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Unformatted text preview: !" !" # & % $ & ' !"π & ' (π & ' (π)* & ' π)!" $ !" # + , *" - . $ / / & & ' !"" & ' (" & '* & '( 0 $ 3 + , 1" - . !2 # / 3 4 5 / 3 *"" ) 3 $ + *" - . $ 3 / + , , # 16 # $% 0 , 2 # • > • $ / 7 89")22" : ; *" - . 7 (" <:= ' !*"× ? / + , *" - . @ / / A '(9= 7 • ? • 3 % B / / ' !" = 7 0 ' *1" : / + 0 + , C 5 C D , / ((")89" : ; *" - . 7 ( <:= 7 !*"" ) • $ • $ $ % / ' *("× $$ 5 / '"(= 7 ? + '*= D $ / / / ϕ ' " E9 = F $ '"9= 3 3 / 0 + • @ G ' !*"" ) 3 / ? 3 / / ' 2" × F '"*Ω • • 89" : $ ' " "1 - $ $ A 3 ? 5 '(= 5 + & = % !" <:= 7 ((")89" : 7 !*"" ) ((")89" : ; *" - . 7 *" - . F '"*Ω F D '!*Ω $ / = 4 % 4 8"H 3 0 ' 8E9 : $$ ' 89! : , 4 I / ? 0 89")22" : ; *" - . 2 # • 7 89")22" : ; *" - . 7 (" <:= ' 8× × > F ≈ " Ω 7 D ' !( Ω / • • + $ 3 @ 5/ & ' " !(×GA ) , 3 ? / 3 / !(E)((" : 5 *" - . + ( <:= 7 ((")89" : 7 !*"" ) • ' 9× × > F ' " Ω 7 D ' 2 (* Ω • • $ ? $ / ? @ & 'EG / % / !("" ) 4 / ' # % $ + / 7 η ' L!6 7 ((")89" : 7 *" - . 7 J ' 8E <K 7 G ' !1** ) ' " 9* $ F AF / / ' " ! Ω 7 AF ' " "9 Ω 0 ' 89" : 7 0 ' (1" : $ ? • $ / • $ + # ) J % • $ • $ • $ ? $ + ((")89" : 5 *" - . 7 *E)88 = 7 / ϕ ' " 9E 7 J ' !2 <K 7 !1!" ) F ' " 8* Ω F !(E)((" : ((")89" : 5 *" - . / Y =…A ∆ UY = … V =…A U∆ = … V Réseau …/…V Réseau …/…V Couplage Étoile $ 3 Couplage Triangle !(E)((" : ; *" - . 3 A ' *"" K ( $ 4 + / (8")1"" : 7 1")(8 = 7 *" - . 7 (EL" ) $ 7 F % / • • 3 / 0 ' 1"" : 7 ' !" = 7 J ' " K 7 G ' 8""" ) 0 ' (" = 7 J ' E2" K ' *( : 7 # ? / ? / & & $ =< $ (8")1"" : 5 *" - . @ / & ' 2" G & 3 G ' 8""" ) / 0 + / ((")89" : 7 *" - . 7 E <K 7 ϕ ' " E9 7 G ' !11" ) 7 ' ' ("" K F '!(Ω F 3 $ ((")89" : ; *" - .% 5/ 5 Tem (N.m) 50 Zone linéaire utile Tem (N) 40 30 20 10 1400 $ / 1440 1460 1480 1500 ' !* = G ' !12" ) • ? • 3 ? 1420 / N (tr/min) @ ) 0 + 1 # , / 7 (8")1"" : 7 F ' " ( Ω 3 !88)(8" : 5 *" - . $ 4 • 3 • ? $ / % • ? • 3 M" ' 2 1 </ N" ' 3 3 J" ' " L <K / 4 • % O / ' *! = 7 ' 16 7 / G J ' !* <K ) A / / ' " L*% , / L Réseau triphasée 127/230 V - 50 Hz S L1 L2 L3 C C C F’p = 0.95 Compensateurs •3 •? 3 / $ Moteur Asynchrone * & + $ / / •J J ' ! * <K 7 : • F ' (*" Ω 7 • F '(Ω7 $ G ' !*"" ) '"2= 7 '2*= × ΩA ' ( ** × / 3 F 4 ) P F / ? F / , • 3 • 3 • ? 4 F ' ** Ω P / ' " ** = $ F : F 0 / F ' ("" Ω 7 • • : / G ' !*"" ) : ' ((" : 7 • $ / A: A= ' A (" " ' !( = / !9" " (* $ : ' A : A: A= (E9 " (2" * % (89 " *" (E" " E* / (91 ! 8"" ! *" % (1( !" (!2 !* !9* (" $ • ? • & ! 4 4 ∆: ' A ; : ' A / $ • 3 ( / • ? / 4 4/ :" ' (L1 : " % % , 0 / •3 : ' (2" : 7 ' " E = 7 F ' 82" Ω •3 : ' !(" : 7 ' (" = 7 F ' " 2 Ω •: G ' (("" ) , $ 5 ' Q× ×ΩA $ ) @ & / & '9G ? G ' (*"" ) 4 3 & / / G G ' A: '"E= ' & • • F • ? / % 3 4 % 4 / / G' A G • ? • & % 4 G % G / : : ' !(" : ' & • : ' !(" : G' A "*R R!= 0 • G & AG % / :% / > ' ! 8!×ΩA ) F ' " !* Ω 7 : ' (2" : 7 • ' !E" = • 3 / = G & 4 • 0 • 0 & AG / % / G" ' !99" ) G ' !E"" ) & ' (8" G & & AG $ / & AG 5 - Moment du couple résistant : Tr( N.m) 250 200 150 100 50 0 0 500 1000 1500 2000 Vitesse de rotation N(tr/min) ? • $ &! • $4 / / ! G! 4 , : ' ((" : 7 $ ' *" = 7 G ' !*"" ) F ' " !* Ω 4 , ? & 4 4 G G' A : ' ((" : & 8" R R !"" = 3 % & $ F ' " "* Ω 4 : & ' AG !""" R G R (*"" ) @ & / Tr (N.m) 200 50 N (tr/min) 1500 > : G G ./ !" 0 , @ F / A A * # F G * # A S F + N (π)* !" # % + , A T % !2 # A '9 : GN( ) ) = + , 2" × 5 $ : : 2 # % = *" - . ' 1" - . N = 2" × 1" = 8"" 9 ) *"" ) 5 N + (" 3 # > S *" - . '8 × G N 8 × *"" = = (* - . 2" 2" *" - . 2" × N 2" × *" GN = = = !""" 8 G = GN (! − 16 ) ) = !""" × ( ! − " "1) = L2" ) ./ $% = 2 # 3 7 89")22" : ; *" - . 7 (" <:= 7 / GN = : 2" × = N 2" × *" = !""" 8 ) , B jXs E : s E Vs −: D = jXs s s = : + VD U + Vs π/2 Charge inductive pure F ' !*"× =: +D = ( 8 × *" × ( 9 ) − ( *1" 8 ) !" 0 = !" 9( Ω ((")89" : ; *" - . 7 ( <:= 7 !*"" ) N / Ecc Ecc 5 jXs jXs scc scc A jXs N B Ecc Ecc jXs C N Circuit Étoile équivalent = U F + D = Circuit Monophasé $$ 8 = VD $$ $ 3 A 8 N 80 ( *(" × ) 8 = ( *(" × " ( ) 8 * '"9= ϕ ' " E9 = F (""" = = 8 "1 = 8 × 89" / = = = !( Ω ϕ ' 89 EH # ELL/√3 jXs s j Xs s θ ϕ = 38.7° Vs ELL/√3 Charge inductive cosϕ = 0.78 U = $$ 8 ( Vs s s = : + VD = (: + D : = ϕ) ( − (D ( ( ϕ) + ( D ϕ) − ( D ϕ) ( ) ( (1" ( − (9 ( − ( (8 ) = (!* : & : = & 0 = 8 : = 8 × (!* = 8E( : 0 ' 89" : / = : + VD $ = (: = ( ( ( ((" + (8 ) + ( (9 ) = (1* : = 3 $$ *(" ϕ) + ( D 0 ' ( 7 !*"" ) $ ( 8 × (1* = " 9( = *(" 8 = *(" = ϕ) ( +D 7 ' 2" × 5 Tm Ω s jXs Alternateur Pem Rotor Stator Tem Pméca Moteur ' (= Tr Rs scc Pélec Court-circuit Monophasé Ercc pm pf A N pj Circuit Monophasé équivalent = J F F + VD D = $ ω = $ × Ω = " "1× ( × + = 3 F +D ( ( = 2" × ( " *( + !( *E ( ( π × !*"" = !( *E Ω 2" = L *1 = V J / J =A + +J =J / J = V 3 J = & = 8F Ω V = 8F ( +J = " " = ( & Ω = 8F 8 × " * × L *1( = " 9E G ( π × ( !*"" 2" ) ( V & 3 $ % / s jXs Rs s Vs ϕ 30° Vs jXs Er Zs s s R Er U : = J = 3 = N 80 $ , / $ + VD = / ϕ = " − 1 8 = − 1 8° J = 8: / + 3 $ J 3 8: ( −1 8° ) ≈ 1E <K ϕ = 8 × (!9 × E! EL × 7 89")22" : ; *" - . 7 (" <:= 7 & ' " !( × G 2 # 2" × ) !" """ = !* !L ∠ 1 8° = 8 × 89" : 5 J + ( F + VD = ( (!9 (8 ∠"°) − ( ((" ∠ − 8"° ) = E! EL ∠1 8° = : − = F + VD " * + V! * / ? S +F =J ϕ=& Ω =& × (π G 2" 2" × *" = !""" ) 8 & = " !( × G = " !( × !""" = !(" G G = =/ = & × ( π G 2" !(" × ( π × !""" 2" = = !! "( = 8: 8 × 89" = 3 / s Vs Vs s jXs θ jXs Er Moteur synchrone : = U > 3 5 s Er + VD = : ( + (D = 8× = ) ( = 89" ( + ( !( × !! "( ) = 1"( : 1"( = ( 29 = 8 × *" ( s ' = + $ / 5 % / : P s ϕ Vs ϕ θ Q jXs s S s Er J J = & Ω = !(" × / J ( π × !""" = !( *22 K 2" M = N ( − J ( = ("""" ( − !(*22 ( = !* *2" := F / $ % S + / ( <:= 7 ((")89" : 7 !*"" ) 7 *" - . 3 ((" : !(E)((" : $ / $ / G = + 2" × !*"" ) 2" × *" = =( !*"" 2" × = G $ 1 # @ & 'E*G $ !("" ) / jXs/3 s Vs s A θ j(Xs/3) s Vs Ercc/√3 N Circuit Monophasé $ Diagramme vectoriel =J J 3 !*"" ) 3 5 9 E* × ( π × ( !*"" 2" ) & Ω &Ω = = = 8 2! = 8: ϕ 8: 8 × !(E D = 8 : + 8 ( = ϕ=& Ω 8: E × !*"" = 9 E* G !("" & = QG = = > ⇔ Er/ 3 9× = ( 2 (* = 8 !(E + × 8 2! 8 ((" = " ** = 9 × *" ( ( = ((" : ( ./ # % S + ((")89" : 7 8E <K 7 !1** ) '( G = J G 2" × = 8""" = !*"" ( # ( ' (×( ' 1 : 0 (1" = = = = " 28 : 0 89" F 3 = W = V V J J V V J η 8E""" " L! = = E( 19 = 8: ϕ 8 × ((" × " 9* G − G !*"" − !1** = = 86 G !*"" = " "8 × *" = ! * - . ( = =J + J = ϕ 8: = 8F = J = = S J = > J G ' !1** ) ) ( V 8F 8 ( F ( = J = 8E """ K !− = J " "8 ( ! − " "8 ) × 8E""" = !!11 K ( × !!11 = LE 21 = 8 × " "9 = + ((")89" : 7 *E)88 = 7 !1!" ) 3 ((" : F ((")89" : ((" : F !(E)((" : ((" : Y A 5 A 5 = 33 A ∆ UY = 380 V U∆ = 220 V Réseau 220 / 380 V Réseau 127 / 220 V Couplage Étoile = 57 A Couplage Triangle ) S !(E)((" : ; *" - . ' *E = J = 8: J J ϕ = 8 × !(E × *E × " 9E = !9 9L1 K = 8F X = F ( V V ( = " 8* × *E ( = !!8E K 3 G − G !*"" − !1!" = = 26 G !*"" W = J J =J − J J =J − 3 & = V − V = !99L1 − !!8E − *"" = !E (*E K = J (! − ) = !E (*E × ( ! − " "2 ) = !2 ((( K !2 ((( J = = !"L 92 G Ω ( π × !1!" 2" J = J − J = !2 ((( − !2 """ = ((( K J & = 3 S = Ω ((( = ! *" G ( π × !1!" 2" + (8")1"" : 7 1")(8 = 7 (EL" ) : G 2" × G = + # = 8""" = 8""" ! (EL" ) ) ( ' (×! ' ( G − G 8""" − (EL" = = = E6 G 8""" W N / $ jX’T s R’r/g r jX’r jXs s so so Vs Rm jXm Vs Supposée infinie • J ' G 'G / : ' (8" : 7 '"K ' !" = 7 J ' " K 7 G ≈ G F '" F AF ) →∞ '" ' so so jXm Vso & F r / 0 1"" = (8" : 8 8 : (8" D = = = (8 Ω !" : = = jXm R’r/g jXT * 0 • ' *( : 7 ' (" = 7 J ' E2" K 7 scc jXT R’r rcc '! sm jXm Vscc & ? *( = 8" : 8 J E2" ϕ = = = " 1(( 8: 8 × 8" × (" 5 3 8 = = 8" ∠"° : = = ! 8" ∠ − L"° = VD V(8 4 = / − = !9 98 ∠ − 28 8° = Y 4 = F 4 + VD & = / 8" ∠"° : = = ! *L ∠28 8° Ω 4 !9 98 ∠ − 28 8° Y 4 = ( " E! + V! 1( ) Ω J =& J & = & = Ω =8 F4 J 8 = Ω ω F ' " E! Ω 7 D& ' ! 1( Ω 4( F4 4( = 8 F4 :( ( ω ( F 4 ) + D &( 8 F4 8*9 22 :( = ( ( ω ( F 4 ) + D ( " *"1 + × ( "( & " *"1 J $ ϕ ' 2*H = (" ∠ − 2*° = 5 3 3 0 : = 5 ( "( ≈ & 8*9 22 = E!( × " ( *"1 ) @ & Tem Tem Tr Tem Point de fonctionnement N N Ns & = U : @ & 2" G = " "( × G 8""" =& ⇔ E!( × G = (EE" ) G −G E!( = E!( − × G = " "( × G G 8""" , S + : $ ((")89" : 7 E <K 7 !11" ) G = + 5 2" × 2" × *" = = G ' !18" ) $ @ / 7F '!(Ω 8""" G ' !*"" ) !12" ) Tem (N.m) Tem (N) 50 45 40 Tr (N) 30 20 10 1420 1400 1440 3 & = 1* G J J =& J J =J − 1480 1460 N (tr/min) 1500 !12" = 2 99" K 2" = 299" − ("" = 2 29" K Ω = 1* × ( π × 3 G − G !*"" − !12" = = ( E6 G !*"" W = J J = J X J !− = 8F V J J =J + F η= S 299" = E "E! K ! − " "(E = ( = 8 × ! ( × !*( = 9!" K + V = E"E! + ("" + 9!" = 9 "9! K J 229" = = 9 ( 26 J 9"9! + 1 # $ > / 3 7 (8")1"" : 7 F ' " ( Ω !(E)(8" : 3 M 21 ϕ" = " = = E !! J" " L = / A J" 80 ϕ" = ϕ" = " !1 L"" = !2 !1 = 8 × (8" × " !1 ( J J V / V = 8F = + 8 =F = J" − ( V = " ( × !2 !1( = *( K = L"" − *( = 919 K % '( ' *! = 7 : G = + = J V 2" × *" = !*"" ( = G = G (! − : J 2" × + J J =J − J J J J =J − F η= > > = =( − V = J (! − ( = 919 = 1(1 K ( ) = !1"*2 × (! − " "1) = !8 1L1 K = !8 1L1 − 1(1 = !8"E" K J 80 = !*""" = " E1 8 × (8" × *! / " L* S L1 L2 L3 C C C Fp = 0.74 Compensateurs T / / Moteur Asynchrone M4= M + M 3 M3 = M4− M = J ( ϕ 4− M3 = − 83ω 0 3 = = !*""" − *(" − 1(1 = !1"*2 K F’p = 0.95 J ( = " ( × *!( = *(" K L 127/230 V - 50 Hz = ) !8"E" J = = 9E 6 J !*""" 3 Réseau triphasée ) ) = !*"" × (! − " "1) = !11" = 8F X( = F V ' 16 7 J ' !* <K 3= $ = J( ϕ − 8ω0 J 80 ϕ 4) ( ϕ) ( = = ϕ4 !*""" × ( " L"L − " 8(L ) = 9E (* Z > 8 × ( π × *" × (8" ( !*""" = 8L 21 = 8 × (8" × " L* ./ & + 0 / 7 F ' (*" Ω 7 J ' ! * <K 7 G ' !*"" ) o $ F F = </ = / 4 / '"2= 7F '(Ω7 P = ( ** × Ω = ( ** × </ ' ( **× ×Ω / ( π × !*"" = 1"" Ω 2" / o '2*= 7 / f Rh Ra Va0 E Rf = (F + F ) U :" = −F F F& = = (F + F + F ) ≤ F F = F − (F + F F F ) = 1"" − ( (*" + ( ) = !19 Ω ' " ** = 7 F ' ** Ω / o A f+ a a f Rh Ra Va E > Rf / = ( ** × × Ω = ( ** × " ** × = & F Rch = 55 Ω ( π × !*"" = ((" : 2" ((" − ( ( × " ** ) −F = = 8 91 = F +F ** + ( : =F = ** × 8 91 = (!! : : (!! F = −F = − (*" = !88 Ω " ** F ' ("" Ω 7 : ' ((" : 7 0 ' !( = / E (V) Va (V) Va0 Va ∆Va Er f (A) a (A) > :"' $ ? , A ' (E9 : '"L= ! ∆: ' 3 ; : ' (E9 ; : > a0 f2 Ra Va0 Rf E : " (L1 = = ! 1E = F ("" : ( = > " = : " + ∆: " ∆: " " ∆: " ' 2 : ∆: A [ ' ! 1E = $ " = : " + ∆: " = (L1 + 2 = 8"" : 0 (2" : 5 " E = 5 F ' 82" Ω 7 !(" : 5 (" = 5 " 2 Ω 7 G ' (("" ) $ 5 3 = < / φΩ = < / ( < U : = ? Q= +F : −F Ω )Ω = (< / < ) Ω=Q Ω =Q Ω+F = !(" − ( " 2 × (" ) = " 2E : ) = " E × ( ( π × (("" 2" ) @ / & =< G= 9 G = 8 ( × !" −8 G( (*"" ) ) −! # 3 / / G ' A: > A '"E= = & = & AG 3 $ (Q Ω) J = = Ω Ω Ω : − F = & =Q & (Q ) =− =Q : − (Q Ω) F =Q × ( F : − (Q Ω) F (π G 2" ( ) ) + Q : (Q = − F F ) ( Q : F 5/ Tem (N.m) Tem Point de fonctionnement Tr Tem N (tr/min) N Nv $ @ − (Q ) ( F Q : (π G+ =< G 2" F & − ( ( " 2E × " E ) × ( π " 2 × 2" −8 G= / $ / / " 2E × " E × : = 8 ( × !" −8 G "2 " E9 : = ( 89 1 + 8 ( ) × !" −8 G −89 1 × !" G + " E9 : = 8 ( × !" G −8 G+ '& " E9 ( 89 1 + 8 ( ) × !" −8 : = !9 E* × : GA: N (tr/min) Nn Commande à flux constant Va (V) Van 3 / / G' A A: ' !(" : & − (Q ) F ( Q : (π G+ =< G 2" F − ( E9 8 × !" −8 ) ( G + ( !81 × / ( " 2E ) × × (π ( − ) = 8 ( × !" −8 G ( " 2 × 2" G+ " 2E × × !(" = 8 ( × !" −8 G "2 G 8 ( + ( E9 8 ) × ( × !" −8 = !81 × Ω & !81 × G= / 3 8 ( + ( E9 8 × / ( / ) × !" −8 "*= != "* "2 "E "9 "L ! (L1( (*2! ((*2 ("!! !9!" ! 211 N (tr/min) Nmax Commande à tension constante Nmin f 1 0.5 (A) 0 : ' ((" : 7 $ 7 F ' " !* Ω 7 F ' " "* Ω 7 ' *" = 7 G ' !*"" ) ≈" / Rf a Ra Va E > = < / φΩ = < / ( < 5 3 > + (F + F : = U Q = Q G= / ) ) : − (F + F Q G + (F + F =Q ) G = < / < × (π (π × G = 2" 2" = G= Q G ) ((" − ( " !* + " "* ) × *" = ( 9 × !" −8 *" × !*"" : − (F + F ) Q = ((" − ( " ( × ) ( 9 × !" × −8 8" 1" *" 2" E" 9" L" !"" (*19 !9L8 !*"" !(89 !"*! L!! 9"! E!1 ' N (tr/min) Nmax Nmin a 30 $ / , (A) 100 / / 0 / > & J J =J −( + 3 & =& = G= ((" − ( " ( × ) = ( 9 × !" × −8 = Ω (Q )=J G) ( π × G 2" = Q × 2" (π ( ((" ( G × ( 9 × !"−8 ) + " ( & = ( 2E × !" −( × ((" ( ( G × ( 9 × !" −8 + " () ( = !(L( ( G × ( 9 × !" !""" !*"" (""" (*"" 8""" !18 ** 22 E1 89 1! (1 L( !E 1E $ = (2 E × !" −( × & AG −8 + " () ( / Tm (N.m) Tmax Fonctionnement à puissance constante Tmin N (tr/min) 1000 J / $ @ & % & = − " !G + ("" $ Soit : 3000 @ ( 2E × !" × : −( ( G × ( 9 × !" −8 ( + " () ( = − " !G + ("" & '& ( ...
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