20. AXIS CONTROL FUNCTION
The principle of polygonal turning is explained below. In the figure below
the radius of tool and workpiece are A and B, and the angular speeds of
tool and workpiece are aand b. The origin of XY cartesian coordinates is
assumed to be the center of the workpiece.
Simplifying the explanation, consider that the tool center exists at the
Po (A,0) on the workpiece periphery, and the tool nose starts from
position Pto(A–B, 0).
A ; Workpiece radius
B ; Rool radius
α ; Workpiece angular speed
β ; Tool angular speed
Po (A, 0)
Pto (A–0, 0)
In this case, the tool nose position Pt (Xt,Yt) after time t is expressed by
Pt (Xt, Yt)
Assuming that the rotation ration of workpiece to tool is 1:2, namely,
equation 1 is modified as follows
Xt=Acos αt–Bcos αt=(A–B)cos αt
Xt=Asin αt+Bsin αt=(A+B)sin αt
Equation 2 indicates that the tool nose path draws an ellipse with longer
diameter A+B and shorter diameter A–B.
Then consider the case when one tool is set at 180° symmetrical positions,
for atotal of two. It is seen that a square can be machined with these tools
as shown below.
D Principle of Polygonal