7applications – Lenze DSD User Manual
Page 95
Lenze · Drive Solution Designer · Manual · DMS 4.2 EN · 12/2013 · TD23
95
7
Applications
7.5
Rack drive
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[7-44] Equation 4: Angular acceleration
Forces of the linear motion
First the mass which is to be moved linearly has to be calculated. The payload m
L
can adopt different
values during the travel cycle.
[7-45] Equation 5: Total mass
The friction force F
μ
can for instance occur on the supporting elements of the rack and pinion. Gen-
erally it can be calculated according to the following equation.
• The force acts opposite to the direction of movement and is taken into consideration by the frac-
tion v/|v| in the following equation. For v = 0 the force F
μ
is 0.
[7-46] Equation 6: Friction force
Additionally a force F
vs
can act, e. g. a force due to weight, which occurs during a slope of the linear
movement.
• F
vs
is an external counterforce that can act additionally on the rack and pinion. The direction of
the force is to be observed.
[7-47] Equation 7: Total translatory force
The required torque of the application M
App
has to be calculated in three steps. First the force that
is transmitted via the rack and pinion has to be ascertained:
[7-48] Equation 8: Force that is transmitted to the rack and pinion
The friction force depends on the force F
App
to be transmitted, so that the resulting force that is to
be transmitted via the spindle is calculated by means of the following equation.
• It is assumed that η
Cog
is the leadscrew efficiency in motor mode. The deterioration of the effi-
ciency for operation in generator mode (backward efficiency) is taken into consideration during
this calculation.
[7-49] Equation 9: Force transmitted to the rack and pinion, taking the spindle friction into consideration
α
2000 a
⋅
d
Cog
--------------------
2000 a
⋅
N
Cog
M
Cog
⋅
------------------------------
=
=
m
sum
m
L
m
aux
+
=
F
μ
m
sum
g μ
Gdn
β
cos
v
v
-----
⋅ ⋅
⋅
⋅
=
F
sum
F
vs
m
+
sum
g
β
sin
⋅ ⋅
=
F
App
F
sum
F
μ
+
(
) m
+
sum
a
⋅
=
F
App,η
F
App
F
App
v
v
-----
1
η
Cog
-----------
1
–
⋅
⋅
+
=