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

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.qscienc

Effects of high frequency drive speed modulation on rotor with continuous stator contact

In many mechanical systems, rotating structures experience continuous rotor-stator contact and torsion motions are dominant in the response. Drill strings used in the oil and gas industry represent one example of rotating structures. Torsion vibrations can be deleterious to the components and operations of the drilling system. As a novel approach to mitigate undesired vibrations, the effects of adding a sinusoidal input to the rotation speed of a drill string are studied. The drill string is modeled as an extended Jeffcott rotor with sinusoidal drive speed modulation. After constructing a three degree-of-freedom model to capture lateral and torsion motions, the equations of motion are reduced to a single differential equation governing torsion vibrations during continuous stator contact. An approximate solution has been obtained by applying the Method of Direct Partition of Motions to obtain an analytical approximation for the solution of this governing equation of motion. The results show that for a rotor undergoing either forward whirling or backward whirling, the addition of sinusoidal excitation to the drive speed can cause an increase in the equivalent torsional stiffness, smooth the discontinuous friction force at contact, and reduce regions of negative slope in the variation of friction coefficient with respect to the contact surface relative speed. Experiments with a laboratory scale drill-string apparatus have also been conducted and the experimental results show good agreement with the numerical results obtained from the reduced-order models. These findings suggest that the developed reduced-order models can be useful for studies of rotor dynamics in situations with continuous rotor-stator contact. Furthermore, the results obtained suggest that the considered drive-speed modulation scheme can be useful for attenuating drill-string vibrations. 1 2017 Elsevier LtdThe authors would like to gratefully acknowledge the support received from the Qatar National Research Fund for NPRP Project 7-083-2-041 , to pursue this collaborative work between the University of Maryland, College Park, MD, USA and Qatar University, Doha, Qatar.Scopu