Drill-string with cutting dynamics: A mathematical assessment of two models

Abstract

In this paper, a new model to study drill-string dynamics is developed. Some of the novelties of the paper are: (1) the use of a new bit-rock interaction relation that does not restrict backward rotation of the bit nor bit-bounce; (2) the use of an advection equation to avoid dealing with a system of delay-differential equations in the simulation of the cutting process; (3) the extension of the advection approach treated in previous works to allow rotation in both directions; (4) the combination of the previous items with a distributed approach for the torsional dynamics; (5) the inclusion of the 2-DOF model as a limiting case of the continuous model. For this purpose, a strategy considering an extra parameter α is used. All these aspects lead to a coupled non-linear formulation that can exhibit self-sustained vibrations associated with the regenerative cutting process. The new model is compared, from a numerical point of view, with an established 2-DOF approach. Five scenarios considering a 1200 m column with different friction parameters and top drive conditions are simulated. Dissimilar predictions are observed, showing a more complex response for the continuum model where higher frequencies are excited as well. These results indicate that the more sophisticated model could capture other aspects of the dynamics that are neglected in the 2-DOF approach.