12.1.1.2 Inertia matching calculation Commonly, the following matching relationship is recommended between the motor’s rotor inertia JM and the load inertia JL (converted to the motor shaft) or the total inertia Jr: The motor’s rotor inertia JM can be found in the product sample or instructions. Calculation method of the load inertia is described below: 1) Inertia of axially rotating solid cylindrical rotary bodies Axially rotating cylindrical rotary bodies include ball screws, couplings, gears and sprockets, among others.
or or 2) Inertia of axially rotating hollow cylindrical rotary bodies 3) Inertia of an object switching from linear movement to movement in the rotating direction of the motor 4) When the gear and the synchronous belt transmission decelerate, it is converted into the inertia of the motor shaft. Teeth at the Z 1 motor h ft d Teeth at the Z 2 load d Motor Where, J0 is the motor shaft inertia converted from the load inertia. As inherent inertia is present with gears and ball screws, the final load inertia J L of the motor shaft after conversion is:
205 Technical Manual for EA190 Series Servo Driver V100 ρ Density of rotary body material (kg/m3) L Length of cylindrical rotary body (m) D Diameter of cylindrical rotary body (m) ρ Density of rotary body material (kg/m3) L Length of cylindrical rotary body (m) D Outer diameter of cylindrical rotary body (m) D1 Inner diameter of cylindrical rotary body (m) m Mass of linearly moving object (kg) A Distance moved by the object in one revolution of the motor (in m); if the motor is directly connected with the screw, then A = screw lead hsp JG1 Inertia of gear 1 (kg•m2) JG2 Inertia of gear 2 (kg•m2) JS Inertia of ball screw (kg•m2) m Mass of linearly moving object (kg) A Distance moved by the object in one revolution of the motor (in m); if the motor is directly connected with the screw, then A = screw lead hsp