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Calculating Optimum Gear Ratios of Mechanical Drive Systems Using Two-Stage Helical Gearbox with Second-Stage Double Gear Sets and Chain Drive for Minimum Gearbox Length

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Advances in Engineering Research and Application (ICERA 2019)

Abstract

The paper presents a study on determining optimum gear ratios of mechanical driven systems using a two-stage helical gearbox with second stage double gear sets and a chain drive. In the study, an optimization problem with the objective function as the minimum system length was solved. In addition, the effects of the input parameters including the total gearbox ratio, the wheel face width coefficient, the allowable contact stress and the output torque on the optimal transmission ratios were evaluated by conducting a simulation experiment. Moreover, several equations to find the optimum gear ratios were proposed.

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References

  1. Kudreavtev, V.N., Gierzaves, I.A., Glukharev, E.G.: Design and Calculus of Gearboxes. Mashinostroenie Publishing, Sankt Petersburg (1971). (in Russian)

    Google Scholar 

  2. Chat, T.: Some problems of kinematics calculation of transmission mechanics system. In: Proceedings of the National Conference on Engineering Mechanics, Hanoi, vol. 2, pp. 7–12 (1993). (in Vietnamese)

    Google Scholar 

  3. Milou, G., Dobre, G., Visa, F., Vitila, H.: Optimal design of two step gear units, regarding the main parameters. VDI Berichte 1230, 227 (1996)

    Google Scholar 

  4. Pi, V.N.: A method for optimal calculation of total transmission ratio of two step helical gearboxes. In: Proceedings of the National conference on Engineering Mechanics, Hanoi, p. 12 (2001)

    Google Scholar 

  5. Cam, N.T.H., Pi, V.N., Tuan, N.K., Hung, L.X., Thao, T.T.P.: Determining optimal partial transmission ratios of mechanical driven systems using a V-belt drive and a helical reducer with second-step double gear-sets. In: Fujita, H., et al. (eds.) ICERA 2018. LNNS, vol. 63, pp. 261–269 (2019). https://doi.org/10.1007/978-3-030-04792-4_35

    Google Scholar 

  6. Petrovski, A.N., Sapiro, B.A., Saphonova, N.K.: About optimal problem for multi-step gearboxes. Vestnik Mashinostroenie 10, 13 (1987). (in Russian)

    Google Scholar 

  7. Pi, V.N.: A new study on optimal calculation of partial transmission ratios of two-step helical gearboxes. In: 2nd WSEAS International Conference on Computer Engineering and Applications, CEA 2008, Acapulco, Mexico, 25–27 January, pp. 162–165 (2008)

    Google Scholar 

  8. Nguyen, K.T., Vu, N.P., Nguyen, T.H.C., Tran, T.P.T., Ho, K.T., Le, X.H., Hoang, T.T.: Determining optimal gear ratios of a two-stage helical reducer for getting minimal acreage of cross section. In: MATEC Web of Conferences, vol. 213, p. 01008 (2018). https://doi.org/10.1051/matecconf/201821301008

    Article  Google Scholar 

  9. Pi, V.N., Tuan, N.K.: Optimum determination of partial transmission ratios of Three-step helical gearboxes for getting minimum cross section. J. Environ. Sci. Eng. A 5, 570–573 (2016)

    Google Scholar 

  10. Pi, V.N., Binh, N.D., Dac, V.Q., The, P.Q.: Optimal calculation of total transmission ratio of three-step helical gearboxes for minimum mass of gears. J. Sci. Technol. 6 Eng. Univ., 91 (2006). (in Vietnamese)

    Google Scholar 

  11. Pi, V.N.: A new study on optimal calculation of partial transmission ratio of three-step helical reducers. In: The 3rd IASME/WSEAS International Conference on Continuum Mechanics, Cambridge, UK, p. 23 (2008)

    Google Scholar 

  12. Pi, V.N.: A new study on optimal calculation of partial transmission ratios of three-step helical reducers for getting minimal cross section dimension. In: The 2nd WSEAS International Conference on Computer Engineering and Applications, CEA 2008, Acapulco, Mexico, 25–27 January, pp. 290–293 (2008)

    Google Scholar 

  13. Pi, V.N.: Optimal determination of partial transmission ratios of three-step helical gearboxes with first and third-step double gear-sets for minimal mass of gear. In: American Conference on Applied Mathematics, MATH 2008, Harvard, Massachusetts, USA, 24–26 March, pp. 385–388 (2008)

    Google Scholar 

  14. Romhild, I., Linke, H.: Gezielte Auslegung Von Zahnradgetrieben mit minimaler Masse auf der Basis neuer Berechnungsverfahren. Konstruktion 44, 229–236 (1992)

    Google Scholar 

  15. Pi, V.N.: A new study on the optimal prediction of partial transmission ratios of three-step helical gearboxes with second-step double gear-sets. WSEAS Trans. Appl. Theor. Mech. 2(11) (2007)

    Google Scholar 

  16. Pi, V.N.: Optimal determination of partial transmission ratios for four-step helical gearboxes with first and third step double gear-sets for minimal mass of gears. In: Applied Computing Conference, ACC 2008, Istanbul, Turkey, 27–30 May (2008)

    Google Scholar 

  17. Pi, V.N.: Optimal calculation of partial transmission ratios for four-step helical gearboxes with first and third-step double gear-sets for minimal gearbox length. In: American Conference on Applied Mathematics, MATH 2008, Harvard, Massachusetts, USA, 24–26 March, pp. 29–32 (2008)

    Google Scholar 

  18. Hung, L.X., Pi, V.N., Du, N.V.: Optimal calculation of partial transmission ratios of four-step helical gearboxes with second and fourth-step double gear-sets for minimal mass of gears. In: The International Symposium on Mechanical Engineering, ISME, Ho Chi Minh city, Vietnam, pp. 21–23, September 2009

    Google Scholar 

  19. Pi, V.N.: Optimal determination of partial transmission ratios for four-step helical gearboxes with first and third step double gear-sets for minimal mass of gears. In: Applied Computing Conference, ACC 2008, Istanbul, Turkey, 27–30 May 2008, pp. 53–57 (2008)

    Google Scholar 

  20. Pi, V.N.: A new and effective method for optimal calculation of total transmission ratio of two step bevel - helical gearboxes. In: International colloquium on Mechanics of Solids, Fluids, Structures & Interaction, Nha Trang, Vietnam, pp. 716–719 (2000)

    Google Scholar 

  21. Pi, V.N., Binh, N.D., Dac, V.Q., The, P.Q.: A new and effective method for optimal splitting of total transmission ratio of three step bevel-helical gearboxes. In: The Sixth Vietnam Conference on Automation, Hanoi, pp. 175–180 (2005)

    Google Scholar 

  22. Tuan, N.K., Thao, T.T.P., Cam, N.T.H., Hung, L.X., Pi, V.N.: Optimum calculation of partial transmission ratios of mechanical driven systems using a V-belt and a three-step bevel helical gearbox. In: Fujita, H., et al. (eds.) ICERA 2018. LNNS, vol. 63, pp. 469–476 (2019). https://doi.org/10.1007/978-3-030-04792-4_61

    Google Scholar 

  23. Chernavsky, S.A., et al.: Design of Mechanical Transmissions: Manual for High Technical Schools, p. 560. Mashinostroenie, Moscow (1984)

    Google Scholar 

  24. Pi, V.N., Dac, V.Q.: Calculation of total transmission ratio of two step worm reducers for the best reasonable gearbox housing structure. J. Sci. Technol. Thai Nguyen Univ. 1(41), 65–69 (2007). (in Vietnamese)

    Google Scholar 

  25. Pi, V.N., Dac, V.Q.: Optimal calculation of partial transmission ratios of worm-helical gear reducers for minimal gearbox length. J. Sci. Technol. Tech. Univ. 61, 73–77 (2007)

    Google Scholar 

  26. Pi, V.N., Dac, V.Q.: Optimal calculation of total transmission ratio of worm-helical gear reducers. J. Sci. Technol. Thai Nguyen Univ. 4(36), 70–73 (2005). No. 1

    Google Scholar 

  27. Pi, V.N., Thao, T.T.P., Thao, L.T.P.: A new study on optimum determination of partial transmission ratios of mechanical driven systems using a V-belt and two-step helical gearbox. Vietnam. Mech. Eng. J. 10, 123 (2015)

    Google Scholar 

  28. Pi, V.N., Cam, N.T.H., Tuan, N.K.: Optimum calculation of partial transmission ratios of mechanical driven systems using a V-belt and two-step bevel helical gearbox. J. Environ. Sci. Eng. A 5, 566 (2016)

    Google Scholar 

  29. Pi, V.N., Thao, T.T.P., Tuan, D.A.: Optimum determination of partial transmission ratios of mechanical driven systems using a chain drive and two-step helical gearbox. J. Environ. Sci. Eng. B 6, 80 (2017)

    Google Scholar 

  30. Cam, N.T.H., Pi, V.N., Tuan, N.K., Hung, L.X., Thao, T.T.P.: A study on determination of optimum partial transmission ratios of mechanical driven systems using a chain drive and a three-step helical reducer. In: Fujita, H., et al. (eds.) ICERA 2018. LNNS, vol. 63, pp. 91–99 (2019). https://doi.org/10.1007/978-3-030-04792-4_14

    Google Scholar 

  31. Chat, T., Uyen, L.V.: Design and calculation of Mechanical Transmissions Systems, vol. 1. Educational Republishing House, Hanoi (2007)

    Google Scholar 

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Acknowledgements

The work described in this paper was supported by Thai Nguyen University of Technology for a scientific project.

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Correspondence to Ngoc Pi Vu .

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Cam, N.T.H. et al. (2020). Calculating Optimum Gear Ratios of Mechanical Drive Systems Using Two-Stage Helical Gearbox with Second-Stage Double Gear Sets and Chain Drive for Minimum Gearbox Length. In: Sattler, KU., Nguyen, D., Vu, N., Tien Long, B., Puta, H. (eds) Advances in Engineering Research and Application. ICERA 2019. Lecture Notes in Networks and Systems, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-030-37497-6_18

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