A torsional-axial vibration analysis of drill string endowed with kinematic coupling and stochastic approach

In this paper, a lumped mass model is proposed to investigate the torsional-axial vibration behavior of drill string. This model exclusively involves two statuses of axial vibration, which are the contacted status and the lifted status, and two statuses of torsional vibration, which are the slip status and the stick status. The criteria of identifying these vibration statuses are proposed. The lumped mass model concentrates the masses along the drill string and calibrates the properties of formation rock using a mass-spring-dashpot system. Instead of utilizing force coupling approaches on the bit-rock interaction boundary, a kinematic coupling approach is proposed to correlate the axial displacement of the bit to the rotation angle of the bit. The kinematic coupling function is expressed as a sinusoidal function of rotation angle with certain frequency and amplitude. The drill string responses at different drilling parameters are discussed, including the weight on bit, the rotary velocity, the borehole depth, the rock property, etc. Finally, the drill string responses are proposed in a stochastic sense by setting the kinematic coupling function be white noise. The power spectrum density functions of drilling parameters are discussed. The model in this paper kinematically couples torsional and axial vibration in stochastic sense and casts light on analyzing drill string responses in a different perspective.