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High Precision Planetary Gearboxes
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Wheeled Motion
Calculation
Linear Motion on Wheels
Input
Acceleration Time
t
a
=
s
System Inclination (degrees)
γ=
°
Drive Wheel Diameter
D=
mm
Drive Axle Diameter
d=
mm
System Mass
m
v
=
kg
Load Mass
m=
kg
Speed
v=
m/s
Bearing Friction Coefficient
μ
b
=
Wheel–Surface Rolling Resistance Factor
b
s
=
mm
Additional Reduction Ratio
1
i
ex
=
Service Factor
1.5
K
A
=
System Efficiency
η
v
=
Gearbox Efficiency
η
g
=
Gearbox Moment of Inertia
J
g
=
kg·cm
2
Max. Motor Speed During Cycle
2000
n
1
=
rpm
Motor Moment of Inertia
J
M
=
kg·cm
2
Number of Motors
1
no
tr
=
The formulas used for these calculations are available in
this PDF
.
Results
Machine
Total Mass
m
load
=
kg
System Efficiency
η=
Bearing Friction Force
F
b
=
N
Weight Force
F
w
=
N
Wheel–Surface Rolling Resistance Force
F
s
=
N
Total Resistive Force
F
T
=
N
Acceleration Force
F
acc
=
N
Required Total Motor Power
P
total
=
kW
Total Required Continuous Torque
T
total
=
N·m
Inertias
Inertia Seen by each Motor
J
m
=
kg·m
2
Load to Motor Inertia Ratio
Λ=
Kinematics
Linear Acceleration
a=
m/s
2
Max. Wheel Rotational Speed
n
2 max
=
rpm
Max. Wheel Rotational Speed
ω
max
=
rad/s
Motor
Required Continuous Motor Power
P
1
=
kW
Required Acceleration Motor Power
P
1max
=
kW
Required Motor Torque
T
m
=
N·m
Gearbox
Ideal Gearbox Ratio
i=
Required Output Torque
T
2
=
N·m
Required Output Torque Adjusted for Service Factor
T
2KA
=
N·m
Required Acceleration Torque
T
2a
=
N·m
Required Acceleration Torque Adjusted for Service Factor
T
2aKA
=
N·m
Buttons
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Diagrams
Linear Motion on Wheels
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