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.
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References
Kudreavtev, V.N., Gierzaves, I.A., Glukharev, E.G.: Design and Calculus of Gearboxes. Mashinostroenie Publishing, Sankt Petersburg (1971)
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)
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)
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)
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_35
Petrovski, A.N., Sapiro, B.A., Saphonova, N.K.: About optimal problem for multi-step gearboxes. Vestnik Mashinostroenie 10, 13 (1987)
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)
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/201821301008
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)
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, Vietnamese
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)
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)
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)
Romhild, I., Linke, H.: Gezielte Auslegung Von Zahnradgetrieben mit minimaler Masse auf der Basis neuer Berechnungsverfahren. Konstruktion 44, 229–236 (1992)
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)
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)
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 2009
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)
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)
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)
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_61
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)
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_14
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)
Chernavsky, S.A., et al.: Design of mechanical transmissions: manual for high technical schools. Mashinostroenie, Moscow, p. 560 (1984)
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)
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)
Karl-Heinrich Grote, K., Antonsson, E.: Springer Handbook of Mechanical Engineering. Springer, Berlin (2008)
Chat, T., Van Uyen, L.: Design and Calculation of Mechanical Transmissions Systems, vol. 1. Educational Republishing House, Hanoi (2007)
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The work described in this paper was supported by Thai Nguyen University of Technology for a scientific project.
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Ky, L.H. et al. (2020). Calculation of Optimum Gear Ratios of Mechanical Driven Systems Using Worm-Helical Gearbox and Chain Drive. 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_7
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