Sigma-II Series SGM*H/SGDH USER'S MANUAL - Esco Drives ...

11 Appendix11.1.1 Selection Example for Speed Control11.1 Servomotor Capacity Selection Examples11.1.1 Selection Example for Speed ControlMechanical SpecificationsLinear motionServomotor1Ball screwCoupling• Load speed: V = 15 m/min• Feeding times: n = 40 times/min• Linear motion section mass: M = 500 kg • Feeding distance: = 0.275 m• Ball screw length: L B = 1.4 m• Feeding time: tm = 1.2 s max.• Ball screw diameter: D B = 0.04 m • Friction coefficient: µ = 0.2• Ball screw lead: P B = 0.01 m • Mechanical efficiency: η = 0.9 (90%)• Coupling mass: M C = 1 kg• Coupling outer diameter: D C = 0.06 m(1) Speed DiagramV15 60 60t = n =40= 1.5 (s)Speedwhere ta = td(m/min)ta tc tdTime (s)60 × 60 × 0.2751.2ta = tm −V= 1.2 −15= 0.1 (s)ttc = 1.2 − 0.1 × 2 = 1.0 (s)(2) Rotation Speed• Load axis rotation speedN = V =15-1= 1500 (min )P B 0.01• Motor shaft rotation speed with the direct coupling: Gear ratio 1/R = 1/1Therefore,(3) Load torqueN = N • R = 1500 × 1 = 1500 (min-1M)9.8µ • M • PT L = B 9.8 × 0.2 × 500 × 0.01= = 1.73 (N•m)2πR • η 2π × 1 × 0.9(4) Load Moment of Inertia• Linear motion sectionJ L1 = M ( ) 2 = 500 × ( ) 2 = 12.7 × 10 -4 (kg • m 2 )• Ball screw• CouplingP B2πR0.012π × 1J =π4ρ • L • D =π-34 -42B B B × 7.87 × 10 × 1.4 × (0.04) = 27.7 × 10 (kg • m )3232J = 1 M C • D2C =1× 1 × (0.06) 2 = 4.5 × 10 -4 (kg • m 2 C)8811-2