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In Table 1,
i
denotes stress level
σ
ai
, i.e.
σ
i
, where
σ
a
1
, i.e. just
σ
1
is the largest stress in
the stress spectrum. The relative variable
x
i
=
σ
i
/
σ
1
= 0...1 enables a permanent ratio to be
kept between stress levels. The number of cycles (occurrences) of each of the stress levels
is determined by reading the values of horizontal parts on the step-like diagram (Fig. 8).
Their sum for
k
stress levels satisfies the condition
340
i
1
k
b
b
i
n
n
=
= ∆
∑
.
Table 1. Presentation of the stress spectrum in Fig. 8
i
1
2
3
4
5
6
7
8
σ
ai
N/mm
2
100
98
94
87
74
57
38
19
x
i
=
σ
ai
/
σ
a1
1
0.98
0.94
0.87
0.74
0.57
0.38
0.19
∆
n
bi
50
450
3500 36000 110000 450000 200000 200000
The Stress Spectrum is an ordered set of stress amplitudes of the value
n
b
which shows
the participation of each of the stress amplitudes
σ
i
in the selected number of cycles
n
b
. It
is a statistical (ordered) presentation of random stress fluctuation, it enables a pattern in
behaviour to be defined in the random process and respective calculations and tests to be
completed. The stress spectrum is determined by the value
n
b
, the relative variable
x
i
, and
the largest stress
σ
1
. The number of stress levels may also be greater but also significantly
less than eight. It can be obtained by statistical processing of empirical data obtained from
random function, as has been shown above, or starting from the known cumulative
growing function of stress amplitudes
F
(
σ
a
). Besides this, the stress spectrum can be
obtained by combining the deterministic and statistical approach. In the course of service
length the machine system may operate with different loads (stresses). The load values
(stresses) may be calculated and it is also possible to estimate the possible number of
cycles of each one of them. By joining the blocks of stress cycles defined by the value
and number of cycles, a set of blocks is obtained. By proportional reduction of the total
number of cycles to
n
b
and blocks to
∆
n
bi
, a stress spectrum is obtained. This spectrum
need not satisfy the above given conditions by all its features, but it may be used both for
testing and for calculations, and also for estimates of the service regime. The mentioned
possibilities of stress spectrum formation do not give the same degree of precision. The
choice is made depending on the aims and possibilities of realization.
Machine systems (of the same design) may be exposed to the action of service loads
(stresses), the value of which reaches some upper acceptable limit. In some exploitation
conditions this limit may be reached extremely rare, i.e. loads (stresses) are most often
below this limit. In some other exploitation conditions the loads (stresses) may be most
frequently close to the upper limit. The exploitation regime in this sense represents the
statistical estimate of the presence of stress amplitudes from the same set of their values,
depending on exploitation conditions. This estimate may be made with the help of the
function of probability density
f
(
σ
a
), the cumulative growing function
F
(
σ
a
), and the
logarithmic function of the stress spectrum (Fig. 8). It is possible to speak of light (
l
)
medium (
m
) and heavy exploitation regime (
h
). The light regime entails big participation
of small stress amplitudes, only exceptionally they can be equal to the largest. As per
Fig. 9a, maximum probability density is for
x
m
= 0.2, i.e.
σ
a
= 0.2
σ
a
1
. In the case of
medium exploitation regime the participation of higher amplitudes increases, and they are
most often with amplitudes
σ
a
= 0.5
σ
a
1
(
x
m
= 0.5), whereby the participation of the high
stress amplitudes in the heavy regime is increased (
σ
a
= 0.8
σ
a
1
) on account of the