Derivation and experimental validation of an analytical criterion for the identification of self-excited modes in drilling systems

Drilling system applications are subject to torsional vibrations that are induced by self-excitation mechanisms. A common mechanism is a falling characteristic of contact or cutting forces with respect to the relative velocity between the bit and the formation. To mitigate the effects of this mechanism, it is important to identify modes that are the most likely to be excited. However, in complex structures the identification of critical mode shapes is no trivial task.This paper discusses a criterion derived to identify critical torsional modes in drilling systems that are prone to self-excitation. Basic assumptions are a falling (velocity-weakening) characteristic of the contact forces and only one contributing mode. Multiple contact forces along the structure can be considered with different contact characteristics. Contributing parameters are angular eigenfrequency, deflection of the mode shape at the contact points, modal damping of the examined mode, and the slope of the characteristic of the contact forces at the operating point.In a case study of a drilling system the derived criterion is tested. The case study focuses on torsional vibrations excited by cutting forces observed in field measurements with high amplitudes and accelerations. The corresponding modes are localized to the so-called bottomhole assembly (BHA) at the end of the drilling system. Numerical results from a finite element analysis are compared to downhole measurements to verify the critical modes that are identified with the criterion. In addition, mass and stiffness changes along the structure are intentionally induced to beneficially influence mode shapes. Results indicate that reducing the mode shape at the source of vibration (bit) decreases the excitability of this mode shape.