Selection Calculations - YASKAWA E-V-MD Series User Manual

2.2.2 Selection Calculations

This section describes how to make the calculations and select a servomotor for the following machine speci-
fications.
Mechanical Specifications
Linear motion
Ball screw
(1) Speed Diagram
L
15
Speed
( m/min )
ta tc
tm
(2) Rotation Speed
Load axis rotation speed
Motor shaft rotation speed
(3) Load Torque
9 . 8 μ m P
・ ・
B
=
T
L
2  R
η
・
(4) Load Moment of Inertia
Linear motion section
Ball screw
Coupling
Load moment of
inertia at motor shaft
(5) Load Moving Power
2  n T
・
M L
= =
P
O
60
(6) Load Acceleration Power
2
2 
J
=
Pa n
M
60
ta
• Load speed:
• Linear motion section mass: m = 250 kg
• Ball screw length: l
Servomotor
• Ball screw diameter: d
• Ball screw lead: P
• Ball screw material density
Coupling
Gear ρ
= 7.87 × 10
:
• Gear ratio : 1/2 (R = 2)
Time (s)
td
t
15
L
= = = 1500
n
L
P 0 . 01
B
Gear ratio 1/R = 1/2 (R=2)
=
Therefore, n n
M L
9 . 8  0 . 2  250  0 . 01
= = 0
. 43
2   2  0 . 9
2
P
B = 250 ×
=
J m
L1
2 π R
π
1
=
B 4
J ℓ d
B B
32 R
× 10
= 0
J . 40 -4 kg m 2
G
= + + = 1
J J J J
. 58
L L1 B G
 3000  0
2  . 43
= 135
W
（ ）
60
2
2  2 . 29  10
L
 
= 3000
60 0 . 1
υ
= 15 m/min
L
= 1.0 m
B
= 0.02 m
B
= 0.01 m
B
3 3
kg/m
60 60
= = = 1
t . 5 s
n 40
where ta = td
60 × 0 . 275
60 ℓ
= − = 1 −
ta tm . 2
15
L
= 1 − 0 × 2 = 1
tc . 2 . 1 . 0 s
min -1
= 1500 × 2 = 3000
-1
R min
N m
（ ･ ）
2
0 . 01
× 10
= 1
. 58 -4 2
kg m
2 π × 2
π
× 7 × 10 × 1 × 0
=
. 87 3 . 0 . 02
2 32
× 10
+ 0 + 0 = 2
. 31 . 40 -4 . 29
-4
= 226
W
（ ）
2.2 Selecting Servomotors
• Gear + coupling moment of inertia:
-4 2
= 0.40 × 10
J kgm
G
• Feeding times: n = 40 times/min
• Feeding distance: l = 0.275 m
• Feeding time: tm = 1.2 s max.
μ
• Friction coefficient: = 0.2
η
• Mechanical efficiency: = 0.9 (90%)
= 1 − 1 = 0
. 2 . 1 . 1 s
1
× 10
= 0
4 . 31 -4 2
kg m
2 2
× 10
-4 kg m 2
2
2-5