Abstract
The problem of the self-excitation of the torsional oscillations of a drillstring rotating in a fluid in a deep borehole is stated. Three models describing the mechanical interaction between the drillstring and the viscous fluid are discussed. Governing equations with ordinary and partial derivatives are derived. A method to solve them is developed. Computer simulation shows that the self-oscillations are relaxational and the curves of the functions that describe them have sections of fast and slow motions. The results of simulation can be used to develop a technique for drilling deep oil and gas boreholes
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