Lenze DSD - Manual (Page 157)

Lenze · Drive Solution Designer · Manual · DMS 4.2 EN · 12/2013 · TD23
157
7 Applications
7.14 Synchronous drive - single roll
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7.14.1 Calculations
For a synchronous drive with a single roll according to the drawing the following applies:
Conditions
The force ratio always has to be smaller than the static friction to avoid slippage. The forces F
in
and
F
out
must not be negative. The safety coefficient S provides for a safety reserve that can be individ-
ually adapted to the application. During the application both a motor torque and a regenerative
torque can occur.
For a reliable power transmission from the drive roll to the material the following conditions have
to be met. Otherwise the DSD outputs a message.
[7-148] Equation 1: Balance of forces
Stationary torque
Under the previously mentioned conditions the stationary torque of the roll is calculated as follows:
[7-149] Equation 2: Stationary torque
Friction torque
In order to take the friction into consideration, usually a system efficiency η is specified. Since the
friction torque is a constant torque, a friction torque M
μ
is calculated by means of the efficiency and
the maximum stationary torque which is then considered as a constant torque.
• The direction of the friction torque is always opposed to the direction of movement and is math-
ematically expressed by the fraction v/|v|.
[7-150] Equation 3: Friction torque
Moment of inertia
The total moment of inertia consists of the moments of inertia of the individual components:
[7-151] Equation 4: Total moment of inertia
For the motor torque ( F
in
> F
out
): For the regenerative torque (F
in
< F
out
):
F
in
F
out
------------- e
μ
0
α ⋅
1
S
100
--------- –
 
 
⋅ <
F
out
F
in
------------- e
μ
0
α ⋅
1
S
100
--------- –
 
 
⋅ <
M
sds
F
in
F
out
– ( ) d ⋅
1000 2 ⋅
------------------------------------ =
M
μ
1
η
Brg
---------- 1 –
 
  max M
sds
( ) vv----- ⋅ ⋅ =
J
sum
J J
L
+ =