Abstract
This paper presents a study on the determination of the optimum gear ratios of a two-stage worm gearbox. To find the optimum gear ratios, an optimization problem was performed. Also, the reasonable gearbox structure was chosen as the objective function of the optimization problem. In addition, the effects of the input factors including the total gearbox ratio, the electric motor speed, and the output torque were investigated. Besides, a simulation experiment was designed and performed by computer programs to evaluate the influences of these input factors on the optimum gear ratios. Moreover, some models to calculate the optimum gear ratios of a two-stage worm gearbox were suggested. As these equations are explicit, the determination of the optimum gear ratios is accurate and uncomplicated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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, Hanoi, Vietnamese, vol. 2, pp. 7–12 (1993)
Milou, G., Dobre, G., Visa, F., Vitila, H.: Optimal design of two step gear units, regarding the main parameters. VDI Berichte 1230, 227 (1996)
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)
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
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 2008, 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, vol. 213, p. 01008 (2018)
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., 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)
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., 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, September, pp. 21–23 (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. Env. 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 2018. LNNS, vol. 63, pp. 469–476 (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, pp. 81–88. Springer (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, vol. 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, Moscow, Mashinostroenie, 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 Univ. 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. Tech. Univ. 61, 73–77 (2007)
Grote, K.-H., Antonsson, E.K.: Springer Handbook of Mechanical Engineering. Springer, Heidelberg (2008)
Chat, T., Van Uyen, L.: Design and Calculation of Mechanical Transmissions Systems, vol. 1. Educational Republishing House, Hanoi (2007)
Acknowledgements
The work described in this paper was supported by Thai Nguyen University of Technology for a scientific project.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Tung, L.A. et al. (2020). A Study on Determination of Optimum Gear Ratios of a Two-Stage Worm Gearbox. 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_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-37497-6_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-37496-9
Online ISBN: 978-3-030-37497-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)