GSK GSK983Ma, User Manual

Page: 303 / 373

Appendix 4. Nomographs
291
Appendi
x
=
( )
t T T Vy
T
t
T
T
t
T
T T
Vy Vy
− + −
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− × −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− ×
−
−
2 1 2
2
2
2
1
2
1
2 1
1 2
exp exp
…………
（
6
）
A4.2 Radius Direction Error at Circle Cutting
When a DC servo motor is used, the positioning system will produce a delay between input axis
and output axis. 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, especially for
circular cutting at high speeds. This error can be obtained as follows:
R: maximum radius error
△ （
mm
）
V: feedrate
（
mm/s
）
r: circle radius
（
mm
）
T
1
: exponential acceleration/deceleration time constant
（
s
）
during cutting
（
T
1
= 0
）
T
2
: time constant of positioning system （ s ）（ inverse of position loop gain ）
△
r =
( )
r
V
T T
2
2
2
2
1
2
1
× +
………………………………………………
（
1
）
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/s) is determined by equation (1).
Since the acceleration/deceleration time constant during cutting which is set by this equipment
varies with the machine tools, please refer to the manual issued by the machine tool builder.