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Calculation of load inertia and motor-shaft conversion inertia
Depending on the type of the motor transfer system, calculate the inertia for all parts and convert it
into the motor-shaft inertia.
• Example in hoist application
• Example in conveyor application
• Example in roller application
• Example of conversion into motor-shaft inertia
Load J
Motor-side gear J
M1 Series Standard Type User's Manual (I669)
J
M
= J + J
J
D
=
M
J
J
J
M : Mass of cylinder [kg]
M : Mass of workpiece [kg]
D : Diameter of cylinder [mm]
J [kg·m
M
D
= J + J + J + J
M
J
M
=
D
M
J : Shaft conversion inertia (Cylinder-1-shaft conversion) [kg·m
J : Inertia of cylinder 1 (Cylinder-1-shaft conversion) [kg·m
J : Inertia of cylinder 2 (Cylinder-1-shaft conversion) [kg·m
J : Inertia of workpiece (Cylinder-1-shaft conversion) [kg·m
J : Inertia of belt (Cylinder-1-shaft conversion) [kg·m
M : Mass of cylinder 1 [kg]
M : Mass of cylinder 2 [kg]
M : Mass of workpiece [kg]
M : Mass of belt [kg]
D : Diameter of cylinder 1 [mm]
D : Diameter of cylinder 2 [mm]
J
[kg·m
J
D
J
: Shaft conversion inertia (Roller-1-shaft conversion) [kg·m
J
J
: Inertia of roller 1 (Roller-1-shaft conversion) [kg·m
J
J
: Inertia of roller 2 (Roller-2-shaft conversion) [kg·m
D
M
M : Mass of workpiece [kg]
D : Diameter of roller 1 [mm]
D : Diameter of roller 2 [mm]
Load-side gear J
Motor
J
[kg·m
2
]
2
2
M · D
M · D
-6
+
× 10
8
4
: Shaft conversion inertia [kg·m
: Inertia of cylinder (Shaft conversion) [kg·m
: Inertia of workpiece (Shaft conversion) [kg·m
2
]
M · D
2
M · D
2
D
2
M · D
+
·
+
8
8
D
2
D
2
M · D
2
2
]
= J +
J +
2
D
4
2
2
J [kg·m
] = J + G
(J + J )
J : Motor-shaft conversion inertia [kg·m
J : Load inertia (Load-side gear-shaft conversion) [kg·m
J : Inertia of motor-side gear [kg·m
J : Inertia of load-side gear [kg·m
Z : Number of motor-side gear teeth
Z : Number of load-side gear teeth
G : Gear ratio (Speed reduction ratio) = Z / Z
Appendix
2
]
2
]
2
]
2
M · D
2
+
× 10
-6
4
4
2
]
2
]
2
]
2
]
2
]
-6
× 10
2
]
2
]
2
]
2
]
2
]
2
]
A
2
]
A-11
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