EMA 1 ET5

Formelsammlung Elektrische Maschinen V1.8 19.01.2003
Stromwendermaschine
Reihenschlusserregung
Besonderheit: Ergänzungen:
c ⋅ = Φ '
Betriebskennlinien: IA;n =f(M)
siehe auch Seite 6.10 Skript
Ruckfreier Antrieb: Ruck ist definiert als:
a
() t
π ⎛ π ⎞
= ⋅ a ⋅sin
⎜ ⋅t
T ⎟
2 ⎝ ü ⎠
Mechanische Zusammenhänge:
Erdbeschleunigung:
n
ü =
n
reduziertes Trägheitsmoment: reduziertes Moment:
J red
2
2
2 2
= J1
+ ü ⋅ J 2 + r1
⋅m1
+ r2
⋅ü
⋅m2
Komplette
Masse
M red = M1
+ ü ⋅ M
Anzugsmoment (Beschleunigung): Gesamtmoment (Motor):
dω1
M z = ⋅ J
dt
J
2 ⋅π
I A = ⋅ M i ~
c
red
Auslauf TA:
g =
9,
81m
s
M red
Grundgleichung der Antriebstechnik:
α
2
1
=
m A I
M red ⋅T
ω
dω
R
ω 2 =
ω
1
α 2
α
M
− M
M
Wann wird nx erreicht?
1
* v2
a2
r2
ü = = = ⋅ ü
v a r
1
⇒
1
= const.
⋅T
[ ] 2
1 M red
1 = =
α =
dt J red
Ui = cm
⋅Φ
h ⋅ n = cm
⋅c
m ⋅ I A ⋅ n = cR
⋅ I A ⋅ n
123 '
cm
⋅ Φh
cR
M i = ⋅ I A = ⋅ I
2 ⋅π
2 ⋅π
1
s
a
max
1
π
= ⋅ a
2
A
Vn A
2
red = J M = [ J ] = kg ⋅ m
1
2 ⋅π
⋅ n0
i
M
2
U
c
R
I − R
c
A A
n = =
−
R
⎛ n
t = + ⋅ ⎜
x tg
J ln
⎝ n
a = r ⋅ & ω = r ⋅α
d a
r = = ˆ Ruck
dt
M ⋅ J + M
M = M z + M red = α1
ω 2 ω 1 =
ü
Trägheitszeitkonstante: Grenzdrehzahl:
End
End
2
A
2
4⋅π
⋅ RA
⋅ J
τ =
J
red
s. Versuch 6 4.7 Grenzzeit:
− n
g
− n
M − M
n =
2 ⋅π
⋅ J
x
2⋅π
⋅c
( ) 2
c ⋅Φ
⎞
⎟
⎠
m
U
i
R
h
⋅ M
M red ⋅
Resthochlauf:
Seite 10 von 10 Formelsammlung_EMA_ET5.doc
red
α 2 a2
α1
= =
ü r ⋅ü
τ τ J
( )
A
i
n = n
n
t
End
R
c
2
A
g
R
+ r ⋅ F + r ⋅ ü ⋅ F
−
A
( cR
⋅ n + RA
) I A
U = U + R ⋅ I = ⋅
1 2
a = const ⇒ s = ⋅ a ⋅ t ⇒ v = a ⋅ t
2
v = r ⋅ω
1
U
=
n
t
AN
g
1
End
− RA
⋅ I
c ⋅ Φ
m
2
M
− n
g
h
2
Amax
ng
⋅ 2 ⋅π
⋅ J
=
M − M
⋅e
2
red
t−t
−
g