# Tooth surface equation of gear hob

Based on the gear hob coordinate system: SW, (ow: XW, YW, ZW), the involute helicoid model of gear hob is established. Any point m on the involute helical surface of gear hob can be recorded as M（ ρ,θ)。 As can be seen from the figure,

According to the spatial geometric relationship in the gear hob coordinate system, the position vector of this point is:

Of which:

Where

γ B1 — radius of base cylinder (mm);

λ B1 — spiral rise angle of base circle (RAD)

In the gear hobbing model, the involute helical surface of the gear hob is set to mesh with the gear tooth surface at the node P of the pitch circle, and the coordinates in the ZW direction of this position are set as the coordinate origin of the ZW axis of the gear hob. Therefore, the coordinate origin of ZW axis in the formula needs to be corrected, and the correction value is set to PZ. This value can be obtained from the involute helicoid equation of gear hob and the spatial coordinate value at node P. Amend the formula to read:

The parameter equation on one side of the involute helicoid of the hob can be expressed as:

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