Formelsammlung Kolbenmaschinen I (KMA I) - Fachhochschule ...

Formelsammlung KMA I Seite 14/27
dx(
α)
⋅
λST
Kolbengeschwindigkeit cK
( α)
= = x = rK
⋅ ω ⋅(sin(
α)
+ sin( 2 ⋅ α))
dt
2
dcK
( α)
⋅⋅
2
Kolbenbeschleunigung aK ( α)
= = x = rK
⋅ ω ⋅(cos(
α)
+ λ ST cos( 2 ⋅ α))
dt
Drehwinkel α=ω·t
mittlere Kolbengeschwindigkeit x 2 s n 4 rK
n ⋅ ⋅ = ⋅ ⋅ =
⋅
1
Oszillierende Massen m O = ∑ mi
≈ mK
+ mST
, für λST=0,25
3
rotierende Massen
rWange
2
m R = ∑ m,
Ri ≈ mZapfen
+ mWange
+ mST
rK
3
Oszillierende Kräfte
r
FO
r r
= FI
+ FII
2
r
= mO
⋅rK
⋅ ω (cos( α)
+ λST
cos( 2α))
⋅ ex
Oszillierende Kraft
r
2 r
FI
= mO
⋅rK
⋅ ω ⋅ cos( α)
⋅ ex
Oszillierende Kraft
r
FII
2 r
= λST
⋅mO
⋅rK
⋅ ω ⋅ cos( 2α)
⋅ ex
Rotierende Kraft
r
FR
2 r
= mR
⋅rK
⋅ ω ⋅ er
sin( α + β)
cos( β)
sin( α + β)
cos( β)
Moment Md = FT
⋅rK
= FK
⋅ ⋅rK
= ( FS
− FO
) ⋅ ⋅rK
Gesamtkraft FG
= FI
+ FII
+ FR
r
r
r
r
0 1 2 3 4 5 6
FII
F O
FI
Drehwinkel α [-]
Kraftverläufe aus den Massenkräften in Abhängigkeit des Drehwinkels der Kurbelwelle