Abstract: The present invention provides a five-simultaneously-working axis computerized numerical controlling system tooth cutting machine tool for toroidal worms, comprising two parts a body of the machine tool and a controlling cabinet. The body comprises a bed, a spindle box with a spindle, a longitudinal sliding table, a traverse slider, a vertical guideway mounted on the slider and a tailstock, a cutter rest that supports a rotating cutter head is mounted on the vertical guideway. The spindle rotates about A-axis thereof, the table longitudinally slides along Y-axis relative to the bed, the cutter head rotates about B-axis thereof and transversely shifts X-axis as well as the cutter head makes up or down shift along Z-axis of the vertical guideway.

Abstract: A forming method for milling teeth of variable tooth worms (VTW) with the following features: on a multi-axis simultaneously-working CNC machine-tool a moving coordinate system {?1(?1)[O1;{right arrow over (i)}1(?1),{right arrow over (j)}1(?1),{right arrow over (k)}1 (?1)]} is correlated to the worm blank of the VTW worms, whereon the worm blank of the VTW worms rotates around {right arrow over (k)}1(?1)-axis at angular speed |{right arrow over (?)}1|; another moving coordinate system {?2(?2)[O2; {right arrow over (i)}2(?2), {right arrow over (j)}2(?2), {right arrow over (k)}2(?2)]} is correlated to the milling cutter, whereon the milling-cutter rotates around {right arrow over (k)}2(?2)-axis at angular speed |{right arrow over (?)}2|, |{right arrow over (?)}1|/|{right arrow over (?)}2|=i12 and i12 is a constant; the feed motion of the milling cutter comprises the radial shift along {right arrow over (i)}2(o2)-axis and the peripheral shift around {right arrow over (k)}2(?2)-axis; the equations of the cutting