3.1 Separate SSM Models for Gears and Pinions
On the basis of (Suh S.H.2001), gear and pinion tooth surface models were developed
and shown in Table1 and 2 respectively. The influence factors u, w and δb1, are
shown in Fig.1. By changing u from 0 to Umax, and w from the value of large section
to small section, the spherical involute curve for straight bevel tooth were obtained,
and then after a rotation of an angle named o, the design model for SBGs was
constructed. Umax is a for-loop controlling factor for generating design surfaces, its
definition is shown in equation-1. Since functions for only one pinion surface were
represented in (Suh S.H. 2001), the more detailed introduction in this paper will give
more convenience for understanding SBGs CAD/CAM model.
Referred to (S.H. Suh 2001) dk1 is outer diameter, X1 is axial distance along adden-
dum, δb1 is base cone angle.
In the SBG design model, different rules were implemented for pinion, wheel and
small pinion. For wheel and small pinion milling (when pinion module is not more
than 2 mm, it would be classified as small pinion), double sided blade parameters
would be applied in both calculation of convex surface and concave surface. When
concave surface obtained, the convex surface would be on the adjacent tooth surface
with a rotation of angle called base. As shown in Table 1, Xg, Yg, Zg and Xg1, Yg1,
Zg1 are machining sample points on concave surface and convex surface, separately.
Due to smaller size and larger curvature, the result of SSM models in pinion applica-
tion attracts more attentions. The formulas are shown in Table–2. Single blade disk
applied in most of pinion machining, its diameter and setting-up parameters on a spe-
cial machine for concave surface and convex surface milling were necessary parame-
ters. In table 2, Xp, Yp, Zp are components of a point located on concave surface
model of pinion, while Xp1, Yp1, Zp1 are on convex model. A software system has
been developed to automatically select right parameters. Its software interface was
shown in Figure– 2.
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