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This paper discusses longitudinal and angular drill-string vibrations and supporting field measurements taken with a special downhole recording instrument. Computer programs based on the theory are used to calculate longitudinal and angular vibrations (caused by periodic bit motions) along the drill string; field measurements made during actual drilling operations are used to check computer calculations. The main difference between this and other theory on the same problem is the inclusion of friction, which acts along the length of a drill string and impedes longitudinal and angular vibrations. For the sake of simplicity, the effect of different types of friction, such as fluid, rubbing, and material, which act along the string, is approximated by the effect produced by viscous friction. This approximation is generally accepted and appears to give adequate results for the drill-string vibration problem.
Dareing et al. (Fri,) studied this question.