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Machines Exercices Corrigés .pdf



Nom original: Machines_Exercices Corrigés.pdf
Titre: Microsoft Word - Mach-FC_Trav.Dir..doc
Auteur: XPS

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)

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( <:= 7 ((")89" : 7 !*"" )

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3

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J

3

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5

9 E* × ( π × ( !*"" 2" )
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8
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E
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V

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=

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ϕ

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=
S

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)

(

V

8F

8
(
F
(
= J = 8E """ K

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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)((" : ; *" - .
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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
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W

=

J

J =J −

J

J

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3

&

=

V


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J
=
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J
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3

S

=



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+

(8")1"" : 7 1")(8 = 7 (EL" )

:
G

2" ×

G =

+
#

=

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!

(EL" )

)

( ' (×! ' (
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=
=
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N

/

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s

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r

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s
so

so

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/

: ' (8" : 7

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F
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F

AF )

→∞

'"

'

so
so

jXm

Vso

&
F

r

/

0

1""
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8
8
:
(8"
D =
=
= (8 Ω
!"
: =

=

jXm

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jXT

*
0



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' (" = 7 J ' E2" K 7

scc

jXT

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rcc

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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

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

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= !2 !1 =
8 × (8" × " !1

(

J
J

V

/

V

= 8F

=

+

8

=F

= J" −

(

V

= " ( × !2 !1( = *( K

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:

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+

=

J
V

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(

=

G = G (! −

:

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+

J

J =J −

J

J

J

J =J −

F

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>

> =

=(



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= J (! −

(

=

919
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) = !1"*2 × (! − " "1) = !8 1L1 K
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J
80

=

!*"""
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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=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
=
=




: −
F

=

&

=Q

&

(Q )
=−

=Q

: − (Q Ω)
F

=Q ×
(

F

: − (Q Ω)
F


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 :

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 :

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 ×



&
!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

=



(Q

)=J
G)

( π × G 2"

=

Q × 2"


(

(("
( 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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