Five-simultaneously-working-axis computerized numerical controlled tooth cutting machine tool for plane enveloping toroidal worms

A five-simultaneously-working-axis computerized numerical controlled tooth cutting machine tool for cutting a toroidal worm on a workpiece, comprising:

• a body of the machine tool and a controlling cabinet, the body including a bed, a spindle box with a spindle, a longitudinal sliding table, a traverse slider, a vertical guideway mounted on the traverse slider, and a tailstock;
• wherein a cutter rest that supports a rotating cutter head is mounted on the vertical guideway;
• wherein the spindle rotates about an A-axis thereof, the table longitudinally slides along a Y-axis relative to the bed;
• wherein the cutter head rotates about a B-axis thereof and transversely shifts along an X-axis, as well as the cutter head makes an up or down shift along a Z-axis of the vertical guideway;
• the controlling cabinet being equipped with programs for controlling the five axes of A, Y, X, Z and B simultaneously working together;
• wherein a first coordinate system is associated with the workpiece worm, a second coordinate system is associated with an imaginary gear which meshes with the workpiece worm, a third coordinate system is associated with the rotating cutter head and a fourth coordinate system is associated with the cutting edges which lie on a tooth flank of the imaginary gear, and wherein motion equations of the five axes of the machine tool are determined such that a shift of the cutting edges of the cutter on the cutter head is controlled to simulate a plane which is inclined relative to and rotating around a central axis of the imaginary gear in spatial locations, in order to envelop cut the tooth flanks of a plane enveloping a toroidal worm.