Nonlinear models of cutting process with superposition of ultrasonics are proposed and investigated. It is confirmed that under the influence of high frequency vibration, the phenomenological plasticisation of brittle materials and fluidisation of dry friction occurs. The mechanical characteristics of transformed machining processes are obtained. It is shown that excitation of the high-frequency nonlinear mode of tool-workpiece interaction is the most effective way of ultrasonic influence on dynamic characteristics of machining. The exploitation of this mode needs a new method of nonlinear control called as autoresonant one. An autoresonant system with supervisory computer control was developed and successfully used for the control of the piezoelectric transducer during ultrasonically assisted cutting.

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