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- 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.

- 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 | |
---|---|---|

Shape | ||

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

Sphere | Hexahedron | |
---|---|---|

Shape | ||

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

POLE | ||
---|---|---|

Shape | ||

GD² Equation |
W: : Mass(kgf) D : Outer Diameter(㎝) ℓ : Length(㎝) |
W : Mass(kgf) ℓ : Length(㎝) |

Linear Motion (Horizontal) | Linear Motion (Vertical) | |
---|---|---|

Shape | ||

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 | |
---|---|---|

Shape | ||

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 | ||
---|---|---|

Shape | ||

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.

EXPLICIT CALCULATION METHOD OF MOTOR CAPACITY

SIZE | Output | Allowable inertia load in the motor shaft |
---|---|---|

GD²[kg.fcm] | ||

□ 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