B-63324EN/03 APPENDIX D.NOMOGRAPHS
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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:
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.
∆r : Maximum radius error (mm)
V : Feedrate (mm/s)
R : Circle radius (mm)
: Exponential acceleration/deceleration time constant
(sec) at cutting
: Time constant of positoning system (sec).
(Inverse of positon loop gain)
In the case of bell-shaped acceleration/deceleration and
linear acceleration/deceleration after cutting feed
interpolation, an approximation of this radius error can
be obtained with the following expression:
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, excluding any error caused by a servo
loop time constant.