Linear Positioners Catalog_en-US_revA - Kollmorgen

Rotary System Selection: CalculationsInertia Solid Cylinder Inertia Hollow Cylinder Tangential(Conveyor, Rack and Pinion, etc.)F t , V L , aωαF tT tRLR 2R 1J RL =T tω L , α L , ρ, J L, W LF tω L , α L , ρ, J L, W LR 1 , J G1ω = ω L ω = ω L ω = V LR 1α = α L α = α L α = a R 1• R 2 1LW BW LR 2 , J G2R 3 , J G3L I N E A R P O S I T I O N E R SW L = Lρ R 2JJ T = J L + J MotorTJ L = 1W • R 2 L2 gW L = Lρ [R 2 2 - R 2 1 ]J T = J L + J MotorJ L = [R 21W L 2 + R 2 1 ]2 gW L + W BgJ T = J Motor + J RL + J G1 + J G2R 2+ J 1 G3R 3( )( )R 1 2R 2T RLF t = F Friction + F Applied + F GravityT RL = F t • R + T tF t = F Friction + F Applied + F GravityT RL = F t • R 2 + T tF t = F Friction + F Applied + F GravityT RL = F t • R 1eLeadscrewGear BoxF T , V L , aW LN: 1, JJ s , T PL , pLDJ L , V L , α LRT tF tωαJω = 2 pV Lα = 2 paJ S 0.0012 LD 4(for steel)J RL = W 2L 1g 2 pJ T = J RL + J S + J Motorω = V LNα = α LNJ RL = J LN 2J T = J RL + J Reducer + J MotorGear ReducersFollow these guidelines when selecting anIDC precision gearhead:1. Be sure your application's peak torque isless than the maximum momentary torquerating of the gearhead. Be sure to multiply themotor's torque by the gearhead efficiency andgear ratio when determining output torquefrom the reducer.TF t = F Friction + F Applied + F GravityFT RL = t + T PL2 • p • eF t = F Friction + F Applied + F GravityT RL = (F t • R) + T tN • e2. Be sure your application's RMS torque isless than the rated continuous torque of thegearhead.Unitsa = acceleration rate (rad/sec 2 )α = rotary acceleration (rad/sec 2 )D = diametere = efficiency of mechanismF t = total load force includingfriction, gravity, or otherexternal forces (oz)g = gravity = 386 in/sec 2J = rotary inertia (oz-in-sec 2 )J T = total inertia seen by motor(oz-in-sec 2 )J RL = reflected load inertia(oz-in-sec 2 )L = length (in)ρ = material density (oz/in 3 )p = pitch of screw (rev/in)R = radius (in)t A = acceleration time (sec)T A = acceleration torque (oz-in)t D = deceleration time (sec)T D = deceleration torque (oz-in)T PL = preload torque of lead screw(oz-in)t R = running time (sec)T R = running torque (oz-in)T RL = reflected load torque due tofriction, gravity, or otherexternal forces (oz-in)V L = linear velocity of load (in/sec)ω = rotary velocity (rad/sec)W = weight (oz)www.kollmorgen.com97