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Gear
Loads in a gear application have to be reflected back to the motor shaft by the gear ratio, or the gear
ratio squared. The inertia of the gears have to be included in the calculations. Gear inertia may be
calculated using the formula for cylinder.
Belt and Pulley
The load parameters have to be reflected back to the motor shaft. Although a belt and pulley
arrangement is shown, it can also be a rack and pinion, or timing belt and pulley, or chain and
sprocket. The inertia of the pulleys, sprockets, or pinions must be included.
Application Notes
Speed:
W
Inertia:
J
T
Torque:
T
L
Where:
W
W
N
M
N
L
T
L
T'
J
T
J
L
J
M
J
NM
J
NL
1
Speed:
W
=
M
2π r
W r
Inertia:
J
=
T
g
Torque:
T
=
F
r + F
L
F
Where:
W
=
motor speed (rpm)
M
V
=
linear load speed (inch/min)
L
r
=
pulley radius (in)
T
=
load torque reflected to motor shaft (lb-in)
L
T
=
friction torque (lb-in)
F
F
=
load force (lb)
L
J
=
total system inertia (lb-in-s
T
J
=
motor inertia (lb-in-s
M
J
=
pulley inertia (lb-in-s
P
W
=
load weight including belt (lb)
F
=
frictional force (lb)
F
g
=
gravitational constant (386 in/s
Page 9
=
W
(N
/N
)
M
L
L
M
=
(N
/N
)
(J
+ J
2
M
L
L
NL
=
T' (N
/N
)
M
L
=
motor speed (rpm)
M
=
load speed (rpm)
L
=
number of motor gear teeth
=
number of load gear teeth
=
load torque at motor shaft (lb-in)
=
load torque (lb-in) - not reflected
=
total system inertia (lb-in-s
=
load inertia (lb-in-s
=
motor inertia (lb-in-s
=
motor gear inertia (lb-in-s
=
load gear inertia (lb-in-s
V
L
+ J
+ J
+ J
2
P1
P2
M
r
L
)
2
)
2
) + J
+ J
M
NM
)
2
)
2
)
2
)
2
)
2
)
2
)
2
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Troubleshooting
