Machines Exercices Corrigés

!"

!" #
&

%

$

& ' !"π
& ' (π
& ' (π)*
& ' π)!"
$

!" #

+ ,

*" - . $
/

/
&

& ' !""
& ' ("
& '*
& '(
0
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3

+ ,

1" - .

!2 #
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3

4

5
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3

*"" )

3
$

+
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3

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+ ,
,

#

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 + (""

& '&

(