Linear Positioners Catalog_en-US_revA - Kollmorgen

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