Self-Excited Vibrations in Drillstrings

Abstract

Abstract Vibrations created by drag bits can cause premature failure of drillstring components and fracture cutters. Unfortunately, there has been no theory that adequately explains how drag bits excite drillstrings. Our paper shows that these vibrations are self excited by the interaction of drillstring, bit, and formation. Results show that drag bit design and bit rotational speed dictate conditions of dynamic instability. In general, large drag bits are unstable at low rotational speeds. Introduction Drill bits are a primary source of drillstring vibrations. The interaction of the cutting elements on drill bits with formation create time dependent forces which feed vibration energy into drillstrings. These time dependent bit forces are affected directly by bit type which dictate the character of the source of excitation. When the frequency of excitation is tuned to one of the many natural modes of vibration or natural harmonics of drillstrings, large dynamic forces and stresses are induced by resonance. Drillstrings can vibrate longitudinally, torsionally or laterally depending on the source of excitation. Measurements of drillstring vibration during drilling, help identify the source of excitation and the particular modes which they excite. For example, roller cone rock bits excite longitudinal modes at a driving frequency of three cycles per bit rotation. This driving frequency causes resonance when tuned a longitudinal harmonic. Rotary speeds which cause this tuning are critical rotational speeds. Drag bits, in particular PDC bits, do not excite drillstrings at three cycles per bit rotation because they develop interactive forces with formations basically different from roller cone rock bits; their cutters shear rock instead of chipping rock. Also, drag bits have no moving parts such as roller cones. The basic question then is how does vibration energy get feed into drillstrings through the shearing action of the drag bit cutters. The paper explains how shearing action between drag bit cutters and rock can cause drillstrings to self excite leading to a condition of dynamic instability. The theory behind this explanation has been tested and verified many times in machine tool cutting. A major conclusion of the study is that drag bit design directly affects the limit of stability or the conditions under which drag bits and drillstrings self excite. The analysis also shows that shock absorbers cause drag bits to be dynamically unstable at practically all rotational speeds. Self Excited Vibrations Two types of vibration responses are:forced vibrations andself excited vibrations. Forced vibration responses are produced by an externally time varying force which is independent from the motion it produces. For example, the longitudinal vibrations produced by roller cone rock bits are forced vibration responses because the three lobed pattern in the rock excites longitudinal modes in drillstrings independent of the vibration response. The main concern here is resonance or tuning between the frequency of the external driving force and natural frequency of one of the drillstring modes. P. 117^