A vibration assisted machining system, comprising: a frame; a vibration element mechanically coupled to the frame, the vibration element including a first actuator and a second actuator adapted to generate a substantially elliptical tool path in a vibration plane of the VAM system; a cutting tool holder connected to the vibration element; a workpiece holder coupled to the frame; a third actuator (116, 104) coupled between the frame and one of: the vibration element; or the workpiece holder; wherein the third actuator (116, 104) is coupled to the frame such that a displacement axis of the third actuator (116, 104) is substantially in the vibration plane and substantially perpendicular to a feed direction of the VAM system; and drive circuitry electrically coupled to the vibration element and the third actuator (116, 104), the drive circuitry adapted to provide a first drive signal for driving the first actuator, a second drive signal for driving the second actuator, and a third drive signal for driving the third actuator (116, 104); wherein: the first drive signal has a fundamental frequency and a first stroke amplitude; the second drive signal has the fundamental frequency and a second stroke amplitude; and the first stroke amplitude, the second stroke amplitude, and a relative phase of the first drive signal and the second drive signal are selected such that a tip of a cutting tool mounted in the cutting tool holder follows the substantially elliptical tool path in the vibration plane relative to the vibration element; characterized in that the third drive signal has a perturbation frequency approximately equal to N times the fundamental frequency, where N is an integer greater than 1, and a perturbation amplitude less than a lesser of the first stroke amplitude and the second stroke amplitude. a frame; a vibration element mechanically coupled to the frame, the vibration element including a first actuator and a second actuator adapted to generate a substantially elliptical tool path in a vibration plane of the VAM system; a cutting tool holder connected to the vibration element; a workpiece holder coupled to the frame; a third actuator (116, 104) coupled between the frame and one of: the vibration element; or the workpiece holder; the vibration element; or the workpiece holder; wherein the third actuator (116, 104) is coupled to the frame such that a displacement axis of the third actuator (116, 104) is substantially in the vibration plane and substantially perpendicular to a feed direction of the VAM system; and drive circuitry electrically coupled to the vibration element and the third actuator (116, 104), the drive circuitry adapted to provide a first drive signal for driving the first actuator, a second drive signal for driving the second actuator, and a third drive signal for driving the third actuator (116, 104); wherein: the first drive signal has a fundamental frequency and a first stroke amplitude; the second drive signal has the fundamental frequency and a second stroke amplitude; and the first stroke amplitude, the second stroke amplitude, and a relative phase of the first drive signal and the second drive signal are selected such that a tip of a cutting tool mounted in the cutting tool holder follows the substantially elliptical tool path in the vibration plane relative to the vibration element; the first drive signal has a fundamental frequency and a first stroke amplitude; the second drive signal has the fundamental frequency and a second stroke amplitude; and the first stroke amplitude, the second stroke amplitude, and a relative phase of the first drive signal and the second drive signal are selected such that a tip of a cutting tool mounted in the cutting tool holder follows the substantially elliptical tool path in the vibration plane relative to the vibration element; characterized in that the third drive signal has a perturbation frequency approximately equal to N times the fundamental frequency, where N is an integer greater than 1, and a perturbation amplitude less than a lesser of the first stroke amplitude and the second stroke amplitude.