YASKAWA SGDS Sigma III Series - Servomotor Capacity Selection Examples; Selection Example for Speed Control

11 Appendix
11.1.1 Selection Example for Speed Control
11-2
11.1 Servomotor Capacity Selection Examples
11.1.1 Selection Example for Speed Control
(1) Speed Diagram
(2) Rotation Speed
• Load axis rotation speed
• Motor shaft rotation speed with the direct coupling: Gear ratio 1/R=1/1
Therefore,
(3) Load torque
(4) Load Moment of Inertia
• Linear motion section
• Ball screw
• Coupling
• Load moment of inertia at motor shaft
• Load speed: V = 15 m/min • Feeding times: n=40 times/min
• Linear motion section mass: M = 300 kg • Feeding distance: = 0.275 m
• Ball screw length: L
B
= 1.0 m • Feeding time: tm = 1.2 s max.
• Ball screw diameter: D
B
= 0.03 m • Friction coefficient: µ = 0.2
• Ball screw lead: P
B
= 0.01 m • Mechanical efficiency: η = 0.9 (90%)
• Coupling mass: M
C
= 1 kg
• Coupling outer diameter: D
C
= 0.06 m
where ta = td
1
Ball screw
Servomotor
Linear motion
Coupling
Mechanical Specifications
c
tt
a
d
t
(m/min)
Speed
Time (s)
1.2
t
V
15
t
60
n
------
60
40
------1.5s()===
tc 1.2 0.1 2×–1.0s()==
N = = = 1500 (min )
V
15
P
B
-1
0.01
N = N  R = 1500 × 1 = 1500 (min )
M
-1
T
L
= = = 1.04 (Nm)
9.8µ
 M  P
B
2πR  η
9.8 × 0.2 × 300 × 0.01
2π × 1 × 0.9
J
L1
= M ( )
2
= 300 × ( )
2
= 7.6 × 10
-4
(kg  m
2
)
P
B
2πR
0.01
2π × 1
J = ρ  L  D = × 7.87 × 10 × 1.0 × (0.03) = 6.3 × 10 (kg  m )
π
32
π
32
BBB
-4+344
2
J
C
1
8
---
M
C
D
C
2
⋅
1
8
---
1× 0.06()
2
× 4.5 10
4–
kg m
2
⋅()×== =
J = J + J + J = 18.4 × 10 (kg  m )
L
L1
C
B
-4 2