PSI - Issue 40

Ksenia Syzrantseva et al. / Procedia Structural Integrity 40 (2022) 418–425 Ksenia Syzrantseva at al. / Structural Integrity Procedia 00 (2022) 000 – 000

422

5

where  1 =1.27027;  2 =-0.85566;  3 =0.07521;  4 =-0.52205;  5 =-0.31440;  6 =0.43318; ν i = Т 1 i / Т 1 м ;   0,1   i . The corresponding density function has the form:             6 1 5 2 cos 2 1 ( ) j i j i j P     , (7) and its histogram is shown in Fig. 3. The feature of the function (7) is that it is characterized by the presence of two extreme points and is not described by standard distributions of random values studied in the probability theory. At the same time, the proposed method of probabilistic calculation of rolling bearing durability is free from restrictions of the loading law, so in this case it is implemented without changes. The last line of the Table 1 contains the results of calculations of the bearing failure probability, while the classical method does not allow for obtaining even an approximate evaluation for this mode.

Fig. 3. Histogram of density function P 5 ( F ) of the random value F described by the law (7).

Table 1. Characteristics of samples of the bearing 2207 safety factor { n } at different loading modes. Classical methods Proposed method

Loading mode

Reshetov-Snesarev knowing the law

Average by classical method

Reshetov on assumption of the normal law

Average of sample

Median Failure

Load correction factor

probability

4.909 % 8.424 % 14.475 % 37.647 %

0.813 % 8.424 % 9.269 % 44.953 % 11.509 %

3.874 % 7.739 % 8.148 % 14.017 % 8.496 %

Light

2.571

10.899

7.1196 4.0373 4.3044 2.6182 3.9192

1.625

Average normal

1.5629

5.297

1

Average equal probability

1.531 1.036 1.461

19.646

0.963 0.666 0.936

Heavy

3.084 5.933

Bimodal

The results of calculating the safety factor sampling { n } of length k =1000 and the reconstructed density function of its distribution (continuous curve) for the bearing 2207 at different operation modes are shown in Figures 4...8. Since the researcher is interested, first of all, in the law of the safety factor distribution near the interval [0;1], diagrams show the left range of sampling. For the convenience of comparing the results, diagrams are plotted in the same scale on both axes.