Russian Federation
Russian Federation
In this paper have been considered questions related to automation of the layout for products with high layout density (primarily means of transport). It has been demonstrated how an aircraft’s geometric shape is formed on the basis of infrastructural and layout constraints. Influences of aerodynamic and internal layouts on the aircraft’s geometric shape have been described, taking into account mass-inertia characteristics of units placed in it. The layout’s reverse problem (when a required layout space is initial data for the aircraft’s geometric shape under hard infrastructure restrictions) has been presented. A project task of finding the rational parameters for the aircraft’s geometric shape as the task of multi-criterion discrete optimization has been described in a generalized form. It has been demonstrated that this task can be formulated as a search for the vector of design parameters as a multitude of admissible variants for design-and-engineering solutions. In the paper has been described a physical task formulation for automated layout as a system of restrictions on objects allocation indoor (required orientation, mutual compatibility, serviceability etc.). Mathematical task formulation for automated layout as the optimization problem has been described too. Since the allocation task is a classical geometric problem, it is necessary to develop appropriate geometric models for its solving. It has been shown that this process’s complexity is due to the complexity related to computer representation of information about geometric shape for layout objects of modern transport, especially the aerospace one. In this paper it has been shown that the abundance of models used in modern applied geometry and allowing describe geometric shapes for objects of any complexity, does not provide any solution for automated layout tasks. Possibilities of modern software have been also shown, and the reasons not allowing its direct use in the tasks of automated layout have been proved. The layout task’s mathematical formulation has been described as an optimization problem, specifying its objective function, limitations and efficiency criteria. Has been justified an approach (receptor methods and apparatus of normal equations) allowing, while creating geometric models for the automated layout, go from exhaustive options for allocation of layout objects to intellectual algorithms for automated allocation As has been shown in the paper, fractal theory is a good mathematical tool for study of rigid bodies’ surface geometry and mechanisms influencing on the obtaining surface structure.
geometric models, allocation, automated layout, compact allocation, conditions of mutual non-crossing, objects normal equations.
Введение
Часто качество проектируемых изделий определяется качеством их компоновки, которая достигается использованием современных информационных технологий. Для изделий с высокой плотностью компоновки, прежде всего, современной транспортной техники, требуются разработки математического и программного обеспечения систем автоматизированной компоновки. Основой для создания такого математического и программного обеспечения являются геометрические модели описания формы и процесса размещения компонуемых объектов. При автоматизации проектирования любой техники на результат проектирования оказывает существенное влияние качество компоновки (т.е. размещение необходимого оборудования и полезной нагрузки). Развитие современной техники, прежде всего, транспортной и особенно авиационно-космической, рост требований к ней и повышение плотности компоновки заставляют конструкторов постоянно совершенствовать методы автоматизации проектирования [8; 14; 27; 31]. На рис. 1 для иллюстрации этого положения показаны два самолета разных эпох примерно одинаковой взлетной массы (30 т). Это самолет «Максим Горький» (СССР, 30-е гг. прошлого века (рис. 1, а) и современный самолет Су-24 (рис. 1, б). И это при том, что на современном самолете установлено намного больше различного бортового оборудования. Как уже отмечалось, качество компоновки любого технического изделия во многом определяет его техническое совершенство и эксплуатационные характеристики. Особенно эта проблема актуальна для транспортного машиностроения, где увеличение габаритных размеров вызывает дополнительное сопротивление окружающей среды при движении транспортного средства. И исключительно актуальна эта проблема для авиационной и ракетно-космической техники с ее высокими скоростями полета, сложными геометрическими формами и высокой плотностью компоновки. В общем виде под компоновкой понимают совокупность геометрических тел, пространственное положение которых зафиксировано относительно общей системы координат и удовлетворяет заданным требованиям. Задачи компоновки присутствуют при проектировании любых технических объектов, но наибольшую сложность она представляет при компоновке летательных аппаратов (ЛА). Поэтому заранее оговоримся, что все рассматриваемые геометрические модели компоновки мы будем «примеривать» к компоновке ЛА как наиболее сложному случаю компоновки как в техническом, так и в геометрическом смысле. Это нисколько не снижает ценности этих методов для других объектов проектирования.
1. Aved'yan A.B., Kuprikov M.YU., Markin L.V. Komponovka samoletov [Aircraft Layout]. Moscow, MAI Press Publ., 2012. 294 p. (in Russian)
2. Andreev V.A., Zvorykin V.N., Konorov L.B. Raschyot i postroenie konturov samolyota na plaze [Calculation and construction of airplane contours on the plaza]. Moscow, Oborongiz Publ., 1960. 492 p. (in Russian)
3. Babakov V.V. Proektirovanie poverkhnostej krivymi vtorogo poryadka v samolyotostroenii [Designing surfaces with second-order curves in aircraft construction]. Moscow, Mashinostroenie Publ., 1969. 124 p. (in Russian)
4. Val'kov K.I. Voprosy ispol'zovaniya metodov geometricheskogo modelirovaniya [The use of geometric modeling methods]. Voprosy geometricheskogo modelirovaniya [Questions of geometric modeling]. 1968, V. 52, pp. 7-15. (in Russian)
5. Val'kov K.I. Lektsii po osnovam geometricheskogo modelirovaniya [Lectures on the basics of geometric modeling]. Leningrad, Leningradskii universitet Publ., 1975. 180 p. (in Russian)
6. Vermishev YU.KH. Metody avtomatizirovannogo poiska reshenij pri proektirovanii slozhnykh tekhnicheskikh sistem [Methods of automated solutions search for the design of complex technical systems]. Moscow, Radio i svyaz' Publ., 1982. 152 p. (in Russian)
7. Vermishev YU.KH. Osnovy avtomatizatsii proektirovaniya [Basics of Design Automation]. Moscow, Radio i svyaz' Publ., 1988. 280 p. (in Russian)
8. Voloshin V.V. Avtomatizatsiya proektirovaniya letatel'nykh apparatov [Automation of aircraft design]. Moscow, Mashinostroenie Publ., 1991. 256 p. (in Russian)
9. Gavrilov V.N. Avtomatizirovannaya komponovka pribornykh otsekov letatel'nykh apparatov [Automated arrangement of instrumentation compartments of aircrafts]. Moscow, Mashinostroenie Publ., 1988. 136 p. (in Russian)
10. Glukhoedov A.V. Komp'yuternaya geometriya i grafika: kurs lektsij [Computer geometry and graphics: a course of lectures]. Belgorod: BGTU Publ., 2011. 1817 p. (in Russian)
11. Golovanov N.N. Geometricheskoe modelirovanie [Geometric modeling]. Moscow, Izdatel'stvo fiziko-matematicheskoj literatury Publ., 2002. 472 p. (in Russian)
12. Golovanov N.N., Il'yutko D.P., Nosovskij G.V., Fomenko A.T. Komp'yuternaya geometriya [Computer geometry]. Moscow, "Akademiya" Publ., 2006. 512 p. (in Russian)
13. Deniskin YU.I., Egorov EH.V., Nartova L.G., Kuprikov M.YU. Prikladnaya geometriya. Nauchnye osnovaniya i primenenie v tekhnike [Applied Geometry. Scientific grounds and application in technology]. Moscow, MAI Press Publ., 2010. 385 p. (in Russian)
14. Eger S.M., Lisejtsev N.K., Samojlovich O.S. Osnovy avtomatizirovannogo proektirovaniya samoletov [Fundamentals of Automated Aircraft Design]. Moscow, Mashinostroenie Publ., 1986. 232 p. (in Russian)
15. Egorov EH.V., Tuzov A.D. Modelirovanie poverkhnostej agregatov letatel'nykh apparatov [Modeling of surfaces of aggregates of aircrafts]. Moscow, MAI Publ., 1988. 88 p. (in Russian)
16. Egorov EH.V., Nartova L.G. Konstruktivnaya geometriya [Constructive geometry]. Moscow, MAI Publ., 2012. 160 p. (in Russian)
17. Erckina E.B., Korol'kova N.N. Geometricheskoe modelirovanie v avtomatizirovannom proektirovanii arhitekturnyh ob"ektov [Geometric modeling in computer-aided design of architectural objects]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 2, pp. 48-54. DOI:https://doi.org/10.12737/19833. (in Russian)
18. Zozulevich D.M., Maksimova L.G. Vypolnenie na EHTSVM nekotorykh operatsij s trekhmernymi kusochno-zadannymi ob"ektami [Execution on the digital computer of some operations with three-dimensional piecewise-specified objects]. Vychislitel'naya tekhnika v mashinostroenii [Computing machinery in mechanical engineering]. Minsk, NTK AN BSSR Publ. 1970, pp. 75-84. (in Russian)
19. Zozulevich D.M. Mashinnaya grafika v avtomatizirovannom proektirovanii [Computer graphics in computer-aided design]. Moscow, Mashinostroenie Publ., 1976. 240 p. (in Russian)
20. Zozulevich D.M., SHerling D.R. Metody realizatsii na EHTSVM teoretiko-mnozhestvennykh operatsij nad ploskimi mnogosvyazannymi oblastyami [Methods for realizing on the computer the set-theoretic operations on flat multiply connected domains]. Vychislitel'naya tekhnika v mashinostroenii [Computing machinery in mechanical engineering]. Minsk. NTK AN BSSR Publ. 1969, pp. 26-35. (in Russian)
21. Zozulevich D.M., Lovchev EH.M. Postroenie s pomoshh'yu EHTSVM izobrazhenij trekhmernykh ob"ektov, zadannykh kusochno-analiticheskimi modelyami [The construction of images of three-dimensional objects defined by piecewise analytic models with the help of an electronic digital computer]. Vychislitel'naya tekhnika v mashinostroenii [Computing machinery in mechanical engineering]. Minsk, NTK AN BSSR Publ. 1971, pp. 64-76. (in Russian)
22. Ivanov G.S. Konstruirovanie tekhnicheskikh poverkhnostej (matematicheskoe modelirovanie na osnove nelinejnykh preobrazovanij) [Designing technical surfaces (mathematical modeling based on nonlinear transformations)]. Moscow, Mashinostroenie Publ., 1987. 192 p. (in Russian)
23. Kui Min KHan, Markin L.V., E Vin Tun, Korn G.V. Retseptornye modeli v zadachakh avtomatizirovannoj komponovki tekhniki [Receptor models in problems of automated layout of technology]. Saarbryuken, Lambert Publ., 2016. 110 p. (in Russian)
24. Kui Min KHan, Markin L.V., E Vin Tun, Korn G.V. Diskretnye modeli geomet-richeskogo modelirovaniya komponovki aviatsionnoj tekhniki [Discrete models of geometric modeling of the layout of aviation equipment]. Elektronnyj zhurnal "Trudy" [Electronic Journal "Proceedings of the"]. 2016, I. 86. Available at: http://trudymai.ru/upload/iblock/530/markin_korn_kui_e_rus.pdf (in Russian)
25. Kuprikov M.YU. Strukturno-parametricheskij sintez geometricheskogo oblika samoleta pri zhestkikh ogranicheniyakh. Uchebnoe posobie [Structural-parametric synthesis of the geometric shape of the aircraft under severe constraints. Tutorial]. Moscow, MAI Publ., 2003. 64 p. (in Russian)
26. Kuprikov M.YU., Komissarov A.A. Formirovanie oblika manevrennogo samoleta v usloviyakh zadannykh stoimostnykh ogranichenij [Formation of the appearance of a maneuverable airplane in conditions of given cost constraints]. Zhurnal "Trudy" [Electronic Journal "Proceedings of the MAI"]. 2011, I. 47. Available at: http://trudymai.ru/upload/iblock/22e/formirovanie-oblika-manevrennogo-samoleta-v-usloviyakh-zadannykh-stoimostnykh-ogranicheniy.pdf (in Russian)
27. Mal'chevskij V.V. Avtomatizatsiya protsessa komponovki samoleta: Uchebnoe posobie dlya FPK [Automation of the airplane configuration process: A manual for the FPK]. Moscow, MAI Publ., 1987. 42 p. (in Russian)
28. Markin L.V. Geometricheskie modeli avtomatizirovannoj komponovki letatel'nykh apparatov [Geometrical models of the automated configuration of aircrafts]. Vestnik [Bulletin of the], 2015, I. 1, V. 22, pp. 47-56.
29. Markin L.V. Ispol'zovanie apparata normal'nykh uravnenij v zadachakh geometricheskogo modelirovaniya razmeshheniya ob"ektov [The use of the apparatus of normal equations in problems of geometric modeling of the arrangement of objects]. EHlektronnyj zhurnal «Prikladnaya geometriya» [Electronic Journal "Applied Geometry"]. V. 6, I. 13 (2004), pp. 19-34. Available at: http://www.apg.mai.ru/Volume6/v6_n14. pdf (in Russian)
30. Markin L.V. O putyakh sozdaniya geometricheskikh modelej avtomatizirovannoj komponovki [About ways of creation of geometrical models of the automated configuration]. Geometriya i grafika [Geometry and graphics]. 2015, V. 3, I. 1, pp. 64-69. (in Russian)
31. Osin M.I. Metody avtomatizirovannogo proektirovaniya letatel'nykh apparatov [Methods of automated design of aircraft]. Moscow, Mashinostroenie Publ., 1984. 168 p. (in Russian)
32. Rvachev V.L. Geometricheskie prilozheniya algebra logiki [Geometric applications of algebra of logic]. Kiev: Tekhnika Publ., 1967. 212 p. (in Russian)
33. Rvachev V.L. Teoriya R-funktsij i nekotorye ee prilozheniya [Theory of R-functions and some of its applications]. Kiev: Naukova dumka Publ., 1982. 552 p. (in Russian)
34. Situ L., N'i N'i KHtun, Markin L.V. Retseptornye geometricheskie modeli v zadachakh avtomatizirovannoj komponovki tekhnicheskogo otseka legkogo samoleta [Receptor geometric models in the problems of automated layout of the technical compartment of light aircraft]. Zhurnal "Trudy" [Electronic Journal "Proceedings of the"]. 2011, I. 47. Available at: http://trudymai.ru/upload/iblock/ed4/retseptornye-geometricheskie-modeli-v-zadachakh-avtomatizirovannoy-komponovki-tekhnicheskogo-otseka-legkogo-samoleta.pdf (in Russian)
35. Stoyan YU.G., YAkovlev S.V. Matematicheskie modeli i optimizatsionnye metody geometricheskogo proektirovaniya [Mathematical models and optimization methods of geometric design]. Kiev: Naukova dumka Publ., 1986. 268 p. (in Russian)
36. Stoyan YU.G., Gil' N.I. Metody i algoritmy razmeshheniya ploskikh geometriche-skikh ob"ektov [Methods and algorithms for placing planar geometric objects]. Kiev: Naukova dumka Publ., 1976. 249 p. (in Russian)
