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Ball screw
Calculation
Ballscrew Positioner
Ball Screw-powered Machine Tool
Input
System Inclination (degrees)
0
γ=
°
Ball Screw Lead
p=
mm/rev
Ball Screw Length
L=
mm
Ball Screw Diameter
D=
mm
Ball Screw Efficiency
0.9
η
bs
=
Friction Coefficient
0.05
μ=
Service Factor
1.5
K
A
=
Traveling Mass
m=
kg
Linear Speed
v=
m/s
Acceleration Time
t
a
=
s
Machining Force
0
F
m
=
N
Max. Motor Speed During Cycle
3000
n
1
=
rpm
Gearbox Efficiency
η
r
=
Gearbox Moment of Inertia
0
J
R
=
kg·cm
2
Motor Moment of Inertia
J
M
=
kg·cm
2
The formulas used for these calculations are available in
this PDF
.
Results
Machine
System Efficiency
η
t
=
Weight Force
F
w
=
N
Friction Force
F
f
=
N
Acceleration Force
F
a
=
N
Total Force
F
T
=
N
Total Force
F
T
=
N
Inertias
Traveling Mass Inertia
J
L
=
kg·cm
2
Ball Screw Inertia
J
bs
=
kg·cm
2
Total Inertia
J
T
=
kg·cm
2
Total Inertia as Seen by the Motor
J
T1
=
kg·cm
2
Load to Motor Inertia Ratio
Λ=
Kinematics
Linear Acceleration
a=
m/s
2
Screw Rotational Acceleration
α
bs
=
rad/s
2
Screw Rotational Speed
ω
bs
=
rad/s
Screw Rotational Speed
n
bs
=
rpm
Motor
Motor Power
P
1
=
kW
Motor Power
P
1
=
kW
Required Motor Torque
T
m
=
N·m
Required Motor Torque
T
m
=
N·m
Gearbox
Ideal Gearbox Ratio
i=
Required Gearbox Output Torque
T
2
=
N·m
Required Gearbox Output Torque, Adjusted for Service Factor
T
2KA
=
N·m
Required Gearbox Output Torque
T
2
=
N·m
Required Gearbox Output Torque, Adjusted for Service Factor
T
2KA
=
N·m
Buttons
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