7applications – Lenze DSD User Manual
Page 88
7
Applications
7.4
Omega belt drive
88
Lenze · Drive Solution Designer · Manual · DMS 4.2 EN · 12/2013 · TD23
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For vehicles with a wheel guide instead of a linear guide, here the travelling resistance F’ is to be
used:
[7-33] Equation 8: Specific travelling resistance of the application
Additionally a counterforce F
vs
opposite to the positive direction of movement and a component of
the force due to weight (downhill force) caused by the slope β can act. Constant friction forces of the
guide rails, which are independent of the mass, have to be taken into consideration with the correct
sign in F
vs
.
[7-34] Equation 9: Total translatory force
Required torque of the application
The required torque of the application M
App
has to be calculated in three steps. First the force that
is transmitted via the toothed belt has to be ascertained.
• The mass m
Blt
of the belt is considered by the specific mass m’
Blt
.
[7-35] Equation 10: Force of the slide
For calculating the torque, the mass inertia of the application is required. It has to be divided into
two types:
A. Additional mass inertias on the belt pulley are added to the moment of inertia of the belt pulley:
[7-36] Equation 11: Mass inertia on the toothed belt pulley
B. Additional mass inertias that are connected via the toothed belt and rotate at the same speed
(e.g. deflection pulleys, belt tighteners), are included in the moment of inertia of the deflection
pulleys J
aux
:
[7-37] Equation 12: Mass inertia of the deflection pulleys
Now the required torque at the drive can be calculated:
[7-38] Equation 13: Required torque at the drive
F’
g 2 f
β
cos
⋅ ⋅
d
Whl
---------------------------
d
Brg
μ
Brg
⋅
d
Whl
-------------------------- μ
Gdn
+
+
⋅
=
F
sum
F
vs
m
sum
g
⋅
+
β
sin
⋅
=
F
aux
F’ m
sum
v
v
-----
⋅
⋅
F
sum
+
m
sum
+
a
⋅
=
J
Cog
J
n const
=
J
k
k 1
=
n
n const
=
=
=
J
aux
J
v const
=
J
i
d
Cog
d
i
-----------
2
⋅
i 2
=
m
v const
=
=
=
M
D
d
Cog
2000
-------------
F
aux
⋅
J
aux
α
⋅
+
=