (weight on bit) which essentially exceeds all other forces. It presses the bit to the hole bottom (not to the hole wall) and the bit loses its ability to slide on the bore-hole bottom and begins to roll on its surface, lagging behind or outstripping the drill string rotation. As a result, the point of the bit contact with the reference surface (the instantaneous centre of velocities) may describe extremely complicated trajectories with loops and cuspidal points and to change the motion directions. As examples, whirling of spherical bit is considered