Download - Modelos de degradação 3
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8/13/2019 Modelos de degradao 3
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Y =AX+ B
1
1 F(t)
=
(t) ()
= A
=
(B )
L(p) =n
i=1
f(ti|p)
L(p1,...,pk)
pi= 0 ; i= 1,...,k
t
t
(t) =t
R(t)dt
R(t)
(0) =
0 R(t)dt
R(0) =
0 R(t)dt
1 =
Z(t)
zc
Tc
Tc= {t|Z(t) zc}
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[0, Tci] Tci
i
Z(Tci) = zci)
R(t) =P(Tc> t)
Z(Tc) =zc
Tc= Z
1(zc)
R(t) =P(Z1(zc)> t)
0 200 400 600 800 1000 1200400
600
800
1000
1200
1400
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2200
Degradation law and extrapolated failure time
Units of time
Degradationvalue
Z(t) =a + b t
0 100 200 300 400 500 600400
600
800
1000
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1400
1600
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2000
2200
Degradation law and extrapolated failure time
Units of time
D
egradationvalue
Z(t) =a
(bt)
0 500 1000 1500 2000 2500 3000 3500 4000200
400
600
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1400
1600
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2000
2200Degradation law and extrapolated failure time
Units of time
Degradationvalue
Z(t) =a tb
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0 100 200 300 400 500 600 700 800 900 10000
200
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Wiener degradation and extrapolated failure times
Units of time
Degradationvalue
Z(t) =Z(0) + N(mt,t)
2 87, 5% 87, 5%
12Tfailure 1019 472, 1 1009
2 92, 6% 88, 8% 88, 3% 58, 8
Tfailure
572, 8 358, 4 3196, 2 175
2 97, 3% 92, 3% 89, 8% 75
Tfailure 573, 4 424 1663, 9 565
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0 50 100 150 200 250 300 350 400 4500
200
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1000
1200
1400
1600
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Degradation law and extrapolated failure time
Units of time
Degradationvalue
0 50 100 150 200 250 300 350 400
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
t
R(t)
0 20 40 60 80 100 120 140 1600
200
400
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1000
1200
1400
1600
1800
2000
2200
Degradation law and extrapolated failure time
Units of time
Degr
adationvalue
0 50 100 150
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
t
R(t)
0 100 200 300 400 500 600 700 800 9000
200
400
600
800
1000
1200
1400
1600
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2000
2200
Degradation law and extrapolated failure time
Units of time
Degradationvalue
0 100 200 300 400 500 600 700 800
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
t
R(t)
5, 294 4, 718 5, 820
0, 373 0, 148 0, 4712 99, 3% 97, 5% 99, 5%
64
149
49
311
da
dN =C Km
K
KmaxKmin K
K= (max min)a
mean =0
min
0
da
dN =C m(a)m/2
m
C
Y = X+
da
dN =
C+ m
+
m
2 a +
m
2
m= 2
C=
(
m
m2 )
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8/13/2019 Modelos de degradao 3
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68, 91
0, 005
0, 0455
m
3, 25
C
9, 1 108
1/2
m
m
3, 297
C
7, 772 108
1/2
m
2
99, 9%
0 10 20 30 40 50 60 70 80 90 1000.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Paris law
Number of cycles N [kcycles]
Cracklenghta[m]
5%
m
500
100
0 50 100 150 200 250 300 3500.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Paris crack growth law
Number of cycles N[kilocycles]
Cracklengtha[m]
100
5%
m
500
4, 11
0, 39
99, 17%
100
0 50 100 150 200 250 300
0.0
0.1
0.2
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1.0
t
R(t)
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24, 97
C
Nc= a
(m/2)+1c a(m/2)+10
((m/2) + 1) (C m m/2)
1
a
(m/2)+1c a(m/2)+10
((m/2) + 1) (m m/2) N