Modeling the effect of stochastic defects formed in products during machining on the loss of their functional dependencies
DOI:
https://doi.org/10.15276/opu.1.65.2022.02Keywords:
surface treatment, failure probability, fracture model, distribution, material defect, crack parameters, heat flux, surface layer, stress intensityAbstract
The article investigates the influence of hereditary defects formed in the surface layer of products from metals of heterogeneous structure on the quality of surfaces treated with finishing methods. The research is based on an integrated approach based on the results of the deterministic theory of defect development and methods of probability theory. The treated layer of the product is considered as a medium weakened by random defects that do not interact with each other, namely: structural changes, cracks, inclusions, the parameters of which are random variables with known laws of their probability distribution. The causes of structural changes, crack formation on the treated surface product depending on different types of probability distribution of dimensions are investigated: length, depth of defects, and their orientation. From these positions, technological possibilities of their elimination by definition of branch of combinations of the technological parameters providing necessary quality of the processed surfaces are considered. Modeling of thermomechanical processes in the treated surface containing hereditary defects is carried out based on thermoelastic equations with discontinuous boundary conditions in the places of their accumulation. The research used the apparatus of boundary value problems of mathematical physics equations, the method of singular integral equations for solving problems of fracture mechanics, Fourier-Laplace integral transformations for obtaining exact solutions, the method of constructing discontinuous functions. The dependences determining the intensity of stresses in the vertices of hereditary defects are obtained. A method for predicting the nature of crack formation depending on the probability distribution of defects, the values of heat flux entering the surface layer of the processed product has been developed. It is established that the increase in the homogeneity of the material leads to an increase in the value of heat flux, which corresponds to a fixed probability of failure.
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Beno T., Hulling U. J. P. C. Measurement of cutting edge temperature in drilling. Procedia CIRP. 2012. №3. P. 531-536. DOI: https://doi.org/10.1016/j.procir.2012.07.091.
Dandekar C. R., Shin Y. C. Modeling of machining of composite materials: a review. International Journal of Machine tools and manufacture. 2012. №57. P. 102–121. DOI: https://doi.org/10.1016/j.ijmachtools.2012.01.006.
Liang S. Y., Hecker R. L., Landers R. G. Machining process monitoring and control: the state-of-the-art. J. Manuf. Sci. Eng. 2004. №126 (2). P. 297-310. DOI: https://doi.org/10.1115/1.1707035.
Korotkov A., Korotkova L., Gubaidulina R. Effect on grains form on performances grinding wheels. Applied Mechanics and Materials. 2014. №682. P. 469–473. DOI: https://doi.org/10.4028/www.scientific.net/AMM.682.469.
Stephenson D. A., Agapiou J. S. Metal Cutting Theory and Practice. CRC Press, 2005. 864 p.
Goodstein D. Thermal Physics. Cambridge University Press, 2015. 185 p.
Nowacki W. Thermoelasticity. Amsterdam : Elsevier Science, 2013.
Povstenko Y. Fractional Thermoelasticity. Springer, 2015
Оборский Г. А., Дащенко А. Ф., Усов А. В., Дмитришин Д. В. Моделирование систем: монография. Одесса : Астропринт, 2013. 664 с.
Shin Y. C., Xu C. Intelligent Systems: Modeling, Optimization, and Control. Boca Raton: CRC Press, 2017.
Hurey І., Hurey T., Hurey V. Wear resіstance of hardened nanocrystallіne structures іn the course of frіctіon of steel-grey cast іron haіr іn-abrasіve medіum. Lecture notes іn mechanіcal engіneerіng. Advances іn desіgn, sіmulatіon and manufacturіng. 2019. №1. P. 572–580. DOI: https://doi.org/10.1007/978-3-030-22365-6_57.
Новиков Ф. В., Дитиненко С. А. Повышение эффективности алмазно-искрового шлифования. Машинобудування: збірник наукових праць. 2018. №22. С. 22-27.
Финишная обработка поверхностей при изготовлении деталей. / Клименко С. А., Копейкина М. Ю., Лавриненко В. И. та інш.; за заг. ред. М. Л. Хейфец, С. А. Чижик. Мінськ : Беларуская навука, 2017. 376 с.
Usov A., Tonkonogy V., Rybak O. Modellіng of Temperature Fіeld and Stress-Straіn State of the Workpіece wіth Plasma Coatіngs durіng Surface Grіndіng. Machіnes. 2019. №7(1). 20. DOI: https://doі.org/10.3390/machіnes7010020.
Usov A., Morozov Y., Kunіtsyn M., Tonkonozhenko A. Іnvestіgatіon of the іnfluence of structural іnhomogeneіtіes on the strength of welded joіnts of functіonally gradіent materіals. Праці Одеського політехнічного університету. 2020. №1 (60). 21-34. DOI: https://doi.org/10.15276/opu.1.60.2020.03.
Wu M. F., Chen H. Y., Chang T. C., Wu C. F. Quality evaluation of internal cylindrical grinding process with multiple quality characteristics for gear products. International Journal of Production Research. 2019. №57 (21). P. 6687–6701. DOI: https://doi.org/10.1080/00207543.2019.1567951.
Guerrini G., Lerra F., Fortunato A. The effect of radial infeed on surface integrity in dry generating gear grinding for industrial production of automotive transmission gears. Journal of Manufacturing Processes. 2019. №45. P. 234–241.
Li G., Rahim M. Z., Pan W., Wen C., Ding S. The manufacturing and the application of polycrystalline diamond tools. A comprehensive review. Journal of Manufacturing Processes. 2020. №56. P. 400–416.
Gupta R. On novel integral transform: Rohit Transform and its application to boundary value problems. ASIO Journal of Chemistry, Physics, Mathematics and Applied Sciences. 2020. №4 (1). P. 8–13.
Stakgold I. Boundary Value Problems of Mathematical Physics: 2-Volume Set. SIAM, 2000. 760 p.
Popov G. Y. New Integral Transformations and Their Applications to Some Boundary-Value Problems of Mathematical Physics. Ukrainian Mathematical Journal. 2002. №54 (12). P. 1992–2005.
Popov G. Y. On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics. Ukrainian Mathematical Journal. 2001. №53 (6). P. 951-964.
Prössdorf S. Some Classes of Singular Equations. North-Holland Publishing Company, 1978. 417 p.
Muskhelishvili N. I. Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics. Springer Netherlands, 2013. 441 p.
Lifanov I. K. Singular Integral Equations and Discrete Vortices. Berlin: Walter de Gruyter GmbH & Co KG, 2018.
Arone R. Probabilistic fracture criterion for brittle body under triaxial load. Engineering fracture mechanics. 1989. №32 (2). P. 249–257.
Arone R. A statistical strength criterion for low temperature brittle fracture of metals. Engineering fracture mechanics. 1977. №9 (2). P. 241–249.
Khoroshun L. P. Methods of theory of random functions in problems of macroscopic properties of microinhomogeneous media. Soviet Applied Mechanics. 1978. №14 (2). P. 113–124.
Batdorf S. B., Crose J. G. A statistical theory for the fracture of brittle structures subjected to nonuniform polyaxial stresses. Defense Technical Information Center, 1974.
Forquin P., Hild F. A probabilistic damage model of the dynamic fragmentation process in brittle materials. Advances in applied mechanics. 2010. №44. P. 1–72.
