About Discretization of the Horizontal Drill-string Model with Uncertainty on the Frictional Force by the Lumped Parameters Method

The dynamics of the horizontal drill string considering frictional forces between the column and the borehole is investigated. A model of longitudinal vibrations of columns proposed in T.G. Ritto et al. is considered. The investigated model has a nonlinear character, and is modelled by the lumped parameters method. The drill-string is discretized with 100 nodes of lumped masses. Displacement of the bit, bit speed and also the ratio between the output power (obtained from the bit-rock interaction) and the input power is defined by the authors. The frictional force between the column and the borehole is relevant and uncertain. The frictional coefficient is modelled as a random field with exponential autocorrelation function. The obtained results are qualitatively and quantitatively consistent with the results of Ritto, where the dynamic model calculations are carried out by the finite element method.