Internal gear grinding machine and dressing method for barrel-shaped threaded tool

A method of dressing a barrel-shaped threaded tool by meshing the threaded tool with a disk-shaped dresser, the threaded tool being formed into a barrel shape having a diameter gradually decreasing from an axially intermediate portion of the threaded tool toward axially opposite end portions thereof so that the threaded tool is meshed with a to-be-machined internal gear at a crossed axes angle therebetween during grinding of the to-be-machined internal gear, the to-be-machined internal gear being rotatable about a work rotation axis, the method being comprising:

• rotating the dresser about a dresser rotation axis and turning the dresser about a dresser pivot axis perpendicular to the dresser rotation axis;
• and
• rotating the threaded tool about a tool rotation axis and moving the threaded tool in a vertical direction, a direction in which a distance between the tool rotation axis and the dresser rotation axis is adjusted, and a direction perpendicular to both the tool rotation axis and the direction in which the distance between the tool rotation axis and the dresser rotation axis is adjusted,
• wherein
• the dresser
• turns about the dresser pivot axis such that a turning angle thereof about the dresser pivot axis varies approximately quadratically with respect to an axial position on the threaded tool at which the dresser comes into contact with the threaded tool,
• the threaded tool
• rotates about the tool rotation axis such that a rotation angle thereof about the tool rotation axis varies approximately linearly with respect to the axial position on the threaded tool at which the dresser comes into contact with the threaded tool,
• moves in the vertical direction such that an amount of travel thereof in the vertical direction varies approximately linearly with respect to the axial position on the threaded tool at which the dresser comes into contact with the threaded tool,
• moves in the direction in which the distance between the tool rotation axis and the dresser rotation axis is adjusted such that an amount of travel thereof in the direction in which the distance between the tool rotation axis and the dresser rotation axis is adjusted varies approximately quadratically with respect to the axial position on the threaded tool at which the dresser comes into contact with the threaded tool, and
• moves in the direction perpendicular to both the tool rotation axis and the direction in which the distance between the tool rotation axis and the dresser rotation axis is adjusted such that an amount of travel thereof in the direction perpendicular to both the tool rotation axis and the direction in which the distance between the tool rotation axis and the dresser rotation axis is adjusted varies approximately cubically with respect to the axial position on the threaded tool at which the dresser comes into contact with the threaded tool.