Traditionally, the analysis of stability in drillstrings is based on longitudinal vibrations only. However, field experience indicates the presence of torsional effects in the form of modulations in longitudinal vibrations. Moreover, torsional dynamic forces are significant and lead to joint problems during drilling. In this paper, we discuss the effect of torsional vibrations on the stability and both longitudinal and torsional forces in drillstrings. Using a model of a typical drillstring that incorporates both longitudinal and torsional multi-degree of freedom, we develop the equations governing displacements and forces at any joint. Using time simulation techniques, we obtain the stability diagram and calculate the dynamic forces at any joint as a function of time. We finally show the effect of torsion on the nature of vibrations through frequency analysis, a technique that is useful in the interpretation of field measurements under various drilling conditions.

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