Yaskawa SGDS Sigma III Servo Amplifier - Manual (Page 317)

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 t ta d t
(m/min)
Speed
Time (s)
1.2
t
V
15
t
60
n
------
60
40
------ 1.5 s ( ) = = =
tc 1.2 0.1 2 × – 1.0 s ( ) = =
N = = = 1500 (min )
V 1 5
P
B
-1
0.01
N = N R = 1500 × 1 = 1500 (min )
M
-1
T
L
= = = 1.04 (N m)
9.8 µ M P
B
2 πR η
9.8 × 0.2 × 300 × 0.01
2 π × 1 × 0.9
J
L1
= M
( ) 2
= 300 ×
( ) 2
= 7.6 × 10 -4 (kg m 2 )
P
B
2 πR
0.01
2 π × 1
J = ρ L D = × 7.87 × 10 × 1.0 × (0.03) = 6.3 × 10 (kg m )
π
32
π
32 B B B
-4 +3 4 4 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