DOI: https://doi.org/10.32515/2414-3820.2018.48.45-53
Method of Planning of Experiment and Construction of Mathematical Model of Process of Strengthening of Pistons of Auto of Tractor Engines a Vacuum Nitriding in the Pulsating Bunch of Plasma
About the Authors
Anatoly Rudkovsky, Senior Researcher, PhD in Technics (Candidate of Technics Sciences), National Academy of sciences of Ukraine G.S. Pisarenko institute for problems of strength, Kyiv, Ukraine, e-mail: coating@ipp.kiev.ua
Sergiy Markovych, Associate Professor, PhD in Technics (Candidate of Technics Sciences), Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: marko60@ukr.net
Sergiy Myhajlyta, post-graduate, Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: sergejmihajluta2@gmail.com
Abstract
In-process developed method of planning of experiment and construction of mathematical model by a calculable experiment, which will allow to conduct the search of the optimum technological modes of forming of diffusive layers a vacuum nitriding in a pulsating bunch plasma which will provide the increase of resistance the isothermal and thermal-cycle creep of pistons.
The decision of task was conducted after the followings stages: formalization of task, constructing of plan of experiment, leadthrough of experiment, previous statistical analysis of results of experiment, construction of mathematical models as a result of experiment, analysis of quality of the got model, leadthrough of calculation experiment, forming of conclusions and recommendations.
After the leadthrough of formalization constructing of plan of experiment is executed.
In this work it is suggested to utillize the plan of experiment which is generated on the basis of LРf – numbers.
Constructing of plan of experiment was in-process conducted by PPP PRIAM (application “Planning, regression and analysis of models package»). The got plan is a matrix every line of which contains the encoded values of independent variables for every level.
Construction of mathematical models as a result of experiment passed in two stages: choice of structure of equalization of regression and receipt of values of coefficients of regression and them statistical descriptions.
For that, to estimate the level of informing in number, utillized the criterion of Boksa-Veca. Verification of adequacy of the got model is taken to verification after the criterion of Fishera.
On the last of peat-time conducted generalization of researches, conclusions and recommendations are formulated in relation to introduction of technological process.
Keywords
vacuum nitriding, mathematical model, plan of experimen, criterion
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References
1. Tolbatov, Yu.A. (1994). Matematychna statystyka ta zadachi optymizatsii v alhorytmakh i prohramakh [Mathematical statistics and optimization problems in algorithms and programs]. Kyiv: Vyscha shkola [in Ukrainian].
2. Radchenko, S.G. (1998). Matematicheskoe modelirovanie tehnologicheskih processov v mashinostroenii [Mathematical modeling of technological processes in mechanical engineering]. Kyiv: ZAO «Ukrspecmontazhproekt» [in Russian].
3. Radchenko, S.H. (2001). Matematychne modeliuvannia ta optymizatsiia tekhnolohichnykh system: Navchal'nyj posibnyk [Mathematical Modeling and Optimized Technological Systems]. Kyiv: 1VTs “Politekhnika” [in Russian].
4. Adler, Ju.P. (1969). Vvedenie v planirovanie zksperimenta [Introduction to Experiment Planning]. Moskow: Metallurgija [in Russian].
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6. Ermakov, S.M., Brodskij, V.Z., Zhigljavskij, A.A. (1983). Matematicheskaja teorija planirovanija zksperimenta [Mathematical theory of experiment planning]. Moskow: Nauka [in Russian].
7. Lapach, S.N., Radchenko, S.G., Babich, P.N. (Eds.). (1993). Programmnye produkty Ukrainy. Planirovanie, regressija i analiz modeli PRIAM [Model planning, regression, and analysis]. Kiev: SP «Tekpor» [in Russian].
GOST Style Citations
- Толбатов Ю.А. Математична статистика та задачі оптимізації в алгоритмах і програмах. Київ: Вища школа, 1994. 399 с.
- Радченко С.Г. Математическое моделирование технологических процессов в машиностроении. Киев: ЗАО «Укрспецмонтажпроект», 1998. 274 с.
- Радченко С.Г. Математичне моделювання та оптимізація технологічних систем: навч. посібн. Київ: 1ВЦ “Політехніка”, 2001. 88 с.
- Адлер Ю.П. Введение в планирование эксперимента. Москва: Металлургия, 1969. 158 с.
- Соболь И.М., Статников Р.Б. Выбор оптимальних параметров в задачах со многими критериями. Москва: Наука, 1981. 111 с.
- Ермаков С.М., Бродский В.З., Жиглявский А.А. Математическая теория планирования зксперимента. Москва: Наука, 1983. 392 с.
- Программные продукти Украины. Планирование, регрессия и анализ модели ПРИАМ / НТУ КПИ; под ред. С.Н. Лапач, С.Г. Радченко, П.Н. Бабич. Киев: СП «Текпор», 1993. С. 24-27.
Copyright (c) 2018 Anatoly Rudkovsky, Sergiy Markovych, Sergiy Myhajlyta
Method of Planning of Experiment and Construction of Mathematical Model of Process of Strengthening of Pistons of Auto of Tractor Engines a Vacuum Nitriding in the Pulsating Bunch of Plasma
About the Authors
Anatoly Rudkovsky, Senior Researcher, PhD in Technics (Candidate of Technics Sciences), National Academy of sciences of Ukraine G.S. Pisarenko institute for problems of strength, Kyiv, Ukraine, e-mail: coating@ipp.kiev.ua
Sergiy Markovych, Associate Professor, PhD in Technics (Candidate of Technics Sciences), Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: marko60@ukr.net
Sergiy Myhajlyta, post-graduate, Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: sergejmihajluta2@gmail.com
Abstract
Keywords
Full Text:
PDFReferences
1. Tolbatov, Yu.A. (1994). Matematychna statystyka ta zadachi optymizatsii v alhorytmakh i prohramakh [Mathematical statistics and optimization problems in algorithms and programs]. Kyiv: Vyscha shkola [in Ukrainian].
2. Radchenko, S.G. (1998). Matematicheskoe modelirovanie tehnologicheskih processov v mashinostroenii [Mathematical modeling of technological processes in mechanical engineering]. Kyiv: ZAO «Ukrspecmontazhproekt» [in Russian].
3. Radchenko, S.H. (2001). Matematychne modeliuvannia ta optymizatsiia tekhnolohichnykh system: Navchal'nyj posibnyk [Mathematical Modeling and Optimized Technological Systems]. Kyiv: 1VTs “Politekhnika” [in Russian].
4. Adler, Ju.P. (1969). Vvedenie v planirovanie zksperimenta [Introduction to Experiment Planning]. Moskow: Metallurgija [in Russian].
5. Sobol', I.M., Statnikov, R.B. (1981). Vybor optimal'nih parametrov v zadachah so mnogimi kriterijami [The choice of optimal parameters in problems with many criteria]. Moskow: Nauka [in Russian].
6. Ermakov, S.M., Brodskij, V.Z., Zhigljavskij, A.A. (1983). Matematicheskaja teorija planirovanija zksperimenta [Mathematical theory of experiment planning]. Moskow: Nauka [in Russian].
7. Lapach, S.N., Radchenko, S.G., Babich, P.N. (Eds.). (1993). Programmnye produkty Ukrainy. Planirovanie, regressija i analiz modeli PRIAM [Model planning, regression, and analysis]. Kiev: SP «Tekpor» [in Russian].
GOST Style Citations
- Толбатов Ю.А. Математична статистика та задачі оптимізації в алгоритмах і програмах. Київ: Вища школа, 1994. 399 с.
- Радченко С.Г. Математическое моделирование технологических процессов в машиностроении. Киев: ЗАО «Укрспецмонтажпроект», 1998. 274 с.
- Радченко С.Г. Математичне моделювання та оптимізація технологічних систем: навч. посібн. Київ: 1ВЦ “Політехніка”, 2001. 88 с.
- Адлер Ю.П. Введение в планирование эксперимента. Москва: Металлургия, 1969. 158 с.
- Соболь И.М., Статников Р.Б. Выбор оптимальних параметров в задачах со многими критериями. Москва: Наука, 1981. 111 с.
- Ермаков С.М., Бродский В.З., Жиглявский А.А. Математическая теория планирования зксперимента. Москва: Наука, 1983. 392 с.
- Программные продукти Украины. Планирование, регрессия и анализ модели ПРИАМ / НТУ КПИ; под ред. С.Н. Лапач, С.Г. Радченко, П.Н. Бабич. Киев: СП «Текпор», 1993. С. 24-27.