technical data Drive chain Roller Chain Selection

11. How to calculate the moment of inertia

Rotating body

shape overview I (moment of inertia) calculation method
(SI units)		 {GD 2 Calculation Gravitational Unit}
Right circular cylinder Right circular cylinder I = 1 2 Mr2 (kg・m2) GD2 = 1 2 WD2 (kgf・m2)
Hollow right circular cylinder Hollow right circular cylinder I = 1 2 M(r12+r22) (kg・m2) GD2 = 1 2 W(D12 + D22)
(kgf・m2)
SI units {gravity unit}
Moment of inertia (I) and flywheel effect (GD 2) 1kg・m2(I) 4kgf・m2(GD2)

linear moving body

Drive type overview I (moment of inertia) calculation method
(SI units)		 {GD 2 Calculation Gravitational Unit}
Chain Chain I = Mr2(kg・m2) GD2 = WD2(kgf・m2)
Cart drive Cart drive I = Mr2(kg・m2) GD2 = WD2(kgf・m2)
Pin gear drive Pin gear drive I = Mr2(kg・m2) GD2 = WD2(kgf・m2)
Hanging transmission Hanging transmission I = Mr2(kg・m2) GD2 = WD2(kgf・m2)

When converting the load moment of inertia to the motor shaft

  • n 1: Motor shaft rotation speed
  • ​n2: Load shaft rotation speed
 Load moment of inertia I
​Iℓ​ ​ ​= ​n2n12I ​​
= I i 2 (kg·m 2)
I ℓ = M V 2 π n 1 2 (kg・m 2)		 Load moment of inertia GD 2
GD 2ℓ = n 2 n 1 2 GD 2
= GD 2 i 2 (kgf·m 2)
GD 2ℓ = W V π n 1 2 (kgf・m 2)

Note: The above does not include the mass of the sprocket and chain.

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