Formulas and Units. Transmission technical calculations Main Formulas. Size designations and units according to the SI-units.

Transcription

1 Fomuls nd Units Tnsmission technicl clcultions Min Fomuls Size designtions nd units ccoding to the SI-units Line movement: s v = m/s t s = v t m s = t m v = m/s t P = F v W F = m N Rottion ω = π f d/s v = ω = π f m/s M = F P = M ω W M = J ω& J ω W = Ws o J J = m kgm W = F s Ws m v W = Ws Units used v = velocity in m/s M = mss in kg P= powe in W s = length in m t = time in sec. = cc. in m/s t = cc. time in sec. F= foce in N W = wok in Ws = J = = ng. velocity in d./sec. f = fequency in ev./sec. = dius in m M = toque in J = Rottionl mss moment of ineti in kgm ω& = ngul cc. in d/s M = cceletion toque in

2 Fomule fo the tnsmission technique Powe Rottionl Movement: P s = M ω W (without loss) ω π n = d/s 30 M n π P = W η 30 M n π P = kw η Toque M = F P 9550 M A = η n Line Movement: P = F v W η F v P = kw 000 η Led scew: F p M = 000 π η Toothed belt: v = π D n m/min D m = z z t D = π M = toque in = ngul velocity in d/s n = evolutions/min. = efficiency (moto) F = foce in N z = numbe of teeth t = distnce between teeth in mm v = velocity in m/min M A = deliveed toque in = dius in m P= powe in kw o W D= dimete in m m = module p = pitch in mm/ev P s = tnsmitted shft powe P= necessy moto powe

3 Acceletion toque J n π M = t 30 Fo opetion of electicl motos with ge tnsmission: M Jed n π = t 30 Reduction of ottionl mss moment of ineti n = J = J kgm n mot i J ed Linely moveble msses is educed to the numbe of evolutions of the moto ccoding to: Rottionl mss moment of ineti of solid cylinde: v J ed = 9. m kgm n mot J = m y kgm M = cceletion toque in J = ottionl mss moment of ineti in kgm n = numbe of evolutions in ev./min. t = cceletion time in s v = velocity in m/s J ed = educed ottionl mss moment efeed to the moto shft in kgm n mot = numbe of evolutions of moto in ev/min. m = mss in kg y = oute dius of solid cylinde n mot i = ge tio n 3

4 Acceletion nd deceletion time t J n = s 9.55 M Bking wok M Jed n mot A = Ws M + M 8.4 b b L Necessy powe fo line movement F v P = kw 000 η Foce t sliding fiction F = m g µ N M = cceletion toque in M b = bking toque in M L = lod toque educed to the motoshft in t = cceletion time in s J = ottionl mss moment of ineti in kgm n = Numbe of evolutions in ev./min. W = wok in Ws o J = efficiency of line movement = fiction coefficient J ed = educed ottionl mss moment of ineti efeed to the moto shft n mot = numbe of evolutions of moto in ev/min. P = powe in kw F = foce in N v = line velocity in m/s m = lod in kg g = gvity (9.8 m/s ) 4

5 Fictionl foce duing line movement using wheels o ils m g d F = (µ + f) µ N D By ppoximte clcultions it is often simple to use the specific unning esistnce R in N/ton cige weight by clcultion of the equied powe. R q v P = kw 000 η Hevie ciges on ils, olle beings R = 70 00N/ton Lighte ciges on ils, olle beings R = 00 50N/ton F = foce in N m = lod in kg g = gvity D = wheel- o olle dimete in m f = olling fiction dius d = shft dimete in m = being fiction = il- o side fiction v = velocity in m/s = efficiency q = lod in ton Rolling fiction dius, f (m): Steel ginst steel f = Steel ginst wood f = 0.00 Hd ubbe ginst steel f = Hd ubbe ginst concete f = Inflted ubbe tie ginst concete f = Being, il- nd side fiction: Rolle beings = Sliding beings = Rolle beings =.6 Slide beings =.5 Sideguides with ollebeings =. Rolle guides side fiction =.8 5

6 SI - Units Symbol Mesue Unit SI bsic units m length mete kg mss kilogm s time second A electicl cuent mpee K tempetue Kelvin Designtion Mesue Unit Symbol Fo Motion Contol distnce mete m, ngle din d ngle degee d dimete mete m h height mete m l length mete m dius mete m s distnce mete m V volume cubic-mete m 3 line cceletion m/s ω& ngul cc. d/s f fequency Hetz Hz g gvity m/s n evolutions pe unit ev./min. /s w ngul velocity d/s T time constnt second s t time second s v line velocity m/s Mechnicl F foce Newton N G weight foce Newton N J Rottionl mss kgm moment of ineti M toque Newtonmete m mss kilogm kg P powe Wtt W W enegy Joule J efficiency fiction coefficient i ge tio Electicl I cuent Ampee A P ctive powe Wtt W R esistnce Ohm S,Ps ppeent powe Voltmpee W, VA U voltge Volt V 6

7 The otting mss moment of ineti of otting bodies Body Rottion Symbol Rottionl mss moment of ineti, J in kgm Hollow cylinde Aound own xis m Homogeneous cylinde Aound own xis m Thickwlled cylinde Aound own xis m ( + ) Disc Aound own xis m Disc Aound own plne m 4 Sphee Aound own cente m 5 Thinwlled sphee Aound own cente m 3 Thin od Pependicul ound own xis m l Steines Eqution Rottionl mss moment of ineti eltive to pllel shft in the distnce J = J kgm 0 + m J 0 = ottionl mss moment of ineti kgm eltive to the cente of gvity xis m = mss of the body = shft distnce kg m 7

8 Coeltion between ottionl mss moment of ineti nd otting mss J J = m kgm J = ottionl mss moment of ineti in kgm m = mss in kg J = inetil dius in m The efficiency fo diffeent types of dives e often vlues obtined by expeience: Some noml vlues fo pts with ollebeings: Dive belt with 80 foce tnsmitting ngle = Chin with 80 foce tnsmitting ngle = Toothed od = Tnspoting belt with 80 tnsmitting ngle = Wie with 80 tnsmitting ngle = The fiction vlues e difficult to give coectly nd e dependnt on sufce conditions nd lubiction. Some noml vlues: Steel ginst steel sttic fiction, dy = dynmic fiction, dy = sttic fiction, viscous = dynmic fiction, viscous = Wood ginst steel sttic fiction, dy = Dynmic fiction, viscous = Wood ginst wood Sttic fiction, dy = Dynmic fiction, viscous = Plstic ginst steel sttic fiction, dy = Dynmic fiction, viscous =

9 The twisting toque on shft fom pulling foce is ccoding to the following: d M = F η = F 0 η F = coss foce M = twisting toque d o = effective dimete on toothed wheel o chin wheel Efficiency, Toothed wheel = 0.95 Chin wheel = 0.95 Toothed belt = 0.80 Flt belt = 0.40 Flt belt, pe-tensed = 0.0 = efficiency = dius in m 9