IFMASS8

nor the work stresses are determinant values. The determinant values are stochastic values

which dissipate by rule within a wide range (Fig. 1). The safety factor is the ratio of the

mean (most probable) value of critical stress and the highest work stress, which can be

expected in the work process. There is also a possibility for the occurrence of circum-

stances which cannot be foreseen, thus work stress can be somewhat greater, but this is

not likely. The machine part has absolutely been used, and the safety in work satisfied, if

the safety factor is such that the highest possible value of work stress is lower than the

minimal possible value of critical stress. This condition has been satisfied if the dissipa-

tion presented in Fig. 1 (curve 1) is covered by the value of the safety factor. This value is

= 1.25

…

2.5. Lower limits may be used when data about the critical and work stresses

are well known and reliable.

Stress

[

]

)

f([

])

Probability

density

Figure 1. Relation between service stress distribution

(

) and critical stress

distribution

([

]) in safety factor determination

Large values of safety factor create conditions for work stress to be significantly

smaller than the critical one (curve 3 in Fig. 1). The increased distance between the

curves of the distribution of critical and work stress does not increase the probability that

failures will not occur. This probability is close to zero when these curves are close to

each other (the curve of work stress distribution 1). With increase in safety factor there is

an increase in dimensions, and the safety remains the same. High values of the safety

factor contribute to irrational use of mass of machine parts, and make the design solution

large and massive. In machine systems where mass reduction is of increased significance

for the materialization of the function, rationality is achieved by acting on all factors on

which the machine part mass depends, and thus also onto the safety factor. In these

machine systems it is not sufficient that the safety factor be on the lower limit which

provides the condition that there is no probability for failure to occur. A risk is taken that

in a smaller number of machine systems, some of which failed. After failures they are

replaced by new ones, and the risk taken enables the reduction of safety factor below the

indicated lower limits and reduction of dimensions, i.e. mass of chosen parts and the

entire machine system. The risk of failure is unreliability, and the probability for failure

not to occur in the course of service length is the reliability. Calculation on the basis of

limited risk that failure may still happen is a transition from the range of complete safety

into the range of reliability. The curves of work distribution (2) and critical stresses in

Fig. 1 overlap partly. The ends of these curves are with small (low) probability density

and overlap on the wide range of stress. The difference between critical and service stress

is thereby significantly reduced and dimensions decrease with a relatively small “risk” of

failure. The safety factor determined for the state of partial overlapping of curves of the

distribution of the working and critical stress is significantly smaller than the minimal

required for the provision of full safety. This contributes to significant mass reduction

according to the diagram in Fig. 1. This value of safety factor may be valid for orien-

tational determination of allowed stress for the reliability range. A more precise calcula-

334