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The high performance demands on commercial CNC machine tools have led to the widespread adoption of direct-drive servo axes. In cases where the workpiece is manipulated by the axis, the plant dynamics seen by the control system may vary widely between different workpieces. In practice it is often found that an axis which has been optimally tuned for a given workpiece becomes unstable when a new workpiece with significantly different geometry is loaded. This paper analyses such a situation. It is shown that conventional modelling approaches, in which the low-order vibrational modes of the axis are represented, but in which details of the current servo are neglected, are unable to predict the experimentally observed limit-cycles. Accurate prediction of these phenomena are obtained by a combination of modal analysis for the mechanical dynamics, and a single-rate representation of the multirate control system, which takes account of computational delays and the current servo dynamics.