# ENTROPY-PROBABILISTIC MODEL OF ACCUMULATION OF FATIGUE DAMAGES

• Evgeny Artemenko National Metallurgical Academy of Ukraine, Dnipro, Ukraine
Keywords: resource, model, spectrum, distribution

### Abstract

Purpose. development of a model for the accumulation of fatigue damage for direct assessment of the service life of machine parts in the probabilistic aspect.
Methods. There are more than a dozen well-known models (hypotheses) of the accumulation of fatigue damage. At one time, we performed a comparative analysis of their accuracy and reliability based on the processing of experimental studies of the durability of fatigue samples under conditions of 205 variants of load regimes. As it turned out, the most adequate estimates of average durability are given by the models: Korten-Dolan, Sorensen-Kogaev, and the model is based on the ideas of linear fracture mechanics. All the above models of the accumulation of fatigue damage, operating on the concept of "relative durability", do not determine what these injuries are. Thus, the development of a model for estimating the life of machine parts in the probabilistic aspect, and a certain concept of "damage" - is relevant.
Results. According to information theory, entropy is a measure of the uncertainty of the state of a physical system. The entropy of a system is the sum of the products of the probabilities of various states of the system by the logarithms of these probabilities, taken with the opposite sign. According to information theory, the amount of information acquired when the state of a certain system is fully identified is equal to the entropy of this system. When the base of the logarithm is two, the dimension is Byte. In our case, a certain volume of numerical values of a random variable can be considered as a system. During the cyclic loading of a certain element (part) of the machine, at each degree of the program block, fatigue damages accumulate, for which the change in entropy is taken. The dependence of the latter on the number of cycles in a graphical form has a domed shape, which resembles the probability density function of the new distribution law. On the basis of certain analytical transformations, the dependence of the entropy change on the number of cycles is presented as a probability density function of a new distribution law of a random variable (in our case, the number of load cycles), and its main characteristics are determined.
Originality. The proposed entropy-probability model of fatigue damage accumulation, based on the principles of the Palmgren-Miner linear hypothesis, contains the latest law of durability distribution, which makes it possible to determine both the average (mathematically expected) durability and the direct construction of the machine resource distribution function, its parameters.
Practical implications. The developed model of fatigue damage accumulation is used for calculations related to forecasting or estimating the fatigue life of machine parts operated under conditions of variable load modes. When performing these calculations, as a rule, the average (mathematically expected) characteristics of the fatigue of the parts are used and, accordingly, fairly accurate average (mathematically expected) resources of the determined elements of the machines are determined.

### References

Grebennik, V. M., Tsapko, V. K. (1989). Reliability of metallurgical equipment (assessment of operational reliability and durability): spravochnik. Moskva : Metallurgy

Ventsel, E. S. (1969). Probability theory. Moskva : Science

Smirnov, N. V., Dunin-Barkovsky, I. V. (1965). Course in Probability Theory and Mathematical Statistics for Technical Applications. Moskva : Science

Collins, J. (1984). Damage to materials in structures. Analysis, prediction, prevention: Per. from English. Moskva: Mir

Oleinik, N. V. (1979). Endurance of machine parts. Kiev: Technics

Grinevich, V. I. (1989). Improvement of drive mechanisms and development of methods for assessing the durability of parts of KhPT mills at the design and operation stages: (Avtoref. disss. cand. tech.) Sciences - Dnepropetrovsk

Grinevich, V. I. (2005). Assessment and prediction of the durability of equipment elements in the probabilistic aspect. Proceedings of NTK (NSAU). Dnepropetrovsk

Grinevich, V. I., Tsapko, V. K. (2002). Calculated assessment of dispersion of fatigue characteristics of materials and parts of metallurgical equipment. Theory and practice of metallurgy. (5-6), 88-91

Published
2021-03-30
How to Cite
Artemenko, E., & Grinevich, V. (2021). ENTROPY-PROBABILISTIC MODEL OF ACCUMULATION OF FATIGUE DAMAGES. Metallurgical and Ore Mining Industry, (1), 42-48. https://doi.org/10.34185/0543-5749.2021-1-42-48
Section
Articles