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).

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 device for the machining of curved laminar surfaces, having a first part including a tool for machining the concave face of the surface, and first pressure device in contact with the concave face of the surface, a second part including second pressure device in contact with the convex face of the surface, and devices synchronizing the movements of the first and second parts is provided. The tool has a circular shape for the radial machining of the concave face, and the first pressure device has at least one disc parallel to the tool, the tool and disc disposed on a rotary shaft and both having a radius equal to or less than the radius of curvature of the concave face.

A method for machining of ball tracks of an inner race of a constant velocity joint includes the step of providing a power skiving tool having a plurality of cutting members and a first axis of rotation and providing a work piece having an outer envelope surface extending along an axis of rotation. The first axis of rotation of the power skiving tool is arranged at a first distance from the axis of rotation of the work piece and oriented at a first angle. A first rotational speed to the power skiving tool and a second rotational speed to the work piece and a relative movement between the work piece and the power skiving tool, is applied such that the cutting members engage the outer envelope surface to machine the ball tracks. A cutting insert and a power skiving cutting tool are also provided.

A broaching tool is held during the conduct of repetitive duplicate rotary broaching operations on serially presented workpieces. The broaching tool is engaged serially with each workpiece for rotation with the engaged workpiece during a corresponding rotary broaching operation. Each workpiece has a given configuration and the broaching tool has a prescribed configuration placed at an initial orientation for establishing a broached configuration placed at a same predetermined orientation relative to the given configuration of each workpiece. Upon completion of a rotary broaching operation on a workpiece, the broaching tool is returned to the initial orientation of the prescribed configuration in preparation for a duplicate rotary broaching operation on a subsequent serially presented workpiece.

A device for the machining of curved laminar surfaces, having a first part including a tool for machining the concave face of the surface, and first pressure device in contact with the concave face of the surface, a second part including second pressure device in contact with the convex face of the surface, and devices synchronizing the movements of the first and second parts is provided. The tool has a circular shape for the radial machining of the concave face, and the first pressure device has at least one disc parallel to the tool, the tool and disc disposed on a rotary shaft and both having a radius equal to or less than the radius of curvature of the concave face.

A broaching tool is held during the conduct of repetitive duplicate rotary broaching operations on serially presented workpieces. The broaching tool is engaged serially with each workpiece for rotation with the engaged workpiece during a corresponding rotary broaching operation. Each workpiece has a given configuration and the broaching tool has a prescribed configuration placed at an initial orientation for establishing a broached configuration placed at a same predetermined orientation relative to the given configuration of each workpiece. Upon completion of a rotary broaching operation on a workpiece, the broaching tool is returned to the initial orientation of the prescribed configuration in preparation for a duplicate rotary broaching operation on a subsequent serially presented workpiece.

A broaching tool is held during the conduct of repetitive duplicate rotary broaching operations on serially presented workpieces. The broaching tool is engaged serially with each workpiece for rotation with the engaged workpiece during a corresponding rotary broaching operation. Each workpiece has a given configuration and the broaching tool has a prescribed configuration placed at an initial orientation for establishing a broached configuration placed at a same predetermined orientation relative to the given configuration of each workpiece. Upon completion of a rotary broaching operation on a workpiece, the broaching tool is returned to the initial orientation of the prescribed configuration in preparation for a duplicate rotary broaching operation on a subsequent serially presented workpiece.

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.