5 Spindle Axis Operation
5.3.4 Tapping Control with a Continuous Jerk Function
5-20
5.3.4
Tapping Control with a Continuous Jerk Function
High-speed, highly accurate tapping can be performed by specifying a continuous speed, acceleration rate, and
jerk.
First, generate a quintic speed equation for continuous jerk.
The conditions for the quintic speed equation are as follows:
• The initial speed is 0 mm/s.
• End acceleration at X mm.
• The target speed when acceleration finishes is Y mm/s.
• The acceleration when acceleration begins and ends is 0.
• The jerk when acceleration begins and ends is also 0.
Satisfy the above conditions in the following quintic speed equation to determine the jerk.
When t = 0, v = At
5
+ Bt
4
+ Ct
3
+ Dt
2
+ Et + F
A = 5At
4
+ 4Bt
3
+ 3Ct
2
+ 2Dt + E (differential of the speed)
α
= 20At
3
+ 12Bt
2
+ 6Ct
1
+ 2D (differential of the acceleration)
The initial speed is calculated with a polynomial expression that solves the above formulas.
v, A,
α
= 0, so D, E, F = 0
This results in the following expressions.
v = At
5
+Bt
4
+Ct
3
A = 5At
4
+4Bt
3
+3Ct
2
α
= 20At
3
+12Bt
2
+6Ct
1
If the time to finish acceleration is t1, the acceleration is calculated as A = 5At
1
4
+ 4Bt
1
3
+ 3Ct
1
2
= 0 ... (1)
The speed when acceleration finishes is Y mm/s, so Y = At
1
5
+ Bt
1
4
+ Ct
1
3
... (2)
The distance when acceleration ends is the integral of v, so X = At
1
6
÷
6 + Bt
1
5
÷
5 + Ct
1
4
÷
4 ... (3)
The jerk when acceleration begins and ends is 0, so 0 = 20At
1
3
+ 12Bt
1
2
+ 6Ct
1
1
... (4)
Now let’s calculate the speed Y and distance X during linear acceleration/deceleration from the spindle axis
revolutions, pitch, tap length, acceleration, and jerk, using the spindle axis pulses as a base.
Then, substitute those values into (2) and (3) above to solve equations (1), (2), (3), and (4) to find t
1
, A, B, and
C.
Calculate the spindle axis motor speed, feed axis value corresponding to the speed, and the target positions for
the spindle and feed axes each communications cycle, then send the INTERPOLATE command to the
Σ
-V-SD
drive.
Also, calculate the time in the constant speed area, the speed of the spindle axis during deceleration, and the
value of the feed axis, then send the INTERPOLATE command.