A method for producing a freeform Fresnel surface having a number of Fresnel facets with a respective Fresnel segment surface and a trailing edge includes the production of the freeform Fresnel surface via machining processing of a starting body based on the construction data for the freeform Fresnel surface. With the aid of the circular cylinder casing surfaces and/or cone casing surfaces, the projection of the edges of the Fresnel facets on the x-y-plane represent circular paths for the creation of the construction data.

A controller of a machine tool acquires coordinates of a first machining start point of an eccentric shape in a reference phase of a workpiece around a spindle axis, a second machining start point in an anti-phase, a first machining end point in the reference phase, and a second machining end point in the anti-phase. The controller decides a moving path of the tool in association with rotation of the workpiece at least according to the coordinates of the first start point, the second start point, the first end point, and the second end point to form the eccentric shape around an eccentric axis passing a start point origin between the first start point and the second start point and an end point origin between the first end point and the second end point and thereby controls movement of the tool in association with rotation of the workpiece.

A controller of a machine tool acquires coordinates of a first machining start point of an eccentric shape in a reference phase of a workpiece around a spindle axis, a second machining start point in an anti-phase, a first machining end point in the reference phase, and a second machining end point in the anti-phase. The controller decides a moving path of the tool in association with rotation of the workpiece at least according to the coordinates of the first start point, the second start point, the first end point, and the second end point to form the eccentric shape around an eccentric axis passing a start point origin between the first start point and the second start point and an end point origin between the first end point and the second end point and thereby controls movement of the tool in association with rotation of the workpiece.

A method for machining ribs or grooves on a workpiece such as a shaft or an air or gas axial bearing intended to be rotated about a longitudinal axis of a centrifugal compressor. All of the ribs or grooves are obtained at once by the machining tool on a workpiece portion driven such that it rotates, by moving the workpiece or the tool holder in a longitudinal machining direction, the machining tool moving back and forth with a machining position in contact with the workpiece and a position wherein it is not in contact with the workpiece from the start to the end of the workpiece portion. The back-and-forth movements of the machining tool are synchronised with the sinusoidal program set up in the machining unit, as well as with the desired, programmed arrangement of the ribs or grooves to be produced on the workpiece portion.

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 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 vibration cutting process diagnostic device diagnoses the propriety of a vibration cutting process to machine the sectional shape of a working object into a non-complete round shape by reciprocating a movable shaft. This device includes a frequency analyzer to calculate a frequency component contained in a position command signal for the movable shaft on the basis of shape data, which is machining shape data on a workpiece treated as the working object, and a machining speed set value; and a process diagnosis executor to diagnose the propriety of machining the shape data under the machining speed set value on the basis of the frequency component and a movable shaft parameter of the movable shaft.

A power skiving tool comprising a shank that extends along a longitudinal axis of the tool, and a cutting head that is arranged at an end face of the shank. The cutting head comprises a plurality of circumferentially arranged teeth, wherein, when viewed in a cross-section orthogonal to the longitudinal axis, each of the teeth comprises a convexly rounded contour, which at a first end transitions either directly or via a first concave transition contour into the convexly rounded contour of a first adjacent tooth of the plurality of teeth and at a second end opposite the first end transitions either directly or via a second concave transition contour into the convexly rounded contour of a second adjacent tooth of the plurality of teeth. A width of each tooth of the plurality of teeth, measured in the cross-section as a distance between the first end and the second end, is greater than a height of the respective tooth, measured in the cross-section orthogonal to the width and centrally between the first end and the second end.

A cutting tool includes: a cutting part including a cutting edge having a linear shape; and a fitted part including a fixed section to which the cutting part is fixed, and a fitted part body to be fitted to a cutting device. The cutting edge is located perpendicularly to a virtual line passing through a central axis of the fitted part body, on a plane that is perpendicular to the central axis of the fitted part body. A center of the cutting edge in its longitudinal direction is located on the virtual line.