7. Feed Functions
7.6 Feedrate Dsignation and Effects on Control Axes
119
X-axis feedrate (linear speed) "fx" and C-axis feedrate (angular speed) "
ω
" are expressed as:
fx = f ×
x
x
2
+ c
2
........................................................................................ (1)
ω
= f ×
c
x
2
+ c
2
......................................................................................... (2)
Linear speed "fc" based on C-axis control is expressed as:
fc =
ω
×
π
× r
180
.................................................................................................. (3)
If the speed in the tool advance direction at start point P1 is "ft" and the component speeds in the
X-axis and Y-axis directions are "ftx" and "fty", respectively, then these can be expressed as:
ftx = -rsin (
π
180
θ
) ×
π
180
ω
+ fx ............................................................... (4)
fty = -rcos (
π
180
θ
) ×
π
180
ω
...................................................................... (5)
Where r is the distance between center of rotation and tool (in mm units), and
θ
is the angle
between the P1 point and the X axis at the center of rotation (in units
°
).
The combined speed "ft" according to (1), (2), (3), (4) and (5) is:
ft =
ftx
2
+ fty
2
= f ×
x
2
- x
•
c
•
rsin (
π
180
θ
)
π
90
+ (
π
•
r
•
c
180
)
2
x
2
+ c
2
.................... (6)
Consequently, feedrate "f" designated by the program must be as follows:
f = ft ×
x
2
+ c
2
x
2
- x
•
c
•
rsin (
π
180
θ
)
π
90
+ (
π
•
r
•
c
180
)
2
.................... (7)
"ft" in formula (6) is the speed at the P1 point and the value of
θ
changes as the C axis rotates,
which means that the value of "ft" will also change.
Consequently, in order to keep the cutting feed "ft" as constant as possible the angle of rotation
which is designated in one block must be reduced to as low as possible and the extent of the
change in the
θ
value must be minimized.