Lateral buckling of drill strings revisited: localised “snaking”

The classical lateral buckling of a straight drill string confined within an inclined cylindrical borehole is formulated as a singularly perturbed boundary-value problem which is subsequently explored using asymptotic techniques. In particular, the localised nature of the critical eigenmodes is discussed with the help of a special multiple-scale technique that yields simple and accurate approximations for the corresponding critical loads. The asymptotic formulae obtained capture the dependence of these loads on the magnitude of the frictional forces as well as the inclination angle of the confining borehole.