A cutting apparatus includes a management unit having a measuring unit for measuring an amount of light emitted from a light emitter and received by a light receiver while a cutting blade is positioned between the light emitter and the light receiver, a measured waveform forming section for forming a measured waveform representing the configuration of an outer circumferential region of the cutting blade, and an ideal waveform recognizing section for recognizing one of the comparative waveforms that has the greatest number of waveform regions similar to the measured waveform as an ideal waveform, a difference calculating section for calculating the area of a region where there is a difference between the measured waveform and the ideal waveform.

A controller uses detection information of a contact sensor or time-series data of a detection value related to a drive motor included in a rotation mechanism and/or a feed mechanism to acquire a coordinate value when a cutting tool comes into contact with a to-be-cut object or a component. The controller determines a relative positional relationship between the cutting tool and a rotation center of the to-be-cut object based on coordinate values when the cutting tool comes into contact with the to-be-cut object subjected to turning work or a reference surface whose relative positional relationship with the rotation center of the to-be-cut object is known at least at two positions different from a rotation angle position of the cutting tool during the turning work.

A cutting apparatus includes a management unit having a measuring unit for measuring an amount of light emitted from a light emitter and received by a light receiver while a cutting blade is positioned between the light emitter and the light receiver, a measured waveform forming section for forming a measured waveform representing the configuration of an outer circumferential region of the cutting blade, and an ideal waveform recognizing section for recognizing one of the comparative waveforms that has the greatest number of waveform regions similar to the measured waveform as an ideal waveform, a difference calculating section for calculating the area of a region where there is a difference between the measured waveform and the ideal waveform.