written 5.8 years ago by |
Minimum speed =240 rpm=N1,r=140 mm
Mass of fly ball =m=5 kg/4 kg
∴ mean speed = N1+N22=20(N2–N1)
=240+N22=20(N2–240)
∴ N2=252.3076 rpm
N2=212.903 rpm
∴ w1=2π×24060=25.132 rad/sec
∴ w2=2π×252.307660=26.4215 rad/sec
=22.295 rad/sec.
90 mm = 0.09 m
Radius of rotation @ N1=r1=110 mm=0.110 m
Sleeve lift =h=50 mm140 mm
Sleeve arm = horizontal arm =Y=100 mm180 mm
Ball arm = vertical arm =X=120 mm1100 mm
h=YX(r2–r1) [r2=140 mm]
50=100120 (r2–110)
r2=170 mm
Fc1=mr1w21
=5×0.11×25.1322
Fc1=347.389N
Fc1=157.85N
a=r–r1
=140 – 110=30 mm
a=r–r1
=150 – 90=25
{ X1=√x2–a2=√1202–302=116.82 mm
=√1002–252=96.82
Y1=√y2–h21=√1002–252=96.82 mm
=√802–202=77.4596mm }
∑Mo=0↷ +
(Mg+S1)2(Y1)–Fc1(X1)+mg(a)=0
S12(96.82)–347.389(116.82)+5×9.81×0.03
S1=748.29 N=369.29 N
b=r2–r
=170 – 140=30 mm
b=140 – 115
b=25 mm
X2=√x2–b2=√1202−302=116.82 mm
=√1002–252=96.82 mm
Y2=√y2–h2=√1002–252=96.82 mm
=√802–202=77.4596 mm
Fc2=mr2w2=593.3813 rad/sec
fc2=278.357 rad/sec
∑Mo=0↷+
(mg+s2)2(y2)–Fc2(X2)–mg(b)=0
s22(0.9682)–593.3812(116.82)–5×9.81×0.030=0
S2=1431.880 N 1454.291 N
721.195 N
s=S2–S1h=1454.291–748.2950
=14.12 N/mm 8.97
δ=S1S=748.2914.121
δ=52.98mm/42.09
Spring force @ mid position (S):
s=S–S1h1
14.12=S–748.2925
S=1101.29 N/545.09 N
N=Nmean=N1+N22=240+252.30762=246.15 r.p.m.
=20645.5 rpm.
For alteration of speed.
N1=Nmean√s−fS . . . . . (sleeve moving downward) . . . . . .( S = spring force @ mid-position)
=246.15√1101.29–301101.29
N”=2427rpm/203.293rpm.
=246.15√1101.29+3021101.29
N”=249.48 rpm/208.967
Alteration in speed =249.48 – 242.7
=6.78 rpm . . . . (ANS)
=5.674 rpm.