ABB
76
ABB |
Motors and Generators | Abb AC Servo motors
5
The torque required to start the load moving, termed acceleration torque (Tacc), is that torque which is needed to overcome the
mechanical friction and inertia.
Expressed mathematically, the equation is:
T
acc
= (J
t
)
(accel rate)
+
T
f
where
T
acc
is acceleration torque (lb-in)
J
t
is the total inertia (load and motor lb-in-s
2
)
accel is rotary acceleration of the motor shaft (rad/sec
2
)
T
f
is the total friction torque of the package (lb-in)
As an example, the application calls for moving a 200 lb (90.6 Kg)load thru a ballscrew (having an inertia of .00313 lb-in-s
2
), (3.6 gm-
cm-s
2
) at an acceleration rate of 1741.6 rad/sec
2
. Typical motor parameters which will be used in this analysis are indicated in Figure 8.
T
acc
= (J
t
)
(accel rate)
+
T
f
T
acc
= (J
l
+ J
ls
+ J
m
) (accel rate)
+
T
f
T
acc
=
(0.00052 + 0.00313 + 0.0037) (1741.6)
+
0.95 Metric = (0.61 + 3.6 + 4.26) 1741.6 + 1094
= 12.8
+
0.95
Metric = 14751 + 1094
= 13.75 lb-in
Metric = 15845 gm-cm (=1.55 Nm)
The motor must be capable of providing torque to accelerate the entire mechanics of the load (friction plus inertia), as well as torque to
move itself.
In this example, the motor must be capable of supplying a total acceleration torque of 13.75 lb-in (15.8 kg-cm).
Torque over the duty cycle
The motor must also be capable of providing a certain amount of torque continuously over the duty cycle, or move profile as was
defined earlier.
In order to determine this, we must look at the rest of the move profile and determine the torques associated with them.
During run time, the torque required is:
T
run
= T
f
T
run
= 0.95 lb-in
Metric = (1094 gm-cm)
During the stopping cycle, or deceleration, the torque required is:
T
dec
= - (J
t
) (accel rate)
+
T
f
T
dec
=
- (.00052 + .00313 + .0037) (1741.6)
+
.95
Metric = - (0.61 + 3.6 + 4.26)(1741.6) + 1094
T
dec
= - 12.8
+
.95
Metric = - 14751 + 1094
T
dec
= - 11.85 lb-in
Metric = - 13657 gm-cm
Now that these torques are identified, the amount of torque required over the move profile can be calculated.
This is termed
“determining the RMS torque”.
It is calculated by simply inserting the figures from the previous page in to the following equation:
T
2
RMS
= (T
2
acc
x t
acc
) + (T
2
run
x t
run
) + (T
2
dec
x t
dec
)
t
acc
+ t
run
+ t
dec
+ t
idle
T
2
RMS
= (13.75)
2
x 0.12 + (0.95)
2
x 0.12 + (11.85)
2
x 0.12 Metric = (15.8)
2
x 0.12 +(1 )
2
x 0.12 + (13.6)
2
x 0.12
0.12 + 0.12 + 0.12 + 0.3
0.12 + 0.12 + 0.12 + 0.3
T
2
RMS
=
22.6 + 0.108 + 16.8
=
59.86
Metric = 29.9 + 0.12 + 22.1 = 78.9 kg-cm
0.66
0.66
T
RMS
= 7.73 lb-in
Metric = 8.8 Kg-cm (= 0.86 Nm)
Thus, this application requires 7.73 lb-in (0.86 Nm) of torque.
The motor for this example has the capability of providing a continuous
torque of 14 lb-in (1.6 Nm).
Acceleration torque
Abb AC Servo motors