ElmoMC SimplIQ Digital Servo Drives-Bell Getting Started - Manual (Page 87)

The SimplIQ for Steppers Getting Started & Tuning and Commissioning Guide
MAN-BELGS (Ver. 1.1)
87
Suppose that in the system of Figure 79 the motor is brought abruptly to some
constant torque. Initially the load will not react. This is because the axis must be
deformed in order to convey torque to the load. When the load finally moves, its
acceleration will oscillate. The oscillations in the load will induce oscillations in
the motor, as shown in Figure 80 for a step command. This oscillation
phenomenon is called Resonance.
0 2 4 6 8 10
0
0.3
0.6
0.9
1.2
1.5
1.8
time
Figure 80: Typical response of an oscillating system to torque step
Mathematically, the following equations describe the system:
( )
( )
ML L M ML L M L
T M
L M M M M M
DL L L L L L
d n c n T
iK T
n T B T J
T B T J
θ − θ + θ − θ =
=
− θ − = θ
+ θ − = θ
& &
& & &
& & & (10)
where,
L
J is the load inertia,
L
θ
load angle,
L
T load torque,
L
B load viscous
friction,
DL
T disturbance moment on the load,
M
J motor inertia,
M
θ
motor shaft
angle,
M
T motor torque,
M
B motor shaft viscous friction,
n
gear ratio,
i
motor
current,
T
K motor e.m.f. constant,
ML
c transmission spring factor and
ML
d the
transmission damping factor. Equations (10) where B is neglected, is
schematically described in Figure 81.