In oil exploration and production, drilling is one of the most important processes. Undesirable vibrations, intrinsic to the drilling process, can lead to fatigue failure, resulting in loss of efficiency due to downtime and, consequently, loss of productivity and high costs. The present work proposes the analysis of fatigue in drill strings under torsional vibrations with the stick–slip phenomenon, considering the frequency domain (or spectral) approach as an alternative to the time domain approach. The stick–slip occurs when the torque imposed by the top drive is not enough to overcome the resistance offered by the environment and, in the process of rock-bit interaction, the bit becomes stationary for a period, causing large fluctuations in the angular speed and, in turn, in shear stress, characterizing failure by fatigue. Spectral Methods for fatigue life analysis, although recent, have shown great potential in several applications and therefore, there is much to be explored given their viability in engineering problems due to the lower computational cost and time processing, being advantageous for complex problems with large amounts of data. In this approach, concepts such as Power Spectral Density (PSD) are used to calculate the Spectral Moments, employed in the various methods of this nature for determining fatigue life. The Dirlik and Tovo-Benasciutti Methods, being widely used not only in academia, have proved to be advantageous. These methods are compared with the rainflow method, used as a reference.
