186 3. THE DIMENSION OF A COMPONENT WITH REQUIRED RELIABILITY
e component fatigue strength index K can be calculated per Equation (2.79):
K D
.
k
a
k
b
k
c
/
m
K
0
: (f)
e surface finish modification factor k
a
follows a normal distribution. Its mean and standard
deviation can be determined per Equations (2.14), (2.15), and (2.16). k
b
is treated as a determin-
istic value and can be calculated per Equation (2.17). Its value will be updated in each iterative
step by using the newly available diameter of the pin. e mean and the standard deviation of
the load modification factor k
c
can be calculated per Equations (2.18), (2.19), and (2.20).
e limit state function of the double-shear pin under model #1 cyclic shearing loading
spectrum per Equation (2.87) is:
g
.
K
0
; k
a
; k
c
; V
a
; d
/
D
.
k
a
k
b
k
c
/
m
K
0
n
L
2V
a
S
ut
.
d
2
S
ut
2V
m
/
8:21
D
8
ˆ
ˆ
<
ˆ
ˆ
:
> 0 Safe
0 Limit state
< 0 Failure:
(g)
ere are five random variables in the limit state function (g). K
0
is a lognormal distribution. e
rests are normal distributions. e dimension d can be treated as a normal distribution, and its
mean and standard deviation can be calculated per Equation (1.1). e distribution parameters
in the limit state function (g) are listed in Table 3.55.
Table 3.55: e distribution parameters of random variables in Equation (g)
K (lognormal) k
a
k
c
V
a
(klb) d (in)
μ
lnK
σ
lnK
μ
k
a
σ
k
a
μ
k
c
σ
k
c
μ
V
a
σ
V
a
μ
d
σ
d
41.738 0.357 0.8588 0.05153 0.774 0.1262 4.815 0.6
μ
d
0.00125
(4) Use the modified Monte Carlo method to determine the diameter d .
We will use the modified Monte Carlo method to conduct this component dimension
design, which has been discussed in Section 3.2.5. We can follow the procedure discussed in
Section 3.2.5 and the program flowchart shown in Figure 3.5 to compile a MATLAB program.
e iterative results are listed in Table 3.56.
According to the result obtained from the program, the mean of the diameter with a
reliability 0.99 is
d
D 0:550
00
: (h)
erefore, the diameter of the pin with the required reliability 0.99 under the specified loading
will be
d D 0:550 ˙ 0:005
00
: