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Moment of Inertia J Calculation Formula

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Moment of Inertia Calculation Formula

Moment of Inertia of a Hollow Cylinder

D : Outer diameter of the cylinder[m]
d : Inner diameter of the cylinder[m]
M : Mass of the cylinder[kg]

J= 1 M (D2 + d2 ) [kg･m2 ]
8

Moment of Inertial of a Cylinder with a Displaced Center-of-Rotation

r : Radius of gyration[m]
M : Mass of the cylinder[kg]
J A : Moment of inertia of the cylinder rotating around r the center axis A [kg・m 2 ]

J=JA + M･r2 [kg･m2]

Moment of Inertia of a Rotating Rod

L : Length of the rod[m]
M : Mass of the rod[kg]

J= 1 M･L2 [kg･m2 ]
3

Moment of Inertial of a Rod with a Displaced Center-of-Rotation

L1, L2 : Distance from the center of rotation [m]
M : Mass of the rod[kg]

J= 1 M(L12 + L1L2 + L22) [kg･m2 ]
3

Moment of Inertia of the Winding Mechanism

JA : Moment of inertia of the drum[kg・m2]
D : Diameter of the drum[m]
M : Mass of the load[kg]

J=JA + 1 M･D2 [kg･m2 ]
4

Moment of Inertia with Counterbalance

JA : Moment of inertia of the drum[kg・m2]
D: Diameter of the drum[m]
M 1,M2 : Mass[kg]

J=JA + 1 (M1+M2) D2 [kg･m2 ]
4

Moment of Inertia of a Cuboid

a, b : Side length[m]
M : Mass of the cuboid[kg]

J= 1 M(a2 + b2)[kg・m2 ]
12

Moment of Inertia of an Object that Moves in a Straight Line

JA : Moment of inertia of the feed screw[kg・m2]
P : Feed screw lead[m]
M : Mass of the load[kg]

J=JA + M･P2 [kg･m2 ]
4π2

Moment of Inertia of the Rack and Pinion

JA : Moment of inertia of thepinion[kg・m2]
D : Diameter of the pinion[m]
M : Mass of the rack and load[kg]

J=JA + 1 M･D2 [kg･m2 ]
4

Moment of Inertia of the Belt Conveyor

JA : Moment of inertia of the roller[kg・m2]
D : Diameter of the roller[m]
M : Mass of the load[kg]

J=JA + 1 M･D2 [kg･m2 ]
4

Moment of Inertia when a Workpiece Is Held by the Rollers

JA : Moment of inertia of the roller A[kg・m2]
J B : Moment of inertia of the roller B[kg・m2]
D A : Diameter of the roller[m]
D B : Diameter of the roller B[m]
M: Equivalent mass of the workpiece[kg]

J=JA+ ( DA )2JB + 1 M･DA2 [kg・m2 ]
DB 4

Motor Shaft Conversion Moment of Inertia

Z1: Teeth number of the motor-side gear
Z 2 : Teeth number of the load-side gear
R : Speed reduction ratio Z2/Z1
J A : Moment of inertia of load[kg・m2]
J 1 : Moment of inertia of the motor-side gear[kg・m2]
J 2 : Moment of inertia of the load-side gear[kg・m2]

J=J1 +(JA + J2)･( 1 )2 [kg･m2 ]
R

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