Printed in the Federal Republic of Germany TR-Electronic GmbH 2016, All Rights Reserved
09/29/2020 TR-EMO-BA-GB-0022 v03 Page 65 of 153
2. Ramp calculation:
Drive with slide, powered by a screw link actuator (translatory movement)
Feed = 1 mm/spindle revolution
Gear reduction = 40:1 = 40 motor revolutions per spindle revolution
Slide movement s = 1000 mm
Acceleration from standstill = 20 rpm/sec
Further acceleration from 20 rpm/sec to 240 rpm, then constant
Deceleration = 60 rpm/sec, until stationary
Position factor = 2
16
*40
1 mm feed = 2
16
*40 position increments.
The following results for the speed factor:
speed factor = 40*2
31
/300000.
This results in
VelocityToPositionUnitFactor = [(40*2
31
/300000)*2
16
]/[(40*2
16
)*(2
31
/5000)]
= 5000/300000 = 1/60
AccelerationToPositionUnitFactor = 1/60
The acceleration phase lasts t
acc
= 12 sec, the braking phase t
dec
= 4 sec.
The following results for the acceleration:
a = 20*(1/60) = 1/3 mm/sec²,
and for the deceleration
b = 60*(1/60) = 1 mm/sec²,
The end speed of 240 rpm corresponds to
v
end
= 240*(1/60) = 4 mm/sec.
During the acceleration phase, the distance covered is
s
a
= 0.5* a* t
acc
2
= 0.5*(1/3)*12² = 24 mm
The deceleration distance is likewise
s
b
= t
dec
* v
end
– 0.5* b* t
dec
2
= 4*4
– 0.5*1*4² = 8 mm.
Therefore, for travel at constant speed v
end
s – (s
a
+ s
b
) = 1000 – 28 = 968 mm still remain.
This phase therefore lasts 968/4 = 242 sec.
In total, the ramp is (theoretically) traveled in 258 sec.
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