THE HOPF BIFURCATIONS IN THE WAVE MODELS OF TORSIONAL VIBRATIONS OF SUPERDEEP DRILL COLUMNS
Valery Gulyayev, Sergey Hudoliy, Olga Glushakova
With the aim to simulate the bifurcations of cycle birth in superdeep drill columns the nonlinear wave model of torsion pendulum is elaborated. The constitutive differential equation with delay argument is constructed. The analysis results testify that the self-excited torsional oscillations of the drill column proceed in the manner of quantized time, when the rotation speed continues to be constant during time quantum equal the duration of the torsion wave forth and back propagation through the DC length.
The states of the limit cycle birth and death in the superdeep DC are found, the modes of DC motion are constructed for the critical states. It is established that the auto-oscillations are predominant at low values of the DC rotation velocities.