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2.4 Tool path generation
In an NC machining of a die/mold, the deter-
mination of an effective tool path is important to
the enhancement of precision and productivity. In
this study, tool path is generated for precision
machining. The cusp height predicted in previous
section is important to determine tool path inter-
val. Cusp heights on the sculptured surface ma-
chined by five-axis milling with the end mill
cutter are much smaller than those by three-axismilling with the ball end mill cutter. Thus, in
five-axis machining with the end mill cutter, the
grinding process may be omitted and the ma-
chined part may be completed by the polishing
process. Thus, a tool path interval had better be
determined from cusp heights predicted in previ-
ous section. There are two kinds of tool paths.
One is a curved tool path having uniform cusp
height for polishing with spiral motion and the
other is a straight tool path having less than given
cusp height for polishing with straight motion.
2.5 Post processing
In the NC part program for the five-axis ma-
chine of Type I used in this study, the tool
position (X,Y,Z) is the position of the pivot
point, and the cutter direction (A,B) is expressed
by the angle of the cutter axis rotating around the
pivot point (Cincinnati Milacron Marketing
Company, 1989).
Figure 5 shows the position of the pivot point.
The position vector can be calculated from the
summation of vectors and is expressed
p~,j) =0 11 ,))- R·uT~i.))+ (Lt
+ Lp)'uT~,i) (9)
Where, uTil,i) is the vector which center point
vector (0, - Rcosacpath, - Rsinacpath) in Xp-Xp-Zp
coordinate is translated to XG -YG-ZG coordinate.
Also, uTa lI,i) is the vector which ZCt in XT -YrZT
coordinate is translated to XG -YG-ZG coordinate.
Further, in the five-axis end milling of Type 2 and
Type 3, translation of coordinates can be applied
with rotational characteristics. Thus, considering(10)
Fig. I and Eq. (2), (3) and (4), NC-code can be
generated from the principle that coordinates are
translated by the translation method on the basis
of the cc-point.
Five-axis end milling produces the machined
surface of edge shapes in feed direction and is
termed the cutter mark. The magnitude of the
edge height for five-axis milling is dependent
upon rotation speed and feed. Thus, the cutter
mark is expressed by
E"=~2 f
where I' is the feed rate at (i,j )-th cc-point. n is the
number of cutter flute, ail,j) is 'Sturz' angle, and Ev
is the cutter mark along the feed direction as
shown in Fig. 6. Thus, for fine surfaces, rotation
speed or feed rate can be adjusted.
In the five-axis machining process by the NC-
code with constant feed rate, machining speed may
be very slow. This is due to the fact that both
rotational and traverse movements are required
simultaneously in programming (Cincinnati Mila-
cron Marketing Company, 1989). This effect
should be considered in five-axis post-processing.
Therefore, for constant feed rate of the cuttingedge at the cc-point, the feed rate of the pivot point
must be varied along with the length of traversing
and rotating path. Also, when machining from
current position to command position with differ-
ential axis direction vector each other, an over-cut
occurs by swivel movements around the pivot
point. In order to solve this problem, the linear-
ization of the tool path must be applied (Takeuch
et al, 1992).
3. Experiments
The CINCINATI MILACRON five-axis ma-
chining center (model 20Y-80) and three- dimen-
sional coordinate measuring machine (CMM)