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Abb AC Servo motors
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73
5
Tangential drive
where
Sm
=
motor speed (rpm)
V
1
=
load speed (in/min) (cm/min)
R
=
radius
T
1
=
torque reflected to motor
F
1
=
load force
T
f
=
friction torque
F
f
=
friction force
J
t
=
total inertia
W
=
load weight
+
belt weight
J
p
=
pulley inertia
J
m
=
motor inertia
g
=
gravitational constant (386
in/s
2
)
(980 cm/s
2
)
speed (motor) =
1 x speed (load)
2π
radius
Sm =
1 x
V
1
2π
R
load torque =
load force x radius
T
1
=
F
1
R
friction torque =
frictional force
x
radius
T
f
=
F
f
R
total inertia =
(weight
x radius
2
) ÷ (gravity)
+
inertia (pulley #1)
+
inertia (pulley #2)
+
inertia (motor)
J
t
=
W
R
2
+
J
p1
+
J
p2
+
J
m
g
Figure 4
Tangential drive:
Motor
Load
For this type of drive, the load parameters have to be reflected back to the motor shaft. A tangential drive can be a timing belt
and pulley, chain and sprocket, or rack and pinion. See Figure 4 for formulas.
As an example, a belt and pulley arrangement will be moving a weight of 10 lbs (4530 gm). The pulleys are hollow cylinders of 5
pounds (2265 gm) each with an outer radius of 2.5 inches (6.35 cm) and an inner radius of 2.3 inches (5.8 cm). The total inertia
would be determined by:
calculating inertia for a hollow cylinder pulley:
J
p
=
1
W
(R
0
2
+ R
i
2
)
=
1
5
(2.5
2
+ 2.3
2
)
=
0.0747 lb-in-s
2
2
g
2
386
Metric
=
1
2265
(6.35
2
+ 5.8
2
)
=
85.39 gm-cm-s
2
2
980
calculating load inertia:
J
1
=
W R
2
=
10 (2.5)
2
=
0.1619 lb-in-s
2
g
386
Metric
=
4530(6.35)
2
=
186.3 gm-cm-s
2
980
the total inertia reflected to the motor shaft would be the sum of the above:
J = J
1
+ J
P1
+ J
P2
=
0.1619 + 0.0747 + 0.0747 = 0.3113 lb-in-s
2
Metric
=
357 gm-cm-s
2
Don’t forget to include the inertia of the pulleys, sprockets, or pinion gears in the determination of total inertia.
Abb AC Servo motors