Advertisement

Calculation of Optimum Gear Ratios of Mechanical Driven Systems Using Worm-Helical Gearbox and Chain Drive

  • Le Hong Ky
  • Tran Thi Hong
  • Nguyen Van Cuong
  • Luu Anh Tung
  • Nguyen Thanh Tu
  • Hoang Thi Tham
  • Le Xuan HungEmail author
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 104)

Abstract

A study on the calculation of the optimum gear ratios of mechanical driven systems using a worm-helical gearbox and a chain drive was presented. To find the optimum gear ratios, an optimization problem in which the height of the system was selected as the objective function was conducted. Also, the influences of the input parameters including the total gear ratio of the system, the calculated coefficient of the worm diameter coefficient, the coefficient of wheel face width and the allowable contact stress of helical gear unit, and the output torque were examined. To weigh the effect of these parameters on the optimum gear ratios, a simulation experiment was performed by computer programming. Additionally, equations to calculate the optimum gear ratios were introduced. Using these equations, the optimum gear ratios can be found easily and accurately because the equations are all in the explicit form.

Keywords

Optimum gearbox design Gear ratio Optimum gear ratio Worm-helical gearbox 

Notes

Acknowledgements

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

References

  1. 1.
    Kudreavtev, V.N., Gierzaves, I.A., Glukharev, E.G.: Design and Calculus of Gearboxes. Mashinostroenie Publishing, Sankt Petersburg (1971)Google Scholar
  2. 2.
    Chat, T.: Some problems of kinematics calculation of transmission mechanics system. In: Proceedings of the National Conference on Engineering Mechanics, vol. 2, Hanoi, Vietnamese, pp. 7–12 (1993)Google Scholar
  3. 3.
    Milou, G., Dobre, F., Visa, H.: Vitila: optimal design of two step gear units, regarding the main parameters. VDI Berichte no. 1230, p. 227 (1996)Google Scholar
  4. 4.
    Ngoc Pi, V.: A method for optimal calculation of total transmission ratio of two step helical gearboxes. In: Proceedings of the National conference on Engineering Mechanics, Ha Noi, p. 12 (2001)Google Scholar
  5. 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 63, pp. 261–269 (2019).  https://doi.org/10.1007/978-3-030-04792-4_35Google Scholar
  6. 6.
    Petrovski, A.N., Sapiro, B.A., Saphonova, N.K.: About optimal problem for multi-step gearboxes. Vestnik Mashinostroenie 10, 13 (1987)Google Scholar
  7. 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’08), Acapulco, Mexico, 25–27 January, pp. 162–165 (2008)Google Scholar
  8. 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 213, 01008 (2018).  https://doi.org/10.1051/matecconf/201821301008CrossRefGoogle Scholar
  9. 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. 10.
    Pi, V.N., Binh, N.D., Dac, V.Q., Quang, P.: The optimal calculation of total transmission ratio of three-step helical gearboxes for minimum mass of gears. J. Sci. Technol. 6, 91 (2006). Engineering Universities, VietnameseGoogle Scholar
  11. 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. 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. 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. 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. 15.
    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
  16. 16.
    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
  17. 17.
    Hung, L.X., Pi, V.N., Van Du, N.: 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, September, pp. 21–23, September 2009Google Scholar
  18. 18.
    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, pp. 53–57 (2008)Google Scholar
  19. 19.
    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
  20. 20.
    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
  21. 21.
    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, LNNS 63, pp. 469–476 (2018, 2019).  https://doi.org/10.1007/978-3-030-04792-4_61Google Scholar
  22. 22.
    Pi, V.N., Tuan, N.K., Hung, L.X., Cam, N.T.H., Thao, T.T.P.: Determining optimum partial transmission ratios of mechanical driven systems using a V-belt drive and a three-stage helical reducer. In: Advances in Material Sciences and Engineering. Springer, pp. 81–88 (2019)Google Scholar
  23. 23.
    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 63, pp. 91–99 (2019).  https://doi.org/10.1007/978-3-030-04792-4_14Google Scholar
  24. 24.
    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
  25. 25.
    Chernavsky, S.A., et al.: Design of mechanical transmissions: manual for high technical schools. Mashinostroenie, Moscow, p. 560 (1984)Google Scholar
  26. 26.
    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 University, Vietnamese 1(41), 65–69 (2007)Google Scholar
  27. 27.
    Pi, V.N., Dac, V.Q.: Optimal calculation of partial transmission ratios of worm-helical gear reducers for minimal gearbox length. J. Sci. Technol. - Technical Universities, Vietnamese 61, 73–77 (2007)Google Scholar
  28. 28.
    Karl-Heinrich Grote, K., Antonsson, E.: Springer Handbook of Mechanical Engineering. Springer, Berlin (2008)Google Scholar
  29. 29.
    Chat, T., Van Uyen, L.: Design and Calculation of Mechanical Transmissions Systems, vol. 1. Educational Republishing House, Hanoi (2007)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Le Hong Ky
    • 1
  • Tran Thi Hong
    • 2
  • Nguyen Van Cuong
    • 3
  • Luu Anh Tung
    • 4
  • Nguyen Thanh Tu
    • 4
  • Hoang Thi Tham
    • 4
  • Le Xuan Hung
    • 4
    Email author
  1. 1.Vinh Long University of Technology EducationVinh LongVietnam
  2. 2.Nguyen Tat Thanh UniversityHo Chi MinhVietnam
  3. 3.University of Transport and CommunicationsHa NoiVietnam
  4. 4.Thai Nguyen University of TechnologyThai NguyenVietnam

Personalised recommendations