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Motor And Inertua Load

  • The equation to calculate the torque that is required for the motor to make the inertia load shaft rotating is as follows.

T : Torque
J : Inertia moment
ω : Angular velocity
t : Time
n : Rotational velocity
GD² : FLYHEEL 효과 [GD² =4J]
g : Gravitational acceleration (g = 9.8[m/sec2]
α : Angular acceleration

  • In case of an induction motor, the starting torque would be changed by rotating speed.
  • Thus, the average value of it that from the starting speed to the normal constant speed is called an average acceleration torque, a value commonly used in practice.
  • The average acceleration torque TA required for the inertia load GD² to be accelerated up to the speed n[r/min] within t[sec] is represented by the following equation.

Calculation Of Flywheel Effect GD²

  • In case that a load is acquired through the connection of a gearhead, the motor shaft component of the load inertia should be calculated to select the motor.
  • Also, the calculation method of GD² is different depending on the type of a load, and the following table provides GD² calculation method for each shape.
Circulular Disk Hollow
GD² Equation
W : Mass(kgf)
D : Outer Diameter(㎝)

W : Mass(kgf)
D : Outer Diameter(㎝)
Sphere Hexahedron
GD² Equation
W : Mass(kgf)
D : Outer Diameter(㎝)

W : Mass(kgf)
a,b : Length of Side(㎝)
GD² Equation
W: : Mass(kgf) D : Outer Diameter(㎝)
ℓ : Length(㎝)

W : Mass(kgf)
ℓ : Length(㎝)
Linear Motion (Horizontal) Linear Motion (Vertical)
GD² Equation
V : Conveyor Speed (cm/min)
N : Drum Rotational Speed (rpm)
W : Weight Over Conveyor(kgf)
D : Drum Outside Diameter (㎝)
(Not included GD² for belt and drum)
GD² : WD² [kgf·㎠]
W : Mass(kgf)
D : Diameter(㎝)
Gearhead Operation of Ball Screw
GD² Equation a-axis component of tatal GD²

n₁ : Rotational speed of a-axis
n₂ : Rotational speed pf b-axis
Reduction ratio is n₁/n₂(i >1)

GD²1 : Ball Screw GD²
P : Pitch of Ball Screw(㎝)
W : Total weight of table and work
GD² of Arbitrary shaft
GD² Equation
D : Diameter (㎝), W : Mass (kgf), S : Radius of Rotation (㎝)
  • When the brake motor is used, the inertia moment of a load has a greater impact on stop time, overrun, and stop precision. The relationship between the inertia moment J and the flywheel effect GD² expressed as the following equation.

Flywheel Effect
J : Inertia Moment

  • When the deceleration is applied using a gearhead, the motor shaft component of GD² is represented by 1/(Gear Ratio)². The equation is as follows.

GDM : Motor Axis Component of GD²
GDL² : Assembled Load of GD² on Gearhead
i : Reduction Ratio of a Gearhead

  • For example, if a gearhead with a ratio of 1/18 is used and the inertia of a load (GDL²) is 1000[kgf , cm²], the component of the motor shaft is
  • If converted to Sl units of the inertia moment, the inertia moment is expressed as l in Sl units and this is represented as an equation below.

g : Gravitational Acceleration 9.80665 [m/sec²]

  • Indicated allowable inertia load in below chart. Please use in less than value indicated.


SIZE Output Allowable inertia load in the motor shaft
□ 60 6W 0.25
□ 70 15W 0.57
□ 80 15W,25W 1.20
□ 90 40W 3.00
□ 90 60W 3.00
□ 90 90W,120W,150W 4.60
□ 90 80W,200W 6.00
  • Allowable inertia load in the gearhead shaft is as below according to gear ratio.

Gear ratio 1/3~1/5

Gear ratio 1/60우

GD²G : Allowable inertia in gearhead shaft
GD²M : Allowable inertia in motor shaft
i : Gear ratio of Gear Head