Appendix 2-5 Expressions For Load Inertia Calculation - Mitsubishi Electric MELDAS MDS-R Series Technical Specification And Instruction Manual

Appendix 2-5 Expressions for load inertia calculation

The calculation method for a representative load inertia is shown.
Type Mechanism
Rotary
shaft is
cylinder
center
Cylinder
When rotary shaft and cylinder
shaft are deviated
Rotary shaft
Column
a
Rotary shaft
Object that
moves
Servomotor
linearly
Suspended
object
W
N
3
J
21
Converted
load
Servomotor
Appendix 2. Selection
D
Ø 1.
D
Ø 2.
J
ρ : Density of cylinder material [kg . cm
L : Length of cylinder
D
D
W : Mass of cylinder
Rotary shaft
R
D
R
b
a
b
V
W
N
D
Load B
J
J
B
31
J
22
N
2
Load A
N J
1 A
N
1
J
11
Calculation expression
π·ρ·L
. (D
4 4
-
J = D ) =
L
1 2
32
: Load inertia
L
: Outer diameter of cylinder [cm]
1
: Inner diameter of cylinder
2
W
. (D
2 2
J = + 8R )
L
8
J : Load inertia
L
W : Mass of cylinder
D : Outer diameter of cylinder
R : Distance between rotary axis and
cylinder axis
2 2
a + b
2
J = W ( + R )
L
3
J : Load inertia
L
W : Mass of cylinder
a.b.R : Left diagram
1
V
2
J = W ( · ) = W (
L
2πN 10
J : Load inertia
L
W : Mass of object that moves linearly
N : Motor speed
V : Speed of object that moves linearly
∆S : Object movement amount per motor rotation [mm]
D
2
J = W ( ) + J
L P
2
J : Load inertia
L
W : Object mass
D : Diameter of pulley
J : Inertia of pulley
P
J = J + (J + J + J ) ·(
L
11 21 22 A
J : Load inertia
L
J ,J : Inertia of load A, B
A B
J ~J : Inertia
11 31
N ~N : Each shaft's speed
1 3
A2 - 15
W
. (D
2 2
-
D )
8
1 2
Reference data
[kg . cm
2
]
Material densities
3
]
Iron
..... 7.80×10
[cm]
Aluminum
..... 2.70×10
[cm]
Copper
[kg]
..... 8.96×10
[kg . cm 2
]
[kg]
[cm]
[cm]
[kg . cm 2
]
[kg]
[cm]
∆S
2
)
20π
[kg . cm 2
]
[kg]
[cm]
[kg . cm
2
]
N N
2
2 ) + (J + J ) · ( 3 )
31 B
N N
1 1
[kg . cm 2
]
[kg . cm 2
]
[kg . cm 2
]
[r/min]
–3 3
[kg/cm ]
–3 3
[kg/cm ]
–3 3
[kg/cm ]
[kg . cm 2
]
[kg]
[r/min]
[mm/min]
2