Motion Control Formulas

Transcription

1 ems: A = acceleation ate {in/sec } C = caiage thust foce {oz} D = deceleation ate {in/sec } d = lead of scew {in/ev} e = lead scew efficiency ball scew 90% F = total fictional foce {oz} GR = gea atio J BEL = belt/ack inetia {oz-in } J LOAD = load inetia {oz} J LS = lead scew inetia {oz-in } J MOOR = moto inetia {oz-in } J PULLEY = pulley/pinion inetia {oz-in } L = lead scew length {inch} L RMS = RMS value of load L = load duing time peiod L = load duing time peiod t = Duation of time peiod t = Duation of time peiod ϕ ρ = angle fom hoizontal {degees} = mateial density (lead scew) steel 4.48 {oz/in 3 } N = numbe of teeth in gea N = numbe of teeth in gea = adius of lead scew {in} = adius of gea {in} = adius of gea {in} SF = safety facto.5-.5 ecommended = total move time {sec} a = acceleation toque c d 564 = constant velocity toque = deceleation toque = acceleation time {sec} t c = constant time {sec} t d = deceleate time {sec} t e ACC = constant velocity time = toque to acceleate load {sec} {oz-in} BREAKAWAY = beakaway toque {oz-in} FRICION GRAVIY MOOR OHER SYS μ V LOAD V avg = equied toque to ovecome fiction {oz-in} = equied toque to ovecome gavity {oz-in} = moto output toque at desied speed {oz-in} = function of mechanical system selected = equied toque to move the load {oz-in} = coefficient of fiction = maximum linea velocity {in/sec} = angula velocity {ad/sec} = aveage velocity {in/sec} = maximum velocity {in/sec} W GEAR = weight of gea {oz} W GEAR = weight of gea {oz} W LOAD = weight of load {oz} W PULLEY Duty Cycle Calculation L RMS = = weight of pulley/pinion {oz} W OHER = weight of caiage {oz} L t + L t t + t Note: 6 oz-in = lb-in

2 oque Equations Hoizontal Applications a = ACC + FRICION + OHER c = FRICION + OHER d = ACC + FRICION + OHER Vetical Applications Upwad Move a = ACC + FRICION + OHER + GRAVIY c = FRICION + OHER + GRAVIY d = ACC FRICION OHER GRAVIY Downwad Move a = ACC + FRICION + OHER GRAVIY c = FRICION + OHER GRAVIY d = ACC FRICION OHER + GRAVIY Lead Scew Equations (Linea Motion) SYS = [ ACC + FRICION + BREAKAWAY + GRAVIY ] ACC = 386 J LOAD e + J LS + J MOOR d (W LOAD + W OHER ) J LOAD = (π) J LS = πρl4 C = π SYS d J MOOR = See Moto Data = πv LOAD d FRICION = df πe F = (W LOAD + W OHER )μ d(w LOAD + W OHER )Sinφ GRAVIY = πe NOES:. SYS is the toque the moto must delive a velocity of (adians/second). his usually occus duing the acceleation potion of a move pofile fo hoizontal applications and an upwad move fo vetical applications. Duing the deceleation potion of a move pofile, FRICION and BREAKAWAY ae subtactions fom SYS. Fo hoizontal applications GRAVIY has a zeo value.. he diviso 386 in the ACC equation epesents acceleation due to gavity (386 in/sec o 3. ft/sec ) and convets inetia fom units of oz-in to oz-in-sec. 3. Veify that the angula velocity of the lead scew is below the manufactue s ecommended ating fo citical speed. 565

3 hust Equations πe MOOR C = d Diect Dive Equations (Rotay Motion) SYS = [ ACC + FRICION ]SF 386 [J LOAD + J MOOR ] ACC = Solid Cylindes W LOAD * J LOAD = = πρl4 W LOAD = πρl J MOOR = See Moto Data L Hollow Cylindes J = W LOAD LOAD [ ] = πρl [ 4 4 ] W LOAD = πρl[ ] J MOOR = See Moto Data L Gea Dive Equations (Rotay Motion) LOAD SYS = ACC + BREAKAWAY + SF e(gr) N Gea ACC = 386 J LOAD + J GEARS + J MOOR e(gr) = V LOAD πgr GR = N N Gea N NOES:. SYS is the toque the moto must delive a velocity of (adians/second). he diviso 386 in the ACC equation epesents acceleation due to gavity (386 in/sec o 3. ft/sec ) and convets inetia fom units of oz-in to oz-in-sec. 566

4 Gea Dive Equations (Rotay Motion) (Continued) J GEARS = J GEAR + J GEAR J GEAR = W GEAR * (GR) W GEAR * J GEAR = N N Wom Gea Belt/angential Dive Equations (Linea Motion) SYS = [ ACC + FRICION + BREAKAWAY + GRAVIY ]SF ACC = [J 386 LOAD + J PULLEY + J BEL + J MOOR ] J LOAD = W LOAD * ( ) W PULLEY J PULLEY = Multiply by Numbe of Pulleys J BEL = W BEL * J MOOR = See Moto Data FRICION = W LOAD μcosφ W GRAVIY = W LOAD μsinφ = V LOAD NOES:. SYS is the toque the moto must delive a velocity of (adians/second). his usually occus duing the acceleation potion of a move pofile fo hoizontal applications and an upwad move fo vetical applications. Duing the deceleation potion of a move pofile, FRICION and BREAKAWAY ae subtactions fom SYS. Fo hoizontal applications GRAVIY has a zeo value.. he diviso 386 in the ACC equation epesents acceleation due to gavity (386 in/sec o 3. ft/sec ) and convets inetia fom units of oz-in to oz-in-sec. 567

5 Move Pofiles iangula Move V avg Velocity (in/sec) (time in sec) t d X (distance in inches) X = V avg = = t d = A = D = = 4X apezoidal Move Velocity (in/sec) t c (time in sec) X (distance in inches) t d.5x Assume: = t c = t d = hen: Vmax = 3 A = D = 4.5X Selected Coefficients of Fiction Mateials Conditions Coefficient of Fiction Had Steel on Had Steel Dy Static 0.78 Geasy Sliding 0.5 Mild Steel on Cast Ion Geasy Sliding 0.83 Mild Steel on Mild Steel Dy Static 0.74 Geasy Sliding 0.6 Mild Steel on Babbit Dy Sliding 0.4 Geasy Sliding 0.7 eflon on eflon Dy Static 0.04 eflon on Steel Dy Static 0.04 Bass on Steel Dy Static 0.5 Bass on Cast Ion Dy Static 0.35 Cast Ion on Oak Dy Static Leadscew Efficiencies ype Efficiency (%) High Median Low Ball-Nut Acme with Metal Nut Acme Plastic Nut Since viscous lubicant is equied, the coefficient of fiction is both speed and tempeatue dependent.