{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3adw000059 - DC or AC Drives A guide for users of...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: DC or AC Drives? A guide for users of variable-speed drives (VSDs) ~ Load ~ ~ ~ ~ Load 1 2 ytilibitapmoc-erutuf evitavonni rof :sevird BBA sevird CD gnitsixe fo noitazinredoM sgnidnuorrus eht no stceffe yna sevird tnardauq-4 rellortnoc rewop sa retrevnoc eht ssecorp eht ot ecafretni eht sa rotom evird eht moor lortnoc eht morf noitapissid taeH rotom dna retrevnoc rof ecaps deriuqeR G F CME krowten ylppus :sgnidnuorrus eht no stceffe ynA E sriaper "tops-eht-no" ;ecivres noitcetorp :stniop gniwollof eht revoc woleb snoitces ehT fo seerged ;snoitidnoc latnemnorivne .cte ,LU ,ASC ;CME-EC .egreme gninoitcnuf fo dohtem lacisyhp eht ni dna serutaef ,NE ,CEI ekil snoitaluger lanoitanretni fo ytilibaliava ,ytilibadneped lanoitarepO eb nac secnereffid tnacifingis yna yldrah ,nosirapmoc laicifrepus tsrif a nI :sevird eht evird eht ni secnereffid ,ylesolc erom deziniturcs nehw ,revewoh ;dnuof D ygolonhcet CD erutuf-eht-ot-pu thgiew ;stnemeriuqer ecaps Fig. 1 Fig. 2 .cte ,POTS ~ YCNEGREME ;noitarepo tnardauq-4 ;emit pu-pmar ,esnopser cimanyd :stcepsa evitavonnI/lacigolonhceT C stnemeriuqer ecaps ~ Load ~ ~ ~ Load .cte ,slevel ycneiciffe/stsoc ssecorp ecnanetniam A )s(metsys DSV eht rof stsoc esahcrup latoT B :stsoc gnitarepo tnerruC :era kcehc siht rof gniylppa airetirc niam ehT .sessecorp/stnemeriuqer DC Drive AC Drive cificeps reh/sih rof ygolonhcet evird CA dna CD ni elbaliava yltnerruc snoitpo eht tuo kcehc retrevnoc MWP CA P rotom .norhcnysa CA mpr 0051/Wk 0002 ... mpr 0003/Wk 57.0 objectively V 096 ... V 083 = CA U ;AVk 0052 ... AVk 5.0 = CA retrevnoc rotsiryht CD P rotom CD mpr 009/Wk 0023 ... mpr 0006/Wk 5 V 0911 ... V 002 = CA U ;Wk 0025 ... Wk 11 = CD ot si od dluohs resu a gniht tsrif ehT Main criteria for the user .devlovni era egnar gnittes deeps egral a tuohguorht ytilibapac dnatshtiw daolrevo rof stnemeriuqer tnegnirts nehw ,ekila snosaer lacisyhp dna lacinhcet rof evirD dna euqrot daol tnatsnoc a htiw sevird cimanyd tnenopmoc segnar BBA fo yrogetac gnitar lacipyT ,elor tnatropmi na yalp ot eunitnoc lliw )stnairav tnardauq-4 dna tnardauq-1 sti htob ni( evird CD CD htiw htob deldnah eb ot boj evird yna tsomla sa woleb ot derrefer[ srotom esahp-eerht suonorhcnysa lanoitnevnoc eht ,sselehtreveN .sevird CA dna :seirogetac gnitar lacipyt gniwollof M eht ni ,]s selbane )smret lacigolonhcet ylerup ni( hcihw htiw sretrevnoc ecruos egatlov( ngised MWP htdi W AC htiw )noitaludo eslu P -noc rewop dellortnoc-rossecorporcim latigiD scitsiretcarahc evird-CA dna evird-CD cisab fo nosirapmoc gniwollof ehT sah ,sevird CA dna CD rof htob ,ygolonhcet retrev CD deticxe yllanretxe htiw sevird rotsiryht esahp-3 eslup-6 ylno srevoc noitacitsihpos lacinhcet fo level a dehcaer won ni sretrevnoc ycneuqerf esahp-3 dna ,]s sa woleb ot derrefer[ srotom Handling drive jobs: DC or AC drives? DC Comparison of the basic characteristics of DC and AC drives in industrial applications This overview is intended to outline to users, plant managers, industrial design engineers or the persons responsible for a particular process the features offered by DC drives as compared to AC drives. The annual growth rate for variable-speed drives (abbreviated to VSDs in the following text) is approx. 6 %, while the growth rate for AC drives is around 8 % p.a., with the market's volume for DC drives remaining more or less stable. 3 ... euqrot daol ... ,sredurtxe ,syawelbac lairea ,srotarepo tfil gnisaercni yllacitardauq a htiw .cte ,snaf ,spmup ,srosserpmoc notsip ,senihcam gniward-eriw :)4 .giF( sdeeps eht revo euqrot tnatsnoc a rof snoitacilppa lacipyT -carahc euqrot gnillaf eht erehw snoitacilppa lacipyT :egnar deeps cisab eritne llams ta rotcaf ecnabrutsid a ton si srotom CA fo citsiret .lla ta elbissop yldrah si sessol rotor eht fo noitapissid ,sdeeps llams tA .noitapissid .rotom CD eht ni gnitanigiro sessol rotor eht fo noitapissid doog serusne )Wk 052 ≤ taeh secuder yllaitnatsbus srotom dradnats CA rof )Wk 052 sDSV fo % 09 .xorppa( desu yliramotsuc noitalitnev ecafruS ≤ sDSV fo % 58 .xorppa( desu yliramotsuc erutaef noitalitnev decrof ehT Fig. 3 nG x G n1 y y F 1 2 3 4 n n 5 Fig. 4 nG x G G 0,5 n n F 1 Commutation limit of motor 2 3 4 5 G 0,5 Self-ventilated motor 1,0 Breakdown torque limit of motor 1,0 Motor with forced ventilation G F n G n1 1,5 Current limit of thyristor converter = = = = 1,5 Basic speed range Field control range Basic speed Black-band speed G = Basic speed range F = Field control range n = Basic speed G Current limit of frequency converter 2,0 2,0 M MN M MN segnar gnitarepo :citsiretcarahc euqroT segnar gnitarepo :citsiretcarahc euqroT )noitciped cisab( )noitciped cisab( DC Drive AC Drive !yniturcs deliated erom ot tcidrev gnipeews siht tcejbus ot elbasivda sselehtenon si ti ;snoitacilppa elpmis ynam rof eurt eb llew yam noitazirogetac sihT .niagrab eht otni noitcetorp fo eerged rehgih a sessessop dna ,evisnepxe ssel erofereht si ,ecnanetniam hcum deen ton seod ,ydruts dna elpmis si ,dnah rehto eht no ,rotom CA ehT .noitcetorp fo eerged rewol a sah osla ti ;nur ot evisnepxe ti sekam hcihw ,ecnanetniam fo tol a seriuqer dna detacilpmoc si rotom CD eht :weiv citsilpmis rehtar gniwollof eht tpoda sresu ynam ,noitaulave rotom lareneg roF Differences between DC and AC motors mgk ni 2 4 .woleb 1 elbaT nosirapmoC eht ees ;euqrot emas eht ot ecnerefer htiw ,srotor eht rof rotor J aitreni fo stnemom ssam tnereffid dna srotom eht rof )H thgieh tfahs ^ = ( sezis tnereffid liatne osla noitapissid ssol -rewop dna noitamrof dleif-citengam ni srotom dradnats CA dna CD neewteb secnereffid detaler-ngised dna lacinhcet cisab ehT Sizes, moments of inertia and ramp-up times: n srelioc :noitacilppa lacipyT .egnar deeps ediw a ni rewop evird tnatsnoc a eriuqer hcihw sessecorp tius ot detpada eb nac noitseuq ni rotom eht retteb eht ,rewop mumixam sti tuptuo nac rotom a hcihw ni egnar deeps eht regral ehT . llew sa retrevnoc ycneuqerf CA / retrevnoc rotsiryht CD detaicossa eht fo gninoisnemid eht no eerged hgih a ot tub sretemarap rotom eht no ylno ton sdneped ytud emit-trohs ni daolrevo elbissop ehT .rewop tnatsnoc ta segnar gnittes hgih rof dna sdeeps wol ta noitarepo suounitnoc rof rotom suonorhcnysa eht ot suoegatnavda si rotom tnerruc-tcerid eht taht swohs srotom CA dna CD fo scitsiretcarahc gnitarepo fo nosirapmoc A Fig. 5 nG x G F 1 y y F 2 3 4 n n 5 G { 0,5 z ¬ ­ Power limitation is caused by the breakdown torque of AC motor decreasing as the square of speed (1/n2). ¯ n 1 DC Depending on the size of the DC motors, on the basic speed specified and the design involved (either as compensated or non-compensated DC machines), the field weakening range is either 1 : 3 or 1 : 5 (see section entitled "High speed setting range at constant power" on Page 6). ® n 1 AC In contrast to the AC standard motor with fixed basic speeds (synchronous speeds of 3000/ 1500/1000/... rpm at 50 Hz), the DC motor's basic speed can be designed from approx. 300 rpm to about 4000 rpm for each working point. Power limitation is caused by the commutation of DC motor. 1,0 = AC Motor = DC Motor 1,5 G G = Basic speed range F = Field control range n = Basic speed 2,0 P PN dna DC AC Motor )noitciped cisab( edom 1S ni deeps tsniaga dettolp rewop :citsiretcarahC x ces 916.0 649.0 51.1 37.1 37.1 24.2 75.1 02.2 5 t t ces a 52 01 5.2 161.0 ²mgk a rotoM rotoM 0051 0002 0002 0002 nim J lanretxe J emas n 065 923 521 51 Wk P 5653 0751 975 17 4 3 2 1 mN N M rotoM CA dna CD rof atad tuptuo war emas ).xE = ( elpmaxE a 17 ces 649.0 = = a ces 916.0 = t 0002 x )161.0 + 161.0( mgk 161.0 = aitreni fo tnemom rotom = ^ lanretxe J A :1 .xE 55.9 x 17 = = J lanretxe J 211 = H thgieh tfahs ;mN 17 / Wk 51 rotoM CD :rof mpr 0002 = n a M htiw srotoM CA rof 0002 x )161.0 + 50.0( rotoM CA sa eulav emas ; mgk 161.0 = 2 081 = H thgieh tfahs ;mN 17 / Wk 51 rotoM CA mpr 0002 = n N M= 1- lanretxe rotoM CA dna CD rof :2 elbaT egnar gnittes deeps cisab eht ni atad rotom evoba eht no desab t semit pu-pmaR AC 55.9 DC ∆ N t emit pu-pmaR M= A M htiw srotoM CD rof :kcabdeef laciripme morf deniatbo seulaV a :1 .xE :rof t emit pu-pmaR :kcabdeef laciripme morf deniatbo seulaV J m ra ta ∆n = = = = = MA Jmot Jexternal 55.9 ces[ n ∆ 2 ≈ ∆ = = = mass moment of inertia in kgm2 mass in kg radius of the solid cylinder (rotor) ramp-up time in sec differential between highest und lowest speed in rpm starting (acceleration) torque in Nm motor moment of inertia external moment of inertia A x M = = lanretxe x) J tom J+ J( :emit pu-pmaR a mgk[ 2 2 r x m x 2/ 1 J = :aitreni fo tnemom ssaM a .)sedom gnikarb dna gnivird( noitarepo tnardauq-ruof ni esnopser cimanyd s'rotom eht dna t e m i t p u - p m a r e h t n o ecneulfni dekram a sah ti ecnis ,sevird gnisrever dna ,sraehs gniylf ,sgir tset sa hcus ,snoitacilppa cimanyd ylhgih rof elbairav tnatropmi na si aitreni fo tnemom ssam siht tuB .llew sa srotom CD htiw rellams yllaitnatsbus gnieb yltneuqesnoc rotor J rotor eht fo aitreni fo tnemom ssam eht htiw ,srotom CA od naht thgiew dna H thgieh tfahs rewol yltnacifingis a evah srotom CD 081 571 513 078 553 0081 054 0893 H thgieh )45PI( gk 00.52 ­ 5952 ­ 2521 ­ 575 ¬ 511 4GL054 02.8 4AMS553 03.2 4AMS513 161.0 tfahS thgieW 4M081 mgk epyT 2 rotor J rotoM CA 45PI 211 011 081 554 522 2301 513 0012 32PI gk thgieW ­ Wk mpr 51 0002 L4-211PMD 521 0002 BL4-081PMD 86.01 923 0002 S522IMD 0051 M513+AMD 00.3 96.0 50.0 H thgieh mgk epyT 2 rotor tfahS J rotoM CD 065 n dna AC Standard Motors rof sthgiew dna sthgieh tfahs/sezis ,srotor eht rof aitreni fo stnemom ssaM 5653 0751 975 ¬ 4 3 2 17 1 mN N P M elpmaxE Cooling system IC86W AC Standard Motor )selpmaxe( Available in version IC37 DC Motor DC :1 elbaT nosirapmoC 6 .srotom CA htiw ycneciffe rehgih elbissop a ni stluser sihT . noitalusni ot gnidrocca dezilitu eb ot desu era srotom CA dradnatS . B H ssalc ssalc noitalusni ot gnidrocca dezilitu netfo era srotom CD .)dohtem gnilooc no gnidneped % 4 ... 1 .xorppa :Wk 55 >( retteb si srotom CA fo ycneiciffe eht revewoH .stnemeriuqer ssecorp eht ot gnidnopserroc srotom CD fo tniop lanimon eht ngised ot elbissop ti sekam tnatsnoc rotom ehT Efficiency and operating point of DC and AC standard motors: n .).cte ,sesserp gnitnirp ,snoitacilppa eniram ,snoitallatsni tfiliks ,sgir gnillird( muimerp a ta si ecaps erehw smetsys ni ro ,)"hcniw gnillevart yellort" eht ni senarc ezis-egral rof .g.e( daol eht htiw rehtegot devom eb ot sah rotom eht erehw snoitacilppa rof laicurc era )45 PI noitcetorp fo eerged lausu( srotom CA eht ot derapmoc sa )32 PI noitcetorp fo eerged lausu( ezis rellams dna thgiew rewol 'srotom CD ehT Weight and space requirements: n .ria gnilooc eht ni tsud dna trid fo eerged hgih a dna snoitidnoc tneibma evissergga yb deziretcarahc yrtsudni fo srotces esoht ni yllaicepse tsom ytilitu lacitcarp sti devorp dna noitisop mrif a flesti now sah rotom CA eht taht snaem sihT .ylevisulcxe tsomla desu era srotom CA detcetorp-noisolpxe ,saera suodrazah ni sboj evird roF .noitcurtsnoc ydruts dna elpmis rieht ot etubirt a si dradnats sa 45 PI noitcetorp fo eerged ni deilppus era Wk 0041 .xorppa ot pu fo sgnitar htiw srotom CA taht tcaf ehT .dedulcnoc neeb tey ton sah sretrevnoc CA htiw sevird deeps-elbairav rof gniylppa stnemeriuqer eht ot srotom dradnats esahp-eerht eht gnihctam fo ssecorp eht suhT .)Wk 052 ≤ sDSV fo % 09 .xorppa( noitalitnev ecafrus erutaef yltsom hcihw ,s08/s07 eht ecnis dezilitu neeb yltnanimoderp evah srotom dradnats suonorhcnysa ,sevird CA deeps-elbairav roF .)Wk 052 ≤ sDSV fo % 58 .xorppa( noitalitnev decrof/lanretni htiw desu yliramotsuc era srotom CD taht tnaem sah seitnewt eht fo gninnigeb eht ecnis evird deeps-elbairav cirtcele na sa rotom CD eht fo tnempoleved lacirotsih ehT Degree of protection for motors: n .srotom CD ni sehsurb eht fo emitefil lufesu eht naht retrohs eb yam srotom CA/CD fo sgniraeb eht rof slavretni noitacirbuler eht ,devlovni snoitidnoc lacinahcem eht no gnidnepeD .desu stinu ylppus dleif dezimitpo dna sehsurb nobrac ,srotcelloc detacitsihpos eht ot sknaht ,)h( sruoh 00021 ... 0007 .xorppa ta si srotom CD ni sehsurb fo emitefil lufesu eht ,devlovni noitacilppa eht no gnidneped ,yadoT Motor maintenance: 005 0521 031 031 3842 339 xam n G 3842 )mN( euqroT 0 503 728 0052 )mpr( n deepS 08 )Wk( P rewoP 0 031 0051 xam n 1 n )5 .giF ees( 21LL054... rotoM dradnatS CA :elpmaxE n 3842 031 005 G 3842 0 0 n )mN( euqroT )Wk( P rewoP )mpr( n deepS n )5 .giF ees( K 082 + AMD rotoM CD detasnepmoc :elpmaxE .5 : 1 si )mN 00542 ... 0042 = M( Wk 0041 ... 521 fo yrogetac gnitar eht ni mm 052 ≥ fo thgieh tfahs a htiw srotom CD detasnep -moc ta egnar gninekaew dleif eht rof eulav mumixam ehT .srotoM CA dradnats lla rof 5.2 : 1 fo .3 : 1 si )mN 0092 ≤ M( Wk 063 ... 5 srotoM CD fo egnar gninekaew dleif eht rof eulav lacipyt A M euqrot tuo-llup eht ot euD fo yrogetac gnitar eht ni mm 522 ... 211 fo thgieh tfahs a htiw mumixam a ot pu 5.1 : 1 ylno si egnar gninekaew dleif eht rof eulav lacipyt eht ,5,2 x N M ≈ k :kcabdeef laciripme morf deniatbo seulaV :kcabdeef laciripme morf deniatbo seulaV . 1 rotcaf gninoisnemidrevo eht rellams eht ,) n o t G )daol(xam P/ )rotom(xam P tpek eb nac n morf ,5 .giF ni citsiretcarahc eht fo noitces latnoziroh eht fo htgnel( rewop mumixam sti tuptuo nac rotom a hcihw ni egnar deeps eht regral eht :snaem sihT .tneiciffe-tsoc ylralucitrap noitatnemelpmi sekam enihcam CD deticxe yllanretxe na htiw noitarepo gninekaew dleif lanoitnevnoc ,sesac eseht nI .detalupits era rewop tnatsnoc ta segnar gnittes egral yrev ,.cte ,sredniwnu dna sredniw ,sgir tset ,sevird relioc ekil ,sboj evird dezilaiceps roF High speed setting range at constant power (field weakening operation or field control range): n 7 rewop elbarapmoc ta deriuqer ecaps eroM .)melborp CME ,egatlov rotom eht ni ecnerefretni FH( ecnerefretni fo level rehgih a etareneg erofereht dna retsaf nur senituor noitatummoc ehT : sretrevnoc rotsiryht CD ot derapmoc nehw segatnavdasid gniwollof eht yb tesffo si sretrevnoc ycneuqerf CA htiw tniop ffo-nrut/no-nrut elbatceles-resu a fo egatnavda ehT Result: .devlovni egatlov enil eht fo evitcepserri emit yna ta elbissop si tub ,lortnoc egatlov rednu nur ton seod dnik siht fo enituor noitatummoc A .elop egatlov CD etisoppo eht ta edoid leehw-eerf a ot sessap tnerruc eht ,ffo sehctiws TBGI na ro OTG a nehW .tnerruc tuptuo eht tpurretni ylevitca ot elba eb ot evah yeht ,esiwirartnoC .lortnoc egatlov rednu ffo hctiws tonnac )sTBGI ro sOTG( stnemele gnihctiws eht ,orez hguorht segassap yna evah ton seod egatlov CD ecniS .egdirb retrevni maertsnwod eht ni tnerruc esahp-eerht otni kcab "detrevnoc" eb ot sah detareneg ylsuoiverp tnerruc tcerid eht ,llew sa retrevnoc rewop detatummoc-enil a sa noitces tupni sti ni skrow )retrevnoc ycneuqerf( retrevnoc CA eht hguohtlA .eulav tnerruc .s.m.r emit-gnol eht rof tub tnerruc kaep s'evird a rof denoisnemid eb ot evah ton od srotsiryht eht yhw si sihT .dedaolrevo ylivaeh gnieb si retrevnoc rotsiryht CD eht nehw neve smelborp yna tuohtiw snoitcnuf ssecorp ffo-nrut siht ,noitatummoc enil ot sknahT .orez ot nwod "rossecederp" eht ni tnerruc eht secuder ylgnidnopserroc suht dna sesir rotsiryht derif ylwen eht ni tnerruc eht taht yaw a hcus ni dezi Fig. 8 -ralop neeb sah sesahp sniam gnitatummoc eht neewteb egatlov eht taht snaem sihT .edom detat -ummoc-enil ni sdeecorp taht retfa dna ,eslup gnirif a htiw snigeb )noitatummoc( gniwollof U V W ~ eht ot hcnarb rotsiryht eno morf refsnart tnerruC Fig. 6 -detalusn =( sTBGI htiw )b 6 I 2 G ralopi -eta 4 B T )srotsisnar us R=0 Fig. 7 uL Ud = E ik X k iL 1 ~ U V W 3 5 Id -nru -eta T O )srotsiryhT ff G =( sOTG htiw )a )sevird tnardauq-eno( )sevird tnardauq-eno( mmargaid kcolb- AC frequency converter mmargaid kcolb- DC thyristor converter Commutation and energy conversion: n Differences between DC thyristor converters and AC frequency converters 8 Fig. 12a ~ ~ ~ .stnemeriuqer lla rof ,noitareneger rof ,ylppus rewop dellortnoc TBGI htiw 4-quadrant AC drive Fig. 11 Fig. 12 ~~ .stnemeriuqer lla rof ,noitareneger rof ,egdirb tupni rotsiryht dellortnoc ylluf htiw stnemeriuqer lla rof ,noitareneger fo elbapac 4-quadrant DC drive 4-quadrant AC drive Fig. 9 Fig. 10 ~~ .cte ,POTS YCNEGREME ,noitarepo tnettimretni rof ,rotsiser gnikarb dna reppohc htiw lasrever dleif htiw ,noitareneger fo elbapac 4-quadrant-DC-drive 4-quadrant AC drive .snoitacilppa evird lairtsudni detacitsihpos ni htrow rieht devorp evah hcihw ereh elbaliava era snoitulos owT .cte ,sevird gnisrever ,sevird sraehs ,sevird enim ,senarc ,srotavele ,stfiliks :era ereh selpmaxe lacipyT ."yltneg ylemertxe" ro "ylneddus" edom gnikarb ot gnivird morf lasrever etucexe ot evah osla dna ,)edom evitareneger ni yltneuqerf( noitator fo snoitcerid htob eldnah ot elba eb ot evah sevird eht ,sessecorp noitcudorp dna snoitacilppa evird ynam nI 4-quadrant drives (reversing drives) for both directions of rotation: n .)gninoitidnoc ria rof tsoC( erutaef tnatropmi na era sessol rewop wol dna ecaps llams revenehw ,sevird CD rof egatnavda na ni stluser sihT .% 003 ... % 031 .xorppa CA ê % 001 CD : ^ = )Wk 001 >( rewop detar ot ecnerefer htiw sevird laudividni sa stenibac retrev -noc rewop rof tnemeriuqer ecapS ;rewop detar eht ot ecnerefer htiw % 5.3 ... % 2 ;rewop detar eht ot ecnerefer htiw % 5.1 ... % 8.0 ≈ ≈ sretrevnoc CA ta ssol rewoP sretrevnoc rotsiryht CD ta ssol rewoP .sretrevnoc rotsiryht CD fo taht elbuod naht erom si ssol rewop eht .e.i ,)CA ê C D ê CA( senituor noisrevnoc ygrene owt era ereht ,retrevnoc ycneuqerf CA eht nI ê CA( enituor noisrevnoc ygrene ylno si ereht ,retrevnoc rotsiryht CD eht nI :kcabdeef laciripme morf deniatbo seulaV and CD .)CD :deunitnoC one 9 .sevird CD htiw thgils ylevitarapmoc si )senilediug .yrassecen serusaem lan yaltuo noitallatsni eht ,evoba denoitnem snosaer eht roF ,sevird CA htiw gnirrucco snoissime citengam-ortcele ehT CME( -oitidda redner yam ,ecnerefretni detaler-elbac htiw rehtegot snoissime citengamortcele gnicuder rof deriuqer :CME • :CME • .sdael s'rotom eht ni srotcaer lanoitidda ro noitalusni gnidniw desaercni yb ,elpmaxe rof ,deidemer eb nac tI .noitalusni s'rotom eht no lla evoba dna ,denrecnoc selbac eht no sserts lanoitidda ot sdael sihT .egatlov detar s'rotom eht eciwt ot pu fo skaep egatlov ni tluser yam )m 01 >( selbac yhtgnel fo .) 2 •√ N U( egatlov enil eht fo eulav kaep eht ot lauqe si slanimret rotom esac eht ni hcihw ,sesir egatlov peets sniatnoc sOTG ro sTBGI eht ta deretnuocne egatlov mumixam eht ,sevird CD htiW htiw sretrevnoc CA dellortnoc-eslup morf tnerruc tuptuo ehT :noitalusni gnidniw/egatlov rotoM :noitalusni gnidniw/egatlov rotoM ..cte senihcam gnitaoc ,sredniwnu -nopmoc lacinahcem ,noissimsnart ,hctulc ,rotom( niart evird • • .)lortnoc CTD htiw BBA morf sret -revnoc :noitpecxe( retaerg yltnatimocnoc suht si ).cte ,stne /sredniw ekil snoitacilppa rof smelborp on eb lliw ereht eht ni snoitallicso citehtapmys fo ytilibaborp ehT .denrecnoc nosaer siht roF .raf yb metsys evird fo seicneuqerf ecnan retrevnoc eht fo elpicnirp lanoitcnuf eht dna tniop gnikrow -oser lacinahcem eht sdeecxe yllareneg dna euqrot evird eht no tnedneped ylesolc yrev ycneuqerf dna edutilpma eht no desopmirepus si elppir tnerruc eht morf gnitluser ni si )enis laedi eht morf noitaived( egatlov dna tnerruc )zH 063 ro zH 003 = fo tnetnoc cinomrah eht morf gnitluser euqrot gnitaslup ehT enil fx6= llicso f( euqrot gnitallicso ehT :euqrot rotom fo snoitallicsO • :euqrot rotom eht fo tnetnoc cinomrah evitaleR · • .thgils ylemertxe era sevird CD htiw deretnuocne smelborp esion eht ,noitarugifnoc siht ot sknahT .ycneuqerf enil dlof-6 .esac htiw tnenopmoc gnitanretla na desopmirepus si hcihw no hcae ni detceles ycneuqerf kcolc eht dna ssecorp kcolc eht tnerruc tcerid a si tnerruc rotom ehT .egatlov enil ladiosunis no tnedneped ylesolc era sevird CA morf snoissime esion ehT eht morf stnemges fo stsisnoc srotom eht ot def egatlov ehT :noitareneg esion/tnerruc rotoM • :snoissime esion/tnerruc rotoM • t - UD Fig. 13...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern