Siemens SINAMICS S200 - Page 758

Typical load inertia equations
Mechanism Equation Mechanism Equation
a
b
Axis of rotation on center
=
W
J
12
(
+ )
a
2
b
2
W: Mass (kg)
a: Length (m)
b: Width (m)
D2
D1
Axis of rotation on center
=
W
J
8
( + )
D1
2
D2
2
W: Mass (kg)
D
1
: External diameter (m)
D
2
: Internal diame
ter (m)
a
R
b
Axis of rotation o󹪜 cent
er
= WJ
+
+
3
( )
a
2
b
2
R
2
W: Mass (kg)
a: Length (m)
b: Width (m)
R: Rot
ational diameter (m)
D
R
Axis of rotation o󹪜 center
=
W
J
8
8( + )
D
2
R
2
W: Mass (kg)
D: Workpiece diameter (m)
R: Ro
tational diameter (m)
'
Conveyor
=
W
J
4
D
2
W: Mass (kg)
D: Pulley wheel diameter (m)
3
Ball screw
=
W
J
4
P
2
2
π
+ Jb
W: Mass (kg)
P: Lead (m)
J
b
: Ball screw inertia (kg·m
2
)
'
:
0
Object hung with pulley
= W +
( )
JpJ
2
D
2
W: Mass (kg)
D: Pulley wheel diameter (m)
J
p
: Pulley iner
tia (kg·m
2
)
0
0
Q
Q
Reducer
= J1 J2J
n2
2
n1
2
W: Mass (kg)
n
1
/n
2
: Speed of each motor
(rpm)
J
1
/J
2
: Inertia of eac
h motor
(kg·m
2
)
A.5.2 Selection examples
Descr
ip
tion
This section uses a ball scr
e
w mec
hanism as an example to illustrate the motor selection
procedure.
Exemplary data
The following table lists the data related to the ball screw mechanism and operation pattern.
Workpiece weight W 40 kg
Material density of the ball screw ρ 7.9 × 10
3
kg/m
3
Appendix
A.5Motor selection
SINAMICS S200 pulse train servo drive system with SIMOTICS S-1FL2
756 Operating Instructions, 11/2023, FW V6.3, A5E51646767B AA