Cross cutter – Lenze EVS93xx CrossCutter User Manual
Page 102
Cross Cutter
Features of the "Cross Cutter" prepared solution
Prepared Solution Servo PLC / ECSxA 1.1 EN
2-88
Generally, torque load on a drive comprises the following components:
)
(
)
(
)
(
)
(
)
(
2
t
M
t
c
dt
t
d
D
dt
t
d
d
J
t
M
S
+
⋅
+
⋅
+
⋅
=
ϕ
ϕ
ϕ
ϕ
ϕ
where:
φ(t)
= Angle of rotation of the drive
J =
Rotary
mass
inertia
D
φ
= Rotary attenuation factor
c
φ
= Rotary spring force constant
M
S
(t) = External load torque
The dynamic component in particular affects the accuracy of the motion of the drive. In the
cross-cutter application, this component is determined essentially by the rotary
acceleration/deceleration of the knife drum and its mass inertia. Therefore, as a first
approximation, a signal proportionate to acceleration/deceleration can be used as a suitable
torque precontrol signal. The second mathematical derivation of the function s = f(x) produces a
signal proportionate to acceleration/deceleration dependent upon the master value position x:
2
)
(
dx
ds
d
x
a
=
The torque component proportionate to acceleration is the product of the rotary acceleration
and the (constant) mass inertia:
( )
2
2
)
(
)
(
)
(
⎟
⎠
⎞
⎜
⎝
⎛
⋅
⋅
=
dt
t
dx
dx
t
x
d
d
K
t
M
J
ϕ
At constant master speed, a torque precontrol signal can be generated accordingly by
multiplying the square of the master speed by the scaled acceleration curve and an adaptation
factor (representing the constant mass inertia of the drive system). The signal flow must
therefore look like this:
2
The designation s(t) is used generally for translatory and rotary systems. The designation φ(t) is used specifically for rotary systems.
Scaled acceleration profile as a
function of the master position x
Master position x(t)
Master speed (dx(t)/dt)
2
(clock-pulse rate)
Adaptation factor to the actual mass inertia
(K
J
factor)
Torque precontrol signal
(MCTRL_nMAdd_a)
Adaptation factor K
J
for
adaptation to the actual mass
inertia of the drive system
(usually calculated as an
experimental value)
Scaled acceleration
characteristic as a function
of the master position x(t)
Taking into account the
likelihood that the master
position will change over