GSK GSK983Ma, Руководство пользователя

Страница: 302 / 373

GSK983M3Ma Milling Machine Center CNC System User Manual
290
Appendi
x
V
X
2 = V·cos φ 2
V
Y
2 = V·sin φ 2
π
－（
φ 1- φ 2
）
= θ
[Description of symbols]
V: Feedrate at both blocks before and after cornering
V
X
1: X-axis component of feedrate of preceding block
V
Y
1: Y-axis component of feedrate of preceding block
V
X
2: X-axis component of feedrate of following block
V
Y
2: X-axis component of feedrate of following block
θ : Corner angle
φ 1: Angle formed by specified path direction of preceding block and X-axis
φ 2: Angle formed by specified path direction of following block and X-axis
Initial value
Initial value calculation
The initial value when cornering starts, that is, the X and Y coordinates at the end of command
distribution by the controller, is determined by the feedrate and the positioning system time constant
of the DC servo motor.
X
0
= Vx
1
（ T
1
+T
2
） ……… （ 1 ） Y
0
= Vy
1
（ T
1
+T
2
） ……… （ 2 ）
T1: Exponential acceleration/deceleration time constant. (T=0)
T2: Time constant of positioning system (inverse of position loop gain)
Analysis of corner tool path
The equations below represent the feedrate for the corner section in X-axis direction and Y-axis
direction.
Vx
（
t
）
=
（
Vx
2
－
Vx
1
）
[1
－
{ }
Vx1] exp exp
Vx1
2
2
1
1
2 1
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− × −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− ×
−
T
t
T
T
t
T
T T
= Vx
2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− × −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− ×
+
−
2
2
1
1
2 1
exp exp
T
Vx1
1
T
t
T
T
t
T
T
………………
（
3
）
Vy
（
t
）
=
2
2
2
1
1
2 1
2 1
Vy exp exp
T
Vy Vy
+
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− × −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− ×
−
−
T
t
T
T
t
T
T
………………
（
4
）
The coordinates of tool path at time t are calculated from following equations:
X
（
t
）
=
0
0
) ( X dt t Vx
t
−
∫
=
( )
t T T Vx
T
t
T
T
t
T
T T
Vx Vx
− + −
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− × −
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
− ×
−
−
2 1 2
2
2
2
1
2
1
2 1
1 2
exp exp
…………
（
5
）
Y （ t ） =
0
0
) ( Y dt t Vy
t
−
∫