An example method includes performing a machining operation by providing linear movement of a tool along a feed axis relative to a workpiece while superimposing oscillation of the tool onto the feed axis and providing rotation of the tool relative to the workpiece. During an optimization mode, the machining operation is performed on a first workpiece portion while providing the linear movement at an initial feed velocity, and sequentially superimposing the oscillating at a plurality of different frequencies. An optimal oscillation frequency is determined from the plurality of different frequencies which causes the tool to apply less force to the first workpiece portion at the initial feed velocity than others of the frequencies. During a run mode, the machining operation is performed on a second workpiece portion having a same composition as the first workpiece portion while superimposing the oscillation at the optimal oscillation frequency.