Influence of Sinusoidal Drive Speed Modulation on Rotor with Continuous Stator Contact

Abstract

Torsional vibrations experienced by drill strings can be detrimental to drilling operations. With a goal of understanding torsional vibrations experienced by drill strings and determining means to attenuate undesired vibrations, the authors have studied the effect of adding a sinusoidal modulation to a constant rotation speed of a drill string. A combination of modeling, analysis, and experiments is used to explore the influence of this rotation input modulation on the system response. The drill string is modeled as a modified Jeffcott rotor, which is described by a system with three degrees of freedom. Considering the case of forward whirling of a rotor in continuous contact with a stator, the equations of motion are reduced to a single degree-of-freedom nonlinear oscillator describing the torsional motions. In order to understand the fast time scale and slow time scale components of the motion, the method of direct partitions of motions is used to determine an approximate response to the nonlinear oscillator. The obtained results of the analysis illustrate that with the sinusoidal modulation of the rotor drive speed, the equivalent torsion stiffness can be enhanced and the character of the friction force at the contact can be made smooth. The analyses helps bring forth the stabilizing influence of the added sinusoidal input to the rotor drive speed. Over the considered parameter ranges, the numerical results obtained with the full three degree-of-freedom model and the reduced single degree-of-freedom model are found to be in agreement with each other. Furthermore, the results from these models are found to compare well with those obtained by using the method of direct partition of motions. Experiments with a laboratory scale drill-string arrangement are to be carried out to validate the analytical and numerical findings and further explore the effectiveness of the drive speed modulation on the rotor dynamics.