Most drill-collar-connection failures are attributed to cumulative fatigue caused by bending vibration. An important class of bending vibration is whirl, which is formed by the eccentricity of the rotational drill collar. The contact between the drill collar and the borehole causes extreme harmful backward whirl, even chaotic whirl. A two-degree-of-freedom nonlinear lumped-mass model is used to represent the drill collar in whirl. Unlike other studies, the stick/slip vibration causing fluctuation of rotary speed is taken into account. In this lumped-element model, the contact forces obey the Hertzian contact law, which leads to lateral bounce of the drill collar and affects the borehole wall chaotically. The modified Karnopp friction model is adopted to simulate the stick/slip rotary vibration of the bottomhole assembly (BHA). On the basis of the time-domain responses of whirl, the continuous-bending-stress history is broken down into individual stress ranges with an associated number of stress cycles using the rainflow-counting method. The cumulative fatigue damage is estimated using Miner's rule. The conclusion of this paper indicates that chaotic lateral vibration and fatigue damage happen at a lower rotational speed than previously reported.

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