Mitsubishi Electric MELDAS MDS-B-SVJ2 Series - Example of Servo Selection; Motor Selection Calculation

Chapter 11 Selection
11-15
11-5 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 2
Ball screw diameter mm 40 40 40
Ball screw length mm 900 800 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
2.0 2.0
−
Weight of moving object installed on the
machine (table, etc.)
kg 500 400 400
Weight of standard added object
(workpiece, etc.)
kg 100 100 10
Rapid traverse rate mm/min 30000 30000 20000
Target acceleration/deceleration time
constant
msec 120 120 120
Rapid traverse positioning frequency times/min. 20 20 20
Motor brakes Not available Not available Available
11-5-1 Motor selection calculation
The selection calculation is carried out in order using the Z axis
as 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.
• Primary side rotation load inertia: J
R1
This is the primary side gear inertia.
J
R1 = 1.6 (kg·cm
2
)
• Secondary 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 "11-7 Load inertia calculation"
J
R2 = JB + 8.1 =
π · ρ · L
32
D
4
+ 8.1 =
π × 7.80 × 10
−
3
× 100
32
× 4
4
+ 8.1
= 19.6 + 8.1 = 27.7 (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.
J
R = JR1 + (
2
3
)
2
× JR2 = 1.6 +
4
9
× 27.7 = 1.6 + 12.3 = 13.9 (kg·cm
2
)
• Linear movement load inertia: J
T
The inertia is calculated when a standard workpiece, tool, etc., is attached. The conversion to the
motor shaft by the deceleration ratio is included in the travel increment per motor rotation. Refer to
section "11-7 Load inertia calculation".
J
T = W · (
ΔS
20π
)
2
= (400 + 10) · (
10 × 2
20π × 3
)
2
= 4.6 (kg·cm
2
)
Servomoto
r
Deceleration ratio = 2/3
400kg
10kg
Primary side
gear
1.6kg·cm
2
Ball screw
φ
40, 1000mm
Fig. 11-3 Z axis configuration
Secondary
side gear
8.1kg·cm
2