However, high precision obtained from a special machine tools is associated with a
less flexible manufacturing process, while general NC machine tools make manufac-
turing business more flexible. Therefore, due to differences in finance situations and
business models and technology of companies, special machines and NC machines
have its own applications. The precision factor has to be considered in connection
with the above factors. In traditional methods, shape, scale and position of the con-
nected ellipses on a pair of gear and pinion tooth surfaces are influenced by a set of
adjustment parameters on the special machines. It not only really takes some time to
get the parameters right for a designed surface, but also can not meet exactly high
precision requirements because of unavoidable errors in a complex mechanism. As
for the simple-structured NC machines, due to different coordination definition, the
gap on spherical involute surfaces of SBGs between design models and machining
models produces uneven machining points. Because of the SBGs complexity, direct
online measurement and control are very difficult as well.
In this paper, a precise SBGs CAD/CAM model was developed with the Loop sub-
division algorithm. It would be more convenient in NC machining and simpler in
precision assessment than the traditional NC algorithm. In the future, a database of
various gear standards for precision-decision and an on-line compensation system can
be developed for SBGs NC machining. Then a Loop subdivision process can be con-
trolled automatically based on required precisions in a real-time machining applica-
tion. It would lead to a complete new CAD/CAM/CNC modelling for intelligent
SBGs manufacturing.
2 Related Work
Based on the gear geometry, a design model, named as Sculptured Surface Machining
(SSM) model, was introduced by (Suh S.H. 2001). Also the specific machining tooth
path was planned, and NC code for 4 axis and 3/4-axis was obtained. Experimental
cuts were done to prove its validity and effectiveness. Later the precision of NC ma-
chining was checked in (Suh S.H. 2002) by testing several parameters, such as tooth
profile error, tooth trace error and pitch errors. The results showed a well coherence
of the tooth surface under SSM model to that of the traditional machining model.
As for machining points data processing, many researches could be applied in our
CAD/CAM model for optimal machining points. Fitting surfaces to 3D cloud points
generated by laser range scanning systems is one of the most important problems in
CAD modelling. The ordinary representation for fitting such data in geometric model-
ling is the tensor product B-spline surfaces. However, it is extremely difficult for
them to handle surfaces with arbitrary topology, and to maintain continuity conditions
near the extraordinary points (Derose T 1998). Then subdivision surfaces become
very popular in movie production and game engines as an alternative to the tensor
product B-spline (Ma W.Y. 2005).
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