This paper presents a mathematical method for the computation of torsional resonance frequencies in a drillstring. The torsional resonance frequencies in a drillstring are readily calculated from the nominal drillstring dimensions. A high degree of accuracy is achieved when a correction factor to the torsional propagation velocity in drillpipe due to the offsets at the drillpipe joints is incorporated into the calculations. The theory and computer program were tested against data recorded in a 1000m deep, nearly vertical well. Torsional spectra were recorded with the bit off bottom at 450m, 550m, and 1000m and while drilling. Well defined torsional resonances were observed for frequencies up to 40 Hz. The calculated resonance frequencies are in very good agreement with all experimental data.


Vibrations within a drillstring are associated with drilling problems, and are the subject of many recent publications. If the amplitude of vibration is large, drilling performance is decreased and the drillpipe, drillcollar, casing, and bit are prematurely worn. The drillstring can exhibit three types of vibrational motion, longitudinal, transverse and torsional. Longitudinal, or axial, vibrations are associated with bit and kelly bounce. Transverse vibrations are associated with buckling of the drillpipe. These vibrations are generally observable from the rig floor. Torsional vibrations on the other hand, are less readily observed, but can lead to drilling problems as well. When torsional vibrational amplitudes are high, the drillpipe is continually loaded and unloaded, leading to a deterioration of drillpipe strength. Torsional oscillations at the bit must have a large effect on drilling performance. An additional motivation for studying torsional vibrations, is that some degree of coupling must exist between the torsional motion and the axial and transverse motions of the drillstring. Thus it may be possible to monitor axial and transverse motions through the torsional spectrum.

The intent of this paper is twofold.

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