6 1. INTRODUCTION AND CYCLIC LOADING SPECTRUM
Model #2: A constant stress amplitude of cyclic loading with a distributed cycle number.
Model #2 is a typical cyclic loading spectrum for a component with a single steady function,
that is, a constant cyclic stress amplitude. However, the cycle number n
L
of the cyclic loading is
treated as a random variable and is described by a probabilistic distribution function. How can
this be? It is because, in the reliability-based mechanical design, the components under design
are a batch of “identical” components in service. Each component during its service life had one
value of the number of cycles. All of those can be used to determine the distribution function
of the cycle number. For example, the component under design is subjected to a constant stress
amplitude of a fully reversed cyclic stress
a
D 15 (ksi) with a normally distributed cycle number
n
L
, which has a mean
n
L
D 3 10
5
(cycles), and a standard deviation
n
L
D 3500 (cycles), that
is, n
L
D N.3 10
5
; 3500/. Here, the expression X D N.
x
;
x
/ means that the random variable
X is a normal distribution with a mean
x
; and a standard deviation
x
.
Model #3: A given fatigue life (cycle number) with a distributed amplitude of a cyclic loading.
Model #3 is a typical cyclic loading spectrum for the component with specified service life,
but the fully reversed stress amplitude
a
varies and can be treated as a random variable, and
is described by a probabilistic distribution function. For example, the component under design
with a cycle number n
L
D 8 10
4
(cycles) is subjected to a fully reversed cyclic stress. e stress
amplitude
a
of this cyclic loading follows the uniform distribution between 25 (ksi) and 35 (ksi).
Model #4: Multiple constant amplitudes of cyclic loadings with multiple constant cycle num-
bers.
Typically, model #4 could be used to describe the cyclic loading spectrum of a machine with
several distinguished functions or actions. For example, the cyclic loading spectrum of the com-
ponent under design is:
Cyclic stress level 1 W
a1
D 20 .ksi/; n
L1
D 260;000 .cycles/
Cyclic stress level 2 W
a2
D 30 .ksi/; n
L2
D 50;000 .cycles/:
Model #5: Multiple constant stress amplitudes of cyclic loadings with multiple distributed cycle
numbers.
Model #5 is a common cyclic loading spectrum and can be used to describe many loading condi-
tions for machines with several distinguished functions. For example, the cyclic loading spectrum
of the component under design is:
Cyclic stress level 1 W
a1
D 20 .ksi/I n
L1
D N.260;000; 10;000/
Cyclic stress level 2 W
a2
D 25 .ksi/I ln.n
L2
/ D N.8:425; 0:136/: