Advanced Micro Controls Inc. SMD23E2 User Manual page 51

SMD23E2 and SMD24E2 User's Manual
S-Curve Acceleration Equations (continued)
Determining Waveforms by Values (continued)
Example 2, Jerk = 400
Just as displacement
15,000 steps/sec
Just as speed = at, acceleration = jt
a =
f
a =
f
Because a is greater than the programmed acceleration of 58,000 steps/sec
f
trapezoidal S-curve. As shown in figure R3.7, two additional calculations must be made. The first is the time
(t ) it takes to jerk to the programmed acceleration value. The second is the time (t
1
half of the required change in speed (S
232,000 steps/sec³ t
Determine speed at t 1 : Speed
Determine remaining change in speed and required time
based on programmed acceleration
S = S –
2 m
S
2
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.
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30,000 steps/sec
S = -------------------------------------- -
m
2
100j
Ja

---------- -
J = j = -------- -
a
100

400 58,000 steps/sec²
j = ------------------------------------------------------ -
100
j = 232,000 steps/sec³
2
1
-- - at
= , speed
2
 
232,000 steps/sec³ t
= ---------------------------------------------------- -
2
15,000 steps/sec
2
t = ------------------------------------------- -
116,000 steps/sec³
t = 0.3596 seconds

232,000 steps/sec³ 0.3596 sec
83,427 steps/sec²
).
m
 
= 58,000 steps/sec²
1
t = 0.25 seconds
1
2
1
-- - jt
=
2

232,000 steps/sec³ 0.25
S = ------------------------------------------------------------- -
1
2
S = 7,250 steps/sec
1
  steps/sec
S = 15,000 7,250 –
1
S = 7,750 steps/sec
2

  
= a t t = S a
c 2 2 2
7,750 steps/sec
t = ---------------------------------------- -
2
58,000 steps/sec²
t = 0.1336 seconds
2
C
ALCULATING
= 15,000 steps/sec S

2
1
-- - jt
=
2
2

jt = a
2

c
M
OVE
= midpoint of change in speed
m
J = Acceleration Jerk parameter
j = physical jerk property
a = calculated final acceleration
f
2
, the resulting acceleration is a
) it takes to accelerate to
2
a
f
a
p
t t
1 2
Figure R3.7 Calculating Trapezoidal S-Curve
P
ROFILES
Time
51