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Motors and Generators | Abb AC Servo motors
5
where
S
m
=
motor speed (rpm)
S
1
=
load speed (rpm)
N
=
gear ratio
N
1
=
number of load gear teeth
N
m
=
number of motor gear teeth
T
m
=
motor torque
T
1
=
load torque
e
=
efficiency
J
t
=
total inertia
J
1
=
load inertia
J
m
= motor inertia
speed (motor) = speed (load) x gear ratio
S
m
=
S
1
x N
or S
m
= S
1
x N
1
÷ N
m
torque at motor = torque at load ÷ gear ratio
T
m
=
T
1
Ne
total inertia = inertia (load) ÷ (gear ratio
2
) + inertia (motor)
J
t
= J
1
+ J
m
N
2
Figure 3
Motor
Load
Gear drive:
Gear drive
In a gear application, since there are mechanical linkages between the load and motor, the load parameters must be reflected
back to the motor shaft. Figure 3 presents the equations.
As an example, if a solid cylinder with a diameter of 4 inches (10.16 cm) and weighing 6 pounds (2718 gm) is connected thru a
3:1 gear, the reflected inertia would be determined by the following:
First, calculating inertia for a solid cylinder:
J
load
=
1
W R
2
=
1
6 (2)
2
=
.031 lb-in-s
2
2
g
2
386
Metric
=
1
2718 (5.08)
2
= 35.7 gm-cm-s
2
2
980
reflecting this inertia thru the gear ratio:
J
ref
=
J
load
=
.031
=
.0034 lb-in-s
2
N
2
(3)
2
Metric =
35.7
= 3.96 gm-cm-s
2
(3)
2
The total reflected load inertia which the motor would “see” would be .0034 lb-in-s
2
(or metric: 3.96 gm-cm-s
2
).
The inertia of the gears should be included in the determination of total load inertia to be really accurate (this can be obtained
from literature or calculated using the formulas for the inertia of a cylinder). Efficiencies of the gearing should also be considered
when calculating torques.
Abb AC Servo motors