# Angle relation between gear hob and gear

In the process of gear hobbing, according to the ideal processing conditions, that is, without considering any external error, the gear hob and the processed gear are processed with a fixed transmission ratio. The relationship between the rotation angle of the gear and the transmission ratio of the hob is fixed:

Where:

φ W — angle of gear hob (RAD);

φ G — rotation angle of gear (RAD);

Z1 — number of heads of gear hob;

Z2 — number of teeth of gear.

The involute helicoid of gear hob can be regarded as an ideal involute helicoid without considering any error. Therefore, the influence of the rotation of the gear hob around its axis and the movement along its axis on the meshing process of the gear tooth surface in space is equivalent. Therefore, this replacement relationship can be used to simplify the calculation. The translation distance L of gear hob along its axis is the same as the angle of hob φ The relationship of W is:

Where: PZ – lead of gear hob.

The lead PZ of the gear hob can be illustrated by the triangle formed by the expansion of the helix, as shown in the figure. Lead of gear hob PZ, i.e Δ The length of the BC side in ABC is the distance along the axis of the cylinder when the helix rotates around the cylinder once. Helix angle of gear hob β 1, i.e Δ The ∠ ABC in ABC is the helix angle at the indexing circle of the hob. Spiral rising angle of gear hob λ 1, i.e Δ BAC in ∠ABC, and helix angle β 1. Complementary.

By Δ ABC knows:

Where:

D1 — graduation circle diameter of gear hob (mm);

λ 1 – spiral rise angle of gear hob (RAD)

Therefore, the translation distance L of the gear hob is different from the rotation angle of the gear φ The relationship between G is:

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