Drilling vibrations most frequently occurring in the field are torsional (stick-slip) and axial (bit-bounce).
The random excitation at the bit-rock interaction, which is considered in the bit axial direction, is treated as Gaussian white noise.
Previous studies reported that the peaks of a power spectrum for roller-cone bit axial vibration move to higher frequencies with the progression of bit-tooth wear.
The statistics of the responses, including the means and standard deviations of the bit axial displacement and rotational velocity are obtained and analyzed.
The model can predict how axial and torsional bit-rock reactions are propagated to the surface, and the role that lateral vibrations near the bit play in exciting those vibrations and stressing components in the bottom-hole-assembly.
This effect is associated with deterioration of conditions of contact interaction between the DS and the bore hole wall, enlargement of friction forces, impossibility of transferring the required axial force to the bit, and the DS lockup situation.
For typical deep drilling field conditions, the critical angular velocity Ωc is virtually independent of the axial force acting on the bit and of the bit bluntness.
The axial force and torque of bit of drill string in compound drilling is greater than that in the conventional drilling.
Normalized basis patterns in 2-D (lateral dimensions) are shown in Figure 4 with 8 bit intensity resolution for axial dimension at the nominal focus.
Time-series are isolated where angular rotation is restarted after a connection, with the bit off bottom and before axial motion is re-initiated, to make the data consistent with the model assumptions.
Six production-line factor variables are considered: the experience of the operator, the use of a pilot hole, the length of the bit, the condition of the bit, the axial pressure or feed rate, and the rotational speed of the bit upon withdrawal from the hole.
