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Multi-dimensional semi-analytical model for axial stick–slip of a rod sliding on a surface with Coulomb friction

A multi-dimensional lumped element model of a long non-rotating rod that moves on a slick surface with both dynamic and static Coulomb friction is outlined. The rod is accelerated to a constant velocity, and the free end of the rod experiences the effect of stick and slip. This article describes a new modeling approach, where the model is able to switch between different linear semi-analytical sub-models, depending on how much of the rod is moving. Fundamental understanding of the stick–slip effect is revealed, and a potential shortcoming of the model is also discussed. The model is computationally effective and may be suitable for real-time applications in, for instance, oil-well drilling.