An oscillation component a×sin(Mωt) (M is the number of sides) that becomes the maximum when a tool cuts the center of a machining surface is superimposed on a reference angular velocity 2ω of the tool. The angular velocity of a tool shaft becomes higher as the tool shaft comes close to the center of the machining surface and becomes the maximum when the tool shaft is at the center of the machining surface. It is possible to adjust the flatness of the machining surface by adjusting an adjustment parameter a of the oscillation component a×sin(Mωt).

Oscillation for a direct distance between the centers of a tool T and a workpiece W to meet l+a×l×(1−cos(Mωt)) and vertical oscillation to meet a×l×sin(Mωt) are applied alone or in combination with time t, where ω denotes an angular velocity of a workpiece, M denotes the number of sides of a polygon, and a denotes an adjustment parameter. Such oscillation enables adjustment as to how the machining surface is made concave or convex.

A control device that controls polygon turning to simultaneously rotate a workpiece and a tool and form a polygon on a surface of the workpiece acquires information on misalignment in the radial direction of a cutting tool attached to a tool body and generates pluses to correct the misalignment in the radial direction of the cutting tool. Furthermore, the control device outputs the pulses to an X-axis servo motor and moves a tool in the opposite direction to the misalignment in the radial direction of the cutting tool. Accordingly, the misalignment in the radial direction of the cutting tool is corrected, and thereby the precision of the polygon turning is improved.

A time necessary for phase alignment is shortened in a polygon machining device having a plurality of cutting tools. In phase alignment of polygon machining, a phase R.sub.CURRENT of the workpiece axis and tool axis before phase alignment and a machining-allowing phase command value R.sub.NEW(n) are calculated, a new phase command value R′.sub.NEW is calculated while considering restrictions such as a phase alignment method and a maximum rotation speed. By adjusting a phase to the new phase command value R′.sub.NEW, a time necessary for phase alignment can be shortened.

A numerical control device includes: a first control unit which rotates a workpiece about a rotation axis of the workpiece; a second control unit which rotates a rotary tool at a rotation speed with a constant ratio with respect to the rotation speed of the workpiece about the rotation axis, of the rotary tool, parallel to the rotation axis of the workpiece; and a third control unit which controls the relative positions of the rotation axis of the rotary tool and the center axis of a polygon so that the positional relationship between the rotation axis of the rotary tool and the center axis of the polygon is fixed, and the center axis of the polygon passes through a predetermined position of the workpiece and is parallel to the rotation axis of the workpiece.

An inference device includes: a reception unit for receiving model information of a structure of a machine tool; a determination unit for determining, at the start of machining a polygon, an initial position of a center axis of the polygon, an initial phase of a rotary tool, and a position relationship between the center axis and a rotary axis of the rotary tool; a calculation unit for calculating a movement range of at least one of the rotary axis of the rotary tool and a rotary axis of workpiece based on the initial position of the center axis of the polygon, the initial phase of the rotary tool, and the position relationship between the center axis of the polygon and the rotary axis of the rotary tool; and an inference unit for inferring whether interference will occur in the machine tool, based on the model information and the movement range.

A machining apparatus includes a multi-joint arm provided with a machining tool for machining a workpiece. A control device of the machining apparatus includes: a storage section for storing NC data indicating a machining region of a workpiece by the machining apparatus; a distance measurement sensor placed on the arm and for measuring a distance between the workpiece and the machining apparatus for each machining surface of the workpiece; and a correction section for correcting the NC data for each of the machining surfaces based on a measurement result by the distance measurement sensor. As a result of this, the machining apparatus can perform the correction of machining data in correspondence to deviation of a machining object with higher accuracy.

A polygon machining method whereby first polygon machining using a polygon cutter is carried out on a workpiece, followed by machining using tools other than the polygon cutter, then second polygon machining using the polygon cutter again. The polygon machining method comprises: a first polygon machining step in which a main axis and a tool main axis are synchronously rotated such that the rotation speed of the main axis and the tool main axis are at a ratio required for the first polygon machining, and polygon machining is carried out; a machining step in which the ratio is changed to a second synchronization ratio such that the main axis rotates at a rotation speed required for machining after the first polygon machining, the main axis and the tool main axis are synchronously rotated, and machining is carried out on the workpiece that has received the first polygon machining; and a second polygon machining step in which the main axis and the tool main axis are synchronously rotated such that the rotation speed of the main axis and the tool main axis are at a ratio required for the second polygon machining, and polygon machining is carried out.

A polygon machining method whereby first polygon machining is carried out on a workpiece held by a main axis, by using a polygon cutter attached to a tool main axis, then machining using a tool other than the polygon cutter is carried out, and second polygon machining after said machining is carried out, using the polygon cutter. The polygon machining method comprises: a synchronized stopping step in which the main axis is stopped at a predetermined prescribed rotation position, in a state in which the main and the tool main axis during polygon machining are synchronously rotated when the first polygon machining has been completed; a synchronization release step in which the synchronization of the main axis and the tool main axis is released when starting machining after the first polygon machining; a main axis stopping step in which the main axis is stopped at a prescribed rotation position when the machining after first polygon machining has been completed; and a synchronization starting step in which the main axis and the tool main axis are synchronously rotated when starting second polygon machining.

This machining assistance apparatus, which calculates various types of data relating to the machining by a machine tool that cuts a workpiece into a polygon shape by rotating the workpiece and the tool at a constant rate, receives input of information relating to the machining, including information relating to the number of polygon surfaces of the workpiece formed by cutting and the number of blades attached to the tool, sets in advance the axial rotation speed of the tool and the workpiece, calculates the rotation speed ratio of the tool with respect to the number of polygon surfaces on the basis of the number of polygon surfaces and the number of blades, calculates an axial rotation speed, or a candidate thereof, of the tool and the workpiece on the basis of the rotation speed ratio within the set range of the axial rotation speed of the tool and workpiece, and outputs and displays the calculation result on a display unit that is connected to the machining assistance apparatus.