Selection Example For Speed Control; Servomotor Capacity Selection Examples - YASKAWA SGDH User Manual

11 Appendix

11.1.1 Selection Example for Speed Control

11.1 Servomotor Capacity Selection Examples

11.1.1 Selection Example for Speed Control
Mechanical Specifications
Servomotor
Linear motion
1
Coupling
Ball screw
• Load speed: V = 15 m/min
• Linear motion section mass: M = 500 kg
• Ball screw length: L = 1.4 m
B
• Ball screw diameter: D
B
• Ball screw lead: P = 0.01 m
B
• Coupling mass: M = 1 kg
C
• Coupling outer diameter: D
(1) Speed Diagram
V
15
Speed
(m/min)
t a
(2) Rotation Speed
• Load axis rotation speed
V
N =
P
• Motor shaft rotation speed with the direct coupling: Gear ratio 1/R = 1/1
Therefore,
N = N
M
(3) Load torque
9.8µ M P
T =
L
(4) Load Moment of Inertia
• Linear motion section
J = M
L1
• Ball screw
π
J =
B
32
• Coupling
1
J = M
C
8
• Feeding times: n = 40 times/min
• Feeding distance:
• Feeding time: tm = 1.2 s max.
• Friction coefficient: µ = 0.2
= 0.04 m
• Mechanical efficiency: η = 0.9 (90%)
= 0.06 m
C
Time (s)
c t
d t
1.2
t
15
= = 1500 (min ) -1
0.01
B
×
R = 1500 1 = 1500 (min )
-1
9.8 × 0.2 × 500 × 0.01
B
=
2πR η 2π × 1 × 0.9
2 0.01 2
P
( ) ( )
B
= 500 ×
2π × 1
2πR
π
ρ L × 7.87 × 10 × 1.4 × (0.04) = 27.7 × 10 (kg m )
4
D =
B B
32
1
2 × 1 × (0.06) 2 = 4.5 × 10
D =
C C
8
= 0.275 m
60 60
t = = = 1.5 (s)
n
40
where ta = td
×
60
ta = tm − = 1.2 −
V
tc = 1.2 − 0.1
×
2 = 1.0 (s)
= 1.73 (N m)
= 12.7 × 10
-4 2
(kg m )
-3 4 -4
-4 2
(kg m )
11-2
×
60 0.275
= 0.1 (s)
15
2