
B-63784EN/01 APPENDIX D.NOMOGRAPHS
- 831 -
D.4 RADIUS DIRECTION ERROR AT CIRCLE CUTTING
When a servo motor is used, the positioning system causes an error
between input commands and output results. Since the tool advances
along the specified segment, an error is not produced in linear
interpolation. In circular interpolation, however, radial errors may be
produced, sepecially for circular cutting at high speeds.
This error can be obtained as follows:
Command path
Y
ctual path
r
∆r
∆r : Maximum radius error (mm)
V : Feedrate (mm/s)
R : Circle radius (mm)
T
1
: Exponential
acceleration/deceleration time
constant (sec) at cutting
(T=0)
T
2
: Time constant of positoning
system (sec).
(Inverse of positon loop gain)
An approximation of this radius error can be obtained with the
following expression:
In the case of exponential acceleration/deceleration
V
TTr
2
2
2
2
1
)
2
1
2
1
( +=∆
In the case of leanear acceleration/deceleration after interpolation
V
TTr
2
2
2
2
1
)
2
1
24
1
( +=∆
In the case of bell-shaped acceleration/deceleration
r
V
TTr
2
2
2
2
1
)
2
1
48
1
( +=∆
Thus, the radius error in the case of bell-shaped acceleration/
deceleration and linear acceleration/deceleration after interpolation is
smaller than in case of exponential acceleration/deceleration by a
factor of 12 or 24, excluding any error caused by a servo loop time
constant.
Since the machining radius r (mm) and allowable error ∆r (mm) of the
workpiece is given in actual machining, the allowable limit feedrate v
(mm /sec) is determined by equation (1).
Since the acceleration/deceleration time constant at cutting which is set
by this equipment varies with the machine tool, refer to the manual
issued by the machine tool builder.