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For machining experiments, a free-form surface
was selected. This surface was machined by five-
axis end milling with a 4mm straight tool path
interval. Also the surface was machined with a
curwd tool path for uniform surface and straight
tool path maintaining cusp height to a constant
value. From test results and discussions, it was
concluded that the machining of sculptured sur-
faces on the five-axis CNC machine was a very
effective machining method.2. The Method for 5-Axis End Milling
2.1 Coordinate representation
In most NC machines the work-table moves in
the X and Y directions and the spindle moves in
the Z direction. These are appropriately termed
three-axis machines. Five-axis machine tools on
the other hand, have two rotational freedoms in
addition to the normal three orthogonal move-
ments. These machines can be pided into three
main families: Type I. Machines with a fixed
table and a spindle head capable of rotation in
two perpendicular planes. Type 2. Machines with
a fixed spindle and a table capable of rotation in
two perpendicular planes. Type 3. Machines with
a rotary table and a tilting spindle head.
The five-axis milling process is carried out at
the cc-point as shown in Fig. I, and coordinates
can be represented for the cc-point. In all types of
five-axis milling machines, the position of the NC
command is the position (Pc or PT ) of the pivot
point in the spindle head or the work-table. Since
the workpiece is mounted on the work-table of
the machine, the surface position of a part is
represented by XT- YT-ZT local coordinate of
table. If free-form surfaces are represented byparametric formulation, the surface position W
XYZt in a local coordinate of the table can be
expressed in this way
where ZCt is the cutter axis direction vector in the
local coordinate of a work-table centering on
cc-point, MA(A) is a translation matrix of the
coordinate, and Zc is (0,0, I )T. Thus, if a cutter
axis direction vector is known in the machining of
sculptured surfaces with the end mill cutter, the
A, Band C values can be calculated from Eq. (2),
(3) and (4).
If cutter axis direction vector T a is known in
types of five-axis machines, coordinates for cutter
axis direction vector can be represented as shown
in Fig. 2 (a)-(c). Where, Zc direction is equal to
cutter axis direction vector T a and the center
point 0 is cc-point represented by Eq. (I). If Xc-
Yc-Zc global coordinate is equal to Xr YrZT
local coordinate of a work-table in initial condi-
tion, the cc-point can be the position in global
coordinate and WXYZt can be translated to WXyzgo
In this study, coordinates are translated on the
basis of cc-point. Here, this method is called the
translation method on the basis of cc-point.
In the three types of five-axis machines, cutter
axis direction vectors in the table coordinate
system are represented respectively by
the machining of a sculptured surface on a five-
axis milling machine. In the previous section, the
cutter axis direction vector required cl-data and
NC-code machining sculptured surfaces on a
five-axis milling machine used with the end mill
cutter. The cutter axis direction vector had better
be determined to produce minimum cusp heights
on the machined surfaces at a fixed tool path
interval.
In Fig. 3, Xp-Yp-Zp coordinate is the coor-
dinate that the tool path direction projected on Xr
YT plane is equal to Yp direction. apath and acpath
values are the angles determining the cutter axis
direction vector in Xp -Yp-Zp coordinate. Since all
positions of surface in a local coordinate can be
obtained by translations, the z-values of Fig. 3