96 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
Table 2.53: e distribution parameters of random variables in Equation (e)
K (lognormal) M
a
(klb.in) d (in)
μ
lnK
σ
lnK
μ
M
a
σ
M
a
μ
d
σ
d
32.476 0.279 16.8 3.19 2.500 0.00125
Table 2.54: e iterative results of Example 2.29 by the R-F method
Iterative #
K
*
M
a
*
d
*
β
*
|∆β
*
|
1 1.32E+14 16.8 2.345547 1.557169
2 1.14E+14 21.63949 2.494604 1.624744 0.067575
3 1.12E+14 21.76716 2.499996 1.624707 3.69E-05
2.9.10 RELIABILITY OF A COMPONENT UNDER CYCLIC COMBINED
LOADING
Component under cyclic combined loading is very complicated because the frequencies of in-
dependent loadings might not be in phase. In this section, we will only discuss a rotating shaft
under a combined-torques-bending loading.
For a rotating shaft, the cyclic bending stress on a rotating shaft is mainly due to the
rotation of the shaft under a bending moment. For a combined stress fatigue issue, we can use
the Von Mises stress as the equivalent stress to run related fatigue calculation [2]. We will use
the following assumptions to study the fatigue issue of a rotating shaft.
(1) e cyclic stress due to the combined loading will be a cyclic Von Mises stress.
(2) e mean of the cyclic Von Mises stress is mainly induced by the acting torque on the
rotating shaft.
(3) e stress amplitude of the cyclic Von Mises stress is mainly induced by the acting bending
moment on the rotating shaft.
(4) e modified Goodman approach will be used to consider the effect of mean stress in
cyclic Von Mises stress.
Now, we will discuss the cyclic combined loading
.
n
Li
; T
i
; M
i
; i D 1; 2; : : : ; L
/
, where i
is the ith loading level. n
Li
, T
i
, and M
i
are the number of cycles, the torque and the bending
moment, respectively, in the i th loading level. L is the number of different combined loading
levels. n
Li
could be a constant number or a distributed number of cycles in a combined loading
level. M
i
can be a constant bending moment or a distributed bending moment in a combined
loading level. But T
i
will be a constant in each loading level. In the ith combined loading level