Lenze DSD - Manual (Page 87)

Lenze · Drive Solution Designer · Manual · DMS 4.2 EN · 12/2013 · TD23
87
7 Applications
7.4 Omega belt drive
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7.4.3 Calculations
The following applies to a linear axis with an omega belt drive that is moved, as is shown in the
drawing:
The belt pulley has the following effective diameter, where p
Cog
specifies the belt pitch:
[7-26] Equation 1: Diameter of belt pulley
Conversion of translatory variables into rotary variables
[7-27] Equation 2: Angle
[7-28] Equation 3: Angular velocity
[7-29] Equation 4: Angular acceleration
Forces of the linear motion
First the mass that is to be moved linearly is to be calculated. The payload m
L
can adopt different
values during the travel cycle. The mass of carriage m
aux
and the mass of the drive motor and the
gearbox m
D
are taken into consideration separately.
[7-30] Equation 5: Total mass
The friction force F
μ
can for instance occur on the guide rails of the slide. The force acts opposite to
the direction of movement and is taken into consideration by the fraction v/|v| in the following
equation, where at v = 0 the force F
μis
0. The static friction at standstill is not considered.
[7-31] Equation 6: Friction force
If the friction force F
μ
is related to the mass in motion, a specific travelling resistance results, which
contains all parts depending on the mass:
[7-32] Equation 7: Specific travelling resistance of the application
d
Cog
[mm]
p
Cog
[mm] N
Cog
⋅
π
------------------------------------------- =
ϕ
2000 s ⋅
d
Cog
--------------------
2000 π s ⋅ ⋅
p
Cog
N
Cog
⋅
---------------------------- = =
ω
2000 v ⋅
d
Cog
--------------------
2000 π v ⋅ ⋅
p
Cog
N
Cog
⋅
---------------------------- = =
α
2000 a ⋅
d
Cog
--------------------
2000 π a ⋅ ⋅
p
Cog
N
Cog
⋅
---------------------------- = =
m
sum
m
L
m
aux
m
D
+ + =
F
μ
m
sum
g μ
Gdn
β cos
v
v
----- ⋅ ⋅ ⋅ ⋅ =
F’ g μ
Gdn
β cos ⋅ ⋅ =