Page 126 - Mechatronics for Safety, Security and Dependability in a New Era

Ch23-I044963.fm Page 110 Tuesday, August 1, 2006 9:09 PM
Ch23-I044963.fm
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110 Page 110 Tuesday, August 1, 2006 9:09 PM
Entity (TLE), i.e., the trajectory made by the tool radius, as a key concept corresponding to the OLE to
treat every tool envelope as an ordinary offset loop. The uncut region detection method, namely the
extended ODM is proposed. The conspicuous feature of the devised method is that uncut regions are
detected in an identical way of offsetting and the clean up curves are treated as ordinary offset loops.
Through this study, the problem of obviating uncut regions is resolved.

GENERATION OF OFFSET CURVE FOR POCKETING
To focus the present study on the detection of uncut regions, offset curve generation for pocketing
without or with islands is briefly discussed through an illustrated example shown in Fig.l. The
boundary of the pocket is defined as the Contour curve Entity (CE) and the sequential linkage of the
CEs is defined as the Contour Loop Entity (CLE) as shown in Fig.l(a), by assuming that a CLE is
constructed only with lines and circular arcs. Imagining that a circle with a radius that equals the offset
distance is rolling on the CE, the trajectory of the center of the circle is defined as the Offset curve
Entity (OE), and the sequential linkage of OEs is defined as the inborn OLE as shown in Fig. 1 (b). In
pocket machining, there is a strong possibility that the inborn OLE is formed into an open loop having
local and global self-intersections that result in undesirable cuts. The local OLE reconstruction is
performed inserting additive OEs or by dissecting intersections in two adjacent OEs to create one
crude OLE and to discard four open OLEs as shown in Fig. l(c). However, the crude OLE is
intersected globally by itself at three points as shown in Fig.l(d). Detecting an intersection and
applying a dissection on the crude OLE, the OLE is decomposed into one simple OLE and one crude
OLE. By the second dissection, the OLE is decomposed into one simple OLE and one crude OLE. By
the third dissection, the OLE is decomposed into two simple OLEs. Finally, all OLEs become simple
OLEs as shown in Fig.l(e). The simple OLE obtained by the global OLE reconstruction may still not
be appropriate as an offset curve for machining. The characteristics of OLE, i.e., closeness and
orientation, need to be examined to confirm the validity of OLE for continuity and proper direction of
the tool path. Fixing the orientation of a CLE to be counterclockwise, two OLEs are selected as valid
OLEs, since they are completely closed and counterclockwise. Then, the valid OLEs in Fig.l(f) are
kept to play the role of an offset curve for pocketing and the role of CLEs in the next offsetting turn.

One of the salient features of the ODM is the applicability. The offset curve generation method for one
OLE works as the method for multiple OLEs. To ensure the merits, the ODM is applied to the
generation of an offset curve for a pocket with islands, by shifting the object of intersection detection,
dissection, and validation, from one OLE to multiple OLEs. Using an illustrated example of offset
curve generation for a pocket with an island, the ODM is evaluated. Figure l(g) shows the CLEs from
one pocket and one island in dotted line, and two simple pocket OLEs and one simple island OLE in
solid lines. At an intersection, a pocket OLE and an island OLE are dissected, and reconnected into
one combined OLE conserving orientations and vice versa. Then, applying a dissection one more time
at the other intersection and reconnecting again, one combined OLE is decomposed into two combined
OLEs as shown in Fig.l(h). Performing OLE validation with the rule that the characteristic of the
pocket OLE is transferred to the combined OLE when a pocket OLE and an island OLE are combined
into an OLE, two valid OLEs are kept to play the role of offset curves for pocketing and the role of
CLEs in the next offsetting turn as shown in Fig. 1 (i). Thus, the ODM works for a pocket with islands.

DETECTION OF UNCUT REGIONS
Uncut regions appear mainly on two occasions. The first is due to the improper selection of tool
diameter for pocket boundary. There is no way to avoid this kind of uncut, unless the other tool is
selected. The second is due to the complexity of pocket geometry under the offset distance properly