Справочник Пользователя для Mitsubishi Electronics 60/60S

Appendix 3. 

Circular Cutting Radius Error 

 

 

 

IV-3 

 
 

When circular cutting is performed, an error is caused between the command coordinate and the tracking 
coordinate due to the tracking delay in the smoothing circuit and servo system, and the workpiece ends up 
with a radius smaller than the commanded value. The method for obtaining this error (radius error) is shown 
below. 

 

 

A  : Command coordinate 
B  : Tracking coordinate 
R  : Command radius (mm) 
∆R : Radius error (mm) 

∆θ : Angle error (rad) 
F  : Cutting feed rate (m/min)

A

F 

B 

∆θ 

R 

∆R 

F 

 

 
 

The radius error 

∆R and angle error ∆θ are calculated from the following formula. 

 

Exponential 
acceleration/ 

deceleration 

∆R =       • (       Ts

2

 +       Tp

2

) • (             )

2

   (mm) 

Linear 
acceleration/ 

deceleration 

∆R =       • (      Ts

2

 +      Tp

2

) • (            )

2

   (mm) 

 
 

 

∆θ= tan

–1

 (Ts •      ) + tan

–1

 (Tp •      ) (rad) 

 
 

 

 

TS: Time constant (s) of specified smoothing circuit 

 

 

 

TP: Position loop time constant 

1) When 

the 

∆R radius error applying with circular cutting does not come within the allowable value, 

proceed to reduce the cutting feed rate F, set Ts to a lower value or review the program. 

2)  In the steady state, 

∆R is constant. However, it is not constant with command start and stop 

transitions. Under command start and stop conditions, therefore, the tracking coordinate should 
be as shown in the figure below. 

 
 

 

Start/stop

Command Tracking

∆R

∆R

 

 

1
2

1 
2 

1 

R 

F × 10

3

60 

1 

24 

1
2

1 

R 

F × 10

3

60 

F 

R 

F

R