The feed motion of hobbing helical gear is a helix, which can be divided into the vertical motion VZ of gear hobbing hob along the Z axis and the additional rotary motion of gear blank Δω c. Strict linkage relationship shall be maintained: the gear hobbing hob moves one lead along the axial direction of the gear blank, and the gear blank rotates for an additional cycle. Therefore:
Both sides are derived and reduced to:
Therefore, the speed of gear blank after synthesis ω＊ C is:
Where, when the rotation direction of gear blank and gear hobbing hob is consistent, take “+” and vice versa.
The linkage of high-order elliptical helical gear hobbing in the end face is similar to that of spur gear. Because the end face modulus is MT, Mn in the formula can be replaced by MT, and MT = Mn / cos β ｃ。 According to the formula, the gear hobbing linkage control model is:
Where β C is the gear helix angle.
The formula shows that the hobbing of high-order elliptic helical gears can be realized by four axis four linkage.