Advanced Micro Controls Inc. SMD23E2, User Manual

Page: 51 / 133

20 Gear Drive, Plymouth Ind. Park, Terryville, CT 06786

Tel: (860) 585-1254 Fax: (860) 584-1973 http://www.amci.com
SMD23E2 and SMD24E2 User’s Manual
C
ALCULATING
M
OVE
P
ROFILES
51
S-Curve Acceleration Equations (continued)
Determining Waveforms by Values (continued)
Example 2, Jerk = 400
Because a
f
is greater than the programmed acceleration of 58,000 steps/sec
2
, the resulting acceleration is a
trapezoidal S-curve. As shown in figure R3.7, two additional calculations must be made. The first is the time
(
t
1
) it takes to jerk to the programmed acceleration value. The second is the time ( t
2
) it takes to accelerate to
half of the required change in speed (S
m
).
The time for this acceleration phase is 2(t1 + t2), which equals 2(0.2500 sec + 0.1336 sec) or 0.7672 seconds.
Time spent in the constant acceleration period is (2(0.1336))/0.7672) or 34.8% of the entire phase.
S
m
30,000 steps/sec
2
--------------------------------------- 15,000 steps/sec = = S
m
= midpoint of change in speed
J
100 j
a
-----------
j
Ja
100
--------- =

=
J Acceleration Jerk parameter =
j physical jerk property =
a
f
calculated final acceleration =
j
400 58,000 steps/sec²
 
100
------------------------------------------------------- =
j 232,000 steps/sec³ =
Just as displacement
1
2
---
at
2
, speed
1
2
---
jt
2
= =
15,000 steps/sec
232,000 steps/sec³ t
2
 
2
----------------------------------------------------- =
t
2
15,000 steps/sec
116,000 steps/sec³
-------------------------------------------- =
t 0.3596 seconds =
Just as speed = at, acceleration = jt
a
f
232,000 steps/sec³ 0.3596 sec
 
=
a
f
83,427 steps/sec² =
Figure R3.7 Calculating Trapezoidal S-Curve
A
cce
le
ra
ti
o
n
a
p
a
f
Time
t
2
t
1
232,000 steps/sec³ t
1
 
58,000 steps/sec² = jt a =
t
1
0.25 seconds =
Determine speed at t
1
: Speed
1
2
---
jt
2
=
S
1
232,000 steps/sec³ 0.25
 
2
2
-------------------------------------------------------------- =
S
1
7,250 steps/sec =
Determine remaining change in speed and required time
based on programmed acceleration
S
2
S
m
S –
1
15,000 7,250 –
 
steps/sec = =
S
2
7,750 steps/sec =
S
2
a
c
t
2
 
t
2

S
2
a
c

= =
t
2
7,750 steps/sec
58,000 steps/sec²
----------------------------------------- =
t
2
0.1336 seconds =