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 a workpiece with at least one tool, wherein the workpiece and/or the tool are driven in rotation, wherein the tool has at least one cutting edge that is brought into cutting engagement with the workpiece, namely into a cutting position, in a cutting operation, and wherein, in the cutting operation, the workpiece or the tool is moved in a feed direction with a constant feed, and wherein, in a surface machining operation, the tool and thus the cutting edge remain in the cutting position and the workpiece or the tool is moved in the feed direction, shifted by half the feed.

A turning method for performing a turning on a workpiece in a machine tool includes: feeding a tool in a rotation axis direction and/or a radial direction of a workpiece while rotating the workpiece, the tool including an insert having a side cutting edge, the side cutting edge including a straight line portion; and feeding the tool in the rotation axis direction and the radial direction and in a predetermined inclined direction that is non-parallel to a final machining surface of the workpiece, so as to perform a turning such that a cutting edge angle as an angle formed by the straight line portion of the side cutting edge and the inclined direction becomes less than 90°.

A turning method for performing a turning on a workpiece in a machine tool includes: feeding a tool in a rotation axis direction and/or a radial direction of a workpiece while rotating the workpiece, the tool including an insert having a side cutting edge, the side cutting edge including a straight line portion; and feeding the tool in the rotation axis direction and the radial direction and in a predetermined inclined direction that is non-parallel to a final machining surface of the workpiece, so as to perform a turning such that a cutting edge angle as an angle formed by the straight line portion of the side cutting edge and the inclined direction becomes less than 90°.

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 powder production method includes providing at least one elongated member including a ductile material; providing a rotating or vibrating cutter configured to repeatedly cut an end of the at least one elongated member to produce particles; and advancing the at least one elongated member or the cutter towards the other of the at least one elongated member or the cutter to cut the particles from the at least one elongated member to produce a powder comprising a plurality of the particles. The particles produced by the method can have a diameter ranging from about 10 μm to about 200 μm.

A turning insert includes a top surface, an opposite bottom surface, and a reference plane located parallel to and between the top and the bottom surfaces. A nose portion includes a convex nose cutting edge, and a first and a second cutting edge. The nose cutting edge connects the first and second cutting edges. The first and second cutting edges form a nose angle of 71-85° relative to each other. The nose portion has a third convex cutting edge adjacent to the first cutting edge and a fourth cutting edge adjacent to the third convex cutting edge. The fourth cutting edge forms an angle of 10-30° relative to a bisector. The distance from at least a portion of the fourth cutting edge to the reference plane increases at an increasing distance from the nose cutting edge. A second protrusion is arranged between the nose cutting edge and the first protrusion.

A turning insert includes a top surface, an opposite bottom surface, and a reference plane located parallel to and between the top and the bottom surfaces. A nose portion includes a convex nose cutting edge, and a first and a second cutting edge. The nose cutting edge connects the first and second cutting edges. The first and second cutting edges form a nose angle of 71-85° relative to each other. The nose portion has a third convex cutting edge adjacent to the first cutting edge and a fourth cutting edge adjacent to the third convex cutting edge. The fourth cutting edge forms an angle of 10-30° relative to a bisector. The distance from at least a portion of the fourth cutting edge to the reference plane increases at an increasing distance from the nose cutting edge. A second protrusion is arranged between the nose cutting edge and the first protrusion.