Production geometry analysis, modeling, and rapid prototyping production of manufacturing tool of spiroid face gear

Abstract

The geometric analysis of a face-gear hob is introduced in this article. We examined the logarithmic spiral and the Archimedean spiral backward-turned curves in profile distortion aspect. The cutting edge of the hob defines the face-gear dentation, which is why the equations of the cutting edge have to be known for manufacturing. We worked out the mathematical analysis of the backward-turned curves, the cutting edge, the face surface, and the relief side surface of the hob in general case. Based on these, we designed a conical hob, working out its three-dimensional virtual CAD model. Using rapid prototyping technique, we produced the real physical model of this hob, and the hob was actually manufactured. We carried out three-coordination measuring analysis of the rapid prototyping model and the actually manufactured model. We analyzed the measured results and presented the evaluation of our results.

Appendix

CAD:

Computer aided design

r :

Radius vector

a:

Constant (if φ = 0, then r = a)

m:

Constant exponent

α:

Back angle

K₀ (ξ, η, ζ):

Coordinate system of generator curve motion

K_1F (x_1F, y_1F, z_1F):

Coordinate system following a thread path, joined to worm surface

K₁ (x₁, y₁, z₁):

Worm stationary coordinate system

${\overrightarrow r_g}$ :

Leading curve in the K₀ (ξ, η, ζ) tool coordinate system

${\overrightarrow r_{{1F}}}$ :

The position vector of an oblique point fitted on thread surface

z _ax :

The K₁ (x₁, y₁, z₁) coordinate system removal value

h_r :

Value of relief