OPTIMIZATION OF THERMOMECHANICAL PHENOMENA IN FINISHING OPERATIONS OF PARTS MADE OF MATERIALS PRONE TO DEFECT FORMATION
DOI:
https://doi.org/10.32782/mathematical-modelling/2025-8-1-23Keywords:
thermomechanical phenomena, finishing, defect formation, multicriteria optimization, mathematical modelingAbstract
The study is devoted to the development and application of mathematical models for optimizing thermomechanical processes occurring during finishing operations of machining parts made of materials prone to defect formation. The article analyzes the modern technological requirements associated with the processing of magnetically hard alloys, ferroceramic materials, and high-strength steels, where traditional methods do not always provide the necessary balance between productivity and processing quality. The main goal of the work is to create an integrated mathematical model that takes into account the influence of temperature, force, and geometric parameters on the formation of defects, including cracks, during finishing. The article presents a theoretical framework for formalizing the problem of multicriteria optimization, which allows unifying various partial criteria into a single system for assessing the quality of a working surface. The use of the principles of utility theory contributes to the development of a model that describes the nonlinear distribution of the temperature field, diffusion processes, and the occurrence of force stresses in the contact zone between the tool and the workpiece. Thanks to the use of specialized cooling and lubricating media, adhesion phenomena were reduced, which minimized local temperature overheating and reduced the risk of microcracks. Experimental studies confirmed the effectiveness of the modeling, as a clear dependence of the stress intensity factor on the size of defects and finishing modes was established. The results obtained allow us to formulate practical recommendations for optimizing technological parameters, including the processing temperature, the duration of exposure to the heat flow, and the geometry of the abrasive wheel. This contributes not only to improving the quality of the treated surfaces, but also to reducing economic costs by reducing the rejection rate and increasing production productivity. Thus, the study has significant practical potential for the implementation of innovative solutions in the field of thermomechanical processing of hard-to-machine materials. The developed methodology of mathematical modeling creates the basis for further experimental testing and optimization of production processes, which will help to increase the competitiveness of enterprises in modern conditions of high-tech production.
References
Diegel O., Nordin A., Motte D. Post-processing. A Practical Guide to Design for Additive Manufacturing. Singapore : Springer Singapore, 2019. P. 181–207. DOI: 10.1007/978-981-13-8281-9_12.
Новіков Ф.В., Полянський В.І. Теоретичне визначення температури різання при лезовій обробці. Вісник Національного технічного університету «Харківський політехнічний інститут». Технології в машинобудуванні : збірник наукових праць. 2023. С. 50–57. URL: http://repository.hneu.edu.ua/handle/123456789/30742.
Armarego E.J.A., Herath A.B. Predictive Models for Machining with Multi-Edge Form Tools Based on a Generalised Cutting Approach. CIRP Annals. 2000. Issue 49, № 1. P. 25–30. DOI: 10.1016/S0007-8506(07)62889-3.
Zakeri M., Nosratollahi M., Novinzade A. Multi-Disciplinary System Design Optimization of a Launch Vehicle Upper-Stage. Journal of Aerospace Technology and Management. 2017. Vol. 9, Issue 1. P. 48–62. DOI: 10.5028/jatm.v9i1.681.
Roszkowska E., Burns T.R. Decision-Making Under Conditions of Multiple Values and Variation in Conditions of Risk and Uncertainty. Human-Centric Decision-Making Models for Social Sciences. Ed. Peijun Guo, Witold Pedrycz. Berlin, Heidelberg : Springer Berlin Heidelberg, 2014. P. 315–338. DOI: 10.1007/978-3-642-39307-5_13.
Fu M.C. Stochastic Gradient Estimation. Handbook of Simulation Optimization. ed. Michael C Fu. New York : Springer New York, 2015. P. 105–147. DOI: 10.1007/978-1-4939-1384-8_5.
Сахно В.П., Поляков В.М., Сакно О.П., Колеснікова Т.М. Метод аналізу функціонального резонансу для моделювання контролю безпеки руху автомобіля. Вісник Національного транспортного університету. Серія «Технічні науки». Науково-технічний збірник. 2020. 1(46). С. 293–303. DOI: 10.33744/2308-6645-2020-1-46-293-303.
Wang Z., Xu Y., Ma X. et al. Towards Smart Remanufacturing and Maintenance of Machinery : Review of Automated Inspection, Condition Monitoring and Production Optimisation. 2020 25th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA). (Vienna, Austria, 09.2020). Vienna, Austria : IEEE, 2020. P. 1731–1738. DOI: 10.1109/ETFA46521.2020.9212110.
Підстригач Я.С., Коляно Ю.М. Узагальнена термомеханіка. Київ : Наукова думка, 2013. 312 с.
Freiman S.W., Jr J.J.M. The fracture of brittle materials: testing and analysis. John Wiley & Sons, 2019. 256 p.
Sih G.C. Methods of analysis and solutions of crack problems. Springer Science & Business Media, 2013. 562 p.
Popov G.Y. New Integral Transformations and Their Applications to Some Boundary-Value Problems of Mathematical Physics. Ukrainian Mathematical Journal. Vol. 54, Issue 12. P. 1992–2005.
Моделювання та оптимізація систем / В.М. Дубовой та ін. Вінниця : ПП «ТД «Едельвейс»», 2017. 804 с.
Nesetova V., Lajtai E. Z. Fracture from compressive stress concentrations around elastic flaws. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. 1973. Issue 10, № 4. P. 265–284. DOI: 10.1016/0148-9062(73)90038-7.
Danilov V.G. Mathematical Modelling of Heat and Mass Transfer Processes. Dordrecht : Springer Netherlands, 1995. 1 p.
Allen A.O. Elements of queuing theory for system design. IBM Systems Journal. Vol. 14, Issue 2. P. 161–187. DOI: 10.1147/sj.142.0161.






