LA0011_11GB. Formulas and Units. Rotation 2 W. W = work in Ws = J = Nm. = ang. velocity in rad./sec. f = frequency in rev./sec.

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1 Tnsmission technicl clcultions Min Fomuls Size designtions nd units ccoding to the SI-units Line moement: s m/s t s t m s 1 m t m/s t P F W F m N Rottion ω π f d/s 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 W Ws = elocity 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. elocity in d./sec. f = fequency in e./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 JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge 1 / 9

2 Fomule fo the tnsmission technique Powe Rottionl Moement: P s M ω W (without loss) ω π n 30 d/s M n π P η 30 W M n π 1 P η kw Toque M F Line Moement: 1 P F W η F 1 P kw 1000 η Led scew: F p M 000 π η Toothed belt: π D n m/min M A P 9550 η n D m z z t D π M = toque in = ngul elocity in d/s n = eolutions/min. = efficiency (moto) F = foce in N z = numbe of teeth t = distnce between teeth in mm = elocity in m/min MA = delieed toque in = dius in m P= powe in kw o W D= dimete in m m = module p = pitch in mm/e Ps = tnsmitted shft powe P= necessy moto powe JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge / 9

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 1 J J kgm n mot i Jed Linely moeble msses is educed to the numbe of eolutions of the moto ccoding to Rottionl mss moment of ineti of solid cylinde J ed 91. m kgm n mot J 1 m y kgm M = cceletion toque in J = ottionl mss moment of ineti in kgm n = numbe of eolutions in e./min. t = cceletion time in s = elocity in m/s Jed = educed ottionl mss moment efeed to the moto shft in kgm nmot = numbe of eolutions of moto in e/min. m = mss in kg y = oute dius of solid cylinde n mot i ge tio n JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge 3 / 9

4 Acceletion nd deceletion time t J n s 9.55 M Bking wok Mb Jed n mot A Ws M M 18.4 b L Necessy powe fo line moement F P kw 1000 η Foce t sliding fiction F m g μ N M = cceletion toque in Mb = bking toque in ML = lod toque educed to the motoshft in t = cceletion time in s J = ottionl mss moment of ineti in kgm n = Numbe of eolutions in e./min. W = wok in Ws o J = fiction coefficient Jed = educed ottionl mss moment of ineti efeed to the moto shft nmot = numbe of eolutions of moto in e/min. P = powe in kw F = foce in N = line elocity in m/s m = lod in kg g = gity (9.81 m/s ) = efficiency of line moement JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge 4 / 9

5 Fictionl foce duing line moement using wheels o ils m g d F (μ1 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 P kw 1000 η Heie ciges on ils, olle beings R = N/ton Lighte ciges on ils, olle beings R = N/ton : F = foce in N m = lod in kg g = gity D = wheel- o olle dimete in m f = olling fiction dius 1 = being fiction = il- o side fiction = elocity in m/s = efficiency q = lod in ton d = shft dimete in m Rolling fiction dius, f (m): Steel ginst steel f = Steel ginst wood f = Hd ubbe ginst steel f = Hd ubbe ginst concete f = Inflted ubbe tie ginst concete f = Being, il- nd side fiction: Rolle beings 1 = Sliding beings 1 = Rolle beings = 1.6 Slide beings = 5 Sideguides with ollebeings = Rolle guides side fiction = 1.8 JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge 5 / 9

6 SI - Units Symbol Mesue Unit SI bsic units m length mete kg mss kilogm s time second A electicl cuent mpee K tempetue Kelin 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 olume cubic-mete m 3 line cceletion m/s ω ngul cc. d/s f fequency Hetz Hz g gity m/s n eolutions pe unit e./min. 1/s w ngul elocity d/s T time constnt second s t time second s line elocity 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 ctie powe Wtt W R esistnce Ohm S,Ps ppeent powe Voltmpee W, VA U oltge Volt V JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge 6 / 9

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

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 ( 1 ) 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 1 Steines Eqution Rottionl mss moment of ineti eltie to pllel shft in the distnce J J kgm 0 m J0 = ottionl mss moment of ineti kgm eltie to the cente of gity xis m = mss of the body = shft distnce kg m JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge 7 / 9

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 dies e often lues obtined by expeience: Some noml lues fo pts with ollebeings: Die belt with 180 foce tnsmitting ngle = Chin with 180 foce tnsmitting ngle = Toothed od = Tnspoting belt with 180 tnsmitting ngle = Wie with 180 tnsmitting ngle = The fiction lues e difficult to gie coectly nd e dependnt on sufce conditions nd lubiction. Some noml lues: Steel ginst steel sttic fiction, dy = dynmic fiction, dy = sttic fiction, iscous = dynmic fiction, iscous = Wood ginst steel sttic fiction, dy = Dynmic fiction, iscous = Wood ginst wood Sttic fiction, dy = Dynmic fiction, iscous = Plstic ginst steel sttic fiction, dy = Dynmic fiction, iscous = JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge 8 / 9

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 do = effectie dimete on toothed wheel o chin wheel = efficiency = dius in m Efficiency, Toothed wheel = 0.95 Chin wheel = 0.95 Toothed belt = 0.80 Flt belt = 0.40 Flt belt, pe-tensed = 0.0 JVL Industi Elektonik A/S - Begneødej 17, DK-3460 Bikeød, Denmk - Tel Pge 9 / 9

Physics 111. Uniform circular motion. Ch 6. v = constant. v constant. Wednesday, 8-9 pm in NSC 128/119 Sunday, 6:30-8 pm in CCLIR 468

Physics 111. Uniform circular motion. Ch 6. v = constant. v constant. Wednesday, 8-9 pm in NSC 128/119 Sunday, 6:30-8 pm in CCLIR 468 ics Announcements dy, embe 28, 2004 Ch 6: Cicul Motion - centipetl cceletion Fiction Tension - the mssless sting Help this week: Wednesdy, 8-9 pm in NSC 128/119 Sundy, 6:30-8 pm in CCLIR 468 Announcements