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Appendix 2. Selection
A2 - 9
Appendix 2-3 Example of servo selection
A servomotor is selected using a machining center with the following specifications as an example.
Specification item
Unit
X axis
Y axis
Z axis
Axis
type
Linear Linear Linear
Movement direction
Horizontal Horizontal Vertical
Table support method
Rolling
Rolling
Rolling
Table movement friction coefficient
%
5
5
5
Ball screw diameter
mm
50
50
50
Ball screw length
mm
1200
1000
1000
Ball screw lead
mm
10
10
10
Deceleration ratio
1
1
2/3
Primary side gear inertia
kg.cm
2
1.6
Secondary side gear inertia
kg.cm
2
8.1
Motor/ball screw connection section inertia
kg.cm
2
10.0
10.0
Mass of moving object installed on the machine
(table, etc.)
(table, etc.)
kg
600 500 500
Mass of standard-added-moving object
(workpiece, etc.)
(workpiece, etc.)
kg 100
100
10
Rapid traverse rate
mm/min
30000
30000
20000
Target acceleration/deceleration time constant
ms
120
120
100
Rapid traverse positioning
frequency
times/min
12 12 12
Motor brake
Without
Without
With
Appendix 2-3-1 Motor selection calculation
Servomotor
Deceleration ratio = 2/3
500kg
10kg
Primary side
gear
1.6kg·cm
gear
1.6kg·cm
2
Ball screw
Ø50, 1000mm
Fig. 11-3 Z axis configuration
Secondary
side gear
8.1kg·cm
side gear
8.1kg·cm
2
The selection calculation is carried out in order using the Z axis as
an example.
an example.
(1) Obtaining the load inertia
Calculate the motor shaft conversion load inertia separately
for the rotation load and linear movement load. Furthermore,
calculate the rotation load inertia separately for the primary
and secondary side.
for the rotation load and linear movement load. Furthermore,
calculate the rotation load inertia separately for the primary
and secondary side.
Primary side rotation load inertia: J
R1
This is the primary side gear inertia.
J
R1
= 1.6 (kg.cm
2
)
Secondary side rotation load inertia: J
R2
This is the sum of the ball screw inertia J
B
and secondary side gear inertia. The ball screw is
generally calculated as a cylinder made of steel. Refer to section "Appendix 2-5 Expressions for
load inertia calculation".
load inertia calculation".
J
R2
= J
B
+ 8.1 =
· · L
32
D
4
+ 8.1 =
7.80 10
3
100
32
5
4
+ 8.1
= 47.9 + 8.1 = 56.0 (kg.cm
2
)
Total rotation load inertia: J
R
This is the sum of the primary side load inertia and secondary side load inertia. To convert the
secondary side load inertia to the motor shaft (primary side), multiply by the square of the
deceleration ratio.
secondary side load inertia to the motor shaft (primary side), multiply by the square of the
deceleration ratio.
J
R
= J
R1
+ (
2
3 )
3 )
2
J
R2
= 1.6 +
4
9 56.0 = 1.6 + 24.9 = 26.5 (kg
9 56.0 = 1.6 + 24.9 = 26.5 (kg
.cm
2
)