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

Abstract

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 Ltd