Lenze DSD - Manual (Page 76)

7 Applications
7.3 Belt drive, rotating
76
Lenze · Drive Solution Designer · Manual · DMS 4.2 EN · 12/2013 · TD23
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7.3.3 Calculations
For a linear axis with rotating toothed belts according to the drawing, the following applies:
The belt pulley has the following effective diameter, where p
Cog
specifies the belt pitch:
[7-10] Equation 1: Diameter of belt pulley
Conversion of translatory variables into rotary variables
[7-11] Equation 2: Angle
[7-12] Equation 3: Angular velocity
[7-13] 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. The mass of carriage m
aux
is considered separately.
[7-14] 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.
[7-15] 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:
[7-16] Equation 7: Specific travelling resistance of the application
For vehicles with a wheel guide instead of a linear guide, here the travelling resistance F’ is to be
used:
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
+ =
F
μ
m
sum
g μ
Gdn
β cos
v
v
----- ⋅ ⋅ ⋅ ⋅ =
F’ g μ
Gdn
β cos ⋅ ⋅ =