7applications – Lenze DSD User Manual
Page 77
Lenze · Drive Solution Designer · Manual · DMS 4.2 EN · 12/2013 · TD23
77
7
Applications
7.3
Belt drive, rotating
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
[7-17] Equation 8: Specific travelling resistance of the application for vehicles with a wheel guide
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
.
[7-18] 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 toothed belt is considered by the specific mass m’
Blt
and the length l
Blt
.
[7-19] 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. An additional mass inertia on the belt pulley of the toothed belt is added to the mass inertia of
the belt pulley:
[7-20] Equation 11: Mass inertia on the side of the belt pulley
B. Additional mass inertias that are connected via the toothed belts and rotate at the same speed
(e.g. deflection pulleys, belt tighteners), are included in the moment of inertia J
aux
of the deflec-
tion pulleys:
[7-21] Equation 12: Mass inertia of the deflection pulleys
Now the required torque at the drive can be calculated:
[7-22] Equation 13: Required torque at the drive
The constant torque loss which occurs within the belt is determined under full load from the torque
at the drive with the efficiency in motor mode of the prestressed belt:
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
l
Blt
m’
Blt
⋅
+
(
)
+
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
⋅
+
=