MELSERVO-J4

Rotary Servo Motors

Rotary Servo Motor Sizing Example 1. Selection criteria (1) Configurations

Feed speed of moving part V 0 = 30000 mm/min D B = ball screw diameter

20 mm 500 mm 40 mm 10 mm

V 0

L B = ball screw length

Feed length per cycle Positioning time Number of feed times (Operating cycle Reduction ratio Moving part mass Drive system efficiency Friction coefficient

R = 400 mm t 0 = within 1 s

D G1 = gear diameter (servo motor shaft) 25 mm

D G2 = gear diameter (load shaft) L G = gear tooth thickness

40 times/min

t f = 1.5 s) 1/n = 5/8 W = 60 kg

Servo motor

Gear ratio 5 : 8

h = 0.8 µ = 0.2

P B = 16 mm

Ball screw lead

(2) Servo motor speed N 0 = V

(3) Select a servo motor Selection criteria

0 × 1 = 30000 × 8 = 3000 r/min P B 1/n 16 5

Load torque , Rated torque of servo motor Moment of inertia of all loads , J R × Moment of inertia of servo motor J R : Recommended load to motor inertia ratio Select the following servo motor to meet the criteria above. HG-KR23 (rated torque: 0.64 N•m, max. torque: 2.2 N•m, moment of inertia: 0.221 × 10 -4 kg•m 2 ) (4) Acceleration/deceleration torque Torque required during acceleration T Ma = (J L / h + J M ) × N 0 + T L = 1.84 N•m 9.55 × 10 4 × t psa J M : moment of inertia of servo motor Torque required during deceleration T Md = - (J L × h + J M ) × N 0 + T L = -0.85 N•m 9.55 × 10 4 × t psd Torque required during acceleration/deceleration must be equal to or lower than the max. torque of the servo motor.

(3) Acceleration/deceleration time constant t psa = t psd = t 0 - R - t s = 0.05 s V 0 /60 t s : settling time. Here assumed 0.15 s. (4) Operating pattern

Speed [r/min]

3000

0

Time [s]

0.15

t psa 0.05

0.05 t psd

t s

t

0 1.0

1 cycle t f 1.5

2. Selecting rotary servo motor (1) Load torque (converted into the servo motor shaft) Travel distance per servo motor revolution S = P B × 1 = 10 mm n T L = µ × W × g × S = 0.23 N•m 2 × 10 3 π h (2) Moment of inertia of load (converted into the servo motor shaft) Moving part J L1 = W × ( S × 10 -3 ) 2 = 1.52 × 10 -4 kg•m 2 2 π Ball screw J L2 = π × ρ × L B × D B 4 × ( 1 ) 2 = 0.24 × 10 -4 kg•m 2 32 n ρ = 7.8 × 10 3 kg/m 3 (iron) Gear (servo motor shaft) J L3 = π × ρ × L G × D G1 4 = 0.03 × 10 -4 kg•m 2 32

(5) Continuous effective load torque T rms = T

Ma 2 × t psa + T L 2 × t c + T Md 2 × t psd

= 0.40 N•m

t f

t c = t 0 - t s - t psa - t psd Continuous effective load torque must be equal to or lower than the rated torque of the servo motor.

(6) Torque pattern

Torque [N•m]

1.84

0.23 0

Time [s]

0.05

0.75

0.15 0.05

-0.85

1.5

(7) Result

Select the following: Servo motor: HG-KR23 Servo amplifier: MR-J4-20B [Free capacity selection software]

Gear (load shaft) J L4 = π × ρ × L

G2 4 × ( 1 ) 2

G × D

= 0.08 × 10 -4 kg•m 2

32 n Moment of inertia of all loads (converted into the servo motor shaft) J L = J L1 + J L2 + J L3 + J L4 = 1.87 × 10 -4 kg•m 2

Capacity selection software (MRZJW3-MOTSZ111E) does all the calculations for you. The capacity selection software is available for free download. Contact your local sales office for more details. * Be sure to update your MRZJW3-MOTSZ111E to the latest version.

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