Linear Positioners Catalog_en-US_revA - Kollmorgen

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Linear Sizing Calculations: Move ProfileL I N E A R P O S I T I O N E R SRotary and linear positioner selection begins with thecalculation of speed, thrust and torque requirements. In orderto determine the torque required, the acceleration of the massbeing moved must be calculated. A “move profile”, or a plot ofload velocity vs. time, is sketched in order to simplify the peakacceleration and peak velocity calculations.Typical Machine CycleVelocityV+V-(1) Total distance,(2) Max velocity,Typical Cycle Time Tt1 t2 t3 t4 t5v MAX =[d tot = v MAX t 1 t+ t 32 2 +2 ]d tott( 1 + t 3)2+ t 2Next CycleTimeThe Move Profile sketch contains some important information:• Peak acceleration is the steepest slope on the curve, in thiscase during t 4 or t 5 .• Maximum velocity is at the highest or lowest point over theentire curve, here at the peak between t 4 and t 5 .• Distance is equal to the area under the curve. Area abovethe time axis represents distance covered in the positivedirection, while negative distance falls below this axis. Thedistance equation (1) is just a sum of the areas of two trianglesand a rectangle.Trapezoidal and Triangular ProfilesA couple of assumptions can greatly simplify the generalequations. For the Trapezoidal profile we assume t 1 =t 2 =t 3 ,and for the Triangular we assume t 3 =t 4 . Substituting theseassumptions into equations (2) and (3) yields the equationsshown in the figure below.For a given distance (or area), a triangular profile requireslower acceleration than the trapezoidal profile. This results ina lower thrust requirement, and in turn, a smaller motor. On theother hand, the triangular profile’s peak speed is greater thanthe trapezoidal, so for applications where the motor speed is alimiting factor, a trapezoidal profile is usually a better choice.(3) Acceleration,a =v MAXt ACCELThe figure above is an example of a typical machine cycle,and is made up of two Move Profiles; the first is an exampleof a trapezoidal profile, while the second is a triangularprofile. The horizontal axis represents time and the verticalaxis represents velocity (linear or rotary). The load acceleratesfor a time (t 1 ), has a constant velocity or slew section (t 2 ),and decelerates to a stop (t 3 ). There it dwells for a time,accelerates in the negative direction (t 4 ), and deceleratesback to a stop (t 5 ) without a slew region. The equationsneeded to calculate Peak Velocity and Acceleration for ageneral trapezoidal profile are shown in the figure. A triangularprofile can be thought of as a trapezoidal profile where t 2 = 0.Trapezoidal Move Profilev maxv avgad tott 2Velocity(in/sec)Triangular Move ProfileV maxV avgVelocity(in/sec)t 1 t 3aT (time in sec)t 1 t 3T (time in sec)d totv d AVE = tott tott 1 = t 2= t 3 =t tot3v d MAX = 1.5 tot = 1.5v t AVEtotda = 4.5 tot( t tot) 2v AVE =t 1 = t 3 =v MAX =a =4d tot( t tot) 2d tott tott tot22d tott tot=2v MAXt tott 2 = 0= 2 v AVE86K O L L M O R G E N
Linear Sizing Calculations: Move ProfileExample 1Calculate the peak acceleration and velocity for an object thatneeds to move 30 inches in 2.5 seconds. Assume a TrapezoidalProfile.Solutionv max2.5 sec.d = 30 in.totExample 3This is an example of a case when triangular and trapezoidalmove profiles are not adequate approximations. Assume amaximum positioner speed is 6 inches/sec. Sketch a moveprofile that will complete a 10 inch move in 2 seconds. What isthe minimum allowable acceleration rate in inches/sec 2 ?SolutionvTriangularTrapezoidalActualRequiredMoveL I N E A R P O S I T I O N E R Sv AVE =30 in2.5 sec= 12 in/sectv MAX = 1.5d totd tott tot= 18 in/secExample 2Calculate, in radians/sec, the peak acceleration and velocityfor an cylinder that needs to move 5 revolutions in 0.4 seconds.Assume a Triangular Profile.SolutionTriangularv AVE =10 in2 sec= 5 in/secv MAX = 2 × v AVE = 10 in/sec (v MAX > 6 in/sec – too fast)Trapezoidalv MAX = 1.5 × v AVE = 7.5 in/sec (v MAX > 6 in/sec – too fast)These are too fast, so we need to find t 1 as follows:a = 4.5 = 21.6 in/sec 2 in( t tot) 2 ( t tot – t 2)v max5 revsRequired Profile( t 1 + t 3)( 2 )d tot = v MAX + t 2d tot = 5 revs × 2π rad = 31.42 radrevv 31.42 rad in radAVE = = 78.550.4 secsecv radMAX = 2 v AVE = 157.1secda = 4 tot = 785.5 radT2 sec20.4 sec.d = + t 2 = t tot +22v MAX( )solving for t 2 ,( ) ( )td tot t tot2 sec2 = – × 2 10 inv = MAX 26 in/sec– 2× 2t 2 = 1.33 secNow assume t 1 = t 3 , sot 1 = (t tot - t 2 )/2 = 0.33 sec.Finally, calculate accelerationva = MAX = 6 in/sec = 18t 0.33 sec1sec2t 22www.kollmorgen.com87
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Kollmorgen Linear Positioners Catal
Page 3 and 4:
K O L L M O R G E N L I N E A R P O
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N2 & EC Series Electric Cylinder Se
Page 7 and 8:
Electric Cylinders Are Preferred Wh
Page 9 and 10:
N2 Series Electric Cylinders: Gener
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N2 Series Electric Cylinders: Gener
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EC Series Electric Cylinders: Gener
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Page 21 and 22:
System Performance Summary - N2, EC
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System Performance Summary - EC4 Se
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Thrust Speed Curves - N2 SeriesSPEE
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Thrust Speed Curves - EC1 SeriesSPE
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Page 35 and 36: Thrust Speed Curves - EC4 SeriesSPE
Page 41 and 42: Servo System Current CalculationEC3
Page 43 and 44: N2 DimensionsMF3 Front and Rear Rec
Page 45 and 46: N2 DimensionsMS6 Side Tapped HolesP
Page 47 and 48: N2 DimensionsMT4 Trunnion MountingI
Page 49 and 50: EC Series DimensionsJFTMF1 Front Fl
Page 51 and 52: EC Series DimensionsHETMS2 Side Lug
Page 53 and 54: EC Series DimensionsHICTMS2 SideLug
Page 55 and 56: EC Series Rod End DimensionsFT1 Fem
Page 57 and 58: N2 Dual Rod-End Bearing OptionDB Du
Page 59 and 60: Linear Rod Bearing OptionLR Linear
Page 61 and 62: N2 Environmental OptionsTemperature
Page 63 and 64: Position SensorsPosition Sensor Spe
Page 65 and 66: AKM1x Brushless Servo SystemsAKM11B
Page 67 and 68: AKM42 Brushless Servo SystemsAKM42G
Page 69 and 70: AKM52L Brushless Servo SystemAKM52L
Page 71 and 72: S200 Servo DriveCompact, High-Perfo
Page 73 and 74: S200 Indexer and Linear System Digi
Page 75 and 76: S300 Servo DriveFeatures• CE, UL,
Page 77 and 78: Smart DriveIEC 61131 Machine and Mo
Page 79 and 80: MMC Control SystemThe D16, Drive Re
Page 81 and 82: Linear Actuation Operation: Rotary
Page 83 and 84: Linear Positioning: Mechanical Driv
Page 85: Electric Cylinders vs. Hydraulics &
Page 89 and 90: Linear Sizing Calculations: Thrust
Page 91 and 92: Linear Motion Terminology: Linear P
Page 93 and 94: Linear Motion Terminology: Critical
Page 95 and 96: Introduction to Motion Control Tech
Page 97 and 98: Rotary System Selection: Calculatio
Page 99 and 100: Glossary of Motion Control Terminol
Page 101: Conversion TablesAngular VelocityAL
Page 104 and 105: Application WorksheetL I N E A R P
Page 106 and 107: Application WorksheetL I N E A R P
Page 109 and 110: 1-5 Base Model NumberChoose the mod
Page 111 and 112: 1-5 Base Model NumberChoose the mod
Page 113 and 114: Electric Cylinder Servo Systems - S
Page 115 and 116: Electric Cylinder Servo Systems - S
Page 117 and 118: Dimensional Data - AKM1x Frame+0.30
Page 119 and 120: Dimensional Data - AKM4x Frame+0.30
Page 121 and 122: NOTES :
Page 123 and 124: Removing the Barriers of Design, So
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Linear Positioners Catalog_en-US_revA - Kollmorgen

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