Linear-graph and contour-graph-based models of planetary gears

• Autorzy: Drewniak J. , Zawiślak S.

Warianty tytułu

PL

Grafowe i konturowe modele przekładni planetarnych

• Języki publikacji: EN

Abstrakty

EN

Analysis and synthesis of mechanisms are basic engineering tasks. They can suffer from errors due to versatile reasons. The graph-based methods of analysis and synthesis of planetary gears can be alternative methods for accomplishing of the afore mentioned tasks, which additionally allow for checking of their correctness. In the paper, two graph-based methods of analysis of planetary gears are discussed. An exemplary planetary gear is analysed by means of the graph-based methods as well as the traditional Willis method. Force and torque analyses were performed as well. An algorithmic approach – which implies from the graph models – allows for checking of versatile variants of designs in an easy and schematic way, which can lead to optimisation of the design within a conceptual phase of the design procedure.

PL

Analiza i synteza mechanizmów są podstawowymi działaniami inżyniera. Narażone są one z różnych powodów na niezamierzone błędy. Metody analizy i syntezy przekładni planetarnych oparte na teorii grafów mogą być metodami alternatywnymi dla realizacji tych zadań, które pozwalają sprawdzić poprawność przeprowadzonych rozważań. W artykule rozważa się dwie metody grafowe modelowania przekładni. Przykładową przekładnię planetarną analizuje się tymi metodam, a wyniki porównuje się z metodą Willis'a. Przeprowadzono także analizę sił, momentów i sprawności. Ujęcie algorytmiczne – które wynika z modelowania grafami – pozwala na łatwe sprawdzanie wielu wariantów rozwiązań w łatwym ujęciu schematycznym, co wpływa na optymalizację rozważanych rozwiązań konstrukcyjnych w fazie koncypowania.

Słowa kluczowe

EN

contour equation method; Hsu's graph; f-cycle equation; gear ratio variants

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2010
• Tom: Vol. 48 nr 2
• Strony: 415--433
• Opis fizyczny: Bibliogr. 24 poz., rys., tab.

Twórcy

autor

Drewniak J.

autor

Zawiślak S.

• University of Bielsko-Biala, Department of Mechanical Engineering Fundamentals, Bielsko-Biała, Poland,

Bibliografia

• 1. Abramov B.M., 1976, Typical Problems in Theory of Mechanisms and Machines, Kharkov [in Russian]
• 2. Andrews G.C., Lo L., Wong C., 1997, Graph theory - the key to AI applications in dynamics, Proceedings IEEE Conference on Systems, Man and Cybernetics, Florida, 3, 2939-2944
• 3. Arczewski K., Dul F., 1995, Determination of angular velocities within a multi-body system by means of graphs, ZAMM Z. Angew. Math. Mech., 75, SI, S105-S106
• 4. Bonnell R., Hess R., 1968, Applications of signal-flow graph theory to epicyclic gear trains, IEEE Transactions on Automatic Control, 13, 5, 594-595
• 5. Davies T.H., 1968, An extension of Manolescu’s classification of planar kinematic chains and mechanisms of mobility m > 1, using graph theory, J. Mech., 3, 87-100
• 6. Drewniak J., Zawiślak S., 2010, Kinematical and dynamical analysis of closed kinematic chains using graphs and contour equations, PAMM, after the Conference GAMM2009 in Gdańsk
• 7. Hsu C.H., 2002, An analysis methodology for the kinematic synthesis of epicyclic gear mechanisms, ASME Journal of Mechanical Design, 124, 574-576
• 8. Ivanˇcenko L.N., Suˇskov J.A., Waˇsec A.D., 1974, Avtomatizaciya vybora skhem planetarnykh korobok peredachi, Mashinostroenie, Leningrad [in Russian]
• 9. Marghitu D.B., 2005, Kinematic Chains and Machine Components Design, Academic Press, London as well as Elsevier, San Diego
• 10. Marghitu D.B., Crocker M.J., 2001, Analytical Elements of Mechanisms, Cambridge University Press, Cambridge
• 11. M¨uller L., Wilk A., 1996, Toothed Epicyclic Gears, PWN, Warszawa [In Polish]
• 12. Schmidt L.C., Shetty H., Chase S., 2000, A graph grammar approach to mechanism synthesis, ASME Journal of Mechanical Design, 122, 371-376
• 13. Shai O., 2001, The multidisciplinary combinatorial approach (MCA) and its applications in engineering, Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 15, 2, 109-144
• 14. Shai O., Preiss K., 1999, Graph theory representation of engineering systems and their embedded knowledge, Artificial Intelligence in Engineering, 13, 273-285
• 15. Tsai L.W., 2001, Mechanism Design: Enumeration of Kinematic Structures According to Function, CRC, Boca Raton, USA
• 16. Tuttle E.R., Peterson S.W., Titus J.E., 1989, Enumeration of basic kinematic chains using the theory of finite groups, ASME Journal of Mechanisms, Transmissions, and Automation in Design, 111, 498-503
• 17. Uematsu S., 1997, An application of graph theory to the kinematic analysis of planetary gear trains, International Journal of the Japan Society for Precision Engineering, 31, 2, 141-146
• 18. Uyguro˘glu M., Demirel H., 2005, TSAI-TOKAD (T-T) graph: The combination of non-oriented and oriented graphs for the kinematics of articulated gear mechanisms, Meccanica, 40, 3, 223-232
• 19. Wojnarowski J., Kopeć J., Zawiślak S., 2006, Gears and graphs, Journal of Theoretical and Applied Mechanics, 44, 1, 139-162
• 20. Wojnarowski J., Lidwin A., 1975, The application of signal flow graphs – the kinematic analysis of planetary gear trains, Mechanism and Machine Theory, 10, 1-B, 17-31
• 21. Zawiślak S., 2006, Graph-based methodology as a support of conceptual design of planetary gears, Proc. XX Conference on TMM in Zielona Góra, 405-411
• 22. Zawiślak S., 2007, Artificial intelligence aided design of gears based on graph-theoretical models, Proc. IFToMM2007 Twelfth World Congress in Mechanism and Machine Science, Besancon, France, 1-6 (http://130.15.85.212/proceedings/WorldCongress07/articles/article cd.htm, see Zawislak S.)
• 23. Zawiślak S., 2008,Graph theoretic based models of planetary gears, in: Theory of Machines and Mechanisms, J. Wojnarowski and I. Adamiec-Wojcik (Edit.), Wydawnictwo AT-H, Bielsko-Biała, 2, 67-74
• 24. Zawiślak S., Szypuła Ł., Myśliwiec M., Jagosz A., 2008, Some applications of graph transformations in modelling of mechanical systems, Pre-Proceedings Seventh International Workshop on Graph Transformation and Visual Modelling Techniques (GT-VMT 2008), Budapest, Hungary, 332-345